%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO264+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GEO264+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.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 14:43:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(left_apart_point_type, type, (
% 0.18/0.37 left_apart_point: ( $i * $i ) > $o)).
% 0.18/0.37 tff(reverse_line_type, type, (
% 0.18/0.37 reverse_line: $i > $i)).
% 0.18/0.37 tff(line_connecting_type, type, (
% 0.18/0.37 line_connecting: ( $i * $i ) > $i)).
% 0.18/0.37 tff(tptp_fun_C_1_type, type, (
% 0.18/0.37 tptp_fun_C_1: $i)).
% 0.18/0.37 tff(tptp_fun_B_2_type, type, (
% 0.18/0.37 tptp_fun_B_2: $i)).
% 0.18/0.37 tff(tptp_fun_D_0_type, type, (
% 0.18/0.37 tptp_fun_D_0: $i)).
% 0.18/0.37 tff(tptp_fun_A_3_type, type, (
% 0.18/0.37 tptp_fun_A_3: $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 ((~(left_apart_point(D!0, line_connecting(A!3, B!2)) | (~(left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))) & left_apart_point(D!0, reverse_line(line_connecting(C!1, A!3))))) | (~left_apart_point(C!1, line_connecting(A!3, B!2))))) <=> (~(left_apart_point(D!0, line_connecting(A!3, B!2)) | (~(left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))) & left_apart_point(D!0, reverse_line(line_connecting(C!1, A!3))))) | (~left_apart_point(C!1, line_connecting(A!3, B!2)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A))))) | (~left_apart_point(C, line_connecting(A, B))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A))))) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 ((~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(C, line_connecting(A, B)) => ((left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A)))) => left_apart_point(D, line_connecting(A, B))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A))))) | (~left_apart_point(C, line_connecting(A, B)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(4,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(C, line_connecting(A, B)) => ((left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A)))) => left_apart_point(D, line_connecting(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A))))) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A))))) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A))))) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (~![A: $i, B: $i, C: $i, D: $i] : (left_apart_point(D, line_connecting(A, B)) | (~(left_apart_point(D, reverse_line(line_connecting(B, C))) & left_apart_point(D, reverse_line(line_connecting(C, A))))) | (~left_apart_point(C, line_connecting(A, B))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.18/0.37 tff(9,plain,(
% 0.18/0.37 ~(left_apart_point(D!0, line_connecting(A!3, B!2)) | (~(left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))) & left_apart_point(D!0, reverse_line(line_connecting(C!1, A!3))))) | (~left_apart_point(C!1, line_connecting(A!3, B!2))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[8])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (~(left_apart_point(D!0, line_connecting(A!3, B!2)) | (~(left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))) & left_apart_point(D!0, reverse_line(line_connecting(C!1, A!3))))) | (~left_apart_point(C!1, line_connecting(A!3, B!2))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 (left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))) & left_apart_point(D!0, reverse_line(line_connecting(C!1, A!3)))),
% 0.18/0.37 inference(or_elim,[status(thm)],[10])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))),
% 0.18/0.37 inference(and_elim,[status(thm)],[11])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 ((left_apart_point(D!0, line_connecting(B!2, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))) | (~left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1))))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (left_apart_point(D!0, line_connecting(B!2, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (^[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)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (![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))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![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))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(18,axiom,(![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag10')).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.37 tff(20,plain,(
% 0.18/0.37 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.18/0.37 inference(skolemize,[status(sab)],[19])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(D!0, line_connecting(B!2, C!1)) | left_apart_point(D!0, reverse_line(line_connecting(B!2, C!1)))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------