TSTP Solution File: GEO086+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO086+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 20:34:46 EDT 2022
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO086+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n016.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Aug 31 05:44:17 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % SZS output start Proof
% 0.14/0.38 tff(open_type, type, (
% 0.14/0.38 open: $i > $o)).
% 0.14/0.38 tff(tptp_fun_Cpp_12_type, type, (
% 0.14/0.38 tptp_fun_Cpp_12: $i)).
% 0.14/0.38 tff(tptp_fun_C_13_type, type, (
% 0.14/0.38 tptp_fun_C_13: $i)).
% 0.14/0.38 tff(part_of_type, type, (
% 0.14/0.38 part_of: ( $i * $i ) > $o)).
% 0.14/0.38 tff(1,plain,
% 0.14/0.38 ((~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))) <=> (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(2,plain,
% 0.14/0.38 ((~![C: $i, Cpp: $i] : ((open(C) & part_of(Cpp, C)) => open(Cpp))) <=> (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(3,axiom,(~![C: $i, Cpp: $i] : ((open(C) & part_of(Cpp, C)) => open(Cpp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_2_7_2')).
% 0.14/0.38 tff(4,plain,
% 0.14/0.38 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.38 tff(5,plain,
% 0.14/0.38 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.38 tff(6,plain,
% 0.14/0.38 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.38 tff(7,plain,
% 0.14/0.38 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.38 tff(8,plain,
% 0.14/0.38 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.14/0.38 tff(9,plain,
% 0.14/0.38 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.14/0.38 tff(10,plain,
% 0.14/0.38 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.14/0.38 tff(11,plain,(
% 0.14/0.38 ~(open(Cpp!12) | (~(open(C!13) & part_of(Cpp!12, C!13))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[10])).
% 0.14/0.38 tff(12,plain,
% 0.14/0.38 (open(C!13) & part_of(Cpp!12, C!13)),
% 0.14/0.38 inference(or_elim,[status(thm)],[11])).
% 0.14/0.38 tff(13,plain,
% 0.14/0.38 (part_of(Cpp!12, C!13)),
% 0.14/0.38 inference(and_elim,[status(thm)],[12])).
% 0.14/0.38 tff(14,plain,
% 0.14/0.38 (~open(Cpp!12)),
% 0.14/0.38 inference(or_elim,[status(thm)],[11])).
% 0.14/0.38 tff(15,plain,
% 0.14/0.38 (^[C: $i, C1: $i] : refl(((C1 = C) | open(C1) | (~part_of(C1, C))) <=> ((C1 = C) | open(C1) | (~part_of(C1, C))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(16,plain,
% 0.14/0.38 (![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C))) <=> ![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.14/0.38 tff(17,plain,
% 0.14/0.38 (^[C: $i, C1: $i] : trans(monotonicity(trans(monotonicity(rewrite((part_of(C1, C) & (~(C1 = C))) <=> (~((~part_of(C1, C)) | (C1 = C)))), ((~(part_of(C1, C) & (~(C1 = C)))) <=> (~(~((~part_of(C1, C)) | (C1 = C)))))), rewrite((~(~((~part_of(C1, C)) | (C1 = C)))) <=> ((~part_of(C1, C)) | (C1 = C))), ((~(part_of(C1, C) & (~(C1 = C)))) <=> ((~part_of(C1, C)) | (C1 = C)))), ((open(C1) | (~(part_of(C1, C) & (~(C1 = C))))) <=> (open(C1) | ((~part_of(C1, C)) | (C1 = C))))), rewrite((open(C1) | ((~part_of(C1, C)) | (C1 = C))) <=> ((C1 = C) | open(C1) | (~part_of(C1, C)))), ((open(C1) | (~(part_of(C1, C) & (~(C1 = C))))) <=> ((C1 = C) | open(C1) | (~part_of(C1, C)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(18,plain,
% 0.14/0.38 (![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C))))) <=> ![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.38 tff(19,plain,
% 0.14/0.38 (![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C))))) <=> ![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(20,plain,
% 0.14/0.38 (^[C: $i, C1: $i] : rewrite(((part_of(C1, C) & (~(C1 = C))) => open(C1)) <=> (open(C1) | (~(part_of(C1, C) & (~(C1 = C))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(21,plain,
% 0.14/0.38 (![C: $i, C1: $i] : ((part_of(C1, C) & (~(C1 = C))) => open(C1)) <=> ![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.14/0.38 tff(22,axiom,(![C: $i, C1: $i] : ((part_of(C1, C) & (~(C1 = C))) => open(C1))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','c1')).
% 0.14/0.38 tff(23,plain,
% 0.14/0.38 (![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.14/0.38 tff(24,plain,
% 0.14/0.38 (![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.38 tff(25,plain,(
% 0.14/0.38 ![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[24])).
% 0.14/0.38 tff(26,plain,
% 0.14/0.38 (![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.14/0.38 tff(27,plain,
% 0.14/0.38 (![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.14/0.38 tff(28,plain,
% 0.14/0.38 (((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | (open(Cpp!12) | (~part_of(Cpp!12, C!13)) | (Cpp!12 = C!13))) <=> ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | open(Cpp!12) | (~part_of(Cpp!12, C!13)) | (Cpp!12 = C!13))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(29,plain,
% 0.14/0.38 (((Cpp!12 = C!13) | open(Cpp!12) | (~part_of(Cpp!12, C!13))) <=> (open(Cpp!12) | (~part_of(Cpp!12, C!13)) | (Cpp!12 = C!13))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(30,plain,
% 0.14/0.38 (((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | ((Cpp!12 = C!13) | open(Cpp!12) | (~part_of(Cpp!12, C!13)))) <=> ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | (open(Cpp!12) | (~part_of(Cpp!12, C!13)) | (Cpp!12 = C!13)))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[29])).
% 0.14/0.38 tff(31,plain,
% 0.14/0.38 (((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | ((Cpp!12 = C!13) | open(Cpp!12) | (~part_of(Cpp!12, C!13)))) <=> ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | open(Cpp!12) | (~part_of(Cpp!12, C!13)) | (Cpp!12 = C!13))),
% 0.14/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.14/0.38 tff(32,plain,
% 0.14/0.38 ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | ((Cpp!12 = C!13) | open(Cpp!12) | (~part_of(Cpp!12, C!13)))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(33,plain,
% 0.14/0.38 ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | open(Cpp!12) | (~part_of(Cpp!12, C!13)) | (Cpp!12 = C!13)),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.38 tff(34,plain,
% 0.14/0.38 (Cpp!12 = C!13),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[33, 27, 14, 13])).
% 0.14/0.38 tff(35,plain,
% 0.14/0.38 (open(Cpp!12) <=> open(C!13)),
% 0.14/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.14/0.38 tff(36,plain,
% 0.14/0.38 (open(C!13) <=> open(Cpp!12)),
% 0.14/0.38 inference(symmetry,[status(thm)],[35])).
% 0.14/0.38 tff(37,plain,
% 0.14/0.38 (open(C!13)),
% 0.14/0.38 inference(and_elim,[status(thm)],[12])).
% 0.14/0.38 tff(38,plain,
% 0.14/0.38 (open(Cpp!12)),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.14/0.38 tff(39,plain,
% 0.14/0.38 ($false),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[14, 38])).
% 0.14/0.38 % SZS output end Proof
%------------------------------------------------------------------------------