TSTP Solution File: GRP659+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP659+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %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 : 600s
% DateTime : Sat Jul 16 11:20:22 EDT 2022
% Result : Theorem 0.95s 1.21s
% Output : Refutation 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP659+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %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 : 600
% 0.13/0.34 % DateTime : Mon Jun 13 10:30:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.95/1.21 ============================== Prover9 ===============================
% 0.95/1.21 Prover9 (32) version 2009-11A, November 2009.
% 0.95/1.21 Process 2916 was started by sandbox2 on n026.cluster.edu,
% 0.95/1.21 Mon Jun 13 10:30:21 2022
% 0.95/1.21 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2762_n026.cluster.edu".
% 0.95/1.21 ============================== end of head ===========================
% 0.95/1.21
% 0.95/1.21 ============================== INPUT =================================
% 0.95/1.21
% 0.95/1.21 % Reading from file /tmp/Prover9_2762_n026.cluster.edu
% 0.95/1.21
% 0.95/1.21 set(prolog_style_variables).
% 0.95/1.21 set(auto2).
% 0.95/1.21 % set(auto2) -> set(auto).
% 0.95/1.21 % set(auto) -> set(auto_inference).
% 0.95/1.21 % set(auto) -> set(auto_setup).
% 0.95/1.21 % set(auto_setup) -> set(predicate_elim).
% 0.95/1.21 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.95/1.21 % set(auto) -> set(auto_limits).
% 0.95/1.21 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.95/1.21 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.95/1.21 % set(auto) -> set(auto_denials).
% 0.95/1.21 % set(auto) -> set(auto_process).
% 0.95/1.21 % set(auto2) -> assign(new_constants, 1).
% 0.95/1.21 % set(auto2) -> assign(fold_denial_max, 3).
% 0.95/1.21 % set(auto2) -> assign(max_weight, "200.000").
% 0.95/1.21 % set(auto2) -> assign(max_hours, 1).
% 0.95/1.21 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.95/1.21 % set(auto2) -> assign(max_seconds, 0).
% 0.95/1.21 % set(auto2) -> assign(max_minutes, 5).
% 0.95/1.21 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.95/1.21 % set(auto2) -> set(sort_initial_sos).
% 0.95/1.21 % set(auto2) -> assign(sos_limit, -1).
% 0.95/1.21 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.95/1.21 % set(auto2) -> assign(max_megs, 400).
% 0.95/1.21 % set(auto2) -> assign(stats, some).
% 0.95/1.21 % set(auto2) -> clear(echo_input).
% 0.95/1.21 % set(auto2) -> set(quiet).
% 0.95/1.21 % set(auto2) -> clear(print_initial_clauses).
% 0.95/1.21 % set(auto2) -> clear(print_given).
% 0.95/1.21 assign(lrs_ticks,-1).
% 0.95/1.21 assign(sos_limit,10000).
% 0.95/1.21 assign(order,kbo).
% 0.95/1.21 set(lex_order_vars).
% 0.95/1.21 clear(print_given).
% 0.95/1.21
% 0.95/1.21 % formulas(sos). % not echoed (6 formulas)
% 0.95/1.21
% 0.95/1.21 ============================== end of input ==========================
% 0.95/1.21
% 0.95/1.21 % From the command line: assign(max_seconds, 300).
% 0.95/1.21
% 0.95/1.21 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.95/1.21
% 0.95/1.21 % Formulas that are not ordinary clauses:
% 0.95/1.21 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 5 (all C all B all A mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B))) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 6 -(exists X0 all X1 (mult(X1,X0) = X1 & mult(X0,X1) = X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.95/1.21
% 0.95/1.21 ============================== end of process non-clausal formulas ===
% 0.95/1.21
% 0.95/1.21 ============================== PROCESS INITIAL CLAUSES ===============
% 0.95/1.21
% 0.95/1.21 ============================== PREDICATE ELIMINATION =================
% 0.95/1.21
% 0.95/1.21 ============================== end predicate elimination =============
% 0.95/1.21
% 0.95/1.21 Auto_denials:
% 0.95/1.21 % copying label goals to answer in negative clause
% 0.95/1.21
% 0.95/1.21 Term ordering decisions:
% 0.95/1.21
% 0.95/1.21 % Assigning unary symbol f1 kb_weight 0 and highest precedence (5).
% 0.95/1.21 Function symbol KB weights: mult=1. ld=1. rd=1. f1=0.
% 0.95/1.21
% 0.95/1.21 ============================== end of process initial clauses ========
% 0.95/1.21
% 0.95/1.21 ============================== CLAUSES FOR SEARCH ====================
% 0.95/1.21
% 0.95/1.21 ============================== end of clauses for search =============
% 0.95/1.21
% 0.95/1.21 ============================== SEARCH ================================
% 0.95/1.21
% 0.95/1.21 % Starting search at 0.01 seconds.
% 0.95/1.21
% 0.95/1.21 ============================== PROOF =================================
% 0.95/1.21 % SZS status Theorem
% 0.95/1.21 % SZS output start Refutation
% 0.95/1.21
% 0.95/1.21 % Proof 1 at 0.21 (+ 0.01) seconds: goals.
% 0.95/1.21 % Length of proof is 53.
% 0.95/1.21 % Level of proof is 17.
% 0.95/1.21 % Maximum clause weight is 15.000.
% 0.95/1.21 % Given clauses 68.
% 0.95/1.21
% 0.95/1.21 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 5 (all C all B all A mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B))) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.95/1.21 6 -(exists X0 all X1 (mult(X1,X0) = X1 & mult(X0,X1) = X1)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.95/1.21 7 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 0.95/1.21 8 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 0.95/1.21 9 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 0.95/1.21 10 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 0.95/1.21 11 mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)) # label(f05) # label(axiom). [clausify(5)].
% 0.95/1.21 12 mult(f1(A),A) != f1(A) | mult(A,f1(A)) != f1(A) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(6)].
% 0.95/1.21 13 ld(rd(A,B),A) = B. [para(9(a,1),8(a,1,2))].
% 0.95/1.21 14 rd(A,ld(B,A)) = B. [para(7(a,1),10(a,1,1))].
% 0.95/1.21 15 mult(mult(A,B),mult(ld(B,C),B)) = mult(mult(A,C),B). [para(7(a,1),11(a,1,1,2)),flip(a)].
% 0.95/1.21 18 mult(mult(rd(A,mult(B,C)),B),mult(C,B)) = mult(A,B). [para(9(a,1),11(a,1,1)),flip(a)].
% 0.95/1.21 19 rd(mult(mult(A,B),mult(C,B)),B) = mult(A,mult(B,C)). [para(11(a,1),10(a,1,1))].
% 0.95/1.21 23 ld(mult(A,B),mult(mult(A,C),B)) = mult(ld(B,C),B). [para(15(a,1),8(a,1,2))].
% 0.95/1.21 43 rd(mult(A,B),mult(C,B)) = mult(rd(A,mult(B,C)),B). [para(18(a,1),10(a,1,1))].
% 0.95/1.21 63 rd(mult(A,mult(B,C)),C) = mult(rd(A,C),mult(C,B)). [para(9(a,1),19(a,1,1,1))].
% 0.95/1.21 66 ld(mult(A,B),mult(C,B)) = mult(ld(B,ld(A,C)),B). [para(7(a,1),23(a,1,2,1))].
% 0.95/1.21 68 mult(ld(A,A),A) = A. [para(23(a,1),8(a,1))].
% 0.95/1.21 77 rd(A,A) = ld(A,A). [para(68(a,1),10(a,1,1))].
% 0.95/1.21 356 mult(rd(ld(A,A),mult(A,B)),A) = rd(A,mult(B,A)). [para(68(a,1),43(a,1,1)),flip(a)].
% 0.95/1.21 610 mult(ld(A,ld(B,B)),mult(A,B)) = B. [para(68(a,1),63(a,1,1)),rewrite([10(2),66(3),10(4)]),flip(a)].
% 0.95/1.21 639 ld(ld(A,ld(B,B)),B) = mult(A,B). [para(610(a,1),8(a,1,2))].
% 0.95/1.21 640 mult(ld(rd(A,B),ld(B,B)),A) = B. [para(9(a,1),610(a,1,2))].
% 0.95/1.21 641 rd(A,mult(B,A)) = ld(B,ld(A,A)). [para(610(a,1),10(a,1,1))].
% 0.95/1.21 684 mult(rd(ld(A,A),mult(A,B)),A) = ld(B,ld(A,A)). [back_rewrite(356),rewrite([641(6)])].
% 0.95/1.21 685 mult(rd(ld(A,A),B),A) = ld(B,A). [para(13(a,1),639(a,1,1)),flip(a)].
% 0.95/1.21 702 ld(mult(A,B),A) = ld(B,ld(A,A)). [back_rewrite(684),rewrite([685(4)])].
% 0.95/1.21 720 ld(rd(A,B),ld(B,B)) = rd(B,A). [para(640(a,1),10(a,1,1)),flip(a)].
% 0.95/1.21 786 ld(rd(ld(A,A),B),ld(B,A)) = A. [para(685(a,1),8(a,1,2))].
% 0.95/1.21 788 rd(ld(A,B),B) = rd(ld(B,B),A). [para(685(a,1),10(a,1,1))].
% 0.95/1.21 832 ld(ld(A,B),ld(A,A)) = ld(B,A). [para(7(a,1),702(a,1,1)),flip(a)].
% 0.95/1.21 835 rd(A,ld(B,ld(A,A))) = mult(A,B). [para(702(a,1),14(a,1,2))].
% 0.95/1.21 976 ld(rd(ld(A,B),B),ld(A,A)) = rd(A,ld(B,B)). [para(788(a,2),720(a,1,1))].
% 0.95/1.21 977 ld(rd(A,ld(B,B)),ld(B,B)) = rd(ld(A,B),B). [para(788(a,2),720(a,2)),rewrite([832(5)])].
% 0.95/1.21 979 rd(ld(ld(A,B),ld(A,B)),rd(ld(B,B),A)) = A. [para(786(a,1),788(a,1,1)),rewrite([14(2)]),flip(a)].
% 0.95/1.21 1037 ld(ld(A,B),B) = mult(ld(B,A),B). [para(832(a,1),639(a,1,1))].
% 0.95/1.21 1070 rd(A,rd(A,B)) = mult(A,rd(B,A)). [para(720(a,1),835(a,1,2))].
% 0.95/1.21 1072 mult(ld(A,A),B) = B. [para(835(a,1),788(a,2)),rewrite([832(3),639(3),10(2)]),flip(a)].
% 0.95/1.21 1217 mult(f1(ld(A,A)),ld(A,A)) != f1(ld(A,A)) # answer(goals). [ur(12,b,1072,a)].
% 0.95/1.21 1218 ld(ld(A,A),B) = B. [para(1072(a,1),7(a,1))].
% 0.95/1.21 1219 ld(A,A) = ld(B,B). [para(1072(a,1),10(a,1,1)),rewrite([77(1)])].
% 0.95/1.21 1253 ld(A,A) = c_0. [new_symbol(1219)].
% 0.95/1.21 1299 ld(c_0,A) = A. [back_rewrite(1218),rewrite([1253(1)])].
% 0.95/1.21 1300 mult(f1(c_0),c_0) != f1(c_0) # answer(goals). [back_rewrite(1217),rewrite([1253(1),1253(3),1253(5)])].
% 0.95/1.21 1334 mult(c_0,A) = A. [back_rewrite(1072),rewrite([1253(1)])].
% 0.95/1.21 1389 rd(A,c_0) = A. [back_rewrite(979),rewrite([1253(3),1253(2),1070(4),1334(4)])].
% 0.95/1.21 1391 rd(ld(A,B),B) = ld(A,c_0). [back_rewrite(977),rewrite([1253(1),1389(2),1253(1)]),flip(a)].
% 0.95/1.21 1392 mult(A,c_0) = A. [back_rewrite(976),rewrite([1391(2),1253(3),1037(4),1299(2),1253(3),1389(4)])].
% 0.95/1.21 1393 $F # answer(goals). [resolve(1392,a,1300,a)].
% 0.95/1.21
% 0.95/1.21 % SZS output end Refutation
% 0.95/1.21 ============================== end of proof ==========================
% 0.95/1.21
% 0.95/1.21 ============================== STATISTICS ============================
% 0.95/1.21
% 0.95/1.21 Given=68. Generated=4130. Kept=1386. proofs=1.
% 0.95/1.21 Usable=40. Sos=670. Demods=828. Limbo=139, Disabled=542. Hints=0.
% 0.95/1.21 Megabytes=2.58.
% 0.95/1.21 User_CPU=0.21, System_CPU=0.01, Wall_clock=0.
% 0.95/1.21
% 0.95/1.21 ============================== end of statistics =====================
% 0.95/1.21
% 0.95/1.21 ============================== end of search =========================
% 0.95/1.21
% 0.95/1.21 THEOREM PROVED
% 0.95/1.21 % SZS status Theorem
% 0.95/1.21
% 0.95/1.21 Exiting with 1 proof.
% 0.95/1.21
% 0.95/1.21 Process 2916 exit (max_proofs) Mon Jun 13 10:30:21 2022
% 0.95/1.21 Prover9 interrupted
%------------------------------------------------------------------------------