TSTP Solution File: GEO227+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO227+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Fri Sep 16 20:35:54 EDT 2022
% Result : Theorem 0.09s 0.48s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.23 % Problem : GEO227+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.02/0.23 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.43 % Computer : n014.cluster.edu
% 0.09/0.43 % Model : x86_64 x86_64
% 0.09/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.43 % Memory : 8042.1875MB
% 0.09/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Wed Aug 31 07:05:18 EDT 2022
% 0.09/0.43 % CPUTime :
% 0.09/0.43 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.43 Usage: tptp [options] [-file:]file
% 0.09/0.43 -h, -? prints this message.
% 0.09/0.43 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.43 -m, -model generate model.
% 0.09/0.43 -p, -proof generate proof.
% 0.09/0.43 -c, -core generate unsat core of named formulas.
% 0.09/0.43 -st, -statistics display statistics.
% 0.09/0.43 -t:timeout set timeout (in second).
% 0.09/0.43 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.43 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.43 -<param>:<value> configuration parameter and value.
% 0.09/0.43 -o:<output-file> file to place output in.
% 0.09/0.48 % SZS status Theorem
% 0.09/0.48 % SZS output start Proof
% 0.09/0.48 tff(unequally_directed_lines_type, type, (
% 0.09/0.48 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.09/0.48 tff(reverse_line_type, type, (
% 0.09/0.48 reverse_line: $i > $i)).
% 0.09/0.48 tff(tptp_fun_M_0_type, type, (
% 0.09/0.48 tptp_fun_M_0: $i)).
% 0.09/0.48 tff(tptp_fun_L_1_type, type, (
% 0.09/0.48 tptp_fun_L_1: $i)).
% 0.09/0.48 tff(line_type, type, (
% 0.09/0.48 line: $i > $o)).
% 0.09/0.48 tff(1,plain,
% 0.09/0.48 ((~![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)))))))),
% 0.09/0.48 inference(rewrite,[status(thm)],[])).
% 0.09/0.48 tff(2,plain,
% 0.09/0.48 ((~![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)))))))),
% 0.09/0.48 inference(rewrite,[status(thm)],[])).
% 0.09/0.48 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/sandbox2/benchmark/theBenchmark.p','con')).
% 0.09/0.48 tff(4,plain,
% 0.09/0.48 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.09/0.48 tff(5,plain,
% 0.09/0.48 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.09/0.48 tff(6,plain,
% 0.09/0.48 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.09/0.48 tff(7,plain,
% 0.09/0.48 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.09/0.48 tff(8,plain,
% 0.09/0.48 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.09/0.48 tff(9,plain,
% 0.09/0.48 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.09/0.48 tff(10,plain,
% 0.09/0.48 (~![L: $i, M: $i] : ((~(line(L) & line(M))) | (~((~unequally_directed_lines(L, M)) & (~unequally_directed_lines(L, reverse_line(M))))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.09/0.48 tff(11,plain,(
% 0.09/0.48 ~((~(line(L!1) & line(M!0))) | (~((~unequally_directed_lines(L!1, M!0)) & (~unequally_directed_lines(L!1, reverse_line(M!0))))))),
% 0.09/0.48 inference(skolemize,[status(sab)],[10])).
% 0.09/0.48 tff(12,plain,
% 0.09/0.48 ((~unequally_directed_lines(L!1, M!0)) & (~unequally_directed_lines(L!1, reverse_line(M!0)))),
% 0.09/0.48 inference(or_elim,[status(thm)],[11])).
% 0.09/0.48 tff(13,plain,
% 0.09/0.48 (~unequally_directed_lines(L!1, reverse_line(M!0))),
% 0.09/0.48 inference(and_elim,[status(thm)],[12])).
% 0.09/0.48 tff(14,plain,
% 0.09/0.48 (~unequally_directed_lines(L!1, M!0)),
% 0.09/0.48 inference(and_elim,[status(thm)],[12])).
% 0.09/0.48 tff(15,plain,
% 0.09/0.48 (line(L!1) & line(M!0)),
% 0.09/0.48 inference(or_elim,[status(thm)],[11])).
% 0.09/0.48 tff(16,plain,
% 0.09/0.48 (line(M!0)),
% 0.09/0.48 inference(and_elim,[status(thm)],[15])).
% 0.09/0.48 tff(17,plain,
% 0.09/0.48 (line(L!1)),
% 0.09/0.48 inference(and_elim,[status(thm)],[15])).
% 0.09/0.48 tff(18,plain,
% 0.09/0.48 (^[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))))),
% 0.09/0.48 inference(bind,[status(th)],[])).
% 0.09/0.48 tff(19,plain,
% 0.09/0.48 (![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)))),
% 0.09/0.48 inference(quant_intro,[status(thm)],[18])).
% 0.09/0.48 tff(20,plain,
% 0.09/0.48 (^[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)))))),
% 0.09/0.48 inference(bind,[status(th)],[])).
% 0.09/0.48 tff(21,plain,
% 0.09/0.48 (![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)))),
% 0.09/0.48 inference(quant_intro,[status(thm)],[20])).
% 0.09/0.48 tff(22,plain,
% 0.09/0.48 (![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))))),
% 0.09/0.48 inference(rewrite,[status(thm)],[])).
% 0.09/0.48 tff(23,plain,
% 0.09/0.48 (^[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)))))),
% 0.09/0.48 inference(bind,[status(th)],[])).
% 0.09/0.48 tff(24,plain,
% 0.09/0.48 (![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))))),
% 0.09/0.48 inference(quant_intro,[status(thm)],[23])).
% 0.09/0.48 tff(25,axiom,(![L: $i, M: $i] : ((line(L) & line(M)) => (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax','oag8')).
% 0.09/0.48 tff(26,plain,
% 0.09/0.48 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.09/0.48 tff(27,plain,
% 0.09/0.48 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.09/0.48 tff(28,plain,(
% 0.09/0.48 ![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~(line(L) & line(M))))),
% 0.09/0.48 inference(skolemize,[status(sab)],[27])).
% 0.09/0.48 tff(29,plain,
% 0.09/0.48 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.09/0.48 tff(30,plain,
% 0.09/0.48 (![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))),
% 0.09/0.48 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.09/0.48 tff(31,plain,
% 0.09/0.48 (((~![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)))),
% 0.09/0.48 inference(rewrite,[status(thm)],[])).
% 0.09/0.48 tff(32,plain,
% 0.09/0.48 ((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)))),
% 0.14/0.48 inference(rewrite,[status(thm)],[])).
% 0.14/0.48 tff(33,plain,
% 0.14/0.48 (((~![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))))),
% 0.14/0.48 inference(monotonicity,[status(thm)],[32])).
% 0.14/0.48 tff(34,plain,
% 0.14/0.48 (((~![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)))),
% 0.14/0.48 inference(transitivity,[status(thm)],[33, 31])).
% 0.14/0.48 tff(35,plain,
% 0.14/0.48 ((~![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)))),
% 0.14/0.48 inference(quant_inst,[status(thm)],[])).
% 0.14/0.48 tff(36,plain,
% 0.14/0.48 ((~![L: $i, M: $i] : (unequally_directed_lines(L, reverse_line(M)) | unequally_directed_lines(L, M) | (~line(M)) | (~line(L)))) | unequally_directed_lines(L!1, M!0) | unequally_directed_lines(L!1, reverse_line(M!0)) | (~line(M!0)) | (~line(L!1))),
% 0.14/0.48 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.14/0.48 tff(37,plain,
% 0.14/0.48 ($false),
% 0.14/0.48 inference(unit_resolution,[status(thm)],[36, 30, 17, 16, 14, 13])).
% 0.14/0.48 % SZS output end Proof
%------------------------------------------------------------------------------