%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO227+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO227+1 : TPTP v9.0.0. Bugfixed v6.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.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 14:41:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(unequally_directed_lines_type, type, (
% 0.20/0.38 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.20/0.38 tff(reverse_line_type, type, (
% 0.20/0.38 reverse_line: $i > $i)).
% 0.20/0.38 tff(tptp_fun_M_0_type, type, (
% 0.20/0.38 tptp_fun_M_0: $i)).
% 0.20/0.38 tff(tptp_fun_L_1_type, type, (
% 0.20/0.38 tptp_fun_L_1: $i)).
% 0.20/0.38 tff(line_type, type, (
% 0.20/0.38 line: $i > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 ((~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((~![L: $i, M: $i] : ((line(L) & line(M)) => (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))) <=> (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,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/theBenchmark.p','con')).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.38 tff(8,plain,(
% 0.20/0.38 ~((~(line(L!1) & line(M!0))) | (~((~unequally_directed_lines(L!1, M!0)) & (~unequally_directed_lines(L!1, reverse_line(M!0))))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~unequally_directed_lines(L!1, M!0)) & (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.20/0.38 inference(or_elim,[status(thm)],[8])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.20/0.38 inference(and_elim,[status(thm)],[9])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (~unequally_directed_lines(L!1, M!0)),
% 0.20/0.38 inference(and_elim,[status(thm)],[9])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (line(L!1) & line(M!0)),
% 0.20/0.38 inference(or_elim,[status(thm)],[8])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (line(M!0)),
% 0.20/0.38 inference(and_elim,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (line(L!1)),
% 0.20/0.38 inference(and_elim,[status(thm)],[12])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (![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))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.38 tff(22,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')).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.38 tff(25,plain,(
% 0.20/0.38 ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[24])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~line(M!0)) | (~line(L!1)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~line(M!0)) | (~line(L!1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, M!0) | (~line(M!0)) | (~line(L!1))) <=> (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~line(M!0)) | (~line(L!1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, M!0) | (~line(M!0)) | (~line(L!1)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~line(M!0)) | (~line(L!1))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, M!0) | (~line(M!0)) | (~line(L!1)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~line(M!0)) | (~line(L!1)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | (unequally_directed_lines(L!1, reverse_line(M!0)) | unequally_directed_lines(L!1, M!0) | (~line(M!0)) | (~line(L!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~line(M!0)) | (~line(L!1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[33, 27, 14, 13, 11, 10])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------