%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO232+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:06:04 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO232+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:43:02 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(unequally_directed_lines_type, type, (
% 0.11/0.37 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_L_0_type, type, (
% 0.11/0.37 tptp_fun_L_0: $i)).
% 0.11/0.37 tff(reverse_line_type, type, (
% 0.11/0.37 reverse_line: $i > $i)).
% 0.11/0.37 tff(line_type, type, (
% 0.11/0.37 line: $i > $o)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 ((~![L: $i] : ((~line(L)) | unequally_directed_lines(L, reverse_line(L)))) <=> (~![L: $i] : ((~line(L)) | unequally_directed_lines(L, reverse_line(L))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 ((~![L: $i] : (line(L) => unequally_directed_lines(L, reverse_line(L)))) <=> (~![L: $i] : ((~line(L)) | unequally_directed_lines(L, reverse_line(L))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(3,axiom,(~![L: $i] : (line(L) => unequally_directed_lines(L, reverse_line(L)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (~![L: $i] : ((~line(L)) | unequally_directed_lines(L, reverse_line(L)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (~![L: $i] : ((~line(L)) | unequally_directed_lines(L, reverse_line(L)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (~![L: $i] : ((~line(L)) | unequally_directed_lines(L, reverse_line(L)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (~![L: $i] : ((~line(L)) | unequally_directed_lines(L, reverse_line(L)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.11/0.37 tff(8,plain,(
% 0.11/0.37 ~((~line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (~unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.11/0.37 inference(or_elim,[status(thm)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (^[L: $i, M: $i, N: $i] : refl((unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (^[L: $i, M: $i, N: $i] : trans(monotonicity(rewrite((unequally_directed_lines(L, N) | unequally_directed_lines(M, N)) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))))), rewrite((unequally_directed_lines(L, M) => (unequally_directed_lines(M, N) | unequally_directed_lines(L, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))), ((unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,axiom,(![L: $i, M: $i, N: $i] : (unequally_directed_lines(L, M) => (unequally_directed_lines(L, N) | unequally_directed_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag6')).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.37 tff(18,plain,(
% 0.19/0.37 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[17])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(21,plain,
% 0.19/0.37 ((unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))) <=> (unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))))),
% 0.19/0.37 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.19/0.37 inference(transitivity,[status(thm)],[22, 20])).
% 0.19/0.37 tff(24,plain,
% 0.19/0.37 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 ((~![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))) | unequally_directed_lines(L!0, reverse_line(L!0)) | (~unequally_directed_lines(L!0, L!0))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (~unequally_directed_lines(L!0, L!0)),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[25, 19, 9])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 (line(L!0)),
% 0.19/0.37 inference(or_elim,[status(thm)],[8])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (^[L: $i, M: $i] : trans(monotonicity(trans(monotonicity(rewrite((line(L) & line(M)) <=> (~((~line(M)) | (~line(L))))), ((~(line(L) & line(M))) <=> (~(~((~line(M)) | (~line(L))))))), rewrite((~(~((~line(M)) | (~line(L))))) <=> ((~line(M)) | (~line(L)))), ((~(line(L) & line(M))) <=> ((~line(M)) | (~line(L))))), ((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | ((~line(M)) | (~line(L)))))), rewrite((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | ((~line(M)) | (~line(L)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))), ((unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (^[L: $i, M: $i] : rewrite(((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) <=> (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) <=> ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.37 tff(35,axiom,(![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax','oag8')).
% 0.19/0.37 tff(36,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.37 tff(38,plain,(
% 0.19/0.37 ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[37])).
% 0.19/0.37 tff(39,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | ((~line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(42,plain,
% 0.19/0.38 ((unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0) | (~line(L!0)) | (~line(L!0))) <=> ((~line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0) | (~line(L!0)) | (~line(L!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | ((~line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0) | (~line(L!0)) | (~line(L!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0))),
% 0.19/0.38 inference(transitivity,[status(thm)],[43, 41])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0) | (~line(L!0)) | (~line(L!0)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (~line(L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)) | unequally_directed_lines(L!0, L!0)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[46, 40, 27, 9, 26])).
% 0.19/0.38 % SZS output end Proof
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------