%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO258+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:06:10 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO258+3 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 14:43:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(before_on_line_type, type, (
% 0.12/0.38 before_on_line: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_C_0_type, type, (
% 0.12/0.38 tptp_fun_C_0: $i)).
% 0.12/0.38 tff(tptp_fun_B_1_type, type, (
% 0.12/0.38 tptp_fun_B_1: $i)).
% 0.12/0.38 tff(tptp_fun_L_3_type, type, (
% 0.12/0.38 tptp_fun_L_3: $i)).
% 0.12/0.38 tff(tptp_fun_A_2_type, type, (
% 0.12/0.38 tptp_fun_A_2: $i)).
% 0.12/0.38 tff(between_on_line_type, type, (
% 0.12/0.38 between_on_line: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[L: $i, A: $i, B: $i, C: $i] : refl((between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C)))))) <=> (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C)))))) <=> ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[L: $i, A: $i, B: $i, C: $i] : rewrite((between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C)))) <=> (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C)))) <=> ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C)))) <=> ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[L: $i, A: $i, B: $i, C: $i] : rewrite((between_on_line(L, A, B, C) <=> ((before_on_line(L, A, B) & before_on_line(L, B, C)) | (before_on_line(L, C, B) & before_on_line(L, B, A)))) <=> (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, A, B) & before_on_line(L, B, C)) | (before_on_line(L, C, B) & before_on_line(L, B, A)))) <=> ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,axiom,(![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, A, B) & before_on_line(L, B, C)) | (before_on_line(L, C, B) & before_on_line(L, B, A))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax','a9_defns')).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.38 tff(11,plain,(
% 0.12/0.38 ![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((before_on_line(L, C, B) & before_on_line(L, B, A)) | (before_on_line(L, A, B) & before_on_line(L, B, C))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, A!2, B!1, C!0) <=> ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (between_on_line(L!3, A!2, B!1, C!0) <=> ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((~![L: $i, A: $i, B: $i, C: $i] : ((~between_on_line(L, A, B, C)) | between_on_line(L, C, B, A))) <=> (~![L: $i, A: $i, B: $i, C: $i] : ((~between_on_line(L, A, B, C)) | between_on_line(L, C, B, A)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) => between_on_line(L, C, B, A))) <=> (~![L: $i, A: $i, B: $i, C: $i] : ((~between_on_line(L, A, B, C)) | between_on_line(L, C, B, A)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,axiom,(~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) => between_on_line(L, C, B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','con')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~![L: $i, A: $i, B: $i, C: $i] : ((~between_on_line(L, A, B, C)) | between_on_line(L, C, B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (~![L: $i, A: $i, B: $i, C: $i] : ((~between_on_line(L, A, B, C)) | between_on_line(L, C, B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (~![L: $i, A: $i, B: $i, C: $i] : ((~between_on_line(L, A, B, C)) | between_on_line(L, C, B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (~![L: $i, A: $i, B: $i, C: $i] : ((~between_on_line(L, A, B, C)) | between_on_line(L, C, B, A))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.12/0.38 tff(23,plain,(
% 0.12/0.38 ~((~between_on_line(L!3, A!2, B!1, C!0)) | between_on_line(L!3, C!0, B!1, A!2))),
% 0.12/0.38 inference(skolemize,[status(sab)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (between_on_line(L!3, A!2, B!1, C!0)),
% 0.12/0.38 inference(or_elim,[status(thm)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~(between_on_line(L!3, A!2, B!1, C!0) <=> ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))))) | (~between_on_line(L!3, A!2, B!1, C!0)) | ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 ((~(between_on_line(L!3, A!2, B!1, C!0) <=> ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))))) | ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 ((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[26, 15])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 ((~![L: $i, A: $i, B: $i, C: $i] : (between_on_line(L, A, B, C) <=> ((~((~before_on_line(L, C, B)) | (~before_on_line(L, B, A)))) | (~((~before_on_line(L, A, B)) | (~before_on_line(L, B, C))))))) | (between_on_line(L!3, C!0, B!1, A!2) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (between_on_line(L!3, C!0, B!1, A!2) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[28, 13])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (~between_on_line(L!3, C!0, B!1, A!2)),
% 0.12/0.39 inference(or_elim,[status(thm)],[23])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~(between_on_line(L!3, C!0, B!1, A!2) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))))))) | between_on_line(L!3, C!0, B!1, A!2) | (~((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~(between_on_line(L!3, C!0, B!1, A!2) <=> ((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))))))) | (~((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (~((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[32, 29])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))))) | ((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))))) | ((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 ((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[36, 33])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~((~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0)))))) | (~((~before_on_line(L!3, C!0, B!1)) | (~before_on_line(L!3, B!1, A!2)))) | (~((~before_on_line(L!3, A!2, B!1)) | (~before_on_line(L!3, B!1, C!0))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 37, 35, 27])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------