%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO227+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:06:03 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO227+3 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 : Thu Jun 19 14:42:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(unequally_directed_lines_type, type, (
% 0.19/0.37 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(reverse_line_type, type, (
% 0.19/0.37 reverse_line: $i > $i)).
% 0.19/0.37 tff(tptp_fun_M_0_type, type, (
% 0.19/0.37 tptp_fun_M_0: $i)).
% 0.19/0.37 tff(tptp_fun_L_1_type, type, (
% 0.19/0.37 tptp_fun_L_1: $i)).
% 0.19/0.37 tff(unequally_directed_opposite_lines_type, type, (
% 0.19/0.37 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(equally_directed_opposite_lines_type, type, (
% 0.19/0.37 equally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(equally_directed_lines_type, type, (
% 0.19/0.37 equally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(1,plain,
% 0.19/0.37 (^[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))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,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')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,(
% 0.19/0.37 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[5])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 ((~![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)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (^[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))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (^[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)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.37 tff(15,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')).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.37 tff(18,plain,(
% 0.19/0.37 ![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[17])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![X: $i, Y: $i] : (~(unequally_directed_opposite_lines(X, Y) <=> equally_directed_opposite_lines(X, Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 ((~![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)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (~(unequally_directed_opposite_lines(L!1, M!0) <=> equally_directed_opposite_lines(L!1, M!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 ((~![L: $i, M: $i] : (~(equally_directed_lines(L, M) & equally_directed_opposite_lines(L, M)))) <=> (~![L: $i, M: $i] : (~(equally_directed_lines(L, M) & equally_directed_opposite_lines(L, M))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(23,axiom,(~![L: $i, M: $i] : (~(equally_directed_lines(L, M) & equally_directed_opposite_lines(L, M)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (~![L: $i, M: $i] : (~(equally_directed_lines(L, M) & equally_directed_opposite_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (~![L: $i, M: $i] : (~(equally_directed_lines(L, M) & equally_directed_opposite_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (~![L: $i, M: $i] : (~(equally_directed_lines(L, M) & equally_directed_opposite_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (~![L: $i, M: $i] : (~(equally_directed_lines(L, M) & equally_directed_opposite_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.19/0.37 tff(28,plain,(
% 0.19/0.37 equally_directed_lines(L!1, M!0) & equally_directed_opposite_lines(L!1, M!0)),
% 0.19/0.37 inference(skolemize,[status(sab)],[27])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (equally_directed_opposite_lines(L!1, M!0)),
% 0.19/0.37 inference(and_elim,[status(thm)],[28])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 ((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))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 ((unequally_directed_opposite_lines(L!1, M!0) <=> equally_directed_opposite_lines(L!1, M!0)) | (~unequally_directed_opposite_lines(L!1, M!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (~unequally_directed_opposite_lines(L!1, M!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[31, 21])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 ((~(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)))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((~(unequally_directed_opposite_lines(L!1, M!0) <=> unequally_directed_lines(L!1, reverse_line(M!0)))) | (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[34, 9])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (^[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)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.38 tff(41,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')).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.38 tff(44,plain,(
% 0.19/0.38 ![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[43])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 ((~![X: $i, Y: $i] : (~(unequally_directed_lines(X, Y) <=> equally_directed_lines(X, Y)))) | (~(unequally_directed_lines(L!1, M!0) <=> equally_directed_lines(L!1, M!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (~(unequally_directed_lines(L!1, M!0) <=> equally_directed_lines(L!1, M!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (equally_directed_lines(L!1, M!0)),
% 0.19/0.38 inference(and_elim,[status(thm)],[28])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 ((unequally_directed_lines(L!1, M!0) <=> equally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, M!0)) | (~equally_directed_lines(L!1, M!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 ((unequally_directed_lines(L!1, M!0) <=> equally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, M!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (~unequally_directed_lines(L!1, M!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(55,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.38 tff(57,plain,(
% 0.19/0.38 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[56])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[61, 58, 51, 35])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------