TSTP Solution File: GRP710+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP710+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 11:20:44 EDT 2022
% Result : Theorem 0.70s 1.08s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP710+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n005.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 : 600
% 0.12/0.33 % DateTime : Mon Jun 13 20:13:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/1.08 ============================== Prover9 ===============================
% 0.70/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.08 Process 11145 was started by sandbox2 on n005.cluster.edu,
% 0.70/1.08 Mon Jun 13 20:13:24 2022
% 0.70/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10992_n005.cluster.edu".
% 0.70/1.08 ============================== end of head ===========================
% 0.70/1.08
% 0.70/1.08 ============================== INPUT =================================
% 0.70/1.08
% 0.70/1.08 % Reading from file /tmp/Prover9_10992_n005.cluster.edu
% 0.70/1.08
% 0.70/1.08 set(prolog_style_variables).
% 0.70/1.08 set(auto2).
% 0.70/1.08 % set(auto2) -> set(auto).
% 0.70/1.08 % set(auto) -> set(auto_inference).
% 0.70/1.08 % set(auto) -> set(auto_setup).
% 0.70/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.08 % set(auto) -> set(auto_limits).
% 0.70/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.08 % set(auto) -> set(auto_denials).
% 0.70/1.08 % set(auto) -> set(auto_process).
% 0.70/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.08 % set(auto2) -> assign(stats, some).
% 0.70/1.08 % set(auto2) -> clear(echo_input).
% 0.70/1.08 % set(auto2) -> set(quiet).
% 0.70/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.08 % set(auto2) -> clear(print_given).
% 0.70/1.08 assign(lrs_ticks,-1).
% 0.70/1.08 assign(sos_limit,10000).
% 0.70/1.08 assign(order,kbo).
% 0.70/1.08 set(lex_order_vars).
% 0.70/1.08 clear(print_given).
% 0.70/1.08
% 0.70/1.08 % formulas(sos). % not echoed (6 formulas)
% 0.70/1.08
% 0.70/1.08 ============================== end of input ==========================
% 0.70/1.08
% 0.70/1.08 % From the command line: assign(max_seconds, 300).
% 0.70/1.08
% 0.70/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.08
% 0.70/1.08 % Formulas that are not ordinary clauses:
% 0.70/1.08 1 (all A mult(A,unit) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 2 (all A mult(unit,A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 3 (all C all B all A mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C)) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 4 (all A mult(A,i(A)) = unit) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 5 (all A mult(i(A),A) = unit) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 6 -((all X0 all X1 exists X2 mult(X0,X2) = X1) & (all X3 all X4 exists X5 mult(X5,X4) = X3)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/1.08
% 0.70/1.08 ============================== end of process non-clausal formulas ===
% 0.70/1.08
% 0.70/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.08
% 0.70/1.08 ============================== PREDICATE ELIMINATION =================
% 0.70/1.08
% 0.70/1.08 ============================== end predicate elimination =============
% 0.70/1.08
% 0.70/1.08 Auto_denials:
% 0.70/1.08 % copying label goals to answer in negative clause
% 0.70/1.08
% 0.70/1.08 Term ordering decisions:
% 0.70/1.08
% 0.70/1.08 % Assigning unary symbol i kb_weight 0 and highest precedence (8).
% 0.70/1.08 Function symbol KB weights: unit=1. c1=1. c2=1. c3=1. c4=1. mult=1. i=0.
% 0.70/1.08
% 0.70/1.08 ============================== end of process initial clauses ========
% 0.70/1.08
% 0.70/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.70/1.08
% 0.70/1.08 ============================== end of clauses for search =============
% 0.70/1.08
% 0.70/1.08 ============================== SEARCH ================================
% 0.70/1.08
% 0.70/1.08 % Starting search at 0.01 seconds.
% 0.70/1.08
% 0.70/1.08 ============================== PROOF =================================
% 0.70/1.08 % SZS status Theorem
% 0.70/1.08 % SZS output start Refutation
% 0.70/1.08
% 0.70/1.08 % Proof 1 at 0.12 (+ 0.00) seconds: goals.
% 0.70/1.08 % Length of proof is 41.
% 0.70/1.08 % Level of proof is 19.
% 0.70/1.08 % Maximum clause weight is 22.000.
% 0.70/1.08 % Given clauses 71.
% 0.70/1.08
% 0.70/1.08 1 (all A mult(A,unit) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 2 (all A mult(unit,A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 3 (all C all B all A mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C)) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 4 (all A mult(A,i(A)) = unit) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 5 (all A mult(i(A),A) = unit) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.08 6 -((all X0 all X1 exists X2 mult(X0,X2) = X1) & (all X3 all X4 exists X5 mult(X5,X4) = X3)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/1.08 7 mult(A,unit) = A # label(f01) # label(axiom). [clausify(1)].
% 0.70/1.08 8 mult(unit,A) = A # label(f02) # label(axiom). [clausify(2)].
% 0.70/1.08 9 mult(A,i(A)) = unit # label(f04) # label(axiom). [clausify(4)].
% 0.70/1.08 10 mult(i(A),A) = unit # label(f05) # label(axiom). [clausify(5)].
% 0.70/1.08 11 mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))) # label(f03) # label(axiom). [clausify(3)].
% 0.70/1.08 12 mult(c1,A) != c2 | mult(B,c4) != c3 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(6)].
% 0.70/1.08 14 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(11(a,1),7(a,1)),rewrite([7(2)]),flip(a)].
% 0.70/1.08 15 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(8(a,1),11(a,1,1,1)),rewrite([8(6)])].
% 0.70/1.08 16 mult(A,mult(B,mult(B,i(mult(A,mult(B,B)))))) = unit. [para(11(a,1),9(a,1)),rewrite([14(2)])].
% 0.70/1.08 19 mult(i(A),mult(A,mult(A,B))) = mult(A,B). [para(10(a,1),11(a,1,1,1)),rewrite([8(2)]),flip(a)].
% 0.70/1.08 27 mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))). [back_rewrite(11),rewrite([14(2)])].
% 0.70/1.08 38 mult(A,mult(i(A),i(A))) = i(A). [para(9(a,1),14(a,1,1)),rewrite([8(3)]),flip(a)].
% 0.70/1.08 39 mult(i(A),mult(A,A)) = A. [para(10(a,1),14(a,1,1)),rewrite([8(2)]),flip(a)].
% 0.70/1.08 46 mult(A,mult(A,i(mult(A,A)))) = unit. [para(15(a,1),9(a,1))].
% 0.70/1.08 51 mult(A,mult(A,mult(i(mult(A,A)),i(mult(A,A))))) = i(mult(A,A)). [para(15(a,1),38(a,1))].
% 0.70/1.08 61 i(i(A)) = A. [para(39(a,1),19(a,1,2,2)),rewrite([10(4),7(4),39(5)])].
% 0.70/1.08 64 mult(A,i(mult(A,A))) = i(A). [para(46(a,1),19(a,1,2)),rewrite([7(3)]),flip(a)].
% 0.70/1.08 66 mult(A,mult(i(mult(A,A)),i(mult(A,A)))) = mult(i(A),i(mult(A,A))). [para(64(a,1),14(a,1,1)),flip(a)].
% 0.70/1.08 68 mult(A,mult(i(A),i(mult(A,A)))) = i(mult(A,A)). [back_rewrite(51),rewrite([66(6)])].
% 0.70/1.08 88 i(mult(A,A)) = mult(i(A),i(A)). [para(68(a,1),19(a,1,2,2)),rewrite([64(4),68(8)]),flip(a)].
% 0.70/1.08 126 mult(i(A),mult(A,B)) = B. [para(10(a,1),27(a,1,1)),rewrite([8(2),88(2),15(6),19(5)]),flip(a)].
% 0.70/1.08 155 mult(A,mult(A,i(mult(B,mult(A,A))))) = i(B). [para(16(a,1),126(a,1,2)),rewrite([7(3)]),flip(a)].
% 0.70/1.08 156 mult(A,mult(i(A),B)) = B. [para(61(a,1),126(a,1,1))].
% 0.70/1.08 199 mult(A,c4) != c3 # answer(goals). [ur(12,a,156,a)].
% 0.70/1.08 220 mult(A,i(mult(B,mult(A,A)))) = mult(i(A),i(B)). [para(155(a,1),126(a,1,2)),flip(a)].
% 0.70/1.08 224 mult(A,i(mult(B,mult(A,mult(A,mult(A,A)))))) = mult(i(A),i(mult(B,mult(A,A)))). [para(14(a,1),220(a,1,2,1)),rewrite([15(3)])].
% 0.70/1.08 225 i(mult(A,mult(B,B))) = mult(i(B),mult(i(B),i(A))). [para(220(a,1),15(a,1)),rewrite([88(2),15(5),15(8),224(11),156(11)]),flip(a)].
% 0.70/1.08 270 mult(A,mult(c4,c4)) != c3 # answer(goals). [para(14(a,1),199(a,1))].
% 0.70/1.08 326 i(mult(i(A),mult(i(A),i(B)))) = mult(B,mult(A,A)). [para(225(a,1),61(a,1,1))].
% 0.70/1.08 348 i(mult(A,mult(A,i(B)))) = mult(B,mult(i(A),i(A))). [para(61(a,1),326(a,1,1,1)),rewrite([61(2)])].
% 0.70/1.08 399 i(mult(A,mult(A,B))) = mult(i(B),mult(i(A),i(A))). [para(61(a,1),348(a,1,1,2,2))].
% 0.70/1.08 409 mult(i(mult(A,B)),mult(A,A)) = i(mult(i(A),B)). [para(126(a,1),399(a,1,1,2)),rewrite([61(7),61(7)]),flip(a)].
% 0.70/1.08 428 i(mult(i(c4),A)) != c3 # answer(goals). [para(409(a,1),270(a,1))].
% 0.70/1.08 505 i(A) != c3 # answer(goals). [para(126(a,1),428(a,1,1))].
% 0.70/1.08 506 $F # answer(goals). [resolve(505,a,61,a)].
% 0.70/1.08
% 0.70/1.08 % SZS output end Refutation
% 0.70/1.08 ============================== end of proof ==========================
% 0.70/1.08
% 0.70/1.08 ============================== STATISTICS ============================
% 0.70/1.08
% 0.70/1.08 Given=71. Generated=2093. Kept=499. proofs=1.
% 0.70/1.08 Usable=34. Sos=221. Demods=214. Limbo=0, Disabled=249. Hints=0.
% 0.70/1.08 Megabytes=0.78.
% 0.70/1.08 User_CPU=0.12, System_CPU=0.00, Wall_clock=0.
% 0.70/1.08
% 0.70/1.08 ============================== end of statistics =====================
% 0.70/1.08
% 0.70/1.08 ============================== end of search =========================
% 0.70/1.08
% 0.70/1.08 THEOREM PROVED
% 0.70/1.08 % SZS status Theorem
% 0.70/1.08
% 0.70/1.08 Exiting with 1 proof.
% 0.70/1.08
% 0.70/1.08 Process 11145 exit (max_proofs) Mon Jun 13 20:13:24 2022
% 0.70/1.08 Prover9 interrupted
%------------------------------------------------------------------------------