TSTP Solution File: GEO504+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO504+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20:36:49 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO504+1 : TPTP v8.1.0. Released v7.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 10:56:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(s_e_type, type, (
% 0.19/0.46 s_e: ( $i * $i * $i * $i ) > $o)).
% 0.19/0.46 tff(s_type, type, (
% 0.19/0.46 s: ( $i * $i ) > $i)).
% 0.19/0.46 tff(tptp_fun_Xa_2_type, type, (
% 0.19/0.46 tptp_fun_Xa_2: $i)).
% 0.19/0.46 tff(tptp_fun_Xb_1_type, type, (
% 0.19/0.46 tptp_fun_Xb_1: $i)).
% 0.19/0.46 tff(tptp_fun_Xc_0_type, type, (
% 0.19/0.46 tptp_fun_Xc_0: $i)).
% 0.19/0.46 tff(isomidpoint_type, type, (
% 0.19/0.46 isomidpoint: ( $i * $i * $i ) > $i)).
% 0.19/0.46 tff(s_m_type, type, (
% 0.19/0.46 s_m: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(s_r_type, type, (
% 0.19/0.46 s_r: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 (^[Xa: $i, Xb: $i, Xc: $i] : refl((~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(2,plain,
% 0.19/0.46 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.46 tff(3,plain,
% 0.19/0.46 (^[Xa: $i, Xb: $i, Xc: $i] : rewrite((((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))) <=> (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(4,plain,
% 0.19/0.46 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.46 tff(5,plain,
% 0.19/0.46 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))) <=> ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(6,plain,
% 0.19/0.46 (^[Xa: $i, Xb: $i, Xc: $i] : 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_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(7,plain,
% 0.19/0.46 (![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_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.46 tff(8,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')).
% 0.19/0.46 tff(9,plain,
% 0.19/0.46 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.46 tff(10,plain,
% 0.19/0.46 (![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.46 tff(11,plain,(
% 0.19/0.46 ![Xa: $i, Xb: $i, Xc: $i] : (((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc))) & ((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[10])).
% 0.19/0.46 tff(12,plain,
% 0.19/0.46 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.46 tff(13,plain,
% 0.19/0.46 (![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))) | (~((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | (~((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_r(Xa!2, Xb!1, Xc!0)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 (~((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | (~((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_r(Xa!2, Xb!1, Xc!0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 (((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | (~((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_r(Xa!2, Xb!1, Xc!0)))) | ((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(17,plain,
% 0.19/0.46 ((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 ((~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))) <=> (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(19,axiom,(~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz8_2')).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[20, 18])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (~![Xa: $i, Xb: $i, Xc: $i] : ((~s_r(Xa, Xb, Xc)) | s_r(Xc, Xb, Xa))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.46 tff(27,plain,(
% 0.19/0.46 ~((~s_r(Xa!2, Xb!1, Xc!0)) | s_r(Xc!0, Xb!1, Xa!2))),
% 0.19/0.46 inference(skolemize,[status(sab)],[26])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (s_r(Xa!2, Xb!1, Xc!0)),
% 0.19/0.46 inference(or_elim,[status(thm)],[27])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | (~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 ((~((~s_r(Xa!2, Xb!1, Xc!0)) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0)))) | s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[30, 17])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 (^[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)))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (![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))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(35,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')).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.47 tff(37,plain,(
% 0.19/0.47 ![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.19/0.47 inference(skolemize,[status(sab)],[36])).
% 0.19/0.47 tff(38,plain,
% 0.19/0.47 (![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.47 tff(39,plain,
% 0.19/0.47 (((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | ((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0)))) <=> ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | (~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(40,plain,
% 0.19/0.47 ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | ((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(41,plain,
% 0.19/0.47 ((~![Xc: $i, Xa: $i, Xb: $i] : ((~s_e(Xc, Xa, Xc, Xb)) | s_m(Xa, isomidpoint(Xa, Xb, Xc), Xb))) | (~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.47 tff(42,plain,
% 0.19/0.47 (s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.19/0.47 tff(43,plain,
% 0.19/0.47 (^[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))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(44,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.47 tff(45,plain,
% 0.19/0.47 (![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)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(46,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')).
% 0.19/0.47 tff(47,plain,
% 0.19/0.47 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.47 tff(48,plain,(
% 0.19/0.47 ![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[47])).
% 0.19/0.47 tff(49,plain,
% 0.19/0.47 (![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.19/0.47 tff(50,plain,
% 0.19/0.47 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))) | (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))) | (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(51,plain,
% 0.19/0.47 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))) | (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(52,plain,
% 0.19/0.47 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(Xc!0, isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), s(Xb!1, Xc!0))) | (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.47 tff(53,plain,
% 0.19/0.47 (s(Xb!1, Xc!0) = s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[52, 49, 42])).
% 0.19/0.47 tff(54,plain,
% 0.19/0.47 (s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0) = s(Xb!1, Xc!0)),
% 0.19/0.47 inference(symmetry,[status(thm)],[53])).
% 0.19/0.47 tff(55,plain,
% 0.19/0.47 (s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0) <=> s_m(s(Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.19/0.47 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.47 tff(56,plain,
% 0.19/0.47 (s_m(s(Xb!1, Xc!0), Xb!1, Xc!0) <=> s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)),
% 0.19/0.47 inference(symmetry,[status(thm)],[55])).
% 0.19/0.47 tff(57,plain,
% 0.19/0.47 (^[Xp: $i, Xa: $i] : refl(s_m(Xp, Xa, s(Xa, Xp)) <=> s_m(Xp, Xa, s(Xa, Xp)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(58,plain,
% 0.19/0.47 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.47 tff(59,plain,
% 0.19/0.47 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp)) <=> ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(60,axiom,(![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_4a')).
% 0.19/0.47 tff(61,plain,
% 0.19/0.47 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.47 tff(62,plain,(
% 0.19/0.47 ![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.47 inference(skolemize,[status(sab)],[61])).
% 0.19/0.47 tff(63,plain,
% 0.19/0.47 (![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.47 tff(64,plain,
% 0.19/0.47 ((~![Xp: $i, Xa: $i] : s_m(Xp, Xa, s(Xa, Xp))) | s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(65,plain,
% 0.19/0.47 (s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.19/0.47 tff(66,plain,
% 0.19/0.47 (^[Xa: $i, Xm: $i, Xb: $i] : refl(((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(67,plain,
% 0.19/0.47 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[66])).
% 0.19/0.47 tff(68,plain,
% 0.19/0.47 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa)) <=> ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(69,axiom,(![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_2')).
% 0.19/0.47 tff(70,plain,
% 0.19/0.47 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.47 tff(71,plain,(
% 0.19/0.47 ![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.19/0.47 inference(skolemize,[status(sab)],[70])).
% 0.19/0.47 tff(72,plain,
% 0.19/0.47 (![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 (((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))) | s_m(s(Xb!1, Xc!0), Xb!1, Xc!0))) <=> ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))) | s_m(s(Xb!1, Xc!0), Xb!1, Xc!0))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | ((~s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))) | s_m(s(Xb!1, Xc!0), Xb!1, Xc!0))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 ((~![Xa: $i, Xm: $i, Xb: $i] : ((~s_m(Xa, Xm, Xb)) | s_m(Xb, Xm, Xa))) | (~s_m(Xc!0, Xb!1, s(Xb!1, Xc!0))) | s_m(s(Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 (s_m(s(Xb!1, Xc!0), Xb!1, Xc!0)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[75, 72, 65])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 (s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[76, 56])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 (((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))))) <=> ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | ((~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 ((~![Xp: $i, Xa: $i, Xq: $i] : ((~s_m(Xp, Xa, Xq)) | (Xq = s(Xa, Xp)))) | (~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 ((~s_m(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xb!1, Xc!0)) | (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[80, 49])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (Xc!0 = s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[81, 77])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)) = Xc!0),
% 0.19/0.47 inference(symmetry,[status(thm)],[82])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2)) <=> s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[54, 83])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2)) <=> s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2))),
% 0.19/0.47 inference(symmetry,[status(thm)],[84])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 ((~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))) <=> (~s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2)))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[85])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 (^[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)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 (![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))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(90,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')).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.47 tff(92,plain,(
% 0.19/0.47 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.19/0.47 inference(skolemize,[status(sab)],[91])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | ((~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i] : ((~s_e(Xa, Xb, Xc, Xd)) | s_e(Xb, Xa, Xd, Xc))) | (~s_e(Xa!2, Xc!0, Xa!2, s(Xb!1, Xc!0))) | s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[96, 93, 31])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 ((~![Xa: $i, Xb: $i, Xc: $i] : (~((~((~s_r(Xa, Xb, Xc)) | s_e(Xa, Xc, Xa, s(Xb, Xc)))) | (~((~s_e(Xa, Xc, Xa, s(Xb, Xc))) | s_r(Xa, Xb, Xc)))))) | (~((~((~s_r(Xc!0, Xb!1, Xa!2)) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)))) | (~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (~((~((~s_r(Xc!0, Xb!1, Xa!2)) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)))) | (~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[98, 13])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (((~((~s_r(Xc!0, Xb!1, Xa!2)) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)))) | (~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2)))) | ((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 ((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (~s_r(Xc!0, Xb!1, Xa!2)),
% 0.19/0.47 inference(or_elim,[status(thm)],[27])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 ((~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2))) | (~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 ((~((~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))) | s_r(Xc!0, Xb!1, Xa!2))) | (~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (~s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : refl((s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) <=> (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 (^[Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : trans(monotonicity(rewrite(((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) <=> ((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))), ((((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)) <=> (((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)))), rewrite((((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)) <=> (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))), ((((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)) <=> (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf)) <=> ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.47 tff(111,axiom,(![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (((~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf))) | s_e(Xa, Xb, Xe, Xf))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz2_3')).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.19/0.48 tff(114,plain,(
% 0.19/0.48 ![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[113])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 (![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))) | (s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)) | (~s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)) | (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))))) <=> ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)) | (~s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)) | (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))) | (s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)) | (~s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)) | (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 ((~![Xa: $i, Xb: $i, Xc: $i, Xd: $i, Xe: $i, Xf: $i] : (s_e(Xa, Xb, Xe, Xf) | (~s_e(Xa, Xb, Xc, Xd)) | (~s_e(Xc, Xd, Xe, Xf)))) | s_e(Xc!0, Xa!2, Xc!0, s(Xb!1, Xa!2)) | (~s_e(Xc!0, Xa!2, s(Xb!1, Xc!0), Xa!2)) | (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 (~s_e(s(Xb!1, Xc!0), Xa!2, Xc!0, s(Xb!1, Xa!2))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[118, 115, 105, 97])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (~s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[119, 86])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 (^[Xp: $i, Xq: $i, Xa: $i] : refl(s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq)) <=> s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq)))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 (![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq)) <=> ![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq)) <=> ![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(124,axiom,(![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aSatz7_13')).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.48 tff(126,plain,(
% 0.19/0.48 ![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.19/0.48 inference(skolemize,[status(sab)],[125])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 ((~![Xp: $i, Xq: $i, Xa: $i] : s_e(Xp, Xq, s(Xa, Xp), s(Xa, Xq))) | s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 (s_e(s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0), Xa!2, s(Xb!1, s(isomidpoint(Xc!0, s(Xb!1, Xc!0), Xa!2), Xc!0)), s(Xb!1, Xa!2))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[129, 120])).
% 0.19/0.48 % SZS output end Proof
%------------------------------------------------------------------------------