TSTP Solution File: GEO216+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO216+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 20:35:46 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO216+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.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 06:55:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(convergent_lines_type, type, (
% 0.21/0.39 convergent_lines: ( $i * $i ) > $o)).
% 0.21/0.39 tff(tptp_fun_L_0_type, type, (
% 0.21/0.39 tptp_fun_L_0: $i)).
% 0.21/0.39 tff(unorthogonal_lines_type, type, (
% 0.21/0.39 unorthogonal_lines: ( $i * $i ) > $o)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((~![L: $i] : unorthogonal_lines(L, L)) <=> (~![L: $i] : unorthogonal_lines(L, L))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 ((~![L: $i] : (~(~unorthogonal_lines(L, L)))) <=> (~![L: $i] : unorthogonal_lines(L, L))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(3,axiom,(~![L: $i] : (~(~unorthogonal_lines(L, L)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (~![L: $i] : unorthogonal_lines(L, L)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.39 tff(5,plain,
% 0.21/0.39 (~![L: $i] : unorthogonal_lines(L, L)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~![L: $i] : unorthogonal_lines(L, L)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (~![L: $i] : unorthogonal_lines(L, L)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.40 tff(8,plain,
% 0.21/0.40 (~![L: $i] : unorthogonal_lines(L, L)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.21/0.40 tff(9,plain,
% 0.21/0.40 (~![L: $i] : unorthogonal_lines(L, L)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.21/0.40 tff(10,plain,
% 0.21/0.40 (~![L: $i] : unorthogonal_lines(L, L)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.21/0.40 tff(11,plain,(
% 0.21/0.40 ~unorthogonal_lines(L!0, L!0)),
% 0.21/0.40 inference(skolemize,[status(sab)],[10])).
% 0.21/0.40 tff(12,plain,
% 0.21/0.40 (^[L: $i, M: $i] : refl((convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(13,plain,
% 0.21/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.40 tff(14,plain,
% 0.21/0.40 (^[L: $i, M: $i] : trans(monotonicity(rewrite(((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))) <=> (~(convergent_lines(L, M) | unorthogonal_lines(L, M)))), ((~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> (~(~(convergent_lines(L, M) | unorthogonal_lines(L, M)))))), rewrite((~(~(convergent_lines(L, M) | unorthogonal_lines(L, M)))) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M))), ((~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> (convergent_lines(L, M) | unorthogonal_lines(L, M))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(15,plain,
% 0.21/0.40 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M)))) <=> ![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(17,axiom,(![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','coipo1')).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.40 tff(19,plain,(
% 0.21/0.40 ![L: $i, M: $i] : (~((~convergent_lines(L, M)) & (~unorthogonal_lines(L, M))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[18])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.40 tff(21,plain,
% 0.21/0.40 (![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))) <=> ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | (convergent_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(24,plain,
% 0.21/0.40 ((~![L: $i, M: $i] : (convergent_lines(L, M) | unorthogonal_lines(L, M))) | convergent_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0)),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (convergent_lines(L!0, L!0)),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (^[L: $i, M: $i, N: $i] : refl(((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M)) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 (^[L: $i, M: $i, N: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) <=> (~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))))), rewrite((~(~(unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), ((~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))) <=> (unorthogonal_lines(L, N) | unorthogonal_lines(L, M)))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))), rewrite(((~convergent_lines(M, N)) | (unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))), (((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (^[L: $i, M: $i, N: $i] : rewrite((((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N))) <=> ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.40 tff(33,axiom,(![L: $i, M: $i, N: $i] : (((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax','couo1')).
% 0.21/0.40 tff(34,plain,
% 0.21/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.21/0.40 tff(36,plain,(
% 0.21/0.40 ![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~unorthogonal_lines(L, M)) & (~unorthogonal_lines(L, N)))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[35])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[37, 27])).
% 0.21/0.40 tff(39,plain,
% 0.21/0.40 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(40,plain,
% 0.21/0.40 (((~convergent_lines(L!0, L!0)) | unorthogonal_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0)) <=> (unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(41,plain,
% 0.21/0.40 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(L!0, L!0)) | unorthogonal_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | (unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.21/0.40 tff(42,plain,
% 0.21/0.40 (((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(L!0, L!0)) | unorthogonal_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))) <=> ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0)))),
% 0.21/0.40 inference(transitivity,[status(thm)],[41, 39])).
% 0.21/0.40 tff(43,plain,
% 0.21/0.40 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | ((~convergent_lines(L!0, L!0)) | unorthogonal_lines(L!0, L!0) | unorthogonal_lines(L!0, L!0))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(44,plain,
% 0.21/0.40 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | unorthogonal_lines(L, N) | unorthogonal_lines(L, M))) | unorthogonal_lines(L!0, L!0) | (~convergent_lines(L!0, L!0))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.40 tff(45,plain,
% 0.21/0.40 ($false),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[44, 38, 11, 25])).
% 0.21/0.40 % SZS output end Proof
%------------------------------------------------------------------------------