%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO228+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 05:06:03 AM UTC 2025
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO228+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 14:42:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(unequally_directed_lines_type, type, (
% 0.19/0.37 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(reverse_line_type, type, (
% 0.19/0.37 reverse_line: $i > $i)).
% 0.19/0.37 tff(tptp_fun_M_0_type, type, (
% 0.19/0.37 tptp_fun_M_0: $i)).
% 0.19/0.37 tff(tptp_fun_L_1_type, type, (
% 0.19/0.37 tptp_fun_L_1: $i)).
% 0.19/0.37 tff(convergent_lines_type, type, (
% 0.19/0.37 convergent_lines: ( $i * $i ) > $o)).
% 0.19/0.37 tff(1,assumption,(~((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))))), introduced(assumption)).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 ((~![L: $i, M: $i] : (~(convergent_lines(L, M) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))) <=> (~![L: $i, M: $i] : (~(convergent_lines(L, M) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 ((~![L: $i, M: $i] : ((~convergent_lines(L, M)) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> (~![L: $i, M: $i] : (~(convergent_lines(L, M) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(4,axiom,(~![L: $i, M: $i] : ((~convergent_lines(L, M)) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (~![L: $i, M: $i] : (~(convergent_lines(L, M) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (~![L: $i, M: $i] : (~(convergent_lines(L, M) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (~![L: $i, M: $i] : (~(convergent_lines(L, M) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (~![L: $i, M: $i] : (~(convergent_lines(L, M) <=> ((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.19/0.37 tff(9,plain,(
% 0.19/0.37 convergent_lines(L!1, M!0) <=> ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ((~convergent_lines(L!1, M!0)) | ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) | (~(convergent_lines(L!1, M!0) <=> ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))))))),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 ((~convergent_lines(L!1, M!0)) | ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (~convergent_lines(L!1, M!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[11, 1])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (^[L: $i, M: $i] : refl((~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))) <=> ![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (^[L: $i, M: $i] : trans(trans(monotonicity(rewrite((unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))))), rewrite((convergent_lines(L, M) <=> (~((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))))), rewrite((~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))), ((convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(18,axiom,(![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','con_def')).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.37 tff(20,plain,(
% 0.19/0.37 ![L: $i, M: $i] : (convergent_lines(L, M) <=> (unequally_directed_lines(L, M) & unequally_directed_lines(L, reverse_line(M))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[19])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 ((~![L: $i, M: $i] : (~(((~unequally_directed_lines(L, M)) | (~unequally_directed_lines(L, reverse_line(M)))) <=> convergent_lines(L, M)))) | (~(((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) <=> convergent_lines(L!1, M!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 (~(((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) <=> convergent_lines(L!1, M!0))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 ((((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) <=> convergent_lines(L!1, M!0)) | ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) | convergent_lines(L!1, M!0)),
% 0.19/0.37 inference(tautology,[status(thm)],[])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) | convergent_lines(L!1, M!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[26, 12, 1])).
% 0.19/0.37 tff(28,plain,((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (convergent_lines(L!1, M!0) | (~((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))))) | (~(convergent_lines(L!1, M!0) <=> ((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (convergent_lines(L!1, M!0) | (~((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[29, 9])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (convergent_lines(L!1, M!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[30, 28])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0)))) <=> convergent_lines(L!1, M!0)) | (~((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))))) | (~convergent_lines(L!1, M!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~((~unequally_directed_lines(L!1, M!0)) | (~unequally_directed_lines(L!1, reverse_line(M!0))))) | (~convergent_lines(L!1, M!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[32, 24])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[33, 31, 28])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------