%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO253+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 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 05:06:09 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO253+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.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 14:43:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(left_apart_point_type, type, (
% 0.12/0.37 left_apart_point: ( $i * $i ) > $o)).
% 0.12/0.37 tff(reverse_line_type, type, (
% 0.12/0.37 reverse_line: $i > $i)).
% 0.12/0.37 tff(tptp_fun_L_0_type, type, (
% 0.12/0.37 tptp_fun_L_0: $i)).
% 0.12/0.37 tff(tptp_fun_A_2_type, type, (
% 0.12/0.37 tptp_fun_A_2: $i)).
% 0.12/0.37 tff(apart_point_and_line_type, type, (
% 0.12/0.37 apart_point_and_line: ( $i * $i ) > $o)).
% 0.12/0.37 tff(parallel_through_point_type, type, (
% 0.12/0.37 parallel_through_point: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_B_1_type, type, (
% 0.12/0.37 tptp_fun_B_1: $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[A: $i, L: $i] : refl((apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L)))) <=> ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,axiom,(![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','apt_def')).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.37 tff(6,plain,(
% 0.12/0.37 ![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[5])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 ((~![A: $i, L: $i] : (apart_point_and_line(A, L) <=> (left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 ((~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & (~apart_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) & (~apart_point_and_line(B, parallel_through_point(L, A))))) | apart_point_and_line(B, L)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 ((~![A: $i, B: $i, L: $i] : ((apart_point_and_line(A, L) & (~apart_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) & (~apart_point_and_line(B, parallel_through_point(L, A))))) | apart_point_and_line(B, L)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(12,axiom,(~![A: $i, B: $i, L: $i] : ((apart_point_and_line(A, L) & (~apart_point_and_line(B, parallel_through_point(L, A)))) => apart_point_and_line(B, L))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & (~apart_point_and_line(B, parallel_through_point(L, A))))) | apart_point_and_line(B, L))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & (~apart_point_and_line(B, parallel_through_point(L, A))))) | apart_point_and_line(B, L))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & (~apart_point_and_line(B, parallel_through_point(L, A))))) | apart_point_and_line(B, L))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (~![A: $i, B: $i, L: $i] : ((~(apart_point_and_line(A, L) & (~apart_point_and_line(B, parallel_through_point(L, A))))) | apart_point_and_line(B, L))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.12/0.38 tff(17,plain,(
% 0.12/0.38 ~((~(apart_point_and_line(A!2, L!0) & (~apart_point_and_line(B!1, parallel_through_point(L!0, A!2))))) | apart_point_and_line(B!1, L!0))),
% 0.12/0.38 inference(skolemize,[status(sab)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (apart_point_and_line(A!2, L!0) & (~apart_point_and_line(B!1, parallel_through_point(L!0, A!2)))),
% 0.12/0.38 inference(or_elim,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (apart_point_and_line(A!2, L!0)),
% 0.12/0.38 inference(and_elim,[status(thm)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))) | (~apart_point_and_line(A!2, L!0)) | (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((~(apart_point_and_line(A!2, L!0) <=> (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))) | (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[21, 9])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(26,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag10')).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,(
% 0.12/0.38 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(A!2, L!0) | left_apart_point(A!2, reverse_line(L!0))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 29, 22])).
% 0.12/0.38 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------