TSTP Solution File: GEO217+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO217+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO217+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 07:01:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(convergent_lines_type, type, (
% 0.20/0.41 convergent_lines: ( $i * $i ) > $o)).
% 0.20/0.41 tff(tptp_fun_N_0_type, type, (
% 0.20/0.41 tptp_fun_N_0: $i)).
% 0.20/0.41 tff(tptp_fun_L_2_type, type, (
% 0.20/0.41 tptp_fun_L_2: $i)).
% 0.20/0.41 tff(tptp_fun_M_1_type, type, (
% 0.20/0.41 tptp_fun_M_1: $i)).
% 0.20/0.41 tff(1,assumption,(~convergent_lines(N!0, N!0)), introduced(assumption)).
% 0.20/0.41 tff(2,assumption,(convergent_lines(M!1, M!1)), introduced(assumption)).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(6,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.41 tff(8,plain,(
% 0.20/0.41 ![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(skolemize,[status(sab)],[7])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (![X: $i] : (~convergent_lines(X, X))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(M!1, M!1))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.20/0.41 tff(12,plain,(~convergent_lines(M!1, M!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 ((~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))) <=> (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 ((~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~convergent_lines(L, N))) => (~convergent_lines(M, N)))) <=> (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(15,axiom,(~![L: $i, M: $i, N: $i] : (((~convergent_lines(L, M)) & (~convergent_lines(L, N))) => (~convergent_lines(M, N)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (~![L: $i, M: $i, N: $i] : ((~convergent_lines(M, N)) | (~((~convergent_lines(L, M)) & (~convergent_lines(L, N)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.20/0.41 tff(23,plain,(
% 0.20/0.41 ~((~convergent_lines(M!1, N!0)) | (~((~convergent_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 ((~convergent_lines(L!2, M!1)) & (~convergent_lines(L!2, N!0))),
% 0.20/0.41 inference(or_elim,[status(thm)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (~convergent_lines(L!2, M!1)),
% 0.20/0.41 inference(and_elim,[status(thm)],[24])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.41 tff(31,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.41 tff(34,plain,(
% 0.20/0.41 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[33])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, M!1) | convergent_lines(M!1, M!1) | (~convergent_lines(M!1, L!2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (~convergent_lines(M!1, L!2)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[38, 35, 25, 12])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (convergent_lines(M!1, N!0)),
% 0.20/0.41 inference(or_elim,[status(thm)],[23])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0))) <=> ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2))),
% 0.20/0.42 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(N!0, L!2) | convergent_lines(M!1, L!2) | (~convergent_lines(M!1, N!0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(M!1, N!0)) | convergent_lines(M!1, L!2) | convergent_lines(N!0, L!2)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (convergent_lines(N!0, L!2)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[46, 35, 40, 39])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (~convergent_lines(L!2, N!0)),
% 0.20/0.42 inference(and_elim,[status(thm)],[24])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | convergent_lines(L!2, N!0) | convergent_lines(N!0, N!0) | (~convergent_lines(N!0, L!2))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 35, 48, 47, 1])).
% 0.20/0.42 tff(53,plain,(convergent_lines(N!0, N!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(N!0, N!0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[54, 9, 53])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------