%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO232+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:06:04 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
% 0.03/0.12 % Problem : GEO232+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 14:44:11 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_L_0_type, type, (
% 0.19/0.37 tptp_fun_L_0: $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(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!0, L!0) <=> unequally_directed_lines(L!0, reverse_line(L!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!0, L!0) <=> unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ((~![L: $i] : unequally_directed_opposite_lines(L, L)) <=> (~![L: $i] : unequally_directed_opposite_lines(L, L))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(11,axiom,(~![L: $i] : unequally_directed_opposite_lines(L, L)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[12, 10])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.37 tff(16,plain,(
% 0.19/0.37 ~unequally_directed_opposite_lines(L!0, L!0)),
% 0.19/0.37 inference(skolemize,[status(sab)],[15])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 ((~(unequally_directed_opposite_lines(L!0, L!0) <=> unequally_directed_lines(L!0, reverse_line(L!0)))) | unequally_directed_opposite_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 ((~(unequally_directed_opposite_lines(L!0, L!0) <=> unequally_directed_lines(L!0, reverse_line(L!0)))) | (~unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (~unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[18, 9])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(L, N) | unequally_directed_lines(M, N)) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))))), rewrite((unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[23])).
% 0.19/0.37 tff(25,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax6_basics')).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_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 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[27])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(L!0, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!0, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 ((unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))) <=> ((~unequally_directed_lines(L!0, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | ((~unequally_directed_lines(L!0, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!0, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[32, 30])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (~unequally_directed_lines(L!0, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (~unequally_directed_lines(L!0, L!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[35, 29, 19])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (^[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))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[37])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (![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)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(40,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')).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.37 tff(42,plain,(
% 0.19/0.37 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[41])).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(45,plain,
% 0.19/0.37 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(46,plain,
% 0.19/0.37 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.37 tff(47,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 43, 36, 19])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------