%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO238+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:06:05 AM UTC 2025
% Result : Theorem 0.16s 0.35s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GEO238+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.02/0.10 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n006.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Jun 19 14:42:50 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.16/0.35 % SZS status Theorem
% 0.16/0.35 % SZS output start Proof
% 0.16/0.35 tff(left_apart_point_type, type, (
% 0.16/0.35 left_apart_point: ( $i * $i ) > $o)).
% 0.16/0.35 tff(reverse_line_type, type, (
% 0.16/0.35 reverse_line: $i > $i)).
% 0.16/0.35 tff(tptp_fun_L_0_type, type, (
% 0.16/0.35 tptp_fun_L_0: $i)).
% 0.16/0.35 tff(tptp_fun_C_1_type, type, (
% 0.16/0.35 tptp_fun_C_1: $i)).
% 0.16/0.35 tff(tptp_fun_B_2_type, type, (
% 0.16/0.35 tptp_fun_B_2: $i)).
% 0.16/0.35 tff(divides_points_type, type, (
% 0.16/0.35 divides_points: ( $i * $i * $i ) > $o)).
% 0.16/0.35 tff(tptp_fun_A_3_type, type, (
% 0.16/0.35 tptp_fun_A_3: $i)).
% 0.16/0.35 tff(1,assumption,(left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0))), introduced(assumption)).
% 0.16/0.35 tff(2,plain,
% 0.16/0.35 (^[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)))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(3,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[2])).
% 0.16/0.35 tff(4,plain,
% 0.16/0.35 (![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 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/GEO007+0.ax','oag10')).
% 0.16/0.35 tff(6,plain,
% 0.16/0.35 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.16/0.35 tff(7,plain,(
% 0.16/0.35 ![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.16/0.35 inference(skolemize,[status(sab)],[6])).
% 0.16/0.35 tff(8,plain,
% 0.16/0.35 (![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.16/0.35 tff(9,plain,
% 0.16/0.35 ((~![A: $i, L: $i] : (~(left_apart_point(A, L) | left_apart_point(A, reverse_line(L))))) | (~(left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0))))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(10,plain,
% 0.16/0.35 ($false),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.16/0.35 tff(11,plain,(~(left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0)))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.35 tff(12,plain,
% 0.16/0.35 ((left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(B!2, L!0))),
% 0.16/0.35 inference(tautology,[status(thm)],[])).
% 0.16/0.35 tff(13,plain,
% 0.16/0.35 (~left_apart_point(B!2, L!0)),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.16/0.35 tff(14,plain,
% 0.16/0.35 (((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))) | left_apart_point(B!2, L!0)),
% 0.16/0.35 inference(tautology,[status(thm)],[])).
% 0.16/0.35 tff(15,plain,
% 0.16/0.35 ((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0)))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.16/0.35 tff(16,plain,
% 0.16/0.35 ((left_apart_point(B!2, L!0) | left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(B!2, reverse_line(L!0)))),
% 0.16/0.35 inference(tautology,[status(thm)],[])).
% 0.16/0.35 tff(17,plain,
% 0.16/0.35 (~left_apart_point(B!2, reverse_line(L!0))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[16, 11])).
% 0.16/0.35 tff(18,plain,
% 0.16/0.35 (((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))) | left_apart_point(B!2, reverse_line(L!0))),
% 0.16/0.35 inference(tautology,[status(thm)],[])).
% 0.16/0.35 tff(19,plain,
% 0.16/0.35 ((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.16/0.35 tff(20,plain,
% 0.16/0.35 (^[A: $i, B: $i, L: $i] : refl((divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L)))))) <=> (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L)))))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(21,plain,
% 0.16/0.35 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L)))))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[20])).
% 0.16/0.35 tff(22,plain,
% 0.16/0.35 (^[A: $i, B: $i, L: $i] : rewrite((divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L)))) <=> (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L)))))))),
% 0.16/0.35 inference(bind,[status(th)],[])).
% 0.16/0.35 tff(23,plain,
% 0.16/0.35 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L)))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))),
% 0.16/0.35 inference(quant_intro,[status(thm)],[22])).
% 0.16/0.35 tff(24,plain,
% 0.16/0.35 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L)))) <=> ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(25,axiom,(![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','div_def')).
% 0.16/0.35 tff(26,plain,
% 0.16/0.35 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.16/0.35 tff(27,plain,(
% 0.16/0.35 ![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((left_apart_point(A, L) & left_apart_point(B, reverse_line(L))) | (left_apart_point(A, reverse_line(L)) & left_apart_point(B, L))))),
% 0.16/0.35 inference(skolemize,[status(sab)],[26])).
% 0.16/0.35 tff(28,plain,
% 0.16/0.35 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.16/0.35 tff(29,plain,
% 0.16/0.35 (![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.16/0.35 tff(30,plain,
% 0.16/0.35 ((~![A: $i, B: $i, L: $i] : (divides_points(L, A, B) <=> ((~((~left_apart_point(A, L)) | (~left_apart_point(B, reverse_line(L))))) | (~((~left_apart_point(A, reverse_line(L))) | (~left_apart_point(B, L))))))) | (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(31,plain,
% 0.16/0.35 (divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0)))))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.16/0.35 tff(32,plain,
% 0.16/0.35 ((~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))) <=> (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C)))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(33,plain,
% 0.17/0.36 ((~![A: $i, B: $i, C: $i, L: $i] : ((divides_points(L, A, B) & divides_points(L, A, C)) => (~divides_points(L, B, C)))) <=> (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C)))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(34,axiom,(~![A: $i, B: $i, C: $i, L: $i] : ((divides_points(L, A, B) & divides_points(L, A, C)) => (~divides_points(L, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.17/0.36 tff(35,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.17/0.36 tff(36,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[35, 32])).
% 0.17/0.36 tff(37,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.17/0.36 tff(38,plain,
% 0.17/0.36 (~![A: $i, B: $i, C: $i, L: $i] : ((~divides_points(L, B, C)) | (~(divides_points(L, A, B) & divides_points(L, A, C))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[37, 32])).
% 0.17/0.36 tff(39,plain,(
% 0.17/0.36 ~((~divides_points(L!0, B!2, C!1)) | (~(divides_points(L!0, A!3, B!2) & divides_points(L!0, A!3, C!1))))),
% 0.17/0.36 inference(skolemize,[status(sab)],[38])).
% 0.17/0.36 tff(40,plain,
% 0.17/0.36 (divides_points(L!0, B!2, C!1)),
% 0.17/0.36 inference(or_elim,[status(thm)],[39])).
% 0.17/0.36 tff(41,plain,
% 0.17/0.36 ((~(divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))) | (~divides_points(L!0, B!2, C!1)) | ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0)))))),
% 0.17/0.36 inference(tautology,[status(thm)],[])).
% 0.17/0.36 tff(42,plain,
% 0.17/0.36 ((~(divides_points(L!0, B!2, C!1) <=> ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))))) | ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0)))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.17/0.36 tff(43,plain,
% 0.17/0.36 ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[42, 31])).
% 0.17/0.36 tff(44,plain,
% 0.17/0.36 ((~((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0)))))) | (~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))),
% 0.17/0.36 inference(tautology,[status(thm)],[])).
% 0.17/0.36 tff(45,plain,
% 0.17/0.36 ((~((~left_apart_point(B!2, L!0)) | (~left_apart_point(C!1, reverse_line(L!0))))) | (~((~left_apart_point(B!2, reverse_line(L!0))) | (~left_apart_point(C!1, L!0))))),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.17/0.36 tff(46,plain,
% 0.17/0.36 ($false),
% 0.17/0.36 inference(unit_resolution,[status(thm)],[45, 19, 15])).
% 0.17/0.36 % SZS output end Proof
% 0.17/0.36 % E exiting
%------------------------------------------------------------------------------