TSTP Solution File: GEO495+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO495+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 20:36:47 EDT 2022
% Result : Theorem 0.51s 0.58s
% Output : Proof 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO495+1 : TPTP v8.1.0. Released v7.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 10:32:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.51/0.58 % SZS status Theorem
% 0.51/0.58 % SZS output start Proof
% 0.51/0.58 tff(s_e_type, type, (
% 0.51/0.58 s_e: ( $i * $i * $i * $i ) > $o)).
% 0.51/0.58 tff(tptp_fun_Xd_0_type, type, (
% 0.51/0.58 tptp_fun_Xd_0: $i)).
% 0.51/0.58 tff(ext_type, type, (
% 0.51/0.58 ext: ( $i * $i * $i * $i ) > $i)).
% 0.51/0.58 tff(tptp_fun_Xb_2_type, type, (
% 0.51/0.58 tptp_fun_Xb_2: $i)).
% 0.51/0.58 tff(tptp_fun_Xa_3_type, type, (
% 0.51/0.58 tptp_fun_Xa_3: $i)).
% 0.51/0.58 tff(tptp_fun_Xc_1_type, type, (
% 0.51/0.58 tptp_fun_Xc_1: $i)).
% 0.51/0.58 tff(gamma_type, type, (
% 0.51/0.58 gamma: $i)).
% 0.51/0.58 tff(alpha_type, type, (
% 0.51/0.58 alpha: $i)).
% 0.51/0.58 tff(insert_type, type, (
% 0.51/0.58 insert: ( $i * $i * $i * $i ) > $i)).
% 0.51/0.58 tff(ins_type, type, (
% 0.51/0.58 ins: ( $i * $i * $i * $i ) > $i)).
% 0.51/0.58 tff(s_t_type, type, (
% 0.51/0.58 s_t: ( $i * $i * $i ) > $o)).
% 0.51/0.58 tff(le_type, type, (
% 0.51/0.58 le: ( $i * $i * $i * $i ) > $o)).
% 0.51/0.58 tff(1,plain,
% 0.51/0.58 (^[Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : refl((insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb)) <=> (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb)))),
% 0.51/0.58 inference(bind,[status(th)],[])).
% 0.51/0.58 tff(2,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.51/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.51/0.58 tff(3,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.51/0.58 inference(rewrite,[status(thm)],[])).
% 0.51/0.58 tff(4,axiom,(![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_insert')).
% 0.51/0.58 tff(5,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.51/0.58 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.51/0.58 tff(6,plain,(
% 0.51/0.58 ![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.51/0.58 inference(skolemize,[status(sab)],[5])).
% 0.51/0.58 tff(7,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))),
% 0.51/0.58 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.51/0.58 tff(8,plain,
% 0.51/0.58 ((~![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))) | (insert(Xa!3, Xb!2, Xc!1, Xd!0) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.51/0.58 inference(quant_inst,[status(thm)],[])).
% 0.51/0.58 tff(9,plain,
% 0.51/0.58 (insert(Xa!3, Xb!2, Xc!1, Xd!0) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)),
% 0.51/0.58 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.51/0.58 tff(10,plain,
% 0.51/0.58 (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = insert(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.51/0.58 inference(symmetry,[status(thm)],[9])).
% 0.51/0.58 tff(11,assumption,(Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)), introduced(assumption)).
% 0.51/0.58 tff(12,plain,
% 0.51/0.58 (Xd!0 = insert(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.51/0.58 inference(transitivity,[status(thm)],[11, 10])).
% 0.51/0.58 tff(13,plain,
% 0.51/0.58 (s_e(Xa!3, Xb!2, Xc!1, Xd!0) <=> s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.51/0.58 inference(monotonicity,[status(thm)],[12])).
% 0.51/0.58 tff(14,plain,
% 0.51/0.58 (s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)) <=> s_e(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.51/0.58 inference(symmetry,[status(thm)],[13])).
% 0.51/0.58 tff(15,plain,
% 0.51/0.58 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : refl((~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))))),
% 0.51/0.58 inference(bind,[status(th)],[])).
% 0.51/0.58 tff(16,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.51/0.58 inference(quant_intro,[status(thm)],[15])).
% 0.51/0.58 tff(17,plain,
% 0.51/0.58 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : trans(monotonicity(rewrite(((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))) <=> ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))), ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))), rewrite((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))), ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))))),
% 0.51/0.58 inference(bind,[status(th)],[])).
% 0.51/0.58 tff(18,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.51/0.58 inference(quant_intro,[status(thm)],[17])).
% 0.51/0.58 tff(19,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.51/0.58 inference(rewrite,[status(thm)],[])).
% 0.51/0.58 tff(20,plain,
% 0.51/0.58 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : trans(monotonicity(rewrite((((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd)) <=> ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))), (((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & (((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd))) <=> ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))))), rewrite(((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y)))) <=> (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))), (((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & (((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd))) <=> (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.51/0.58 inference(bind,[status(th)],[])).
% 0.51/0.58 tff(21,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & (((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.51/0.58 inference(quant_intro,[status(thm)],[20])).
% 0.51/0.58 tff(22,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) & (((~s_t(Xc, Y, Xd)) | (~s_e(Xa, Xb, Xc, Y))) | le(Xa, Xb, Xc, Xd)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d_Defn5_4')).
% 0.51/0.58 tff(23,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.51/0.58 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.51/0.58 tff(24,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.51/0.58 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.51/0.58 tff(25,plain,(
% 0.51/0.58 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd)) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd))) & ((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))),
% 0.51/0.58 inference(skolemize,[status(sab)],[24])).
% 0.51/0.58 tff(26,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.51/0.58 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.51/0.58 tff(27,plain,
% 0.51/0.58 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))),
% 0.51/0.58 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.51/0.58 tff(28,plain,
% 0.51/0.58 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0)))))))),
% 0.51/0.58 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(29,plain,
% 0.51/0.59 ((~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~s_t(Xc!1, Xd!0, Xd!0)) | le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)))))) <=> (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(30,plain,
% 0.51/0.59 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~s_t(Xc!1, Xd!0, Xd!0)) | le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0)))))))),
% 0.51/0.59 inference(monotonicity,[status(thm)],[29])).
% 0.51/0.59 tff(31,plain,
% 0.51/0.59 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~s_t(Xc!1, Xd!0, Xd!0)) | le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0)))))))),
% 0.51/0.59 inference(transitivity,[status(thm)],[30, 28])).
% 0.51/0.59 tff(32,plain,
% 0.51/0.59 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~s_t(Xc!1, Xd!0, Xd!0)) | le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0))))))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(33,plain,
% 0.51/0.59 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.51/0.59 tff(34,plain,
% 0.51/0.59 (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0)))))),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[33, 27])).
% 0.51/0.59 tff(35,plain,
% 0.51/0.59 (((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))) | ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))),
% 0.51/0.59 inference(tautology,[status(thm)],[])).
% 0.51/0.59 tff(36,plain,
% 0.51/0.59 ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.51/0.59 tff(37,plain,
% 0.51/0.59 ((~(s_e(Xa!3, Xb!2, Xc!1, Xd!0) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)))) <=> (~(s_e(Xa!3, Xb!2, Xc!1, Xd!0) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (~le(Xc!1, Xd!0, Xa!3, Xb!2))))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(38,plain,
% 0.51/0.59 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))) <=> (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb))))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(39,plain,
% 0.51/0.59 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb))) | s_e(Xa, Xb, Xc, Xd))) <=> (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb))))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(40,axiom,(~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb))) | s_e(Xa, Xb, Xc, Xd))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz5_9')).
% 0.51/0.59 tff(41,plain,
% 0.51/0.59 (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.51/0.59 tff(42,plain,
% 0.51/0.59 (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.51/0.59 tff(43,plain,
% 0.51/0.59 (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.51/0.59 tff(44,plain,
% 0.51/0.59 (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.51/0.59 tff(45,plain,
% 0.51/0.59 (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.51/0.59 tff(46,plain,
% 0.51/0.59 (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.51/0.59 tff(47,plain,
% 0.51/0.59 (~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_e(Xa, Xb, Xc, Xd) | (~le(Xa, Xb, Xc, Xd)) | (~le(Xc, Xd, Xa, Xb)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.51/0.59 tff(48,plain,(
% 0.51/0.59 ~(s_e(Xa!3, Xb!2, Xc!1, Xd!0) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)))),
% 0.51/0.59 inference(skolemize,[status(sab)],[47])).
% 0.51/0.59 tff(49,plain,
% 0.51/0.59 (~(s_e(Xa!3, Xb!2, Xc!1, Xd!0) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[48, 37])).
% 0.51/0.59 tff(50,plain,
% 0.51/0.59 (le(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.51/0.59 inference(or_elim,[status(thm)],[49])).
% 0.51/0.59 tff(51,plain,
% 0.51/0.59 ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.51/0.59 inference(tautology,[status(thm)],[])).
% 0.51/0.59 tff(52,plain,
% 0.51/0.59 ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.51/0.59 tff(53,plain,
% 0.51/0.59 (s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[52, 36])).
% 0.51/0.59 tff(54,plain,
% 0.51/0.59 (s_e(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[53, 14])).
% 0.51/0.59 tff(55,plain,
% 0.51/0.59 (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.51/0.59 inference(or_elim,[status(thm)],[49])).
% 0.51/0.59 tff(56,plain,
% 0.51/0.59 ($false),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.51/0.59 tff(57,plain,(~(Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.59 tff(58,plain,
% 0.51/0.59 (s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1) <=> s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.51/0.59 inference(monotonicity,[status(thm)],[10])).
% 0.51/0.59 tff(59,plain,
% 0.51/0.59 (s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1) <=> s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.51/0.59 inference(symmetry,[status(thm)],[58])).
% 0.51/0.59 tff(60,plain,
% 0.51/0.59 (((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~(le(Xa!3, Xb!2, Xc!1, Xd!0) | (~s_e(Xa!3, Xb!2, Xc!1, Xd!0)) | (~s_t(Xc!1, Xd!0, Xd!0))))) | ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.51/0.59 inference(tautology,[status(thm)],[])).
% 0.51/0.59 tff(61,plain,
% 0.51/0.59 ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[60, 34])).
% 0.51/0.59 tff(62,plain,
% 0.51/0.59 ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.51/0.59 inference(tautology,[status(thm)],[])).
% 0.51/0.59 tff(63,plain,
% 0.51/0.59 ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[62, 50])).
% 0.51/0.59 tff(64,plain,
% 0.51/0.59 (s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[63, 61])).
% 0.51/0.59 tff(65,plain,
% 0.51/0.59 (^[Xa: $i, Xb: $i, Xc: $i] : refl(((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)))),
% 0.51/0.59 inference(bind,[status(th)],[])).
% 0.51/0.59 tff(66,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.51/0.59 inference(quant_intro,[status(thm)],[65])).
% 0.51/0.59 tff(67,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(68,axiom,(![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_2')).
% 0.51/0.59 tff(69,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.51/0.59 tff(70,plain,(
% 0.51/0.59 ![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.51/0.59 inference(skolemize,[status(sab)],[69])).
% 0.51/0.59 tff(71,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.51/0.59 tff(72,plain,
% 0.51/0.59 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) | s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) | s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(73,plain,
% 0.51/0.59 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) | s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.51/0.59 inference(quant_inst,[status(thm)],[])).
% 0.51/0.59 tff(74,plain,
% 0.51/0.59 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) | s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.51/0.59 tff(75,plain,
% 0.51/0.59 (s_t(Xd!0, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.51/0.59 inference(unit_resolution,[status(thm)],[74, 71, 64])).
% 0.51/0.59 tff(76,plain,
% 0.51/0.59 (s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[75, 59])).
% 0.51/0.59 tff(77,plain,
% 0.51/0.59 (^[Xa: $i, Xb: $i, Xc: $i] : refl(((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) <=> ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))))),
% 0.51/0.59 inference(bind,[status(th)],[])).
% 0.51/0.59 tff(78,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.51/0.59 inference(quant_intro,[status(thm)],[77])).
% 0.51/0.59 tff(79,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(80,plain,
% 0.51/0.59 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) <=> ((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)) <=> (((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)))), rewrite((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)) <=> ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)) <=> ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))))),
% 0.51/0.59 inference(bind,[status(th)],[])).
% 0.51/0.59 tff(81,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.51/0.59 inference(quant_intro,[status(thm)],[80])).
% 0.51/0.59 tff(82,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc))) | (Xa = Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_4')).
% 0.51/0.59 tff(83,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.51/0.59 tff(84,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.51/0.59 tff(85,plain,(
% 0.51/0.59 ![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.51/0.59 inference(skolemize,[status(sab)],[84])).
% 0.51/0.59 tff(86,plain,
% 0.51/0.59 (![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))),
% 0.51/0.59 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.51/0.59 tff(87,plain,
% 0.51/0.59 (((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(88,plain,
% 0.51/0.59 (((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1))) <=> ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(89,plain,
% 0.51/0.59 (((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[88])).
% 0.51/0.60 tff(90,plain,
% 0.51/0.60 (((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.51/0.60 inference(transitivity,[status(thm)],[89, 87])).
% 0.51/0.60 tff(91,plain,
% 0.51/0.60 ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(92,plain,
% 0.51/0.60 ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.51/0.60 tff(93,plain,
% 0.51/0.60 ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[92, 86])).
% 0.51/0.60 tff(94,plain,
% 0.51/0.60 ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[93, 76])).
% 0.51/0.60 tff(95,plain,
% 0.51/0.60 (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[94, 57])).
% 0.51/0.60 tff(96,plain,
% 0.51/0.60 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(97,plain,
% 0.51/0.60 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(98,plain,
% 0.51/0.60 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.51/0.60 tff(99,plain,
% 0.51/0.60 (~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[98, 71, 95])).
% 0.51/0.60 tff(100,plain,
% 0.51/0.60 (^[X: $i, Y: $i, W: $i, V: $i] : refl((~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V)))) <=> (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V)))))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(101,plain,
% 0.51/0.60 (![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V)))) <=> ![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[100])).
% 0.51/0.60 tff(102,plain,
% 0.51/0.60 (^[X: $i, Y: $i, W: $i, V: $i] : rewrite((s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V)) <=> (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V)))))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(103,plain,
% 0.51/0.60 (![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V)) <=> ![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[102])).
% 0.51/0.60 tff(104,plain,
% 0.51/0.60 (![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V)) <=> ![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(105,axiom,(![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax','aA4')).
% 0.51/0.60 tff(106,plain,
% 0.51/0.60 (![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.51/0.60 tff(107,plain,(
% 0.51/0.60 ![X: $i, Y: $i, W: $i, V: $i] : (s_t(X, Y, ext(X, Y, W, V)) & s_e(Y, ext(X, Y, W, V), W, V))),
% 0.51/0.60 inference(skolemize,[status(sab)],[106])).
% 0.51/0.60 tff(108,plain,
% 0.51/0.60 (![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.51/0.60 tff(109,plain,
% 0.51/0.60 (![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.51/0.60 tff(110,plain,
% 0.51/0.60 ((~![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))) | (~((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.51/0.60 inference(quant_inst,[status(thm)],[])).
% 0.51/0.60 tff(111,plain,
% 0.51/0.60 (~((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.51/0.60 tff(112,plain,
% 0.51/0.60 (((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.51/0.60 inference(tautology,[status(thm)],[])).
% 0.51/0.60 tff(113,plain,
% 0.51/0.60 (s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.51/0.60 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.51/0.60 tff(114,plain,
% 0.51/0.60 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl((s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) <=> (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(115,plain,
% 0.51/0.60 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[114])).
% 0.51/0.60 tff(116,plain,
% 0.51/0.60 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(117,plain,
% 0.51/0.60 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) <=> ((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)) <=> (((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)))), rewrite((((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)) <=> (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)) <=> (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))))),
% 0.51/0.60 inference(bind,[status(th)],[])).
% 0.51/0.60 tff(118,plain,
% 0.51/0.60 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.51/0.60 inference(quant_intro,[status(thm)],[117])).
% 0.51/0.60 tff(119,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xd))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_6b')).
% 0.51/0.60 tff(120,plain,
% 0.51/0.60 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.51/0.60 tff(121,plain,
% 0.51/0.60 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.51/0.60 tff(122,plain,(
% 0.51/0.60 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.51/0.60 inference(skolemize,[status(sab)],[121])).
% 0.51/0.60 tff(123,plain,
% 0.51/0.60 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))),
% 0.51/0.60 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.51/0.60 tff(124,plain,
% 0.51/0.60 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(125,plain,
% 0.51/0.60 ((s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.51/0.60 inference(rewrite,[status(thm)],[])).
% 0.51/0.60 tff(126,plain,
% 0.51/0.60 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))))),
% 0.51/0.60 inference(monotonicity,[status(thm)],[125])).
% 0.51/0.60 tff(127,plain,
% 0.51/0.60 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.51/0.61 inference(transitivity,[status(thm)],[126, 124])).
% 0.51/0.61 tff(128,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(129,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xa, Xb, Xd) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xa, Xc, Xd)))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.51/0.61 tff(130,plain,
% 0.51/0.61 (~s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[129, 123, 113, 99])).
% 0.51/0.61 tff(131,plain,
% 0.51/0.61 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)) | s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)) | s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(132,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)) | s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(133,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)) | s_t(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.51/0.61 tff(134,plain,
% 0.51/0.61 (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[133, 71, 130])).
% 0.51/0.61 tff(135,plain,
% 0.51/0.61 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl((~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))))),
% 0.51/0.61 inference(bind,[status(th)],[])).
% 0.51/0.61 tff(136,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))),
% 0.51/0.61 inference(quant_intro,[status(thm)],[135])).
% 0.51/0.61 tff(137,plain,
% 0.51/0.61 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : rewrite((((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))))),
% 0.51/0.61 inference(bind,[status(th)],[])).
% 0.51/0.61 tff(138,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))),
% 0.51/0.61 inference(quant_intro,[status(thm)],[137])).
% 0.51/0.61 tff(139,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(140,plain,
% 0.51/0.61 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : rewrite(((((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))))),
% 0.51/0.61 inference(bind,[status(th)],[])).
% 0.51/0.61 tff(141,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd)))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.51/0.61 inference(quant_intro,[status(thm)],[140])).
% 0.51/0.61 tff(142,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz5_5a')).
% 0.51/0.61 tff(143,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.51/0.61 tff(144,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.51/0.61 tff(145,plain,(
% 0.51/0.61 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb))) & ((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd)) & ((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))),
% 0.51/0.61 inference(skolemize,[status(sab)],[144])).
% 0.51/0.61 tff(146,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.51/0.61 tff(147,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[146, 136])).
% 0.51/0.61 tff(148,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(149,plain,
% 0.51/0.61 (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.51/0.61 tff(150,plain,
% 0.51/0.61 (((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) | ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.51/0.61 inference(tautology,[status(thm)],[])).
% 0.51/0.61 tff(151,plain,
% 0.51/0.61 ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.51/0.61 tff(152,plain,
% 0.51/0.61 (le(Xc!1, Xd!0, Xa!3, Xb!2)),
% 0.51/0.61 inference(or_elim,[status(thm)],[49])).
% 0.51/0.61 tff(153,plain,
% 0.51/0.61 ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.51/0.61 inference(tautology,[status(thm)],[])).
% 0.51/0.61 tff(154,plain,
% 0.51/0.61 ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.51/0.61 tff(155,plain,
% 0.51/0.61 (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[154, 151])).
% 0.51/0.61 tff(156,plain,
% 0.51/0.61 (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ins(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.51/0.61 inference(symmetry,[status(thm)],[155])).
% 0.51/0.61 tff(157,plain,
% 0.51/0.61 (^[Xa: $i, Xb: $i] : refl(s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)) <=> s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)))),
% 0.51/0.61 inference(bind,[status(th)],[])).
% 0.51/0.61 tff(158,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)) <=> ![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.51/0.61 inference(quant_intro,[status(thm)],[157])).
% 0.51/0.61 tff(159,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma)) <=> ![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(160,axiom,(![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_14a')).
% 0.51/0.61 tff(161,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.51/0.61 tff(162,plain,(
% 0.51/0.61 ![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.51/0.61 inference(skolemize,[status(sab)],[161])).
% 0.51/0.61 tff(163,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.51/0.61 tff(164,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i] : s_t(Xa, Xb, ext(Xa, Xb, alpha, gamma))) | s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(165,plain,
% 0.51/0.61 (s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.51/0.61 tff(166,plain,
% 0.51/0.61 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(167,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(168,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xd!0, Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.51/0.61 tff(169,plain,
% 0.51/0.61 (s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)),
% 0.51/0.61 inference(unit_resolution,[status(thm)],[168, 71, 165])).
% 0.51/0.61 tff(170,plain,
% 0.51/0.61 (s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) <=> s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.51/0.61 inference(monotonicity,[status(thm)],[10])).
% 0.51/0.61 tff(171,plain,
% 0.51/0.61 (s_t(Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0) <=> s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.51/0.61 inference(symmetry,[status(thm)],[170])).
% 0.51/0.61 tff(172,plain,
% 0.51/0.61 (s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[64, 171])).
% 0.51/0.61 tff(173,plain,
% 0.51/0.61 (^[Xa: $i, Xb: $i, Xd: $i, Xc: $i] : refl(((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd)) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd)))),
% 0.51/0.61 inference(bind,[status(th)],[])).
% 0.51/0.61 tff(174,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.51/0.61 inference(quant_intro,[status(thm)],[173])).
% 0.51/0.61 tff(175,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(176,plain,
% 0.51/0.61 (^[Xa: $i, Xb: $i, Xd: $i, Xc: $i] : trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)))), ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) | s_t(Xa, Xc, Xd)) <=> (((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd))) | s_t(Xa, Xc, Xd)))), rewrite((((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd))) | s_t(Xa, Xc, Xd)) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))), ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) | s_t(Xa, Xc, Xd)) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))))),
% 0.51/0.61 inference(bind,[status(th)],[])).
% 0.51/0.61 tff(177,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.51/0.61 inference(quant_intro,[status(thm)],[176])).
% 0.51/0.61 tff(178,axiom,(![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (((~s_t(Xa, Xb, Xd)) | (~s_t(Xb, Xc, Xd))) | s_t(Xa, Xc, Xd))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_5b')).
% 0.51/0.61 tff(179,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.51/0.61 tff(180,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.51/0.61 tff(181,plain,(
% 0.51/0.61 ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.51/0.61 inference(skolemize,[status(sab)],[180])).
% 0.51/0.61 tff(182,plain,
% 0.51/0.61 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))),
% 0.51/0.61 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.51/0.61 tff(183,plain,
% 0.51/0.61 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(184,plain,
% 0.51/0.61 (((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) <=> ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)))),
% 0.51/0.61 inference(rewrite,[status(thm)],[])).
% 0.51/0.61 tff(185,plain,
% 0.51/0.61 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))))),
% 0.51/0.61 inference(monotonicity,[status(thm)],[184])).
% 0.51/0.61 tff(186,plain,
% 0.51/0.61 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)))),
% 0.51/0.61 inference(transitivity,[status(thm)],[185, 183])).
% 0.51/0.61 tff(187,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))),
% 0.51/0.61 inference(quant_inst,[status(thm)],[])).
% 0.51/0.61 tff(188,plain,
% 0.51/0.61 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xd!0))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.51/0.62 tff(189,plain,
% 0.51/0.62 (s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[188, 182, 172, 169])).
% 0.51/0.62 tff(190,plain,
% 0.51/0.62 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(191,plain,
% 0.51/0.62 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(192,plain,
% 0.51/0.62 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.51/0.62 tff(193,plain,
% 0.51/0.62 (s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[192, 71, 189])).
% 0.51/0.62 tff(194,assumption,(~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)), introduced(assumption)).
% 0.51/0.62 tff(195,assumption,(~(Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))), introduced(assumption)).
% 0.51/0.62 tff(196,assumption,(~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))), introduced(assumption)).
% 0.51/0.62 tff(197,plain,
% 0.51/0.62 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl((s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) <=> (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(198,plain,
% 0.51/0.62 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[197])).
% 0.51/0.62 tff(199,plain,
% 0.51/0.62 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(200,plain,
% 0.51/0.62 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((Xa = Xb) | (~s_t(Xa, Xb, Xc))) <=> ((~s_t(Xa, Xb, Xc)) | (Xa = Xb))), ((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) <=> (((~s_t(Xa, Xb, Xc)) | (Xa = Xb)) | (~s_t(Xa, Xb, Xd))))), rewrite((((~s_t(Xa, Xb, Xc)) | (Xa = Xb)) | (~s_t(Xa, Xb, Xd))) <=> ((~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))), ((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) <=> ((~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))))), (((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) <=> (((~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)))), rewrite((((~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) <=> (s_t(Xb, Xc, Xd) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))), (((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) <=> (s_t(Xb, Xc, Xd) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))))), ((((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) | s_t(Xb, Xd, Xc)) <=> ((s_t(Xb, Xc, Xd) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xd, Xc)))), rewrite(((s_t(Xb, Xc, Xd) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xd, Xc)) <=> (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))), ((((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) | s_t(Xb, Xd, Xc)) <=> (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(201,plain,
% 0.51/0.62 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) | s_t(Xb, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[200])).
% 0.51/0.62 tff(202,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (((((Xa = Xb) | (~s_t(Xa, Xb, Xc))) | (~s_t(Xa, Xb, Xd))) | s_t(Xb, Xc, Xd)) | s_t(Xb, Xd, Xc))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz5_2')).
% 0.51/0.62 tff(203,plain,
% 0.51/0.62 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.51/0.62 tff(204,plain,
% 0.51/0.62 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.51/0.62 tff(205,plain,(
% 0.51/0.62 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.51/0.62 inference(skolemize,[status(sab)],[204])).
% 0.51/0.62 tff(206,plain,
% 0.51/0.62 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.51/0.62 tff(207,plain,
% 0.51/0.62 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(208,plain,
% 0.51/0.62 ((s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(209,plain,
% 0.51/0.62 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))))),
% 0.51/0.62 inference(monotonicity,[status(thm)],[208])).
% 0.51/0.62 tff(210,plain,
% 0.51/0.62 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.51/0.62 inference(transitivity,[status(thm)],[209, 207])).
% 0.51/0.62 tff(211,plain,
% 0.51/0.62 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(212,plain,
% 0.51/0.62 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (s_t(Xb, Xc, Xd) | s_t(Xb, Xd, Xc) | (~s_t(Xa, Xb, Xc)) | (Xa = Xb) | (~s_t(Xa, Xb, Xd)))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.59/0.63 tff(213,plain,
% 0.59/0.63 ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[212, 206, 76, 196])).
% 0.59/0.63 tff(214,plain,
% 0.59/0.63 (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[213, 195, 194])).
% 0.59/0.63 tff(215,plain,
% 0.59/0.63 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(216,plain,
% 0.59/0.63 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(217,plain,
% 0.59/0.63 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.59/0.63 tff(218,plain,
% 0.59/0.63 (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[217, 71, 214])).
% 0.59/0.63 tff(219,plain,
% 0.59/0.63 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(220,plain,
% 0.59/0.63 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(221,plain,
% 0.59/0.63 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.59/0.63 tff(222,plain,
% 0.59/0.63 ((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[221, 71])).
% 0.59/0.63 tff(223,plain,
% 0.59/0.63 (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[222, 113])).
% 0.59/0.63 tff(224,plain,
% 0.59/0.63 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(225,plain,
% 0.59/0.63 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(226,plain,
% 0.59/0.63 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.59/0.63 tff(227,plain,
% 0.59/0.63 ((~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[226, 182, 223])).
% 0.59/0.63 tff(228,plain,
% 0.59/0.63 (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[227, 76])).
% 0.59/0.63 tff(229,plain,
% 0.59/0.63 (^[Xa: $i, Xb: $i, Xd: $i, Xc: $i] : refl((s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd))) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd))))),
% 0.59/0.63 inference(bind,[status(th)],[])).
% 0.59/0.63 tff(230,plain,
% 0.59/0.63 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.59/0.63 inference(quant_intro,[status(thm)],[229])).
% 0.59/0.63 tff(231,plain,
% 0.59/0.63 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd))) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(232,plain,
% 0.59/0.63 (^[Xa: $i, Xb: $i, Xd: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) <=> ((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd)))), ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) <=> (((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)))), rewrite((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd)))), ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))))), (((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xb)) <=> ((s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xc, Xb)))), rewrite(((s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xc, Xb)) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))), (((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xb)) <=> (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))))),
% 0.59/0.63 inference(bind,[status(th)],[])).
% 0.59/0.63 tff(233,plain,
% 0.59/0.63 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xb)) <=> ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.59/0.63 inference(quant_intro,[status(thm)],[232])).
% 0.59/0.63 tff(234,axiom,(![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((((~s_t(Xa, Xb, Xd)) | (~s_t(Xa, Xc, Xd))) | s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz5_3')).
% 0.59/0.63 tff(235,plain,
% 0.59/0.63 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.59/0.63 tff(236,plain,
% 0.59/0.63 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.59/0.63 tff(237,plain,(
% 0.59/0.63 ![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.59/0.63 inference(skolemize,[status(sab)],[236])).
% 0.59/0.63 tff(238,plain,
% 0.59/0.63 (![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.59/0.63 tff(239,plain,
% 0.59/0.63 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(240,plain,
% 0.59/0.63 ((s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))) <=> ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(241,plain,
% 0.59/0.63 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[240])).
% 0.59/0.64 tff(242,plain,
% 0.59/0.64 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.59/0.64 inference(transitivity,[status(thm)],[241, 239])).
% 0.59/0.64 tff(243,plain,
% 0.59/0.64 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))),
% 0.59/0.64 inference(quant_inst,[status(thm)],[])).
% 0.59/0.64 tff(244,plain,
% 0.59/0.64 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : (s_t(Xa, Xb, Xc) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xb) | (~s_t(Xa, Xc, Xd)))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.59/0.64 tff(245,plain,
% 0.59/0.64 (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[244, 238, 223, 228, 218])).
% 0.59/0.64 tff(246,plain,
% 0.59/0.64 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl(((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd)))),
% 0.59/0.64 inference(bind,[status(th)],[])).
% 0.59/0.64 tff(247,plain,
% 0.59/0.64 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.59/0.64 inference(quant_intro,[status(thm)],[246])).
% 0.59/0.64 tff(248,plain,
% 0.59/0.64 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(249,plain,
% 0.59/0.64 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) <=> ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) <=> (((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))) | (Xb = Xc)))), rewrite((((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))) | (Xb = Xc)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))))), (((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) | s_t(Xa, Xc, Xd)) <=> (((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))) | s_t(Xa, Xc, Xd)))), rewrite((((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc))) | s_t(Xa, Xc, Xd)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))), (((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) | s_t(Xa, Xc, Xd)) <=> ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))))),
% 0.59/0.64 inference(bind,[status(th)],[])).
% 0.59/0.64 tff(250,plain,
% 0.59/0.64 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) | s_t(Xa, Xc, Xd)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.59/0.64 inference(quant_intro,[status(thm)],[249])).
% 0.59/0.64 tff(251,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((((~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xc, Xd))) | (Xb = Xc)) | s_t(Xa, Xc, Xd))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_7a')).
% 0.59/0.64 tff(252,plain,
% 0.59/0.64 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.59/0.64 tff(253,plain,
% 0.59/0.64 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.59/0.64 tff(254,plain,(
% 0.59/0.64 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.59/0.64 inference(skolemize,[status(sab)],[253])).
% 0.59/0.64 tff(255,plain,
% 0.59/0.64 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[254, 247])).
% 0.59/0.64 tff(256,plain,
% 0.59/0.64 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(257,plain,
% 0.59/0.64 (((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) <=> ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(258,plain,
% 0.59/0.64 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))),
% 0.59/0.64 inference(monotonicity,[status(thm)],[257])).
% 0.59/0.64 tff(259,plain,
% 0.59/0.64 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.64 inference(transitivity,[status(thm)],[258, 256])).
% 0.59/0.64 tff(260,plain,
% 0.59/0.64 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | ((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.64 inference(quant_inst,[status(thm)],[])).
% 0.59/0.64 tff(261,plain,
% 0.59/0.64 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((Xb = Xc) | (~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xc)) | s_t(Xa, Xc, Xd))) | (Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_t(Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.59/0.65 tff(262,plain,
% 0.59/0.65 (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[261, 255, 195, 245, 193])).
% 0.59/0.65 tff(263,plain,
% 0.59/0.65 ((~![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))) | (~((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_e(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xa!3, Xb!2))))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(264,plain,
% 0.59/0.65 (~((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_e(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xa!3, Xb!2)))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[263, 109])).
% 0.59/0.65 tff(265,plain,
% 0.59/0.65 (((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (~s_e(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xa!3, Xb!2))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(266,plain,
% 0.59/0.65 (s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.59/0.65 tff(267,plain,
% 0.59/0.65 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(268,plain,
% 0.59/0.65 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(269,plain,
% 0.59/0.65 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.59/0.65 tff(270,plain,
% 0.59/0.65 (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[269, 71, 266])).
% 0.59/0.65 tff(271,plain,
% 0.59/0.65 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(272,plain,
% 0.59/0.65 (((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) <=> (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(273,plain,
% 0.59/0.65 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))))),
% 0.59/0.65 inference(monotonicity,[status(thm)],[272])).
% 0.59/0.65 tff(274,plain,
% 0.59/0.65 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))))),
% 0.59/0.65 inference(transitivity,[status(thm)],[273, 271])).
% 0.59/0.65 tff(275,plain,
% 0.59/0.65 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(276,plain,
% 0.59/0.65 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.59/0.65 tff(277,plain,
% 0.59/0.65 (s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[276, 182, 270, 262])).
% 0.59/0.65 tff(278,plain,
% 0.59/0.65 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(279,plain,
% 0.59/0.65 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(280,plain,
% 0.59/0.65 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, ext(Xd!0, Xc!1, alpha, gamma))) | s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.59/0.65 tff(281,plain,
% 0.59/0.65 (s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[280, 71, 277])).
% 0.59/0.66 tff(282,plain,
% 0.59/0.66 ((Xc!1 = ext(Xd!0, Xc!1, alpha, gamma)) <=> (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)),
% 0.59/0.66 inference(commutativity,[status(thm)],[])).
% 0.59/0.66 tff(283,plain,
% 0.59/0.66 ((~(Xc!1 = ext(Xd!0, Xc!1, alpha, gamma))) <=> (~(ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.59/0.66 inference(monotonicity,[status(thm)],[282])).
% 0.59/0.66 tff(284,plain,
% 0.59/0.66 (^[Xb: $i, Xa: $i] : refl((~(Xb = ext(Xa, Xb, alpha, gamma))) <=> (~(Xb = ext(Xa, Xb, alpha, gamma))))),
% 0.59/0.66 inference(bind,[status(th)],[])).
% 0.59/0.66 tff(285,plain,
% 0.59/0.66 (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma))) <=> ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.59/0.66 inference(quant_intro,[status(thm)],[284])).
% 0.59/0.66 tff(286,plain,
% 0.59/0.66 (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma))) <=> ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(287,axiom,(![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz3_14b')).
% 0.59/0.66 tff(288,plain,
% 0.59/0.66 (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.59/0.66 tff(289,plain,(
% 0.59/0.66 ![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.59/0.66 inference(skolemize,[status(sab)],[288])).
% 0.59/0.66 tff(290,plain,
% 0.59/0.66 (![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.59/0.66 tff(291,plain,
% 0.59/0.66 ((~![Xb: $i, Xa: $i] : (~(Xb = ext(Xa, Xb, alpha, gamma)))) | (~(Xc!1 = ext(Xd!0, Xc!1, alpha, gamma)))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(292,plain,
% 0.59/0.66 (~(Xc!1 = ext(Xd!0, Xc!1, alpha, gamma))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.59/0.66 tff(293,plain,
% 0.59/0.66 (~(ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[292, 283])).
% 0.59/0.66 tff(294,plain,
% 0.59/0.66 (s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2) <=> s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.59/0.66 inference(monotonicity,[status(thm)],[156])).
% 0.59/0.66 tff(295,plain,
% 0.59/0.66 (s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2) <=> s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)),
% 0.59/0.66 inference(symmetry,[status(thm)],[294])).
% 0.59/0.66 tff(296,plain,
% 0.59/0.66 (((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) | ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(297,plain,
% 0.59/0.66 ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[296, 149])).
% 0.59/0.66 tff(298,plain,
% 0.59/0.66 ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(299,plain,
% 0.59/0.66 ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[298, 152])).
% 0.59/0.66 tff(300,plain,
% 0.59/0.66 (s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2)),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[299, 297])).
% 0.59/0.66 tff(301,plain,
% 0.59/0.66 (s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[300, 295])).
% 0.59/0.66 tff(302,plain,
% 0.59/0.66 (^[Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : refl(((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa)) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa)))),
% 0.59/0.66 inference(bind,[status(th)],[])).
% 0.59/0.66 tff(303,plain,
% 0.59/0.66 (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa)) <=> ![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.59/0.66 inference(quant_intro,[status(thm)],[302])).
% 0.59/0.66 tff(304,plain,
% 0.59/0.66 (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa)) <=> ![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(305,plain,
% 0.59/0.66 (^[Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : trans(monotonicity(trans(monotonicity(rewrite(((Xq = Xa) | (~s_t(Xq, Xa, Xd))) <=> ((~s_t(Xq, Xa, Xd)) | (Xq = Xa))), ((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) <=> (((~s_t(Xq, Xa, Xd)) | (Xq = Xa)) | (~s_e(Xa, Xd, Xb, Xc))))), rewrite((((~s_t(Xq, Xa, Xd)) | (Xq = Xa)) | (~s_e(Xa, Xd, Xb, Xc))) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xq = Xa))), ((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xq = Xa)))), (((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) | (Xd = ext(Xq, Xa, Xb, Xc))) <=> (((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xq = Xa)) | (Xd = ext(Xq, Xa, Xb, Xc))))), rewrite((((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xq = Xa)) | (Xd = ext(Xq, Xa, Xb, Xc))) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))), (((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) | (Xd = ext(Xq, Xa, Xb, Xc))) <=> ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))))),
% 0.59/0.66 inference(bind,[status(th)],[])).
% 0.59/0.66 tff(306,plain,
% 0.59/0.66 (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) | (Xd = ext(Xq, Xa, Xb, Xc))) <=> ![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.59/0.66 inference(quant_intro,[status(thm)],[305])).
% 0.59/0.66 tff(307,axiom,(![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((((Xq = Xa) | (~s_t(Xq, Xa, Xd))) | (~s_e(Xa, Xd, Xb, Xc))) | (Xd = ext(Xq, Xa, Xb, Xc)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz2_12')).
% 0.59/0.66 tff(308,plain,
% 0.59/0.66 (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.59/0.66 tff(309,plain,
% 0.59/0.66 (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.59/0.66 tff(310,plain,(
% 0.59/0.66 ![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.59/0.66 inference(skolemize,[status(sab)],[309])).
% 0.59/0.66 tff(311,plain,
% 0.59/0.66 (![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[310, 303])).
% 0.59/0.66 tff(312,plain,
% 0.59/0.66 (((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))) <=> ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(313,plain,
% 0.59/0.66 (((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)) <=> ((~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(314,plain,
% 0.59/0.66 (((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))) <=> ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)))),
% 0.59/0.66 inference(monotonicity,[status(thm)],[313])).
% 0.59/0.66 tff(315,plain,
% 0.59/0.66 (((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))) <=> ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.59/0.66 inference(transitivity,[status(thm)],[314, 312])).
% 0.59/0.66 tff(316,plain,
% 0.59/0.66 ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(317,plain,
% 0.59/0.66 ((~![Xq: $i, Xa: $i, Xd: $i, Xb: $i, Xc: $i] : ((~s_t(Xq, Xa, Xd)) | (~s_e(Xa, Xd, Xb, Xc)) | (Xd = ext(Xq, Xa, Xb, Xc)) | (Xq = Xa))) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.59/0.66 tff(318,plain,
% 0.59/0.66 ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | (ext(Xd!0, Xc!1, alpha, gamma) = Xc!1)),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[317, 311, 301])).
% 0.59/0.66 tff(319,plain,
% 0.59/0.66 ((~s_t(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[318, 293])).
% 0.59/0.66 tff(320,plain,
% 0.59/0.66 (ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[319, 281])).
% 0.59/0.66 tff(321,plain,
% 0.59/0.66 (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.59/0.66 inference(symmetry,[status(thm)],[320])).
% 0.59/0.66 tff(322,plain,
% 0.59/0.66 (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = ins(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.59/0.66 inference(transitivity,[status(thm)],[321, 156])).
% 0.59/0.66 tff(323,plain,
% 0.59/0.66 (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) <=> s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.59/0.66 inference(monotonicity,[status(thm)],[322])).
% 0.59/0.66 tff(324,plain,
% 0.59/0.66 (s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)) <=> s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.59/0.66 inference(symmetry,[status(thm)],[323])).
% 0.59/0.66 tff(325,plain,
% 0.59/0.66 (((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, ins(Xa!3, Xb!2, Xc!1, Xd!0), Xa!3, Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | (ins(Xa!3, Xb!2, Xc!1, Xd!0) = ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) | ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(326,plain,
% 0.59/0.66 ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[325, 149])).
% 0.59/0.66 tff(327,plain,
% 0.59/0.66 ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(328,plain,
% 0.59/0.66 ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)))) | s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[327, 152])).
% 0.59/0.66 tff(329,plain,
% 0.59/0.66 (s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[328, 326])).
% 0.59/0.66 tff(330,plain,
% 0.59/0.66 (s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[329, 324])).
% 0.59/0.66 tff(331,plain,
% 0.59/0.66 (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, Xc!1)),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[94, 195])).
% 0.59/0.66 tff(332,plain,
% 0.59/0.66 (~s_t(Xc!1, Xd!0, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[98, 71, 331])).
% 0.59/0.66 tff(333,plain,
% 0.59/0.66 ($false),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[332, 330])).
% 0.59/0.66 tff(334,plain,((Xd!0 = ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.67 tff(335,plain,
% 0.63/0.67 (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[334, 134, 57])).
% 0.63/0.67 tff(336,plain,
% 0.63/0.67 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(337,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(338,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.63/0.67 tff(339,plain,
% 0.63/0.67 (s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[338, 71, 228])).
% 0.63/0.67 tff(340,plain,
% 0.63/0.67 (((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(341,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | ((ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(342,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i] : ((Xa = Xb) | (~s_t(Xa, Xb, Xc)) | (~s_t(Xb, Xa, Xc)))) | (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xc!1, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.63/0.67 tff(343,plain,
% 0.63/0.67 ((ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[342, 86, 339])).
% 0.63/0.67 tff(344,plain,
% 0.63/0.67 (ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2) = Xc!1),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[343, 335])).
% 0.63/0.67 tff(345,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xa, Xb, ins(Xc, Xd, Xa, Xb)))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, ins(Xc, Xd, Xa, Xb), Xc, Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | (ins(Xc, Xd, Xa, Xb) = ext(Xa, Xb, insert(Xa, Xb, Xc, Xd), Xd))))))) | (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xa!3, Xb!2, ins(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))))))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(346,plain,
% 0.63/0.67 (~((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xa!3, Xb!2, ins(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[345, 147])).
% 0.63/0.67 tff(347,plain,
% 0.63/0.67 (((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xa!3, Xb!2, ins(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))))) | ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))),
% 0.63/0.67 inference(tautology,[status(thm)],[])).
% 0.63/0.67 tff(348,plain,
% 0.63/0.67 ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[347, 346])).
% 0.63/0.67 tff(349,plain,
% 0.63/0.67 ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.67 inference(tautology,[status(thm)],[])).
% 0.63/0.67 tff(350,plain,
% 0.63/0.67 ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[349, 50])).
% 0.63/0.67 tff(351,plain,
% 0.63/0.67 (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[350, 348])).
% 0.63/0.67 tff(352,plain,
% 0.63/0.67 (ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0) = ins(Xc!1, Xd!0, Xa!3, Xb!2)),
% 0.63/0.67 inference(symmetry,[status(thm)],[351])).
% 0.63/0.67 tff(353,plain,
% 0.63/0.67 (s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)) <=> s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[10, 344])).
% 0.63/0.67 tff(354,plain,
% 0.63/0.67 (s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1) <=> s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.63/0.67 inference(symmetry,[status(thm)],[353])).
% 0.63/0.67 tff(355,plain,
% 0.63/0.67 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl(((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc)) <=> ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc)))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(356,plain,
% 0.63/0.67 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[355])).
% 0.63/0.67 tff(357,plain,
% 0.63/0.67 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(358,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz2_14')).
% 0.63/0.67 tff(359,plain,
% 0.63/0.67 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.63/0.67 tff(360,plain,(
% 0.63/0.67 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.63/0.67 inference(skolemize,[status(sab)],[359])).
% 0.63/0.67 tff(361,plain,
% 0.63/0.67 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.63/0.67 tff(362,plain,
% 0.63/0.67 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(363,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(364,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.63/0.67 tff(365,plain,
% 0.63/0.67 (s_e(Xb!2, Xa!3, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[364, 361, 53])).
% 0.63/0.67 tff(366,plain,
% 0.63/0.67 (s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[365, 354])).
% 0.63/0.67 tff(367,plain,
% 0.63/0.67 (^[Xb: $i, Xc: $i, Xa: $i] : refl(((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)) <=> ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(368,plain,
% 0.63/0.67 (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)) <=> ![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[367])).
% 0.63/0.67 tff(369,plain,
% 0.63/0.67 (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc)) <=> ![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(370,axiom,(![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz2_13')).
% 0.63/0.67 tff(371,plain,
% 0.63/0.67 (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.63/0.67 tff(372,plain,(
% 0.63/0.67 ![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.63/0.67 inference(skolemize,[status(sab)],[371])).
% 0.63/0.67 tff(373,plain,
% 0.63/0.67 (![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[372, 368])).
% 0.63/0.67 tff(374,plain,
% 0.63/0.67 (((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | ((~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3))) <=> ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | (~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(375,plain,
% 0.63/0.67 ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | ((~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(376,plain,
% 0.63/0.67 ((~![Xb: $i, Xc: $i, Xa: $i] : ((~s_e(Xb, Xc, Xa, Xa)) | (Xb = Xc))) | (~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.63/0.68 tff(377,plain,
% 0.63/0.68 ((~s_e(Xb!2, Xa!3, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))) | (Xb!2 = Xa!3)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[376, 373])).
% 0.63/0.68 tff(378,plain,
% 0.63/0.68 (Xb!2 = Xa!3),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[377, 366])).
% 0.63/0.68 tff(379,plain,
% 0.63/0.68 (Xa!3 = Xb!2),
% 0.63/0.68 inference(symmetry,[status(thm)],[378])).
% 0.63/0.68 tff(380,plain,
% 0.63/0.68 ((~![Xa: $i, Xb: $i, Xa1: $i, Xc1: $i] : (insert(Xa, Xb, Xa1, Xc1) = ext(ext(Xc1, Xa1, alpha, gamma), Xa1, Xa, Xb))) | (insert(Xc!1, Xd!0, Xa!3, Xb!2) = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(381,plain,
% 0.63/0.68 (insert(Xc!1, Xd!0, Xa!3, Xb!2) = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[380, 7])).
% 0.63/0.68 tff(382,plain,
% 0.63/0.68 (ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0) = insert(Xc!1, Xd!0, Xa!3, Xb!2)),
% 0.63/0.68 inference(symmetry,[status(thm)],[381])).
% 0.63/0.68 tff(383,plain,
% 0.63/0.68 (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3) <=> s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[382, 379])).
% 0.63/0.68 tff(384,plain,
% 0.63/0.68 (s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) <=> s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.63/0.68 inference(symmetry,[status(thm)],[383])).
% 0.63/0.68 tff(385,plain,
% 0.63/0.68 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2)))))))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(386,plain,
% 0.63/0.68 ((~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~s_t(Xa!3, Xb!2, Xb!2)) | le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)))))) <=> (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2))))))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(387,plain,
% 0.63/0.68 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~s_t(Xa!3, Xb!2, Xb!2)) | le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2)))))))),
% 0.63/0.68 inference(monotonicity,[status(thm)],[386])).
% 0.63/0.68 tff(388,plain,
% 0.63/0.68 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~s_t(Xa!3, Xb!2, Xb!2)) | le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2))))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2)))))))),
% 0.63/0.68 inference(transitivity,[status(thm)],[387, 385])).
% 0.63/0.68 tff(389,plain,
% 0.63/0.68 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~s_t(Xa!3, Xb!2, Xb!2)) | le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2))))))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(390,plain,
% 0.63/0.68 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Y: $i] : (~((~((~le(Xa, Xb, Xc, Xd)) | s_t(Xc, insert(Xa, Xb, Xc, Xd), Xd))) | (~((~le(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xc, insert(Xa, Xb, Xc, Xd)))) | (~((~s_t(Xc, Y, Xd)) | le(Xa, Xb, Xc, Xd) | (~s_e(Xa, Xb, Xc, Y))))))) | (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2))))))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.63/0.68 tff(391,plain,
% 0.63/0.68 (~((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2)))))),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[390, 27])).
% 0.63/0.68 tff(392,plain,
% 0.63/0.68 (((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_e(Xc!1, Xd!0, Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~(le(Xc!1, Xd!0, Xa!3, Xb!2) | (~s_e(Xc!1, Xd!0, Xa!3, Xb!2)) | (~s_t(Xa!3, Xb!2, Xb!2))))) | ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.68 inference(tautology,[status(thm)],[])).
% 0.63/0.68 tff(393,plain,
% 0.63/0.68 ((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[392, 391])).
% 0.63/0.68 tff(394,plain,
% 0.63/0.68 ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.68 inference(tautology,[status(thm)],[])).
% 0.63/0.68 tff(395,plain,
% 0.63/0.68 ((~((~le(Xc!1, Xd!0, Xa!3, Xb!2)) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[394, 152])).
% 0.63/0.68 tff(396,plain,
% 0.63/0.68 (s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[395, 393])).
% 0.63/0.68 tff(397,plain,
% 0.63/0.68 (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[396, 384])).
% 0.63/0.68 tff(398,plain,
% 0.63/0.68 (^[X: $i, Y: $i] : refl(((~s_t(X, Y, X)) | (X = Y)) <=> ((~s_t(X, Y, X)) | (X = Y)))),
% 0.63/0.68 inference(bind,[status(th)],[])).
% 0.63/0.68 tff(399,plain,
% 0.63/0.68 (![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y)) <=> ![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[398])).
% 0.63/0.68 tff(400,plain,
% 0.63/0.68 (![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y)) <=> ![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(401,axiom,(![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax','aA6')).
% 0.63/0.68 tff(402,plain,
% 0.63/0.68 (![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.63/0.68 tff(403,plain,(
% 0.63/0.68 ![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.63/0.68 inference(skolemize,[status(sab)],[402])).
% 0.63/0.68 tff(404,plain,
% 0.63/0.68 (![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[403, 399])).
% 0.63/0.68 tff(405,plain,
% 0.63/0.68 (((~![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))) | ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))) <=> ((~![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))) | (~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(406,plain,
% 0.63/0.68 ((~![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))) | ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))),
% 0.63/0.68 inference(quant_inst,[status(thm)],[])).
% 0.63/0.68 tff(407,plain,
% 0.63/0.68 ((~![X: $i, Y: $i] : ((~s_t(X, Y, X)) | (X = Y))) | (~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.63/0.68 tff(408,plain,
% 0.63/0.68 (Xa!3 = ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[407, 404, 397])).
% 0.63/0.68 tff(409,plain,
% 0.63/0.68 (ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0) = Xa!3),
% 0.63/0.68 inference(symmetry,[status(thm)],[408])).
% 0.63/0.68 tff(410,plain,
% 0.63/0.68 (s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0) <=> s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.63/0.68 inference(monotonicity,[status(thm)],[409, 352, 344])).
% 0.63/0.68 tff(411,plain,
% 0.63/0.68 (s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0) <=> s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.63/0.68 inference(symmetry,[status(thm)],[410])).
% 0.63/0.68 tff(412,plain,
% 0.63/0.68 (((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_t(Xa!3, Xb!2, ins(Xc!1, Xd!0, Xa!3, Xb!2)))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | (ins(Xc!1, Xd!0, Xa!3, Xb!2) = ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))))) | ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))),
% 0.63/0.68 inference(tautology,[status(thm)],[])).
% 0.63/0.68 tff(413,plain,
% 0.63/0.68 ((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[412, 346])).
% 0.63/0.68 tff(414,plain,
% 0.63/0.68 ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | (~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.63/0.68 inference(tautology,[status(thm)],[])).
% 0.63/0.68 tff(415,plain,
% 0.63/0.68 ((~((~le(Xa!3, Xb!2, Xc!1, Xd!0)) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0))) | s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.63/0.68 inference(unit_resolution,[status(thm)],[414, 50])).
% 0.63/0.69 tff(416,plain,
% 0.63/0.69 (s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[415, 413])).
% 0.63/0.69 tff(417,plain,
% 0.63/0.69 (s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[416, 411])).
% 0.63/0.69 tff(418,plain,
% 0.63/0.69 (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) <=> s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[344, 156])).
% 0.63/0.69 tff(419,plain,
% 0.63/0.69 (s_t(Xc!1, Xd!0, ins(Xa!3, Xb!2, Xc!1, Xd!0)) <=> s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.69 inference(symmetry,[status(thm)],[418])).
% 0.63/0.69 tff(420,plain,
% 0.63/0.69 (s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[329, 419])).
% 0.63/0.69 tff(421,plain,
% 0.63/0.69 (s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) <=> s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[378])).
% 0.63/0.69 tff(422,plain,
% 0.63/0.69 (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)) <=> s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.69 inference(symmetry,[status(thm)],[421])).
% 0.63/0.69 tff(423,plain,
% 0.63/0.69 (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2) <=> s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.69 inference(monotonicity,[status(thm)],[382])).
% 0.63/0.69 tff(424,plain,
% 0.63/0.69 (s_t(Xa!3, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) <=> s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)),
% 0.63/0.69 inference(symmetry,[status(thm)],[423])).
% 0.63/0.69 tff(425,plain,
% 0.63/0.69 (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[396, 424])).
% 0.63/0.69 tff(426,plain,
% 0.63/0.69 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(427,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(428,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.63/0.69 tff(429,plain,
% 0.63/0.69 ((~s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[428, 71])).
% 0.63/0.69 tff(430,plain,
% 0.63/0.69 (s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[429, 425])).
% 0.63/0.69 tff(431,plain,
% 0.63/0.69 ((~![X: $i, Y: $i, W: $i, V: $i] : (~((~s_t(X, Y, ext(X, Y, W, V))) | (~s_e(Y, ext(X, Y, W, V), W, V))))) | (~((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(432,plain,
% 0.63/0.69 (~((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[431, 109])).
% 0.63/0.69 tff(433,plain,
% 0.63/0.69 (((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(434,plain,
% 0.63/0.69 (s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[433, 432])).
% 0.63/0.69 tff(435,plain,
% 0.63/0.69 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(436,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(437,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.63/0.69 tff(438,plain,
% 0.63/0.69 ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[437, 71])).
% 0.63/0.69 tff(439,plain,
% 0.63/0.69 (s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[438, 434])).
% 0.63/0.69 tff(440,plain,
% 0.63/0.69 (((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))) <=> ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(441,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | ((~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(442,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xd: $i, Xc: $i] : ((~s_t(Xb, Xc, Xd)) | (~s_t(Xa, Xb, Xd)) | s_t(Xa, Xc, Xd))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xb!2, Xa!3)) | s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.63/0.69 tff(443,plain,
% 0.63/0.69 (s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[442, 182, 439, 430])).
% 0.63/0.69 tff(444,plain,
% 0.63/0.69 (((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(445,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | ((~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(446,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_t(Xa, Xb, Xc)) | s_t(Xc, Xb, Xa))) | (~s_t(ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xa!3)) | s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.63/0.69 tff(447,plain,
% 0.63/0.69 (s_t(Xa!3, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[446, 71, 443])).
% 0.63/0.69 tff(448,plain,
% 0.63/0.69 (s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[447, 422])).
% 0.63/0.69 tff(449,plain,
% 0.63/0.69 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl(((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc)) <=> ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc)))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(450,plain,
% 0.63/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[449])).
% 0.63/0.69 tff(451,plain,
% 0.63/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(452,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz2_5')).
% 0.63/0.69 tff(453,plain,
% 0.63/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.63/0.69 tff(454,plain,(
% 0.63/0.69 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.63/0.69 inference(skolemize,[status(sab)],[453])).
% 0.63/0.69 tff(455,plain,
% 0.63/0.69 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[454, 450])).
% 0.63/0.69 tff(456,plain,
% 0.63/0.69 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xd!0, Xc!1)) | s_e(Xa!3, Xb!2, Xc!1, Xd!0))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xd!0, Xc!1)) | s_e(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(457,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xd!0, Xc!1)) | s_e(Xa!3, Xb!2, Xc!1, Xd!0))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(458,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xd!0, Xc!1)) | s_e(Xa!3, Xb!2, Xc!1, Xd!0)),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.63/0.69 tff(459,plain,
% 0.63/0.69 (~s_e(Xa!3, Xb!2, Xd!0, Xc!1)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[458, 455, 55])).
% 0.63/0.70 tff(460,plain,
% 0.63/0.70 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i] : refl(((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb)) <=> ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb)))),
% 0.63/0.70 inference(bind,[status(th)],[])).
% 0.63/0.70 tff(461,plain,
% 0.63/0.70 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[460])).
% 0.63/0.70 tff(462,plain,
% 0.63/0.70 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(463,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz2_2')).
% 0.63/0.70 tff(464,plain,
% 0.63/0.70 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.63/0.70 tff(465,plain,(
% 0.63/0.70 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.63/0.70 inference(skolemize,[status(sab)],[464])).
% 0.63/0.70 tff(466,plain,
% 0.63/0.70 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[465, 461])).
% 0.63/0.70 tff(467,plain,
% 0.63/0.70 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xd!0, Xc!1, Xa!3, Xb!2)) | s_e(Xa!3, Xb!2, Xd!0, Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xd!0, Xc!1, Xa!3, Xb!2)) | s_e(Xa!3, Xb!2, Xd!0, Xc!1))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(468,plain,
% 0.63/0.70 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xd!0, Xc!1, Xa!3, Xb!2)) | s_e(Xa!3, Xb!2, Xd!0, Xc!1))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(469,plain,
% 0.63/0.70 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xd!0, Xc!1, Xa!3, Xb!2)) | s_e(Xa!3, Xb!2, Xd!0, Xc!1)),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.63/0.70 tff(470,plain,
% 0.63/0.70 (~s_e(Xd!0, Xc!1, Xa!3, Xb!2)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[469, 466, 459])).
% 0.63/0.70 tff(471,plain,
% 0.63/0.70 (^[X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : refl((s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) <=> (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))))),
% 0.63/0.70 inference(bind,[status(th)],[])).
% 0.63/0.70 tff(472,plain,
% 0.63/0.70 (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) <=> ![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[471])).
% 0.63/0.70 tff(473,plain,
% 0.63/0.70 (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) <=> ![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(474,plain,
% 0.63/0.70 (^[X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : trans(monotonicity(rewrite(((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) <=> ((~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))), ((((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) | s_e(Z, V, Z2, V2)) <=> (((~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) | s_e(Z, V, Z2, V2)))), rewrite((((~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V))) | s_e(Z, V, Z2, V2)) <=> (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))), ((((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) | s_e(Z, V, Z2, V2)) <=> (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))))),
% 0.63/0.70 inference(bind,[status(th)],[])).
% 0.63/0.70 tff(475,plain,
% 0.63/0.70 (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) | s_e(Z, V, Z2, V2)) <=> ![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.63/0.70 inference(quant_intro,[status(thm)],[474])).
% 0.63/0.70 tff(476,axiom,(![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (((~s_e(X, Y, Z, V)) | (~s_e(X, Y, Z2, V2))) | s_e(Z, V, Z2, V2))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO011+0.ax','aA2')).
% 0.63/0.70 tff(477,plain,
% 0.63/0.70 (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.63/0.70 tff(478,plain,
% 0.63/0.70 (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.63/0.70 tff(479,plain,(
% 0.63/0.70 ![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.63/0.70 inference(skolemize,[status(sab)],[478])).
% 0.63/0.70 tff(480,plain,
% 0.63/0.70 (![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[479, 472])).
% 0.63/0.70 tff(481,plain,
% 0.63/0.70 (((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(Xd!0, Xc!1, Xa!3, Xb!2) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))) <=> ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | s_e(Xd!0, Xc!1, Xa!3, Xb!2) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(482,plain,
% 0.63/0.70 ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(Xd!0, Xc!1, Xa!3, Xb!2) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(483,plain,
% 0.63/0.70 ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | s_e(Xd!0, Xc!1, Xa!3, Xb!2) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xa!3, Xb!2)) | (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.63/0.70 tff(484,plain,
% 0.63/0.70 (~s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[483, 480, 470, 301])).
% 0.63/0.70 tff(485,plain,
% 0.63/0.70 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)) | s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)) | s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(486,plain,
% 0.63/0.70 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)) | s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(487,plain,
% 0.63/0.70 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)) | s_e(Xc!1, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xd!0, Xc!1)),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.63/0.70 tff(488,plain,
% 0.63/0.70 (~s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[487, 361, 484])).
% 0.63/0.70 tff(489,plain,
% 0.63/0.70 (s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0) <=> s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0)),
% 0.63/0.70 inference(monotonicity,[status(thm)],[352])).
% 0.63/0.70 tff(490,plain,
% 0.63/0.70 (s_e(Xa!3, ins(Xc!1, Xd!0, Xa!3, Xb!2), Xc!1, Xd!0) <=> s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)),
% 0.63/0.70 inference(symmetry,[status(thm)],[489])).
% 0.63/0.70 tff(491,plain,
% 0.63/0.70 (s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[416, 490])).
% 0.63/0.70 tff(492,plain,
% 0.63/0.70 (((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | ((~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))) <=> ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(493,plain,
% 0.63/0.70 ((s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1))) <=> ((~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(494,plain,
% 0.63/0.70 (((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))) <=> ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | ((~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1))))),
% 0.63/0.70 inference(monotonicity,[status(thm)],[493])).
% 0.63/0.70 tff(495,plain,
% 0.63/0.70 (((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))) <=> ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))),
% 0.63/0.70 inference(transitivity,[status(thm)],[494, 492])).
% 0.63/0.70 tff(496,plain,
% 0.63/0.70 ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)))),
% 0.63/0.71 inference(quant_inst,[status(thm)],[])).
% 0.63/0.71 tff(497,plain,
% 0.63/0.71 ((~![X: $i, Y: $i, Z: $i, V: $i, Z2: $i, V2: $i] : (s_e(Z, V, Z2, V2) | (~s_e(X, Y, Z2, V2)) | (~s_e(X, Y, Z, V)))) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), Xc!1, Xd!0)) | s_e(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1, Xc!1, Xd!0) | (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1))),
% 0.63/0.71 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.63/0.71 tff(498,plain,
% 0.63/0.71 (~s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1)),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[497, 480, 491, 488])).
% 0.63/0.71 tff(499,plain,
% 0.63/0.71 (s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1) <=> s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.63/0.71 inference(monotonicity,[status(thm)],[10])).
% 0.63/0.71 tff(500,plain,
% 0.63/0.71 (s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1) <=> s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.63/0.71 inference(symmetry,[status(thm)],[499])).
% 0.63/0.71 tff(501,plain,
% 0.63/0.71 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.63/0.71 inference(rewrite,[status(thm)],[])).
% 0.63/0.71 tff(502,plain,
% 0.63/0.71 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1))),
% 0.63/0.71 inference(quant_inst,[status(thm)],[])).
% 0.63/0.71 tff(503,plain,
% 0.63/0.71 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xa!3, Xb!2, Xc!1, insert(Xa!3, Xb!2, Xc!1, Xd!0))) | s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.63/0.71 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.63/0.71 tff(504,plain,
% 0.63/0.71 (s_e(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xc!1)),
% 0.63/0.71 inference(unit_resolution,[status(thm)],[503, 455, 53])).
% 0.63/0.71 tff(505,plain,
% 0.63/0.71 (s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)),
% 0.63/0.71 inference(modus_ponens,[status(thm)],[504, 500])).
% 0.63/0.71 tff(506,plain,
% 0.63/0.71 (^[Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : refl(((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) <=> ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))))),
% 0.63/0.71 inference(bind,[status(th)],[])).
% 0.63/0.71 tff(507,plain,
% 0.63/0.71 (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) <=> ![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.63/0.71 inference(quant_intro,[status(thm)],[506])).
% 0.63/0.71 tff(508,plain,
% 0.63/0.71 (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) <=> ![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.63/0.71 inference(rewrite,[status(thm)],[])).
% 0.63/0.71 tff(509,plain,
% 0.63/0.71 (^[Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) <=> ((~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) <=> (((~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))) | (~s_e(Xa, Xb, XB, XC))))), rewrite((((~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))) | (~s_e(Xa, Xb, XB, XC))) <=> ((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)))), ((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) <=> ((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))))), (((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) <=> (((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))) | (~s_e(Xb, Xc, XA, XB))))), rewrite((((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc))) | (~s_e(Xb, Xc, XA, XB))) <=> ((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))), (((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) <=> ((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))))), ((((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)) <=> (((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)))), rewrite((((~s_e(Xa, Xb, XB, XC)) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)) <=> ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))), ((((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)) <=> ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))))),
% 0.63/0.71 inference(bind,[status(th)],[])).
% 0.63/0.71 tff(510,plain,
% 0.63/0.71 (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : (((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC)) <=> ![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.63/0.71 inference(quant_intro,[status(thm)],[509])).
% 0.63/0.71 tff(511,axiom,(![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : (((((~s_t(Xa, Xb, Xc)) | (~s_t(XA, XB, XC))) | (~s_e(Xa, Xb, XB, XC))) | (~s_e(Xb, Xc, XA, XB))) | s_e(Xa, Xc, XA, XC))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSatz2_15')).
% 0.63/0.71 tff(512,plain,
% 0.63/0.71 (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.63/0.71 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.63/0.71 tff(513,plain,
% 0.63/0.71 (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.63/0.71 inference(modus_ponens,[status(thm)],[512, 508])).
% 0.63/0.71 tff(514,plain,(
% 0.63/0.71 ![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.63/0.71 inference(skolemize,[status(sab)],[513])).
% 0.63/0.71 tff(515,plain,
% 0.63/0.71 (![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))),
% 0.63/0.71 inference(modus_ponens,[status(thm)],[514, 507])).
% 0.63/0.71 tff(516,plain,
% 0.63/0.71 (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.63/0.71 inference(rewrite,[status(thm)],[])).
% 0.63/0.71 tff(517,plain,
% 0.63/0.71 (((~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.63/0.71 inference(rewrite,[status(thm)],[])).
% 0.63/0.71 tff(518,plain,
% 0.63/0.71 (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))))),
% 0.63/0.71 inference(monotonicity,[status(thm)],[517])).
% 0.63/0.71 tff(519,plain,
% 0.63/0.71 (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.63/0.72 inference(transitivity,[status(thm)],[518, 516])).
% 0.63/0.72 tff(520,plain,
% 0.63/0.72 ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))))),
% 0.63/0.72 inference(quant_inst,[status(thm)],[])).
% 0.63/0.72 tff(521,plain,
% 0.63/0.72 ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (~s_t(Xa!3, Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(Xa!3, Xb!2, ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | s_e(Xa!3, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xc!1) | (~s_t(ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xc!1)) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.63/0.72 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.63/0.72 tff(522,plain,
% 0.63/0.72 (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.63/0.72 inference(unit_resolution,[status(thm)],[521, 515, 434, 505, 228, 498])).
% 0.63/0.72 tff(523,plain,
% 0.63/0.72 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.63/0.72 inference(rewrite,[status(thm)],[])).
% 0.63/0.72 tff(524,plain,
% 0.63/0.72 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2)))),
% 0.63/0.72 inference(quant_inst,[status(thm)],[])).
% 0.63/0.72 tff(525,plain,
% 0.63/0.72 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2))),
% 0.63/0.72 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.63/0.72 tff(526,plain,
% 0.63/0.72 (~s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.72 inference(unit_resolution,[status(thm)],[525, 455, 522])).
% 0.63/0.72 tff(527,plain,
% 0.63/0.72 (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2) <=> s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.72 inference(monotonicity,[status(thm)],[382])).
% 0.63/0.72 tff(528,plain,
% 0.63/0.72 (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2) <=> s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)),
% 0.63/0.72 inference(symmetry,[status(thm)],[527])).
% 0.63/0.72 tff(529,plain,
% 0.63/0.72 (((~s_t(Xc!1, Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.72 inference(tautology,[status(thm)],[])).
% 0.63/0.72 tff(530,plain,
% 0.63/0.72 (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)),
% 0.63/0.72 inference(unit_resolution,[status(thm)],[529, 111])).
% 0.63/0.72 tff(531,plain,
% 0.63/0.72 (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)),
% 0.63/0.72 inference(modus_ponens,[status(thm)],[530, 528])).
% 0.63/0.72 tff(532,plain,
% 0.63/0.72 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))),
% 0.63/0.72 inference(rewrite,[status(thm)],[])).
% 0.63/0.72 tff(533,plain,
% 0.63/0.72 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0)))),
% 0.63/0.72 inference(quant_inst,[status(thm)],[])).
% 0.63/0.72 tff(534,plain,
% 0.63/0.72 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xa, Xb, Xd, Xc))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.63/0.72 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.63/0.72 tff(535,plain,
% 0.63/0.72 ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xb!2)) | s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.63/0.72 inference(unit_resolution,[status(thm)],[534, 455])).
% 0.63/0.72 tff(536,plain,
% 0.63/0.72 (s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))),
% 0.63/0.72 inference(unit_resolution,[status(thm)],[535, 531])).
% 0.63/0.72 tff(537,plain,
% 0.63/0.72 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))) | s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))) | s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.63/0.72 inference(rewrite,[status(thm)],[])).
% 0.63/0.72 tff(538,plain,
% 0.63/0.72 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))) | s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.63/0.72 inference(quant_inst,[status(thm)],[])).
% 0.63/0.72 tff(539,plain,
% 0.63/0.72 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2), Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0))) | s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.72 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.63/0.72 tff(540,plain,
% 0.63/0.72 (s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))),
% 0.63/0.72 inference(unit_resolution,[status(thm)],[539, 466, 536])).
% 0.63/0.72 tff(541,plain,
% 0.63/0.72 (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.63/0.73 inference(rewrite,[status(thm)],[])).
% 0.63/0.73 tff(542,plain,
% 0.63/0.73 (((~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))) <=> (s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.63/0.73 inference(rewrite,[status(thm)],[])).
% 0.63/0.73 tff(543,plain,
% 0.63/0.73 (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | (s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))))),
% 0.63/0.73 inference(monotonicity,[status(thm)],[542])).
% 0.63/0.73 tff(544,plain,
% 0.63/0.73 (((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))))),
% 0.63/0.73 inference(transitivity,[status(thm)],[543, 541])).
% 0.63/0.73 tff(545,plain,
% 0.63/0.73 ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | ((~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)))),
% 0.63/0.73 inference(quant_inst,[status(thm)],[])).
% 0.63/0.73 tff(546,plain,
% 0.63/0.73 ((~![Xa: $i, Xb: $i, Xc: $i, XA: $i, XB: $i, XC: $i] : ((~s_e(Xa, Xb, XB, XC)) | s_e(Xa, Xc, XA, XC) | (~s_t(XA, XB, XC)) | (~s_t(Xa, Xb, Xc)) | (~s_e(Xb, Xc, XA, XB)))) | s_e(Xb!2, ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)) | (~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)) | (~s_e(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2)))),
% 0.63/0.73 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.63/0.73 tff(547,plain,
% 0.63/0.73 ((~s_t(ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0, ext(Xc!1, Xd!0, insert(Xc!1, Xd!0, Xa!3, Xb!2), Xb!2))) | (~s_t(Xb!2, ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0))) | (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0))),
% 0.63/0.73 inference(unit_resolution,[status(thm)],[546, 515, 540, 526])).
% 0.63/0.73 tff(548,plain,
% 0.63/0.73 (~s_e(ext(ext(Xb!2, Xa!3, alpha, gamma), Xa!3, Xc!1, Xd!0), ext(Xa!3, Xb!2, insert(Xa!3, Xb!2, Xc!1, Xd!0), Xd!0), ext(ext(Xd!0, Xc!1, alpha, gamma), Xc!1, Xa!3, Xb!2), Xd!0)),
% 0.63/0.73 inference(unit_resolution,[status(thm)],[547, 448, 420])).
% 0.63/0.73 tff(549,plain,
% 0.63/0.73 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[548, 417])).
% 0.70/0.74 % SZS output end Proof
%------------------------------------------------------------------------------