TSTP Solution File: GEO526+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO526+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:36:52 EDT 2022
% Result : Theorem 0.63s 0.65s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO526+1 : TPTP v8.1.0. Released v7.0.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 11:12:56 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.63/0.65 % SZS status Theorem
% 0.63/0.65 % SZS output start Proof
% 0.63/0.65 tff(s_r_type, type, (
% 0.63/0.65 s_r: ( $i * $i * $i ) > $o)).
% 0.63/0.65 tff(s_type, type, (
% 0.63/0.65 s: ( $i * $i ) > $i)).
% 0.63/0.65 tff(tptp_fun_Xc_2_type, type, (
% 0.63/0.65 tptp_fun_Xc_2: $i)).
% 0.63/0.65 tff(midpoint_type, type, (
% 0.63/0.65 midpoint: ( $i * $i ) > $i)).
% 0.63/0.65 tff(tptp_fun_Xc1_0_type, type, (
% 0.63/0.65 tptp_fun_Xc1_0: $i)).
% 0.63/0.65 tff(tptp_fun_Xa_4_type, type, (
% 0.63/0.65 tptp_fun_Xa_4: $i)).
% 0.63/0.65 tff(isomidpoint_type, type, (
% 0.63/0.65 isomidpoint: ( $i * $i * $i ) > $i)).
% 0.63/0.65 tff(tptp_fun_Xa1_1_type, type, (
% 0.63/0.65 tptp_fun_Xa1_1: $i)).
% 0.63/0.65 tff(tptp_fun_Xb_3_type, type, (
% 0.63/0.65 tptp_fun_Xb_3: $i)).
% 0.63/0.65 tff(s_m_type, type, (
% 0.63/0.65 s_m: ( $i * $i * $i ) > $o)).
% 0.63/0.65 tff(s_e_type, type, (
% 0.63/0.65 s_e: ( $i * $i * $i * $i ) > $o)).
% 0.63/0.65 tff(1,plain,
% 0.63/0.65 (^[Xa: $i, Xb: $i] : refl(s_m(Xa, midpoint(Xa, Xb), Xb) <=> s_m(Xa, midpoint(Xa, Xb), Xb))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(2,plain,
% 0.63/0.65 (![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb) <=> ![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.63/0.65 inference(quant_intro,[status(thm)],[1])).
% 0.63/0.65 tff(3,plain,
% 0.63/0.65 (![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb) <=> ![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(4,axiom,(![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_22')).
% 0.63/0.65 tff(5,plain,
% 0.63/0.65 (![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.63/0.65 tff(6,plain,(
% 0.63/0.65 ![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.63/0.65 inference(skolemize,[status(sab)],[5])).
% 0.63/0.65 tff(7,plain,
% 0.63/0.65 (![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.63/0.65 tff(8,plain,
% 0.63/0.65 ((~![Xa: $i, Xb: $i] : s_m(Xa, midpoint(Xa, Xb), Xb)) | s_m(Xc!2, midpoint(Xc!2, Xc1!0), Xc1!0)),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(9,plain,
% 0.63/0.65 (s_m(Xc!2, midpoint(Xc!2, Xc1!0), Xc1!0)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.63/0.65 tff(10,plain,
% 0.63/0.65 (^[Xp: $i, Xa: $i, Xq: $i] : refl(((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(11,plain,
% 0.63/0.65 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[10])).
% 0.63/0.65 tff(12,plain,
% 0.63/0.65 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp))) <=> ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(13,axiom,(![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_6')).
% 0.63/0.65 tff(14,plain,
% 0.63/0.65 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.63/0.65 tff(15,plain,(
% 0.63/0.65 ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.63/0.65 inference(skolemize,[status(sab)],[14])).
% 0.63/0.65 tff(16,plain,
% 0.63/0.65 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.63/0.65 tff(17,plain,
% 0.63/0.65 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xc!2, midpoint(Xc!2, Xc1!0), Xc1!0)) | (Xc1!0 = s(midpoint(Xc!2, Xc1!0), Xc!2)))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xc!2, midpoint(Xc!2, Xc1!0), Xc1!0)) | (Xc1!0 = s(midpoint(Xc!2, Xc1!0), Xc!2)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(18,plain,
% 0.63/0.65 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xc!2, midpoint(Xc!2, Xc1!0), Xc1!0)) | (Xc1!0 = s(midpoint(Xc!2, Xc1!0), Xc!2)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(19,plain,
% 0.63/0.65 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xc!2, midpoint(Xc!2, Xc1!0), Xc1!0)) | (Xc1!0 = s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.63/0.65 tff(20,plain,
% 0.63/0.65 (Xc1!0 = s(midpoint(Xc!2, Xc1!0), Xc!2)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.63/0.65 tff(21,plain,
% 0.63/0.65 (s(midpoint(Xc!2, Xc1!0), Xc!2) = Xc1!0),
% 0.63/0.66 inference(symmetry,[status(thm)],[20])).
% 0.63/0.66 tff(22,plain,
% 0.63/0.66 ((~(s_e(Xa!4, Xc!2, Xa1!1, Xc1!0) | (Xc!2 = Xc1!0) | (~s_e(Xb!3, Xc!2, Xb!3, Xc1!0)) | (~(Xb!3 = midpoint(Xc!2, Xc1!0))) | (~s_e(Xa!4, Xb!3, Xa1!1, Xb!3)) | (~s_r(Xa1!1, Xb!3, Xc1!0)) | (~s_r(Xa!4, Xb!3, Xc!2)))) <=> (~(s_e(Xa!4, Xc!2, Xa1!1, Xc1!0) | (Xc!2 = Xc1!0) | (~s_e(Xb!3, Xc!2, Xb!3, Xc1!0)) | (~(Xb!3 = midpoint(Xc!2, Xc1!0))) | (~s_e(Xa!4, Xb!3, Xa1!1, Xb!3)) | (~s_r(Xa1!1, Xb!3, Xc1!0)) | (~s_r(Xa!4, Xb!3, Xc!2))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(23,plain,
% 0.63/0.66 ((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc)))) <=> (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(24,plain,
% 0.63/0.66 ((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (((((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb))) | (~s_e(Xb, Xc, Xb, Xc1))) | s_e(Xa, Xc, Xa1, Xc1)) | (~(Xb = midpoint(Xc, Xc1)))) | (Xc = Xc1))) <=> (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(25,axiom,(~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (((((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb))) | (~s_e(Xb, Xc, Xb, Xc1))) | s_e(Xa, Xc, Xa1, Xc1)) | (~(Xb = midpoint(Xc, Xc1)))) | (Xc = Xc1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz10_12c')).
% 0.63/0.66 tff(26,plain,
% 0.63/0.66 (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.63/0.66 tff(27,plain,
% 0.63/0.66 (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.63/0.66 tff(28,plain,
% 0.63/0.66 (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.63/0.66 tff(29,plain,
% 0.63/0.66 (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.63/0.66 tff(30,plain,
% 0.63/0.66 (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.63/0.66 tff(31,plain,
% 0.63/0.66 (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.63/0.66 tff(32,plain,
% 0.63/0.66 (~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i, Xc1: $i] : (s_e(Xa, Xc, Xa1, Xc1) | (Xc = Xc1) | (~s_e(Xb, Xc, Xb, Xc1)) | (~(Xb = midpoint(Xc, Xc1))) | (~s_e(Xa, Xb, Xa1, Xb)) | (~s_r(Xa1, Xb, Xc1)) | (~s_r(Xa, Xb, Xc)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[31, 23])).
% 0.63/0.66 tff(33,plain,(
% 0.63/0.66 ~(s_e(Xa!4, Xc!2, Xa1!1, Xc1!0) | (Xc!2 = Xc1!0) | (~s_e(Xb!3, Xc!2, Xb!3, Xc1!0)) | (~(Xb!3 = midpoint(Xc!2, Xc1!0))) | (~s_e(Xa!4, Xb!3, Xa1!1, Xb!3)) | (~s_r(Xa1!1, Xb!3, Xc1!0)) | (~s_r(Xa!4, Xb!3, Xc!2)))),
% 0.63/0.66 inference(skolemize,[status(sab)],[32])).
% 0.63/0.66 tff(34,plain,
% 0.63/0.66 (~(s_e(Xa!4, Xc!2, Xa1!1, Xc1!0) | (Xc!2 = Xc1!0) | (~s_e(Xb!3, Xc!2, Xb!3, Xc1!0)) | (~(Xb!3 = midpoint(Xc!2, Xc1!0))) | (~s_e(Xa!4, Xb!3, Xa1!1, Xb!3)) | (~s_r(Xa1!1, Xb!3, Xc1!0)) | (~s_r(Xa!4, Xb!3, Xc!2)))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[33, 22])).
% 0.63/0.66 tff(35,plain,
% 0.63/0.66 (Xb!3 = midpoint(Xc!2, Xc1!0)),
% 0.63/0.66 inference(or_elim,[status(thm)],[34])).
% 0.63/0.66 tff(36,plain,
% 0.63/0.66 (midpoint(Xc!2, Xc1!0) = Xb!3),
% 0.63/0.66 inference(symmetry,[status(thm)],[35])).
% 0.63/0.66 tff(37,plain,
% 0.63/0.66 (s_e(Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1, midpoint(Xc!2, Xc1!0)) <=> s_e(Xa!4, Xb!3, Xa1!1, Xb!3)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[36, 36])).
% 0.63/0.66 tff(38,plain,
% 0.63/0.66 (s_e(Xa!4, Xb!3, Xa1!1, Xb!3) <=> s_e(Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1, midpoint(Xc!2, Xc1!0))),
% 0.63/0.66 inference(symmetry,[status(thm)],[37])).
% 0.63/0.66 tff(39,plain,
% 0.63/0.66 (s_e(Xa!4, Xb!3, Xa1!1, Xb!3)),
% 0.63/0.66 inference(or_elim,[status(thm)],[34])).
% 0.63/0.66 tff(40,plain,
% 0.63/0.66 (s_e(Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1, midpoint(Xc!2, Xc1!0))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.63/0.66 tff(41,plain,
% 0.63/0.66 (^[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)))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(42,plain,
% 0.63/0.66 (![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))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[41])).
% 0.63/0.66 tff(43,plain,
% 0.63/0.66 (![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))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(44,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_14')).
% 0.63/0.66 tff(45,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.63/0.66 tff(46,plain,(
% 0.63/0.66 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.63/0.66 inference(skolemize,[status(sab)],[45])).
% 0.63/0.66 tff(47,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.63/0.66 tff(48,plain,
% 0.63/0.66 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1, midpoint(Xc!2, Xc1!0))) | s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1, midpoint(Xc!2, Xc1!0))) | s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(49,plain,
% 0.63/0.66 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1, midpoint(Xc!2, Xc1!0))) | s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(50,plain,
% 0.63/0.66 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1, midpoint(Xc!2, Xc1!0))) | s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.63/0.66 tff(51,plain,
% 0.63/0.66 ((~s_e(Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1, midpoint(Xc!2, Xc1!0))) | s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.63/0.66 tff(52,plain,
% 0.63/0.66 (s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[51, 40])).
% 0.63/0.66 tff(53,plain,
% 0.63/0.66 (^[Xc: $i, Xa: $i, Xb: $i] : refl(((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb)) <=> ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb)))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(54,plain,
% 0.63/0.66 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb)) <=> ![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[53])).
% 0.63/0.66 tff(55,plain,
% 0.63/0.66 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb)) <=> ![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(56,axiom,(![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_25')).
% 0.63/0.66 tff(57,plain,
% 0.63/0.66 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.63/0.66 tff(58,plain,(
% 0.63/0.66 ![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.63/0.66 inference(skolemize,[status(sab)],[57])).
% 0.63/0.66 tff(59,plain,
% 0.63/0.66 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.63/0.66 tff(60,plain,
% 0.63/0.66 (((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | ((~s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1)) | s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1))) <=> ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | (~s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1)) | s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(61,plain,
% 0.63/0.66 ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | ((~s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1)) | s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(62,plain,
% 0.63/0.66 ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | (~s_e(midpoint(Xc!2, Xc1!0), Xa!4, midpoint(Xc!2, Xc1!0), Xa1!1)) | s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.63/0.66 tff(63,plain,
% 0.63/0.66 (s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[62, 59, 52])).
% 0.63/0.66 tff(64,plain,
% 0.63/0.66 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1)) | (Xa1!1 = s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4)))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1)) | (Xa1!1 = s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(65,plain,
% 0.63/0.66 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1)) | (Xa1!1 = s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4)))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(66,plain,
% 0.63/0.66 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xa!4, isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa1!1)) | (Xa1!1 = s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.63/0.66 tff(67,plain,
% 0.63/0.66 (Xa1!1 = s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[66, 16, 63])).
% 0.63/0.66 tff(68,plain,
% 0.63/0.66 (s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4) = Xa1!1),
% 0.63/0.66 inference(symmetry,[status(thm)],[67])).
% 0.63/0.66 tff(69,plain,
% 0.63/0.66 (s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) <=> s_r(Xa1!1, Xb!3, Xc1!0)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[68, 36, 21])).
% 0.63/0.66 tff(70,plain,
% 0.63/0.66 (s_r(Xa1!1, Xb!3, Xc1!0) <=> s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.66 inference(symmetry,[status(thm)],[69])).
% 0.63/0.66 tff(71,plain,
% 0.63/0.66 (s_r(Xa1!1, Xb!3, Xc1!0)),
% 0.63/0.66 inference(or_elim,[status(thm)],[34])).
% 0.63/0.66 tff(72,plain,
% 0.63/0.66 (s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.63/0.66 tff(73,plain,
% 0.63/0.66 (s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) <=> s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[68])).
% 0.63/0.66 tff(74,plain,
% 0.63/0.66 (s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2)) <=> s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.66 inference(symmetry,[status(thm)],[73])).
% 0.63/0.66 tff(75,plain,
% 0.63/0.66 ((~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))) <=> (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[74])).
% 0.63/0.66 tff(76,plain,
% 0.63/0.66 (^[Xa: $i, Xb: $i, Xc: $i] : refl((~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(77,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[76])).
% 0.63/0.66 tff(78,plain,
% 0.63/0.66 (^[Xa: $i, Xb: $i, Xc: $i] : trans(monotonicity(rewrite((s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))) <=> (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))), ((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))))), rewrite((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))), ((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(79,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[78])).
% 0.63/0.66 tff(80,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(81,axiom,(![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d_Defn8_1')).
% 0.63/0.66 tff(82,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.63/0.66 tff(83,plain,(
% 0.63/0.66 ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & (s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))),
% 0.63/0.66 inference(skolemize,[status(sab)],[82])).
% 0.63/0.66 tff(84,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.63/0.66 tff(85,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.63/0.66 tff(86,plain,
% 0.63/0.66 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))) | (~((~((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)) | s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2)))) | (~(s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2) | (~s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2)))))))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(87,plain,
% 0.63/0.66 (~((~((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)) | s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2)))) | (~(s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2) | (~s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2))))))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.63/0.66 tff(88,plain,
% 0.63/0.66 (((~((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)) | s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2)))) | (~(s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2) | (~s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2)))))) | ((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)) | s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2)))),
% 0.63/0.66 inference(tautology,[status(thm)],[])).
% 0.63/0.66 tff(89,plain,
% 0.63/0.66 ((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)) | s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.63/0.66 tff(90,plain,
% 0.63/0.66 (s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2) <=> s_r(Xa!4, Xb!3, Xc!2)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[36])).
% 0.63/0.66 tff(91,plain,
% 0.63/0.66 (s_r(Xa!4, Xb!3, Xc!2) <=> s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)),
% 0.63/0.66 inference(symmetry,[status(thm)],[90])).
% 0.63/0.66 tff(92,plain,
% 0.63/0.66 (s_r(Xa!4, Xb!3, Xc!2)),
% 0.63/0.66 inference(or_elim,[status(thm)],[34])).
% 0.63/0.66 tff(93,plain,
% 0.63/0.66 (s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.63/0.66 tff(94,plain,
% 0.63/0.66 ((~((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)) | s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2)))) | (~s_r(Xa!4, midpoint(Xc!2, Xc1!0), Xc!2)) | s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.66 inference(tautology,[status(thm)],[])).
% 0.63/0.66 tff(95,plain,
% 0.63/0.66 (s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[94, 93, 89])).
% 0.63/0.66 tff(96,plain,
% 0.63/0.66 (^[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)))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(97,plain,
% 0.63/0.66 (![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))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[96])).
% 0.63/0.66 tff(98,plain,
% 0.63/0.66 (![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))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(99,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_2')).
% 0.63/0.66 tff(100,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.63/0.66 tff(101,plain,(
% 0.63/0.66 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.63/0.66 inference(skolemize,[status(sab)],[100])).
% 0.63/0.66 tff(102,plain,
% 0.63/0.66 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.63/0.66 tff(103,plain,
% 0.63/0.66 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(104,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(105,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xa!4, Xc!2, Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.63/0.67 tff(106,plain,
% 0.63/0.67 (s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[105, 102, 95])).
% 0.63/0.67 tff(107,plain,
% 0.63/0.67 (s_e(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) <=> s_e(Xa1!1, Xc1!0, Xa!4, Xc!2)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[21])).
% 0.63/0.67 tff(108,plain,
% 0.63/0.67 (s_e(Xa1!1, Xc1!0, Xa!4, Xc!2) <=> s_e(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)),
% 0.63/0.67 inference(symmetry,[status(thm)],[107])).
% 0.63/0.67 tff(109,plain,
% 0.63/0.67 ((~s_e(Xa1!1, Xc1!0, Xa!4, Xc!2)) <=> (~s_e(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[108])).
% 0.63/0.67 tff(110,plain,
% 0.63/0.67 (~s_e(Xa!4, Xc!2, Xa1!1, Xc1!0)),
% 0.63/0.67 inference(or_elim,[status(thm)],[34])).
% 0.63/0.67 tff(111,plain,
% 0.63/0.67 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xa1!1, Xc1!0, Xa!4, Xc!2)) | s_e(Xa!4, Xc!2, Xa1!1, Xc1!0))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xa1!1, Xc1!0, Xa!4, Xc!2)) | s_e(Xa!4, Xc!2, Xa1!1, Xc1!0))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(112,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | ((~s_e(Xa1!1, Xc1!0, Xa!4, Xc!2)) | s_e(Xa!4, Xc!2, Xa1!1, Xc1!0))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(113,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xc, Xd, Xa, Xb))) | (~s_e(Xa1!1, Xc1!0, Xa!4, Xc!2)) | s_e(Xa!4, Xc!2, Xa1!1, Xc1!0)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.63/0.67 tff(114,plain,
% 0.63/0.67 (~s_e(Xa1!1, Xc1!0, Xa!4, Xc!2)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[113, 102, 110])).
% 0.63/0.67 tff(115,plain,
% 0.63/0.67 (~s_e(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[114, 109])).
% 0.63/0.67 tff(116,plain,
% 0.63/0.67 (^[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))))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(117,plain,
% 0.63/0.67 (![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)))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[116])).
% 0.63/0.67 tff(118,plain,
% 0.63/0.67 (![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)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(119,plain,
% 0.63/0.67 (^[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)))))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(120,plain,
% 0.63/0.67 (![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)))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[119])).
% 0.63/0.67 tff(121,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/sandbox/benchmark/Axioms/GEO011+0.ax','aA2')).
% 0.63/0.67 tff(122,plain,
% 0.63/0.67 (![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)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.63/0.67 tff(123,plain,
% 0.63/0.67 (![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)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.63/0.67 tff(124,plain,(
% 0.63/0.67 ![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)))),
% 0.63/0.67 inference(skolemize,[status(sab)],[123])).
% 0.63/0.67 tff(125,plain,
% 0.63/0.67 (![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)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.63/0.67 tff(126,plain,
% 0.63/0.67 (((~![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(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)))) <=> ((~![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(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(127,plain,
% 0.63/0.67 ((s_e(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2)))) <=> (s_e(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(128,plain,
% 0.63/0.67 (((~![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(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))))) <=> ((~![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(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2))))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[127])).
% 0.63/0.67 tff(129,plain,
% 0.63/0.67 (((~![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(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))))) <=> ((~![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(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)))),
% 0.63/0.67 inference(transitivity,[status(thm)],[128, 126])).
% 0.63/0.67 tff(130,plain,
% 0.63/0.67 ((~![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(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(131,plain,
% 0.63/0.67 ((~![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(Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.63/0.67 tff(132,plain,
% 0.63/0.67 (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa1!1, s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[131, 125, 115, 106])).
% 0.63/0.67 tff(133,plain,
% 0.63/0.67 (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[132, 75])).
% 0.63/0.67 tff(134,plain,
% 0.63/0.67 (s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0)) <=> s_e(Xa!4, Xb!3, Xa1!1, Xb!3)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[36, 68, 36])).
% 0.63/0.67 tff(135,plain,
% 0.63/0.67 (s_e(Xa!4, Xb!3, Xa1!1, Xb!3) <=> s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))),
% 0.63/0.67 inference(symmetry,[status(thm)],[134])).
% 0.63/0.67 tff(136,plain,
% 0.63/0.67 (s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[39, 135])).
% 0.63/0.67 tff(137,plain,
% 0.63/0.67 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~(s_r(Xa, Xb, Xc) | (~s_e(Xa, Xc, Xa, s(Xb, Xc)))))))) | (~((~((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))) | (~(s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))))))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(138,plain,
% 0.63/0.67 (~((~((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))) | (~(s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)))))))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[137, 85])).
% 0.63/0.67 tff(139,plain,
% 0.63/0.67 (((~((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))) | (~(s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))))) | (s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)))))),
% 0.63/0.67 inference(tautology,[status(thm)],[])).
% 0.63/0.67 tff(140,plain,
% 0.63/0.67 (s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.63/0.67 tff(141,plain,
% 0.63/0.67 (^[Xa: $i, Xp: $i] : refl((s(Xa, s(Xa, Xp)) = Xp) <=> (s(Xa, s(Xa, Xp)) = Xp))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(142,plain,
% 0.63/0.67 (![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp) <=> ![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp)),
% 0.63/0.67 inference(quant_intro,[status(thm)],[141])).
% 0.63/0.67 tff(143,plain,
% 0.63/0.67 (![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp) <=> ![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp)),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(144,axiom,(![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_7')).
% 0.63/0.67 tff(145,plain,
% 0.63/0.67 (![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.63/0.67 tff(146,plain,(
% 0.63/0.67 ![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp)),
% 0.63/0.67 inference(skolemize,[status(sab)],[145])).
% 0.63/0.67 tff(147,plain,
% 0.63/0.67 (![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.63/0.67 tff(148,plain,
% 0.63/0.67 ((~![Xa: $i, Xp: $i] : (s(Xa, s(Xa, Xp)) = Xp)) | (s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) = Xc!2)),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(149,plain,
% 0.63/0.67 (s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) = Xc!2),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.63/0.67 tff(150,plain,
% 0.63/0.67 (s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) <=> s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2)),
% 0.63/0.67 inference(monotonicity,[status(thm)],[149])).
% 0.63/0.67 tff(151,plain,
% 0.63/0.67 (s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, Xc!2) <=> s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)))),
% 0.63/0.67 inference(symmetry,[status(thm)],[150])).
% 0.63/0.67 tff(152,plain,
% 0.63/0.67 (s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[106, 151])).
% 0.63/0.67 tff(153,plain,
% 0.63/0.67 ((~(s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)))))) | s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), Xa!4, s(midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))),
% 0.63/0.67 inference(tautology,[status(thm)],[])).
% 0.63/0.67 tff(154,plain,
% 0.63/0.67 (s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[153, 152, 140])).
% 0.63/0.67 tff(155,plain,
% 0.63/0.67 (^[Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : refl(((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb))) <=> ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb))))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(156,plain,
% 0.63/0.67 (![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[155])).
% 0.63/0.67 tff(157,plain,
% 0.63/0.67 (![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(158,plain,
% 0.63/0.67 (^[Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) <=> ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)))), ((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) | (~s_e(Xa, Xb, Xa1, Xb))) <=> (((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) | (~s_e(Xa, Xb, Xa1, Xb))))), rewrite((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) | (~s_e(Xa, Xb, Xa1, Xb))) <=> ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | (~s_e(Xa, Xb, Xa1, Xb)))), ((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) | (~s_e(Xa, Xb, Xa1, Xb))) <=> ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | (~s_e(Xa, Xb, Xa1, Xb))))), (((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) | (~s_e(Xa, Xb, Xa1, Xb))) | s_e(Xa, Xc, Xa1, Xc)) <=> (((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | (~s_e(Xa, Xb, Xa1, Xb))) | s_e(Xa, Xc, Xa1, Xc)))), rewrite((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | (~s_e(Xa, Xb, Xa1, Xb))) | s_e(Xa, Xc, Xa1, Xc)) <=> ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))), (((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) | (~s_e(Xa, Xb, Xa1, Xb))) | s_e(Xa, Xc, Xa1, Xc)) <=> ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(159,plain,
% 0.63/0.68 (![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) | (~s_e(Xa, Xb, Xa1, Xb))) | s_e(Xa, Xc, Xa1, Xc)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))),
% 0.63/0.68 inference(quant_intro,[status(thm)],[158])).
% 0.63/0.68 tff(160,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc))) | (~s_e(Xa, Xb, Xa1, Xb))) | s_e(Xa, Xc, Xa1, Xc))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz10_12b')).
% 0.63/0.68 tff(161,plain,
% 0.63/0.68 (![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.63/0.68 tff(162,plain,
% 0.63/0.68 (![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.63/0.68 tff(163,plain,(
% 0.63/0.68 ![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))),
% 0.63/0.68 inference(skolemize,[status(sab)],[162])).
% 0.63/0.68 tff(164,plain,
% 0.63/0.68 (![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.63/0.68 tff(165,plain,
% 0.63/0.68 (((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))) | ((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))) | (~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(166,plain,
% 0.63/0.68 (((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0)))) <=> ((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(167,plain,
% 0.63/0.68 (((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))) | ((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))) | ((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)))))),
% 0.63/0.69 inference(monotonicity,[status(thm)],[166])).
% 0.63/0.69 tff(168,plain,
% 0.63/0.69 (((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))) | ((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))) | (~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))))),
% 0.63/0.69 inference(transitivity,[status(thm)],[167, 165])).
% 0.63/0.69 tff(169,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))) | ((~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(170,plain,
% 0.63/0.69 ((~![Xa: $i, Xb: $i, Xc: $i, Xa1: $i] : ((~s_r(Xa, Xb, Xc)) | (~s_r(Xa1, Xb, Xc)) | s_e(Xa, Xc, Xa1, Xc) | (~s_e(Xa, Xb, Xa1, Xb)))) | (~s_r(Xa!4, midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))) | (~s_e(Xa!4, midpoint(Xc!2, Xc1!0), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0))) | s_e(Xa!4, s(midpoint(Xc!2, Xc1!0), Xc!2), s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), s(midpoint(Xc!2, Xc1!0), Xc!2)) | (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.63/0.69 tff(171,plain,
% 0.63/0.69 (~s_r(s(isomidpoint(Xa!4, Xa1!1, midpoint(Xc!2, Xc1!0)), Xa!4), midpoint(Xc!2, Xc1!0), s(midpoint(Xc!2, Xc1!0), Xc!2))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[170, 164, 154, 136, 133])).
% 0.63/0.69 tff(172,plain,
% 0.63/0.69 ($false),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[171, 72])).
% 0.63/0.69 % SZS output end Proof
%------------------------------------------------------------------------------