TSTP Solution File: GEO232+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO232+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 20:35:56 EDT 2022
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO232+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 07:20:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(unequally_directed_lines_type, type, (
% 0.13/0.39 unequally_directed_lines: ( $i * $i ) > $o)).
% 0.13/0.39 tff(reverse_line_type, type, (
% 0.13/0.39 reverse_line: $i > $i)).
% 0.13/0.39 tff(tptp_fun_L_0_type, type, (
% 0.13/0.39 tptp_fun_L_0: $i)).
% 0.13/0.39 tff(unequally_directed_opposite_lines_type, type, (
% 0.13/0.39 unequally_directed_opposite_lines: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl((unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y))) <=> ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,axiom,(![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','a1_defns')).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.39 tff(6,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (unequally_directed_opposite_lines(X, Y) <=> unequally_directed_lines(X, reverse_line(Y)))) | (unequally_directed_opposite_lines(L!0, L!0) <=> unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (unequally_directed_opposite_lines(L!0, L!0) <=> unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ((~![L: $i] : unequally_directed_opposite_lines(L, L)) <=> (~![L: $i] : unequally_directed_opposite_lines(L, L))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(11,axiom,(~![L: $i] : unequally_directed_opposite_lines(L, L)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 10])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (~![L: $i] : unequally_directed_opposite_lines(L, L)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.13/0.39 tff(19,plain,(
% 0.13/0.39 ~unequally_directed_opposite_lines(L!0, L!0)),
% 0.13/0.39 inference(skolemize,[status(sab)],[18])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 ((~(unequally_directed_opposite_lines(L!0, L!0) <=> unequally_directed_lines(L!0, reverse_line(L!0)))) | unequally_directed_opposite_lines(L!0, L!0) | (~unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((~(unequally_directed_opposite_lines(L!0, L!0) <=> unequally_directed_lines(L!0, reverse_line(L!0)))) | (~unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (~unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[21, 9])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (^[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))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (^[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)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.40 tff(28,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/GEO009+0.ax','ax6_basics')).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.40 tff(31,plain,(
% 0.13/0.40 ![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[30])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![L: $i, M: $i, N: $i] : (unequally_directed_lines(M, N) | unequally_directed_lines(L, N) | (~unequally_directed_lines(L, M)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (((~![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, L!0)) | unequally_directed_lines(L!0, reverse_line(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, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 ((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, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (((~![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, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (((~![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, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[35, 33])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ((~![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)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ((~![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, L!0)) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (~unequally_directed_lines(L!0, L!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[38, 32, 22])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (^[L: $i, M: $i] : refl((unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))) <=> (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (![L: $i, M: $i] : (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)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 (![L: $i, M: $i] : (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)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(43,axiom,(![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax','ax8_basics')).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.13/0.40 tff(45,plain,(
% 0.13/0.40 ![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[44])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 (![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.13/0.40 tff(47,plain,
% 0.13/0.40 (((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))) <=> ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | (unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 ((~![L: $i, M: $i] : (unequally_directed_lines(L, M) | unequally_directed_lines(L, reverse_line(M)))) | unequally_directed_lines(L!0, L!0) | unequally_directed_lines(L!0, reverse_line(L!0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[49, 46, 39, 22])).
% 0.13/0.40 % SZS output end Proof
%------------------------------------------------------------------------------