%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO253+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:06:09 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO253+3 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:43:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(left_apart_point_type, type, (
% 0.21/0.38 left_apart_point: ( $i * $i ) > $o)).
% 0.21/0.38 tff(reverse_line_type, type, (
% 0.21/0.38 reverse_line: $i > $i)).
% 0.21/0.38 tff(tptp_fun_L_0_type, type, (
% 0.21/0.38 tptp_fun_L_0: $i)).
% 0.21/0.38 tff(tptp_fun_A_2_type, type, (
% 0.21/0.38 tptp_fun_A_2: $i)).
% 0.21/0.38 tff(right_apart_point_type, type, (
% 0.21/0.38 right_apart_point: ( $i * $i ) > $o)).
% 0.21/0.38 tff(apart_point_and_line_type, type, (
% 0.21/0.38 apart_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.38 tff(incident_point_and_line_type, type, (
% 0.21/0.38 incident_point_and_line: ( $i * $i ) > $o)).
% 0.21/0.38 tff(parallel_through_point_type, type, (
% 0.21/0.38 parallel_through_point: ( $i * $i ) > $i)).
% 0.21/0.38 tff(tptp_fun_B_1_type, type, (
% 0.21/0.38 tptp_fun_B_1: $i)).
% 0.21/0.38 tff(1,assumption,(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))), introduced(assumption)).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (^[A: $i, L: $i] : refl((~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(5,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax10_basics')).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.38 tff(7,plain,(
% 0.21/0.38 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.38 inference(skolemize,[status(sab)],[6])).
% 0.21/0.38 tff(8,plain,
% 0.21/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.38 tff(11,plain,(~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))) | (~left_apart_point(A!2, reverse_line(L!0)))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(13,plain,
% 0.21/0.38 (~left_apart_point(A!2, reverse_line(L!0))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 ((left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))) | (~left_apart_point(A!2, L!0))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (~left_apart_point(A!2, L!0)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(19,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a6_defns')).
% 0.21/0.38 tff(20,plain,
% 0.21/0.38 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.21/0.38 tff(21,plain,(
% 0.21/0.38 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.21/0.38 inference(skolemize,[status(sab)],[20])).
% 0.21/0.38 tff(22,plain,
% 0.21/0.38 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.38 tff(23,plain,
% 0.21/0.38 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | right_apart_point(A, L)))) | (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 ((~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A)))) | apart_point_and_line(B, L))) <=> (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A)))) | apart_point_and_line(B, L)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 ((~![A: $i, B: $i, L: $i] : ((apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A))) => apart_point_and_line(B, L))) <=> (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A)))) | apart_point_and_line(B, L)))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(27,axiom,(~![A: $i, B: $i, L: $i] : ((apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A))) => apart_point_and_line(B, L))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.38 tff(28,plain,
% 0.21/0.38 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A)))) | apart_point_and_line(B, L))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A)))) | apart_point_and_line(B, L))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A)))) | apart_point_and_line(B, L))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & incident_point_and_line(B, parallel_through_point(L, A)))) | apart_point_and_line(B, L))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.21/0.38 tff(32,plain,(
% 0.21/0.38 ~((~(apart_point_and_line(A!2, L!0) & incident_point_and_line(B!1, parallel_through_point(L!0, A!2)))) | apart_point_and_line(B!1, L!0))),
% 0.21/0.38 inference(skolemize,[status(sab)],[31])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 (apart_point_and_line(A!2, L!0) & incident_point_and_line(B!1, parallel_through_point(L!0, A!2))),
% 0.21/0.38 inference(or_elim,[status(thm)],[32])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 (apart_point_and_line(A!2, L!0)),
% 0.21/0.38 inference(and_elim,[status(thm)],[33])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)))) | (~apart_point_and_line(A!2, L!0)) | (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)))) | (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[36, 24])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 ((~(left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0))) | left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (left_apart_point(A!2, L!0) | right_apart_point(A!2, L!0)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 (right_apart_point(A!2, L!0)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[39, 15])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 ((~(right_apart_point(A!2, L!0) <=> left_apart_point(A!2, reverse_line(L!0)))) | (~right_apart_point(A!2, L!0)) | left_apart_point(A!2, reverse_line(L!0))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (~(right_apart_point(A!2, L!0) <=> left_apart_point(A!2, reverse_line(L!0)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[41, 40, 13])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (^[X: $i, Y: $i] : refl((right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(46,axiom,(![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a2_defns')).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.39 tff(48,plain,(
% 0.21/0.39 ![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.39 inference(skolemize,[status(sab)],[47])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 ((~![X: $i, Y: $i] : (right_apart_point(X, Y) <=> left_apart_point(X, reverse_line(Y)))) | (right_apart_point(A!2, L!0) <=> left_apart_point(A!2, reverse_line(L!0)))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[50, 49, 42])).
% 0.21/0.39 % SZS output end Proof
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------