%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO265+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:06:11 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO265+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n013.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 14:44:08 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(unequally_directed_lines_type, type, (
% 0.11/0.37 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(reverse_line_type, type, (
% 0.11/0.37 reverse_line: $i > $i)).
% 0.11/0.37 tff(tptp_fun_M_0_type, type, (
% 0.11/0.37 tptp_fun_M_0: $i)).
% 0.11/0.37 tff(tptp_fun_L_1_type, type, (
% 0.11/0.37 tptp_fun_L_1: $i)).
% 0.11/0.37 tff(unequally_directed_opposite_lines_type, type, (
% 0.11/0.37 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(equally_directed_opposite_lines_type, type, (
% 0.11/0.37 equally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(equally_directed_lines_type, type, (
% 0.11/0.37 equally_directed_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl((~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))) <=> (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : trans(rewrite((equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))), rewrite((~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y))) <=> (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))), ((equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.37 tff(6,axiom,(![X: $i, Y: $i] : (equally_directed_opposite_lines(X, Y) <=> (~unequally_directed_opposite_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a5_defns')).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.37 tff(9,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))) | (~(unequally_directed_opposite_lines(L!1, M!0) <=> equally_directed_opposite_lines(L!1, M!0)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (~(unequally_directed_opposite_lines(L!1, M!0) <=> equally_directed_opposite_lines(L!1, M!0))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 ((~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))) <=> (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 ((~![L: $i, M: $i] : (equally_directed_lines(L, reverse_line(M)) => equally_directed_opposite_lines(L, M))) <=> (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(15,axiom,(~![L: $i, M: $i] : (equally_directed_lines(L, reverse_line(M)) => equally_directed_opposite_lines(L, M))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (~![L: $i, M: $i] : ((~equally_directed_lines(L, reverse_line(M))) | equally_directed_opposite_lines(L, M))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.11/0.37 tff(20,plain,(
% 0.11/0.37 ~((~equally_directed_lines(L!1, reverse_line(M!0))) | equally_directed_opposite_lines(L!1, M!0))),
% 0.11/0.37 inference(skolemize,[status(sab)],[19])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (~equally_directed_opposite_lines(L!1, M!0)),
% 0.11/0.37 inference(or_elim,[status(thm)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 ((unequally_directed_opposite_lines(L!1, M!0) <=> equally_directed_opposite_lines(L!1, M!0)) | unequally_directed_opposite_lines(L!1, M!0) | equally_directed_opposite_lines(L!1, M!0)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ((unequally_directed_opposite_lines(L!1, M!0) <=> equally_directed_opposite_lines(L!1, M!0)) | unequally_directed_opposite_lines(L!1, M!0)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (unequally_directed_opposite_lines(L!1, M!0)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[23, 12])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl((~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : trans(rewrite((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))), rewrite((~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))), ((equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y))) <=> ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.37 tff(30,axiom,(![X: $i, Y: $i] : (equally_directed_lines(X, Y) <=> (~unequally_directed_lines(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a4_defns')).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.11/0.37 tff(33,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[32])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(L!1, reverse_line(M!0)) <=> equally_directed_lines(L!1, reverse_line(M!0))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 (~(unequally_directed_lines(L!1, reverse_line(M!0)) <=> equally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (equally_directed_lines(L!1, reverse_line(M!0))),
% 0.11/0.37 inference(or_elim,[status(thm)],[20])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((unequally_directed_lines(L!1, reverse_line(M!0)) <=> equally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0))) | (~equally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 ((unequally_directed_lines(L!1, reverse_line(M!0)) <=> equally_directed_lines(L!1, reverse_line(M!0))) | (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 ((~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))) | (~unequally_directed_opposite_lines(L!1, M!0)) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[41, 40, 24])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (^[X: $i, Y: $i] : refl((unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(46,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.11/0.37 tff(48,plain,(
% 0.11/0.37 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[47])).
% 0.11/0.37 tff(49,plain,
% 0.11/0.37 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[50, 49, 42])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------