TSTP Solution File: GEO520+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO520+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:36:52 EDT 2022
% Result : Theorem 0.60s 0.67s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO520+1 : TPTP v8.1.0. Released v7.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 11:10:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.60/0.67 % SZS status Theorem
% 0.60/0.67 % SZS output start Proof
% 0.60/0.67 tff(f813_type, type, (
% 0.60/0.67 f813: ( $i * $i * $i * $i * $i ) > $i)).
% 0.60/0.67 tff(tptp_fun_Xc_2_type, type, (
% 0.60/0.67 tptp_fun_Xc_2: $i)).
% 0.60/0.67 tff(tptp_fun_Xb_0_type, type, (
% 0.60/0.67 tptp_fun_Xb_0: $i)).
% 0.60/0.67 tff(tptp_fun_Xq_3_type, type, (
% 0.60/0.67 tptp_fun_Xq_3: $i)).
% 0.60/0.67 tff(tptp_fun_Xp_4_type, type, (
% 0.60/0.67 tptp_fun_Xp_4: $i)).
% 0.60/0.67 tff(s_type, type, (
% 0.60/0.67 s: ( $i * $i ) > $i)).
% 0.60/0.67 tff(il_type, type, (
% 0.60/0.67 il: ( $i * $i * $i * $i ) > $i)).
% 0.60/0.67 tff(s_e_type, type, (
% 0.60/0.67 s_e: ( $i * $i * $i * $i ) > $o)).
% 0.60/0.67 tff(tptp_fun_Xa_1_type, type, (
% 0.60/0.67 tptp_fun_Xa_1: $i)).
% 0.60/0.67 tff(s_r_type, type, (
% 0.60/0.67 s_r: ( $i * $i * $i ) > $o)).
% 0.60/0.67 tff(perp_type, type, (
% 0.60/0.67 perp: ( $i * $i * $i * $i ) > $o)).
% 0.60/0.67 tff(s_col_type, type, (
% 0.60/0.67 s_col: ( $i * $i * $i ) > $o)).
% 0.60/0.67 tff(perpAt_type, type, (
% 0.60/0.67 perpAt: ( $i * $i * $i * $i * $i ) > $o)).
% 0.60/0.67 tff(g813_type, type, (
% 0.60/0.67 g813: ( $i * $i * $i * $i * $i ) > $i)).
% 0.60/0.67 tff(g811_type, type, (
% 0.60/0.67 g811: ( $i * $i * $i * $i * $i ) > $i)).
% 0.60/0.67 tff(f811_type, type, (
% 0.60/0.67 f811: ( $i * $i * $i * $i * $i ) > $i)).
% 0.60/0.67 tff(s_t_type, type, (
% 0.60/0.67 s_t: ( $i * $i * $i ) > $o)).
% 0.60/0.67 tff(1,plain,
% 0.60/0.67 (^[Xa: $i, Xb: $i, Xc: $i] : refl((~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(2,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[1])).
% 0.60/0.67 tff(3,plain,
% 0.60/0.67 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(rewrite((s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))) <=> (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))), ((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))), rewrite((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))), ((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(4,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[3])).
% 0.60/0.67 tff(5,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(6,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_Defn8_1')).
% 0.60/0.67 tff(7,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.60/0.67 tff(8,plain,(
% 0.60/0.67 ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.60/0.67 inference(skolemize,[status(sab)],[7])).
% 0.60/0.67 tff(9,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.60/0.67 tff(10,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.60/0.67 tff(11,plain,
% 0.60/0.67 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))) | (~((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(12,plain,
% 0.60/0.67 (~((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.60/0.67 tff(13,plain,
% 0.60/0.67 (((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) | ((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.60/0.67 inference(tautology,[status(thm)],[])).
% 0.60/0.67 tff(14,plain,
% 0.60/0.67 ((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.60/0.67 tff(15,plain,
% 0.60/0.67 (^[Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : refl((~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))) <=> (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(16,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[15])).
% 0.60/0.67 tff(17,plain,
% 0.60/0.67 (^[Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : trans(monotonicity(rewrite(((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) <=> ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))), rewrite(((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))) <=> ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))), ((((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))), rewrite((((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))), ((((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(18,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[17])).
% 0.60/0.67 tff(19,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(20,plain,
% 0.60/0.67 (^[Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : rewrite((((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | (~s_col(Xa, Xb, Xc))) | (~perp(Xa, Xb, Xc, Xp))) & ((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | s_r(Xc, Xp, Xq)) | (~perp(Xa, Xb, Xc, Xp)))) <=> (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp)))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(21,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | (~s_col(Xa, Xb, Xc))) | (~perp(Xa, Xb, Xc, Xp))) & ((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | s_r(Xc, Xp, Xq)) | (~perp(Xa, Xb, Xc, Xp)))) <=> ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[20])).
% 0.60/0.67 tff(22,axiom,(![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | (~s_col(Xa, Xb, Xc))) | (~perp(Xa, Xb, Xc, Xp))) & ((((((Xa = Xb) | (~s_col(Xa, Xb, Xp))) | (~s_col(Xa, Xb, Xq))) | (Xq = Xp)) | s_r(Xc, Xp, Xq)) | (~perp(Xa, Xb, Xc, Xp))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz8_16a')).
% 0.60/0.67 tff(23,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.60/0.67 tff(24,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.60/0.67 tff(25,plain,(
% 0.60/0.67 ![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp))) & ((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))),
% 0.60/0.67 inference(skolemize,[status(sab)],[24])).
% 0.60/0.67 tff(26,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.60/0.67 tff(27,plain,
% 0.60/0.67 (![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.60/0.67 tff(28,plain,
% 0.60/0.67 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(29,plain,
% 0.60/0.67 ((~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))))) <=> (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(30,plain,
% 0.60/0.68 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.60/0.68 inference(monotonicity,[status(thm)],[29])).
% 0.60/0.68 tff(31,plain,
% 0.60/0.68 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.60/0.68 inference(transitivity,[status(thm)],[30, 28])).
% 0.60/0.68 tff(32,plain,
% 0.60/0.68 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))),
% 0.60/0.68 inference(quant_inst,[status(thm)],[])).
% 0.60/0.68 tff(33,plain,
% 0.60/0.68 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.60/0.68 tff(34,plain,
% 0.60/0.68 (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[33, 27])).
% 0.60/0.68 tff(35,plain,
% 0.60/0.68 (((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xa!1)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.60/0.68 inference(tautology,[status(thm)],[])).
% 0.60/0.68 tff(36,plain,
% 0.60/0.68 ((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.60/0.68 tff(37,plain,
% 0.60/0.68 ((~((Xp!4 = Xq!3) | s_col(Xc!2, Xa!1, Xb!0) | (Xa!1 = Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)))) <=> (~((Xp!4 = Xq!3) | s_col(Xc!2, Xa!1, Xb!0) | (Xa!1 = Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(38,plain,
% 0.60/0.68 ((~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))) <=> (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(39,plain,
% 0.60/0.68 ((~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : (((((Xp = Xq) | (~perpAt(Xp, Xq, Xc, Xa, Xc))) | (~perpAt(Xp, Xq, Xc, Xb, Xc))) | (Xa = Xc)) | s_col(Xc, Xa, Xb))) <=> (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(40,axiom,(~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : (((((Xp = Xq) | (~perpAt(Xp, Xq, Xc, Xa, Xc))) | (~perpAt(Xp, Xq, Xc, Xb, Xc))) | (Xa = Xc)) | s_col(Xc, Xa, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aLemma9_13g')).
% 0.60/0.68 tff(41,plain,
% 0.60/0.68 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.60/0.68 tff(42,plain,
% 0.60/0.68 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.60/0.68 tff(43,plain,
% 0.60/0.68 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.60/0.68 tff(44,plain,
% 0.60/0.68 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.60/0.68 tff(45,plain,
% 0.60/0.68 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.60/0.68 tff(46,plain,
% 0.60/0.68 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.60/0.68 tff(47,plain,
% 0.60/0.68 (~![Xp: $i, Xq: $i, Xc: $i, Xa: $i, Xb: $i] : ((Xp = Xq) | s_col(Xc, Xa, Xb) | (Xa = Xc) | (~perpAt(Xp, Xq, Xc, Xb, Xc)) | (~perpAt(Xp, Xq, Xc, Xa, Xc)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.60/0.68 tff(48,plain,(
% 0.60/0.68 ~((Xp!4 = Xq!3) | s_col(Xc!2, Xa!1, Xb!0) | (Xa!1 = Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)))),
% 0.60/0.68 inference(skolemize,[status(sab)],[47])).
% 0.60/0.68 tff(49,plain,
% 0.60/0.68 (~((Xp!4 = Xq!3) | s_col(Xc!2, Xa!1, Xb!0) | (Xa!1 = Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[48, 37])).
% 0.60/0.68 tff(50,plain,
% 0.60/0.68 (perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)),
% 0.60/0.68 inference(or_elim,[status(thm)],[49])).
% 0.60/0.68 tff(51,plain,
% 0.60/0.68 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : refl(((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq))) <=> ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq))))),
% 0.60/0.68 inference(bind,[status(th)],[])).
% 0.60/0.68 tff(52,plain,
% 0.60/0.68 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.60/0.68 inference(quant_intro,[status(thm)],[51])).
% 0.60/0.68 tff(53,plain,
% 0.60/0.68 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(54,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz8_14c')).
% 0.60/0.68 tff(55,plain,
% 0.60/0.68 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.60/0.68 tff(56,plain,(
% 0.60/0.68 ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.60/0.68 inference(skolemize,[status(sab)],[55])).
% 0.60/0.68 tff(57,plain,
% 0.60/0.68 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.60/0.68 tff(58,plain,
% 0.60/0.68 (((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(59,plain,
% 0.60/0.68 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.60/0.68 inference(quant_inst,[status(thm)],[])).
% 0.60/0.68 tff(60,plain,
% 0.60/0.68 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (Xc = il(Xa, Xb, Xp, Xq)))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.60/0.68 tff(61,plain,
% 0.60/0.68 (Xc!2 = il(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[60, 57, 50])).
% 0.60/0.68 tff(62,plain,
% 0.60/0.68 (il(Xp!4, Xq!3, Xb!0, Xc!2) = Xc!2),
% 0.60/0.68 inference(symmetry,[status(thm)],[61])).
% 0.60/0.68 tff(63,plain,
% 0.60/0.68 (s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> s_col(Xp!4, Xq!3, Xc!2)),
% 0.60/0.68 inference(monotonicity,[status(thm)],[62])).
% 0.60/0.68 tff(64,plain,
% 0.60/0.68 (s_col(Xp!4, Xq!3, Xc!2) <=> s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.60/0.68 inference(symmetry,[status(thm)],[63])).
% 0.60/0.68 tff(65,plain,
% 0.60/0.68 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : refl((~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))) <=> (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))))),
% 0.60/0.69 inference(bind,[status(th)],[])).
% 0.60/0.69 tff(66,plain,
% 0.60/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.60/0.69 inference(quant_intro,[status(thm)],[65])).
% 0.60/0.69 tff(67,plain,
% 0.60/0.69 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : trans(monotonicity(rewrite(((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) <=> ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))), rewrite(((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) <=> ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))), ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))), rewrite((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))), ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))))),
% 0.60/0.69 inference(bind,[status(th)],[])).
% 0.60/0.69 tff(68,plain,
% 0.60/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.60/0.69 inference(quant_intro,[status(thm)],[67])).
% 0.60/0.69 tff(69,plain,
% 0.60/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.60/0.69 inference(rewrite,[status(thm)],[])).
% 0.60/0.69 tff(70,plain,
% 0.60/0.69 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))))), (((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)))), (((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))))), ((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)))), ((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))))), (((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))))), (((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))))), ((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))))), ((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))))), (((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))))), (((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))))), ((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))))), ((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))))), (((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))))), rewrite(((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))), (((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.60/0.69 inference(bind,[status(th)],[])).
% 0.60/0.69 tff(71,plain,
% 0.60/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.60/0.69 inference(quant_intro,[status(thm)],[70])).
% 0.60/0.69 tff(72,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((((((((((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz8_13a')).
% 0.60/0.69 tff(73,plain,
% 0.60/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.60/0.69 tff(74,plain,
% 0.60/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.60/0.69 tff(75,plain,(
% 0.60/0.69 ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc)) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc)))) & ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))),
% 0.60/0.69 inference(skolemize,[status(sab)],[74])).
% 0.60/0.69 tff(76,plain,
% 0.60/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.60/0.69 tff(77,plain,
% 0.60/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.60/0.69 tff(78,plain,
% 0.60/0.69 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : (~((~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xa = Xb)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xp = Xq)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, Xc))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xa, Xb, f813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_col(Xp, Xq, g813(Xa, Xb, Xp, Xq, Xc)))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = f813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | (~(Xc = g813(Xa, Xb, Xp, Xq, Xc))))) | (~((~perpAt(Xa, Xb, Xc, Xp, Xq)) | s_r(f813(Xa, Xb, Xp, Xq, Xc), Xc, g813(Xa, Xb, Xp, Xq, Xc))))))) | (~((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.60/0.69 inference(quant_inst,[status(thm)],[])).
% 0.60/0.69 tff(79,plain,
% 0.60/0.69 (~((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.60/0.69 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.60/0.69 tff(80,plain,
% 0.60/0.69 (((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))),
% 0.60/0.69 inference(tautology,[status(thm)],[])).
% 0.60/0.69 tff(81,plain,
% 0.60/0.69 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2)),
% 0.60/0.69 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.60/0.69 tff(82,plain,
% 0.60/0.69 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2)),
% 0.60/0.69 inference(tautology,[status(thm)],[])).
% 0.60/0.69 tff(83,plain,
% 0.60/0.69 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | s_col(Xp!4, Xq!3, Xc!2)),
% 0.60/0.69 inference(unit_resolution,[status(thm)],[82, 50])).
% 0.60/0.69 tff(84,plain,
% 0.60/0.69 (s_col(Xp!4, Xq!3, Xc!2)),
% 0.60/0.69 inference(unit_resolution,[status(thm)],[83, 81])).
% 0.60/0.69 tff(85,plain,
% 0.60/0.69 (s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[84, 64])).
% 0.60/0.69 tff(86,plain,
% 0.60/0.69 (perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.60/0.69 inference(monotonicity,[status(thm)],[62])).
% 0.60/0.69 tff(87,plain,
% 0.60/0.69 (perp(Xp!4, Xq!3, Xa!1, Xc!2) <=> perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.60/0.69 inference(symmetry,[status(thm)],[86])).
% 0.60/0.69 tff(88,plain,
% 0.60/0.69 (^[Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : refl((~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))))) <=> (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))))))),
% 0.60/0.69 inference(bind,[status(th)],[])).
% 0.60/0.69 tff(89,plain,
% 0.60/0.69 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))))) <=> ![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))),
% 0.60/0.69 inference(quant_intro,[status(thm)],[88])).
% 0.60/0.69 tff(90,plain,
% 0.60/0.69 (^[Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : trans(monotonicity(rewrite((perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))) <=> (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))), ((((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))))), rewrite((((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))), ((((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))))),
% 0.60/0.69 inference(bind,[status(th)],[])).
% 0.60/0.69 tff(91,plain,
% 0.60/0.69 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> ![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))),
% 0.60/0.69 inference(quant_intro,[status(thm)],[90])).
% 0.60/0.69 tff(92,plain,
% 0.60/0.69 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1)))) <=> ![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))),
% 0.60/0.69 inference(rewrite,[status(thm)],[])).
% 0.60/0.69 tff(93,axiom,(![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_Defn8_11b')).
% 0.60/0.69 tff(94,plain,
% 0.60/0.69 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.60/0.69 tff(95,plain,(
% 0.60/0.69 ![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1)) & (perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))),
% 0.60/0.69 inference(skolemize,[status(sab)],[94])).
% 0.60/0.69 tff(96,plain,
% 0.60/0.69 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.60/0.69 tff(97,plain,
% 0.60/0.69 (![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))),
% 0.60/0.69 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.60/0.69 tff(98,plain,
% 0.60/0.69 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))))))),
% 0.60/0.69 inference(rewrite,[status(thm)],[])).
% 0.60/0.69 tff(99,plain,
% 0.60/0.69 ((~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~(perp(Xp!4, Xq!3, Xa!1, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)))))) <=> (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)))))),
% 0.60/0.69 inference(rewrite,[status(thm)],[])).
% 0.60/0.69 tff(100,plain,
% 0.60/0.69 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~(perp(Xp!4, Xq!3, Xa!1, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2))))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))))))),
% 0.68/0.70 inference(monotonicity,[status(thm)],[99])).
% 0.68/0.70 tff(101,plain,
% 0.68/0.70 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~(perp(Xp!4, Xq!3, Xa!1, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2))))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))))))),
% 0.68/0.70 inference(transitivity,[status(thm)],[100, 98])).
% 0.68/0.70 tff(102,plain,
% 0.68/0.70 ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~(perp(Xp!4, Xq!3, Xa!1, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2))))))),
% 0.68/0.70 inference(quant_inst,[status(thm)],[])).
% 0.68/0.70 tff(103,plain,
% 0.68/0.70 ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)))))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.68/0.70 tff(104,plain,
% 0.68/0.70 (~((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))))),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[103, 97])).
% 0.68/0.70 tff(105,plain,
% 0.68/0.70 (((~((~perp(Xp!4, Xq!3, Xa!1, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xa!1, Xc!2), Xa!1, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))),
% 0.68/0.70 inference(tautology,[status(thm)],[])).
% 0.68/0.70 tff(106,plain,
% 0.68/0.70 ((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.68/0.70 tff(107,plain,
% 0.68/0.70 (perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)),
% 0.68/0.70 inference(or_elim,[status(thm)],[49])).
% 0.68/0.70 tff(108,plain,
% 0.68/0.70 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.68/0.70 inference(tautology,[status(thm)],[])).
% 0.68/0.70 tff(109,plain,
% 0.68/0.70 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xa!1, Xc!2)) | perp(Xp!4, Xq!3, Xa!1, Xc!2))) | perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.68/0.70 tff(110,plain,
% 0.68/0.70 (perp(Xp!4, Xq!3, Xa!1, Xc!2)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.68/0.70 tff(111,plain,
% 0.68/0.70 (perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[110, 87])).
% 0.68/0.70 tff(112,plain,
% 0.68/0.70 ((f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = Xc!2) <=> (Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.70 inference(commutativity,[status(thm)],[])).
% 0.68/0.70 tff(113,plain,
% 0.68/0.70 ((f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = Xc!2)),
% 0.68/0.70 inference(monotonicity,[status(thm)],[62])).
% 0.68/0.70 tff(114,plain,
% 0.68/0.70 ((f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> (Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.70 inference(transitivity,[status(thm)],[113, 112])).
% 0.68/0.70 tff(115,plain,
% 0.68/0.70 ((Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) <=> (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.68/0.70 inference(symmetry,[status(thm)],[114])).
% 0.68/0.70 tff(116,plain,
% 0.68/0.70 ((~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) <=> (~(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.68/0.70 inference(monotonicity,[status(thm)],[115])).
% 0.68/0.70 tff(117,plain,
% 0.68/0.70 (((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.68/0.70 inference(tautology,[status(thm)],[])).
% 0.68/0.70 tff(118,plain,
% 0.68/0.70 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[117, 79])).
% 0.68/0.70 tff(119,plain,
% 0.68/0.70 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.70 inference(tautology,[status(thm)],[])).
% 0.68/0.70 tff(120,plain,
% 0.68/0.70 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[119, 50])).
% 0.68/0.70 tff(121,plain,
% 0.68/0.70 (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[120, 118])).
% 0.68/0.70 tff(122,plain,
% 0.68/0.70 (~(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[121, 116])).
% 0.68/0.70 tff(123,plain,
% 0.68/0.70 (((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.70 inference(tautology,[status(thm)],[])).
% 0.68/0.70 tff(124,plain,
% 0.68/0.70 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[123, 79])).
% 0.68/0.70 tff(125,plain,
% 0.68/0.70 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.70 inference(tautology,[status(thm)],[])).
% 0.68/0.70 tff(126,plain,
% 0.68/0.70 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[125, 50])).
% 0.68/0.70 tff(127,plain,
% 0.68/0.70 (s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[126, 124])).
% 0.68/0.70 tff(128,plain,
% 0.68/0.70 (~(Xp!4 = Xq!3)),
% 0.68/0.70 inference(or_elim,[status(thm)],[49])).
% 0.68/0.70 tff(129,plain,
% 0.68/0.70 ((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.71 inference(tautology,[status(thm)],[])).
% 0.68/0.71 tff(130,plain,
% 0.68/0.71 ((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[129, 128, 127])).
% 0.68/0.71 tff(131,plain,
% 0.68/0.71 (s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[130, 122, 111, 85, 36])).
% 0.68/0.71 tff(132,plain,
% 0.68/0.71 ((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.71 inference(tautology,[status(thm)],[])).
% 0.68/0.71 tff(133,plain,
% 0.68/0.71 ((~((~s_r(Xa!1, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.68/0.71 tff(134,plain,
% 0.68/0.71 (s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[133, 14])).
% 0.68/0.71 tff(135,plain,
% 0.68/0.71 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))) | (~((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(136,plain,
% 0.68/0.71 (~((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[135, 10])).
% 0.68/0.71 tff(137,plain,
% 0.68/0.71 (((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) | ((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.68/0.71 inference(tautology,[status(thm)],[])).
% 0.68/0.71 tff(138,plain,
% 0.68/0.71 ((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.68/0.71 tff(139,plain,
% 0.68/0.71 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(140,plain,
% 0.68/0.71 ((~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))))) <=> (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(141,plain,
% 0.68/0.71 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[140])).
% 0.68/0.71 tff(142,plain,
% 0.68/0.71 (((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))) <=> ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.68/0.71 inference(transitivity,[status(thm)],[141, 139])).
% 0.68/0.71 tff(143,plain,
% 0.68/0.71 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)))))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(144,plain,
% 0.68/0.72 ((~![Xa: $i, Xb: $i, Xp: $i, Xq: $i, Xc: $i] : (~((~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | (~s_col(Xa, Xb, Xc)) | (~perp(Xa, Xb, Xc, Xp)))) | (~((Xa = Xb) | (~s_col(Xa, Xb, Xp)) | (Xq = Xp) | (~s_col(Xa, Xb, Xq)) | s_r(Xc, Xp, Xq) | (~perp(Xa, Xb, Xc, Xp))))))) | (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.68/0.72 tff(145,plain,
% 0.68/0.72 (~((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[144, 27])).
% 0.68/0.72 tff(146,plain,
% 0.68/0.72 (((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, Xb!0)) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.72 inference(tautology,[status(thm)],[])).
% 0.68/0.72 tff(147,plain,
% 0.68/0.72 ((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.68/0.72 tff(148,plain,
% 0.68/0.72 (perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.68/0.72 inference(monotonicity,[status(thm)],[62])).
% 0.68/0.72 tff(149,plain,
% 0.68/0.72 (perp(Xp!4, Xq!3, Xb!0, Xc!2) <=> perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.68/0.72 inference(symmetry,[status(thm)],[148])).
% 0.68/0.72 tff(150,plain,
% 0.68/0.72 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))))))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(151,plain,
% 0.68/0.72 ((~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~(perp(Xp!4, Xq!3, Xb!0, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)))))) <=> (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)))))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(152,plain,
% 0.68/0.72 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~(perp(Xp!4, Xq!3, Xb!0, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2))))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[151])).
% 0.68/0.72 tff(153,plain,
% 0.68/0.72 (((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~(perp(Xp!4, Xq!3, Xb!0, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2))))))) <=> ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))))))),
% 0.68/0.72 inference(transitivity,[status(thm)],[152, 150])).
% 0.68/0.72 tff(154,plain,
% 0.68/0.72 ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~(perp(Xp!4, Xq!3, Xb!0, Xc!2) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2))))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(155,plain,
% 0.68/0.72 ((~![Xp: $i, Xq: $i, Xp1: $i, Xq1: $i, X: $i] : (~((~((~perp(Xp, Xq, Xp1, Xq1)) | perpAt(Xp, Xq, il(Xp, Xq, Xp1, Xq1), Xp1, Xq1))) | (~(perp(Xp, Xq, Xp1, Xq1) | (~perpAt(Xp, Xq, X, Xp1, Xq1))))))) | (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)))))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.68/0.72 tff(156,plain,
% 0.68/0.72 (~((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[155, 97])).
% 0.68/0.72 tff(157,plain,
% 0.68/0.72 (((~((~perp(Xp!4, Xq!3, Xb!0, Xc!2)) | perpAt(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2), Xb!0, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.68/0.72 inference(tautology,[status(thm)],[])).
% 0.68/0.72 tff(158,plain,
% 0.68/0.72 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.68/0.72 tff(159,plain,
% 0.68/0.72 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.68/0.72 inference(tautology,[status(thm)],[])).
% 0.68/0.72 tff(160,plain,
% 0.68/0.72 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perp(Xp!4, Xq!3, Xb!0, Xc!2))) | perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[159, 50])).
% 0.68/0.72 tff(161,plain,
% 0.68/0.72 (perp(Xp!4, Xq!3, Xb!0, Xc!2)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[160, 158])).
% 0.68/0.72 tff(162,plain,
% 0.68/0.72 (perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[161, 149])).
% 0.68/0.72 tff(163,plain,
% 0.68/0.72 ((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.72 inference(tautology,[status(thm)],[])).
% 0.68/0.72 tff(164,plain,
% 0.68/0.72 ((~((Xp!4 = Xq!3) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~perp(Xp!4, Xq!3, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[163, 128, 127])).
% 0.68/0.72 tff(165,plain,
% 0.68/0.72 (s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[164, 122, 162, 85, 147])).
% 0.68/0.72 tff(166,plain,
% 0.68/0.72 ((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.72 inference(tautology,[status(thm)],[])).
% 0.68/0.72 tff(167,plain,
% 0.68/0.72 ((~((~s_r(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.68/0.72 tff(168,plain,
% 0.68/0.72 (s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[167, 138])).
% 0.68/0.72 tff(169,plain,
% 0.68/0.72 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))) | (~((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(170,plain,
% 0.68/0.72 (~((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[169, 10])).
% 0.68/0.73 tff(171,plain,
% 0.68/0.73 (((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~(s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) | ((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.68/0.73 inference(tautology,[status(thm)],[])).
% 0.68/0.73 tff(172,plain,
% 0.68/0.73 ((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.68/0.73 tff(173,plain,
% 0.68/0.73 (^[Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : refl((~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))) <=> (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))))),
% 0.68/0.73 inference(bind,[status(th)],[])).
% 0.68/0.73 tff(174,plain,
% 0.68/0.73 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))) <=> ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.68/0.73 inference(quant_intro,[status(thm)],[173])).
% 0.68/0.73 tff(175,plain,
% 0.68/0.73 (^[Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : trans(monotonicity(rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) <=> ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))), rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) <=> ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))), rewrite(((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))), rewrite(((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))), rewrite(((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))), rewrite(((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))), rewrite((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))), ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))))),
% 0.68/0.73 inference(bind,[status(th)],[])).
% 0.68/0.73 tff(176,plain,
% 0.68/0.73 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.68/0.73 inference(quant_intro,[status(thm)],[175])).
% 0.68/0.73 tff(177,plain,
% 0.68/0.73 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(178,plain,
% 0.68/0.73 (^[Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) <=> ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))), (((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))))), (((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))))), rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) <=> ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))), ((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))))), ((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))))), trans(monotonicity(trans(monotonicity(rewrite(((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) <=> ((~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1)))), ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) <=> (((~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))) | (~s_col(Y1, Z1, V))))), rewrite((((~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))) | (~s_col(Y1, Z1, V))) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1)))), ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))))), (((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V)) <=> (((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))) | s_r(U, X, V)))), rewrite((((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | (~perpAt(Y, Z, X, Y1, Z1))) | s_r(U, X, V)) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))), (((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V)) <=> ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))))), (((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))))), (((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) <=> ((Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> (((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)))), rewrite((((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> (((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))))), rewrite((((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))))), ((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))))), ((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) <=> ((Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> (((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)))), rewrite((((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> (((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))))), rewrite((((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))))), (((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))))), (((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) <=> ((Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> (((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)))), rewrite((((Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1))), (((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) <=> ((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> (((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))))), rewrite((((Y1 = Z1) | (Y = Z) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))) <=> (((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))))), rewrite((((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))), ((((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))) <=> ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))))) <=> ((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))))), rewrite(((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))), ((((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))))) <=> (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.68/0.73 inference(bind,[status(th)],[])).
% 0.68/0.73 tff(179,plain,
% 0.68/0.73 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))))) <=> ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.68/0.73 inference(quant_intro,[status(thm)],[178])).
% 0.68/0.73 tff(180,axiom,(![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((((((((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) & ((((~perpAt(Y, Z, X, Y1, Z1)) | (~s_col(Y, Z, U))) | (~s_col(Y1, Z1, V))) | s_r(U, X, V))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) & (((((perpAt(Y, Z, X, Y1, Z1) | (Y = Z)) | (Y1 = Z1)) | (~s_col(Y, Z, X))) | (~s_col(Y1, Z1, X))) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_Defn8_11a')).
% 0.68/0.73 tff(181,plain,
% 0.68/0.73 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.68/0.73 tff(182,plain,
% 0.68/0.73 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.68/0.73 tff(183,plain,(
% 0.68/0.73 ![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X)) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z))) & ((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1))) & ((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X))) & ((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))),
% 0.68/0.73 inference(skolemize,[status(sab)],[182])).
% 0.68/0.73 tff(184,plain,
% 0.68/0.73 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.68/0.73 tff(185,plain,
% 0.68/0.73 (![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[184, 174])).
% 0.68/0.73 tff(186,plain,
% 0.68/0.73 (((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))) <=> ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(187,plain,
% 0.68/0.74 ((~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xp!4 = Xq!3)))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3))))) <=> (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(188,plain,
% 0.68/0.74 (((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xp!4 = Xq!3)))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))))) <=> ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.68/0.75 inference(monotonicity,[status(thm)],[187])).
% 0.68/0.75 tff(189,plain,
% 0.68/0.75 (((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xp!4 = Xq!3)))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))))) <=> ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))))),
% 0.73/0.75 inference(transitivity,[status(thm)],[188, 186])).
% 0.73/0.75 tff(190,plain,
% 0.73/0.75 ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~(Xp!4 = Xq!3)))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(191,plain,
% 0.73/0.76 ((~![Y: $i, Z: $i, X: $i, Y1: $i, Z1: $i, U: $i, V: $i] : (~((~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y, Z, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | s_col(Y1, Z1, X))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y = Z)))) | (~((~perpAt(Y, Z, X, Y1, Z1)) | (~(Y1 = Z1)))) | (~((~s_col(Y1, Z1, V)) | (~s_col(Y, Z, U)) | s_r(U, X, V) | (~perpAt(Y, Z, X, Y1, Z1)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y, Z, f811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1) | s_col(Y1, Z1, g811(Y, Z, Y1, Z1, X)))) | (~((Y1 = Z1) | (Y = Z) | (~s_col(Y, Z, X)) | (~s_r(f811(Y, Z, Y1, Z1, X), X, g811(Y, Z, Y1, Z1, X))) | (~s_col(Y1, Z1, X)) | perpAt(Y, Z, X, Y1, Z1)))))) | (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.73/0.76 tff(192,plain,
% 0.73/0.76 (~((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[191, 185])).
% 0.73/0.76 tff(193,plain,
% 0.73/0.76 (((~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))) | (~((~(Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((~(Xp!4 = Xq!3)) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_col(Xp!4, Xq!3, g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))))) | (~((Xp!4 = Xq!3) | (Xb!0 = il(Xp!4, Xq!3, Xb!0, Xc!2)) | (~s_col(Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2))) | perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | (~s_r(f811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)), il(Xp!4, Xq!3, Xb!0, Xc!2), g811(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3, il(Xp!4, Xq!3, Xb!0, Xc!2)))))) | (~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.73/0.76 inference(tautology,[status(thm)],[])).
% 0.73/0.76 tff(194,plain,
% 0.73/0.76 ((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.73/0.76 tff(195,plain,
% 0.73/0.76 (perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3) <=> perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3)),
% 0.73/0.76 inference(monotonicity,[status(thm)],[62, 62])).
% 0.73/0.76 tff(196,plain,
% 0.73/0.76 (perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3) <=> perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)),
% 0.73/0.76 inference(symmetry,[status(thm)],[195])).
% 0.73/0.76 tff(197,plain,
% 0.73/0.76 (^[Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : refl(((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb)) <=> ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb)))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(198,plain,
% 0.73/0.76 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[197])).
% 0.73/0.76 tff(199,plain,
% 0.73/0.76 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(200,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz8_12a')).
% 0.73/0.76 tff(201,plain,
% 0.73/0.76 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.73/0.76 tff(202,plain,(
% 0.73/0.76 ![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.73/0.76 inference(skolemize,[status(sab)],[201])).
% 0.73/0.76 tff(203,plain,
% 0.73/0.76 (![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.73/0.76 tff(204,plain,
% 0.73/0.76 (((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(205,plain,
% 0.73/0.76 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3))),
% 0.73/0.77 inference(quant_inst,[status(thm)],[])).
% 0.73/0.77 tff(206,plain,
% 0.73/0.77 ((~![Xa: $i, Xb: $i, Xc: $i, Xp: $i, Xq: $i] : ((~perpAt(Xa, Xb, Xc, Xp, Xq)) | perpAt(Xp, Xq, Xc, Xa, Xb))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3)),
% 0.73/0.77 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.73/0.77 tff(207,plain,
% 0.73/0.77 (perpAt(Xb!0, Xc!2, Xc!2, Xp!4, Xq!3)),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[206, 203, 50])).
% 0.73/0.77 tff(208,plain,
% 0.73/0.77 (perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)),
% 0.73/0.77 inference(modus_ponens,[status(thm)],[207, 196])).
% 0.73/0.77 tff(209,plain,
% 0.73/0.77 (s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> s_col(Xb!0, Xc!2, Xc!2)),
% 0.73/0.77 inference(monotonicity,[status(thm)],[62, 62])).
% 0.73/0.77 tff(210,plain,
% 0.73/0.77 (s_col(Xb!0, Xc!2, Xc!2) <=> s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.73/0.77 inference(symmetry,[status(thm)],[209])).
% 0.73/0.77 tff(211,plain,
% 0.73/0.77 (((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xp!4 = Xq!3)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xb!0 = Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, Xc!2))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | (~(Xc!2 = g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_r(f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xc!2, g813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))),
% 0.73/0.77 inference(tautology,[status(thm)],[])).
% 0.73/0.77 tff(212,plain,
% 0.73/0.77 ((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2)),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[211, 79])).
% 0.73/0.77 tff(213,plain,
% 0.73/0.77 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | (~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2)),
% 0.73/0.77 inference(tautology,[status(thm)],[])).
% 0.73/0.77 tff(214,plain,
% 0.73/0.77 ((~((~perpAt(Xp!4, Xq!3, Xc!2, Xb!0, Xc!2)) | s_col(Xb!0, Xc!2, Xc!2))) | s_col(Xb!0, Xc!2, Xc!2)),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[213, 50])).
% 0.73/0.77 tff(215,plain,
% 0.73/0.77 (s_col(Xb!0, Xc!2, Xc!2)),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[214, 212])).
% 0.73/0.77 tff(216,plain,
% 0.73/0.77 (s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.73/0.77 inference(modus_ponens,[status(thm)],[215, 210])).
% 0.73/0.77 tff(217,plain,
% 0.73/0.77 ((~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.73/0.77 inference(tautology,[status(thm)],[])).
% 0.73/0.77 tff(218,plain,
% 0.73/0.77 ((~((~s_col(Xp!4, Xq!3, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~perpAt(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), Xp!4, Xq!3)) | (~s_col(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2))) | s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[217, 127])).
% 0.73/0.77 tff(219,plain,
% 0.73/0.77 (s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[218, 216, 208, 194])).
% 0.73/0.77 tff(220,plain,
% 0.73/0.77 ((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | (~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.73/0.77 inference(tautology,[status(thm)],[])).
% 0.73/0.77 tff(221,plain,
% 0.73/0.77 ((~((~s_r(il(Xp!4, Xq!3, Xb!0, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) | s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.73/0.77 tff(222,plain,
% 0.73/0.77 (s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.73/0.77 inference(unit_resolution,[status(thm)],[221, 172])).
% 0.73/0.77 tff(223,plain,
% 0.73/0.77 (s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) <=> s_t(Xb!0, Xc!2, Xa!1)),
% 0.73/0.77 inference(monotonicity,[status(thm)],[62])).
% 0.73/0.77 tff(224,plain,
% 0.73/0.77 (s_t(Xb!0, Xc!2, Xa!1) <=> s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1)),
% 0.73/0.77 inference(symmetry,[status(thm)],[223])).
% 0.73/0.77 tff(225,plain,
% 0.73/0.77 ((~s_t(Xb!0, Xc!2, Xa!1)) <=> (~s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1))),
% 0.73/0.77 inference(monotonicity,[status(thm)],[224])).
% 0.73/0.77 tff(226,plain,
% 0.73/0.77 (^[Xa: $i, Xb: $i, Xc: $i] : refl((~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))))),
% 0.73/0.77 inference(bind,[status(th)],[])).
% 0.73/0.77 tff(227,plain,
% 0.73/0.77 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.73/0.77 inference(quant_intro,[status(thm)],[226])).
% 0.73/0.77 tff(228,plain,
% 0.73/0.77 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(rewrite((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) <=> (s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))) <=> (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))), (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))), rewrite(((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))), (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))))),
% 0.73/0.77 inference(bind,[status(th)],[])).
% 0.73/0.77 tff(229,plain,
% 0.73/0.77 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.73/0.77 inference(quant_intro,[status(thm)],[228])).
% 0.73/0.77 tff(230,plain,
% 0.73/0.77 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.73/0.77 inference(rewrite,[status(thm)],[])).
% 0.73/0.77 tff(231,plain,
% 0.73/0.77 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(rewrite((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa))) <=> ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))), (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) <=> (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))))), rewrite((((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)))), (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))))), rewrite((s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))) <=> (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))), ((((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> (((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))))), rewrite((((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))), ((((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.73/0.77 inference(bind,[status(th)],[])).
% 0.73/0.77 tff(232,plain,
% 0.73/0.77 (![Xa: $i, Xb: $i, Xc: $i] : (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb)))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.73/0.77 inference(quant_intro,[status(thm)],[231])).
% 0.73/0.77 tff(233,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((((((~s_col(Xa, Xb, Xc)) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) & (s_col(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xc)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xb, Xc, Xa)))) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_Defn4_10')).
% 0.73/0.77 tff(234,plain,
% 0.73/0.77 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.73/0.77 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.73/0.77 tff(235,plain,
% 0.73/0.77 (![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.73/0.77 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.73/0.77 tff(236,plain,(
% 0.73/0.77 ![Xa: $i, Xb: $i, Xc: $i] : ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb)) & ((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc)) & ((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc)) & (s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))),
% 0.73/0.77 inference(skolemize,[status(sab)],[235])).
% 0.73/0.77 tff(237,plain,
% 0.73/0.77 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.73/0.77 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.73/0.77 tff(238,plain,
% 0.73/0.77 (![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))),
% 0.73/0.77 inference(modus_ponens,[status(thm)],[237, 227])).
% 0.73/0.77 tff(239,plain,
% 0.73/0.77 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1))))))),
% 0.73/0.77 inference(rewrite,[status(thm)],[])).
% 0.73/0.77 tff(240,plain,
% 0.73/0.77 ((~((~(s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | (~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xb!0, Xc!2, Xa!1))) | (~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))))) <=> (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))))),
% 0.73/0.77 inference(rewrite,[status(thm)],[])).
% 0.73/0.77 tff(241,plain,
% 0.73/0.77 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | (~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xb!0, Xc!2, Xa!1))) | (~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1))))))),
% 0.73/0.77 inference(monotonicity,[status(thm)],[240])).
% 0.73/0.77 tff(242,plain,
% 0.73/0.77 (((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | (~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xb!0, Xc!2, Xa!1))) | (~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1))))))),
% 0.73/0.77 inference(transitivity,[status(thm)],[241, 239])).
% 0.73/0.77 tff(243,plain,
% 0.73/0.77 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~(s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | (~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xb!0, Xc!2, Xa!1))) | (~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))))))),
% 0.73/0.77 inference(quant_inst,[status(thm)],[])).
% 0.73/0.77 tff(244,plain,
% 0.73/0.77 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~(s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_col(Xa, Xb, Xc)) | s_t(Xc, Xa, Xb))) | (~((~s_t(Xa, Xb, Xc)) | s_col(Xa, Xb, Xc))) | (~((~s_t(Xb, Xc, Xa)) | s_col(Xa, Xb, Xc))) | (~(s_col(Xa, Xb, Xc) | (~s_t(Xc, Xa, Xb))))))) | (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))))),
% 0.73/0.78 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.73/0.78 tff(245,plain,
% 0.73/0.78 (~((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1))))),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[244, 238])).
% 0.73/0.78 tff(246,plain,
% 0.73/0.78 (((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))) | (s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))),
% 0.73/0.78 inference(tautology,[status(thm)],[])).
% 0.73/0.78 tff(247,plain,
% 0.73/0.78 (s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.73/0.78 tff(248,plain,
% 0.73/0.78 (~s_col(Xc!2, Xa!1, Xb!0)),
% 0.73/0.78 inference(or_elim,[status(thm)],[49])).
% 0.73/0.78 tff(249,plain,
% 0.73/0.78 ((~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1))),
% 0.73/0.78 inference(tautology,[status(thm)],[])).
% 0.73/0.78 tff(250,plain,
% 0.73/0.78 ((~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~s_t(Xb!0, Xc!2, Xa!1))),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.73/0.78 tff(251,plain,
% 0.73/0.78 (~s_t(Xb!0, Xc!2, Xa!1)),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[250, 247])).
% 0.73/0.78 tff(252,plain,
% 0.73/0.78 (~s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1)),
% 0.73/0.78 inference(modus_ponens,[status(thm)],[251, 225])).
% 0.73/0.78 tff(253,plain,
% 0.73/0.78 (s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) <=> s_t(Xa!1, Xb!0, Xc!2)),
% 0.73/0.78 inference(monotonicity,[status(thm)],[62])).
% 0.73/0.78 tff(254,plain,
% 0.73/0.78 (s_t(Xa!1, Xb!0, Xc!2) <=> s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.73/0.78 inference(symmetry,[status(thm)],[253])).
% 0.73/0.78 tff(255,plain,
% 0.73/0.78 ((~s_t(Xa!1, Xb!0, Xc!2)) <=> (~s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.73/0.78 inference(monotonicity,[status(thm)],[254])).
% 0.73/0.78 tff(256,plain,
% 0.73/0.78 (((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))) | ((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))),
% 0.73/0.78 inference(tautology,[status(thm)],[])).
% 0.73/0.78 tff(257,plain,
% 0.73/0.78 ((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0)),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[256, 245])).
% 0.73/0.78 tff(258,plain,
% 0.73/0.78 ((~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0)),
% 0.73/0.78 inference(tautology,[status(thm)],[])).
% 0.73/0.78 tff(259,plain,
% 0.73/0.78 ((~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~s_t(Xa!1, Xb!0, Xc!2))),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[258, 248])).
% 0.73/0.78 tff(260,plain,
% 0.73/0.78 (~s_t(Xa!1, Xb!0, Xc!2)),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[259, 257])).
% 0.73/0.78 tff(261,plain,
% 0.73/0.78 (~s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.73/0.78 inference(modus_ponens,[status(thm)],[260, 255])).
% 0.73/0.78 tff(262,plain,
% 0.73/0.78 (s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) <=> s_t(Xc!2, Xa!1, Xb!0)),
% 0.73/0.78 inference(monotonicity,[status(thm)],[62])).
% 0.73/0.78 tff(263,plain,
% 0.73/0.78 (s_t(Xc!2, Xa!1, Xb!0) <=> s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0)),
% 0.73/0.78 inference(symmetry,[status(thm)],[262])).
% 0.73/0.78 tff(264,plain,
% 0.73/0.78 ((~s_t(Xc!2, Xa!1, Xb!0)) <=> (~s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0))),
% 0.73/0.78 inference(monotonicity,[status(thm)],[263])).
% 0.73/0.78 tff(265,plain,
% 0.73/0.78 (((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~((~s_t(Xa!1, Xb!0, Xc!2)) | s_col(Xc!2, Xa!1, Xb!0))) | (~(s_col(Xc!2, Xa!1, Xb!0) | (~s_t(Xb!0, Xc!2, Xa!1)))) | (~((~s_col(Xc!2, Xa!1, Xb!0)) | s_t(Xa!1, Xb!0, Xc!2) | s_t(Xc!2, Xa!1, Xb!0) | s_t(Xb!0, Xc!2, Xa!1)))) | ((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))),
% 0.73/0.78 inference(tautology,[status(thm)],[])).
% 0.73/0.78 tff(266,plain,
% 0.73/0.78 ((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0)),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[265, 245])).
% 0.73/0.78 tff(267,plain,
% 0.73/0.78 ((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0)),
% 0.73/0.78 inference(tautology,[status(thm)],[])).
% 0.73/0.78 tff(268,plain,
% 0.73/0.78 ((~((~s_t(Xc!2, Xa!1, Xb!0)) | s_col(Xc!2, Xa!1, Xb!0))) | (~s_t(Xc!2, Xa!1, Xb!0))),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[267, 248])).
% 0.73/0.78 tff(269,plain,
% 0.73/0.78 (~s_t(Xc!2, Xa!1, Xb!0)),
% 0.73/0.78 inference(unit_resolution,[status(thm)],[268, 266])).
% 0.73/0.78 tff(270,plain,
% 0.73/0.78 (~s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0)),
% 0.73/0.78 inference(modus_ponens,[status(thm)],[269, 264])).
% 0.73/0.78 tff(271,plain,
% 0.73/0.78 (^[Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : refl((s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) <=> (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))),
% 0.73/0.78 inference(bind,[status(th)],[])).
% 0.73/0.78 tff(272,plain,
% 0.73/0.78 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) <=> ![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.73/0.78 inference(quant_intro,[status(thm)],[271])).
% 0.73/0.78 tff(273,plain,
% 0.73/0.78 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) <=> ![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.73/0.78 inference(rewrite,[status(thm)],[])).
% 0.73/0.78 tff(274,plain,
% 0.73/0.78 (^[Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) <=> ((~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), ((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) <=> (((~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | (~s_e(Xb, Xp, Xb, Xq))))), rewrite((((~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | (~s_e(Xb, Xp, Xb, Xq))) <=> ((~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), ((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) <=> ((~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))), (((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) <=> (((~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | (~s_e(Xc, Xp, Xc, Xq))))), rewrite((((~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | (~s_e(Xc, Xp, Xc, Xq))) <=> ((~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), (((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) <=> ((~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))), ((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) <=> (((~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xa, Xb, Xc)))), rewrite((((~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xa, Xb, Xc)) <=> (s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), ((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) <=> (s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))), (((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) <=> ((s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xb, Xc, Xa)))), rewrite(((s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xb, Xc, Xa)) <=> (s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), (((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) <=> (s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)))), ((((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) <=> ((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xc, Xa, Xb)))), rewrite(((s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq)) | s_t(Xc, Xa, Xb)) <=> (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))), ((((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) <=> (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))))),
% 0.73/0.78 inference(bind,[status(th)],[])).
% 0.73/0.78 tff(275,plain,
% 0.73/0.78 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb)) <=> ![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.73/0.78 inference(quant_intro,[status(thm)],[274])).
% 0.73/0.78 tff(276,axiom,(![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (((((((Xp = Xq) | (~s_e(Xa, Xp, Xz, Xq))) | (~s_e(Xb, Xp, Xb, Xq))) | (~s_e(Xc, Xp, Xc, Xq))) | s_t(Xa, Xb, Xc)) | s_t(Xb, Xc, Xa)) | s_t(Xc, Xa, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aA9')).
% 0.73/0.78 tff(277,plain,
% 0.73/0.78 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.73/0.78 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.73/0.78 tff(278,plain,
% 0.73/0.78 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.73/0.78 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.73/0.78 tff(279,plain,(
% 0.73/0.78 ![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.73/0.78 inference(skolemize,[status(sab)],[278])).
% 0.73/0.78 tff(280,plain,
% 0.73/0.78 (![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))),
% 0.73/0.78 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.73/0.78 tff(281,plain,
% 0.73/0.78 (((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.73/0.78 inference(rewrite,[status(thm)],[])).
% 0.73/0.78 tff(282,plain,
% 0.73/0.78 ((s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) <=> (s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.73/0.78 inference(rewrite,[status(thm)],[])).
% 0.73/0.78 tff(283,plain,
% 0.73/0.78 (((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))))),
% 0.73/0.79 inference(monotonicity,[status(thm)],[282])).
% 0.73/0.79 tff(284,plain,
% 0.73/0.79 (((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))) <=> ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.73/0.79 inference(transitivity,[status(thm)],[283, 281])).
% 0.73/0.79 tff(285,plain,
% 0.73/0.79 ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | (s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))))),
% 0.73/0.79 inference(quant_inst,[status(thm)],[])).
% 0.73/0.79 tff(286,plain,
% 0.73/0.79 ((~![Xp: $i, Xq: $i, Xa: $i, Xz: $i, Xb: $i, Xc: $i] : (s_t(Xc, Xa, Xb) | s_t(Xb, Xc, Xa) | s_t(Xa, Xb, Xc) | (~s_e(Xc, Xp, Xc, Xq)) | (~s_e(Xb, Xp, Xb, Xq)) | (~s_e(Xa, Xp, Xz, Xq)) | (Xp = Xq))) | s_t(il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1, Xb!0) | s_t(Xa!1, Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2)) | s_t(Xb!0, il(Xp!4, Xq!3, Xb!0, Xc!2), Xa!1) | (~s_e(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), il(Xp!4, Xq!3, Xb!0, Xc!2), s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xb!0, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xb!0, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (~s_e(Xa!1, f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2), Xa!1, s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)))),
% 0.73/0.79 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.73/0.79 tff(287,plain,
% 0.73/0.79 (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.73/0.79 inference(unit_resolution,[status(thm)],[286, 280, 270, 261, 252, 222, 168, 134])).
% 0.73/0.79 tff(288,plain,
% 0.73/0.79 (s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)),
% 0.78/0.80 inference(symmetry,[status(thm)],[287])).
% 0.78/0.80 tff(289,plain,
% 0.78/0.80 (^[Xa: $i, Xp: $i] : refl(((~(s(Xa, Xp) = Xp)) | (Xp = Xa)) <=> ((~(s(Xa, Xp) = Xp)) | (Xp = Xa)))),
% 0.78/0.80 inference(bind,[status(th)],[])).
% 0.78/0.80 tff(290,plain,
% 0.78/0.80 (![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa)) <=> ![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.78/0.80 inference(quant_intro,[status(thm)],[289])).
% 0.78/0.80 tff(291,plain,
% 0.78/0.80 (![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa)) <=> ![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.78/0.80 inference(rewrite,[status(thm)],[])).
% 0.78/0.80 tff(292,axiom,(![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz7_10a')).
% 0.78/0.80 tff(293,plain,
% 0.78/0.80 (![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.78/0.80 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.78/0.80 tff(294,plain,(
% 0.78/0.80 ![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.78/0.80 inference(skolemize,[status(sab)],[293])).
% 0.78/0.80 tff(295,plain,
% 0.78/0.80 (![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))),
% 0.78/0.80 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.78/0.80 tff(296,plain,
% 0.78/0.80 (((~![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))) | ((~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)))) <=> ((~![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))) | (~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.78/0.80 inference(rewrite,[status(thm)],[])).
% 0.78/0.80 tff(297,plain,
% 0.78/0.80 ((~![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))) | ((~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2)))),
% 0.78/0.80 inference(quant_inst,[status(thm)],[])).
% 0.78/0.80 tff(298,plain,
% 0.78/0.80 ((~![Xa: $i, Xp: $i] : ((~(s(Xa, Xp) = Xp)) | (Xp = Xa))) | (~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))) | (f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2) = il(Xp!4, Xq!3, Xb!0, Xc!2))),
% 0.78/0.80 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.78/0.80 tff(299,plain,
% 0.78/0.80 (~(s(il(Xp!4, Xq!3, Xb!0, Xc!2), f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2)) = f813(Xp!4, Xq!3, Xb!0, Xc!2, Xc!2))),
% 0.78/0.80 inference(unit_resolution,[status(thm)],[298, 295, 122])).
% 0.78/0.80 tff(300,plain,
% 0.78/0.80 ($false),
% 0.78/0.80 inference(unit_resolution,[status(thm)],[299, 288])).
% 0.78/0.80 % SZS output end Proof
%------------------------------------------------------------------------------