%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO086+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 : Sat Jun 21 05:05:33 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO086+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:16:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(open_type, type, (
% 0.20/0.37 open: $i > $o)).
% 0.20/0.37 tff(tptp_fun_Cpp_11_type, type, (
% 0.20/0.37 tptp_fun_Cpp_11: $i)).
% 0.20/0.37 tff(tptp_fun_C_12_type, type, (
% 0.20/0.37 tptp_fun_C_12: $i)).
% 0.20/0.37 tff(part_of_type, type, (
% 0.20/0.37 part_of: ( $i * $i ) > $o)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 ((~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))) <=> (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 ((~![C: $i, Cpp: $i] : ((open(C) & part_of(Cpp, C)) => open(Cpp))) <=> (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(3,axiom,(~![C: $i, Cpp: $i] : ((open(C) & part_of(Cpp, C)) => open(Cpp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','theorem_2_7_2')).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (~![C: $i, Cpp: $i] : (open(Cpp) | (~(open(C) & part_of(Cpp, C))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.37 tff(8,plain,(
% 0.20/0.37 ~(open(Cpp!11) | (~(open(C!12) & part_of(Cpp!11, C!12))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[7])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 (open(C!12) & part_of(Cpp!11, C!12)),
% 0.20/0.37 inference(or_elim,[status(thm)],[8])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (part_of(Cpp!11, C!12)),
% 0.20/0.37 inference(and_elim,[status(thm)],[9])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (~open(Cpp!11)),
% 0.20/0.37 inference(or_elim,[status(thm)],[8])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (^[C: $i, C1: $i] : refl(((C1 = C) | open(C1) | (~part_of(C1, C))) <=> ((C1 = C) | open(C1) | (~part_of(C1, C))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C))) <=> ![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (^[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)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 (![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C))))) <=> ![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C))))) <=> ![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (^[C: $i, C1: $i] : rewrite(((part_of(C1, C) & (~(C1 = C))) => open(C1)) <=> (open(C1) | (~(part_of(C1, C) & (~(C1 = C))))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![C: $i, C1: $i] : ((part_of(C1, C) & (~(C1 = C))) => open(C1)) <=> ![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.37 tff(19,axiom,(![C: $i, C1: $i] : ((part_of(C1, C) & (~(C1 = C))) => open(C1))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','c1')).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.37 tff(22,plain,(
% 0.20/0.37 ![C: $i, C1: $i] : (open(C1) | (~(part_of(C1, C) & (~(C1 = C)))))),
% 0.20/0.37 inference(skolemize,[status(sab)],[21])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | (open(Cpp!11) | (~part_of(Cpp!11, C!12)) | (Cpp!11 = C!12))) <=> ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | open(Cpp!11) | (~part_of(Cpp!11, C!12)) | (Cpp!11 = C!12))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (((Cpp!11 = C!12) | open(Cpp!11) | (~part_of(Cpp!11, C!12))) <=> (open(Cpp!11) | (~part_of(Cpp!11, C!12)) | (Cpp!11 = C!12))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 (((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | ((Cpp!11 = C!12) | open(Cpp!11) | (~part_of(Cpp!11, C!12)))) <=> ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | (open(Cpp!11) | (~part_of(Cpp!11, C!12)) | (Cpp!11 = C!12)))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | ((Cpp!11 = C!12) | open(Cpp!11) | (~part_of(Cpp!11, C!12)))) <=> ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | open(Cpp!11) | (~part_of(Cpp!11, C!12)) | (Cpp!11 = C!12))),
% 0.20/0.37 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | ((Cpp!11 = C!12) | open(Cpp!11) | (~part_of(Cpp!11, C!12)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 ((~![C: $i, C1: $i] : ((C1 = C) | open(C1) | (~part_of(C1, C)))) | open(Cpp!11) | (~part_of(Cpp!11, C!12)) | (Cpp!11 = C!12)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (Cpp!11 = C!12),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[30, 24, 11, 10])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (open(Cpp!11) <=> open(C!12)),
% 0.20/0.37 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (open(C!12) <=> open(Cpp!11)),
% 0.20/0.37 inference(symmetry,[status(thm)],[32])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 (open(C!12)),
% 0.20/0.37 inference(and_elim,[status(thm)],[9])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 (open(Cpp!11)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[11, 35])).
% 0.20/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------