TSTP Solution File: GRP697-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP697-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %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 : 600s
% DateTime : Sat Jul 16 11:20:39 EDT 2022
% Result : Unsatisfiable 0.79s 1.10s
% Output : Refutation 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP697-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.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 18:41:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.79/1.10 ============================== Prover9 ===============================
% 0.79/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.10 Process 3462 was started by sandbox2 on n020.cluster.edu,
% 0.79/1.10 Mon Jun 13 18:41:35 2022
% 0.79/1.10 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3308_n020.cluster.edu".
% 0.79/1.10 ============================== end of head ===========================
% 0.79/1.10
% 0.79/1.10 ============================== INPUT =================================
% 0.79/1.10
% 0.79/1.10 % Reading from file /tmp/Prover9_3308_n020.cluster.edu
% 0.79/1.10
% 0.79/1.10 set(prolog_style_variables).
% 0.79/1.10 set(auto2).
% 0.79/1.10 % set(auto2) -> set(auto).
% 0.79/1.10 % set(auto) -> set(auto_inference).
% 0.79/1.10 % set(auto) -> set(auto_setup).
% 0.79/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.10 % set(auto) -> set(auto_limits).
% 0.79/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.10 % set(auto) -> set(auto_denials).
% 0.79/1.10 % set(auto) -> set(auto_process).
% 0.79/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.10 % set(auto2) -> assign(stats, some).
% 0.79/1.10 % set(auto2) -> clear(echo_input).
% 0.79/1.10 % set(auto2) -> set(quiet).
% 0.79/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.10 % set(auto2) -> clear(print_given).
% 0.79/1.10 assign(lrs_ticks,-1).
% 0.79/1.10 assign(sos_limit,10000).
% 0.79/1.10 assign(order,kbo).
% 0.79/1.10 set(lex_order_vars).
% 0.79/1.10 clear(print_given).
% 0.79/1.10
% 0.79/1.10 % formulas(sos). % not echoed (12 formulas)
% 0.79/1.10
% 0.79/1.10 ============================== end of input ==========================
% 0.79/1.10
% 0.79/1.10 % From the command line: assign(max_seconds, 300).
% 0.79/1.10
% 0.79/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.10
% 0.79/1.10 % Formulas that are not ordinary clauses:
% 0.79/1.10
% 0.79/1.10 ============================== end of process non-clausal formulas ===
% 0.79/1.10
% 0.79/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.79/1.10
% 0.79/1.10 ============================== PREDICATE ELIMINATION =================
% 0.79/1.10
% 0.79/1.10 ============================== end predicate elimination =============
% 0.79/1.10
% 0.79/1.10 Auto_denials:
% 0.79/1.10 % copying label goals to answer in negative clause
% 0.79/1.10
% 0.79/1.10 Term ordering decisions:
% 0.79/1.10
% 0.79/1.10 % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 0.79/1.10 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. i=0.
% 0.79/1.10
% 0.79/1.10 ============================== end of process initial clauses ========
% 0.79/1.10
% 0.79/1.10 ============================== CLAUSES FOR SEARCH ====================
% 0.79/1.10
% 0.79/1.10 ============================== end of clauses for search =============
% 0.79/1.10
% 0.79/1.10 ============================== SEARCH ================================
% 0.79/1.10
% 0.79/1.10 % Starting search at 0.01 seconds.
% 0.79/1.10
% 0.79/1.10 ============================== PROOF =================================
% 0.79/1.10 % SZS status Unsatisfiable
% 0.79/1.10 % SZS output start Refutation
% 0.79/1.10
% 0.79/1.10 % Proof 1 at 0.09 (+ 0.01) seconds: goals.
% 0.79/1.10 % Length of proof is 55.
% 0.79/1.10 % Level of proof is 14.
% 0.79/1.10 % Maximum clause weight is 20.000.
% 0.79/1.10 % Given clauses 66.
% 0.79/1.10
% 0.79/1.10 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 0.79/1.10 2 mult(unit,A) = A # label(c06) # label(axiom). [assumption].
% 0.79/1.10 3 mult(i(A),A) = unit # label(c10) # label(axiom). [assumption].
% 0.79/1.10 4 mult(A,i(A)) = unit # label(c11) # label(axiom). [assumption].
% 0.79/1.10 5 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 0.79/1.10 6 ld(A,mult(A,B)) = B # label(c02) # label(axiom). [assumption].
% 0.79/1.10 8 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 0.79/1.10 9 mult(A,i(mult(B,A))) = i(B) # label(c07) # label(axiom). [assumption].
% 0.79/1.10 10 mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) # label(c08) # label(axiom). [assumption].
% 0.79/1.10 11 mult(rd(mult(A,B),A),mult(A,C)) = mult(A,mult(B,C)). [copy(10),flip(a)].
% 0.79/1.10 12 mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) # label(c09) # label(axiom). [assumption].
% 0.79/1.10 13 mult(mult(A,B),ld(B,mult(C,B))) = mult(mult(A,C),B). [copy(12),flip(a)].
% 0.79/1.10 14 mult(mult(a,b),mult(b,mult(c,b))) != mult(mult(a,mult(b,mult(b,c))),b) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 0.79/1.10 15 mult(mult(a,mult(b,mult(b,c))),b) != mult(mult(a,b),mult(b,mult(c,b))) # answer(goals). [copy(14),flip(a)].
% 0.79/1.10 19 ld(i(A),unit) = A. [para(3(a,1),6(a,1,2))].
% 0.79/1.10 20 ld(A,unit) = i(A). [para(4(a,1),6(a,1,2))].
% 0.79/1.10 21 i(i(A)) = A. [back_rewrite(19),rewrite([20(3)])].
% 0.79/1.10 25 rd(unit,A) = i(A). [para(3(a,1),8(a,1,1))].
% 0.79/1.10 27 mult(ld(A,B),i(B)) = i(A). [para(5(a,1),9(a,1,2,1))].
% 0.79/1.10 28 i(mult(A,B)) = ld(B,i(A)). [para(9(a,1),6(a,1,2)),flip(a)].
% 0.79/1.10 30 mult(ld(A,i(B)),B) = i(A). [para(9(a,1),9(a,1,2,1)),rewrite([28(2),21(4)])].
% 0.79/1.10 31 mult(i(A),mult(A,B)) = mult(A,mult(i(A),B)). [para(3(a,1),11(a,1,1,1)),rewrite([25(3),21(2)]),flip(a)].
% 0.79/1.10 34 rd(mult(A,B),A) = mult(A,mult(B,i(A))). [para(4(a,1),11(a,1,2)),rewrite([1(4)])].
% 0.79/1.10 37 mult(mult(A,mult(B,i(A))),C) = mult(A,mult(B,ld(A,C))). [para(5(a,1),11(a,1,2)),rewrite([34(2)])].
% 0.79/1.10 46 ld(A,mult(B,A)) = mult(mult(i(A),B),A). [para(3(a,1),13(a,1,1)),rewrite([2(4)])].
% 0.79/1.10 47 mult(mult(A,i(B)),B) = mult(mult(A,B),i(B)). [para(3(a,1),13(a,1,2,2)),rewrite([20(3)]),flip(a)].
% 0.79/1.10 55 ld(mult(A,B),mult(mult(A,C),B)) = mult(mult(i(B),C),B). [para(13(a,1),6(a,1,2)),rewrite([46(6)])].
% 0.79/1.10 64 mult(mult(A,B),mult(mult(i(B),C),B)) = mult(mult(A,C),B). [back_rewrite(13),rewrite([46(3)])].
% 0.79/1.10 67 ld(ld(A,B),i(A)) = i(B). [para(27(a,1),6(a,1,2))].
% 0.79/1.10 90 i(ld(A,B)) = mult(i(B),A). [para(67(a,1),27(a,1,1)),rewrite([21(3)]),flip(a)].
% 0.79/1.10 93 mult(A,mult(i(A),i(A))) = i(A). [para(4(a,1),31(a,1,2)),rewrite([1(3)]),flip(a)].
% 0.79/1.10 97 ld(mult(i(A),B),i(A)) = ld(mult(A,B),A). [para(31(a,1),28(a,1,1)),rewrite([28(4),21(7)])].
% 0.79/1.10 100 mult(mult(i(A),B),ld(B,A)) = unit. [para(90(a,1),3(a,1,1))].
% 0.79/1.10 113 mult(mult(i(A),mult(B,A)),C) = mult(i(A),mult(B,ld(i(A),C))). [para(21(a,1),37(a,1,1,2,2))].
% 0.79/1.10 136 mult(A,ld(mult(A,A),A)) = unit. [para(93(a,1),100(a,1,1)),rewrite([21(2),21(2),21(2)])].
% 0.79/1.10 137 ld(mult(A,A),A) = i(A). [para(136(a,1),6(a,1,2)),rewrite([20(2)]),flip(a)].
% 0.79/1.10 158 ld(i(A),A) = mult(A,A). [para(137(a,1),30(a,1,1)),rewrite([21(2),28(5),21(4)]),flip(a)].
% 0.79/1.10 172 mult(A,mult(mult(i(A),B),A)) = mult(B,A). [para(46(a,1),5(a,1,2))].
% 0.79/1.10 180 ld(A,ld(B,A)) = mult(ld(A,i(B)),A). [para(46(a,1),90(a,1,1)),rewrite([28(4),28(3),21(2),28(4)])].
% 0.79/1.10 222 mult(ld(i(A),B),A) = mult(A,mult(B,A)). [para(5(a,1),172(a,1,2,1)),flip(a)].
% 0.79/1.10 229 mult(A,mult(i(A),mult(B,mult(A,A)))) = mult(mult(B,A),A). [para(37(a,1),172(a,1,2)),rewrite([158(3),21(7)])].
% 0.79/1.10 249 mult(A,mult(ld(A,i(B)),A)) = ld(B,A). [para(180(a,1),5(a,1,2))].
% 0.79/1.10 298 mult(A,mult(ld(A,B),A)) = ld(i(B),A). [para(21(a,1),249(a,1,2,1,2))].
% 0.79/1.10 323 ld(ld(A,i(B)),B) = mult(B,mult(A,B)). [para(6(a,1),298(a,1,2,1)),rewrite([28(4)]),flip(a)].
% 0.79/1.10 333 mult(mult(A,mult(B,A)),i(A)) = mult(A,B). [para(298(a,1),172(a,1,2,1)),rewrite([30(4),21(2),47(6),222(4)]),flip(a)].
% 0.79/1.10 342 ld(mult(A,B),B) = mult(mult(i(B),i(A)),B). [para(4(a,1),55(a,1,2,1)),rewrite([2(3)])].
% 0.79/1.10 422 ld(ld(mult(A,B),A),A) = mult(B,A). [para(172(a,1),323(a,2)),rewrite([97(4)])].
% 0.79/1.10 436 ld(ld(A,B),B) = mult(ld(B,A),B). [para(5(a,1),422(a,1,1,1))].
% 0.79/1.10 437 mult(mult(A,B),i(B)) = mult(B,mult(i(B),A)). [para(422(a,1),27(a,1,1)),rewrite([90(6),31(6)])].
% 0.79/1.10 454 mult(mult(ld(A,B),A),A) = mult(i(A),mult(B,mult(A,A))). [para(298(a,1),422(a,1,1,1)),rewrite([436(3),342(4),90(4),21(3),113(4),158(3)]),flip(a)].
% 0.79/1.10 549 mult(mult(A,B),mult(mult(B,mult(i(B),C)),B)) = mult(mult(A,mult(B,C)),B). [para(31(a,1),64(a,1,2,1))].
% 0.79/1.10 606 mult(A,mult(i(A),mult(B,A))) = ld(i(B),A). [para(298(a,1),333(a,2)),rewrite([454(3),229(5),437(4)])].
% 0.79/1.10 615 mult(mult(A,mult(i(A),B)),A) = ld(i(B),A). [para(333(a,1),333(a,1,1,2)),rewrite([31(3),21(5),31(8),606(8)])].
% 0.79/1.10 639 mult(mult(A,mult(B,C)),B) = mult(mult(A,B),ld(i(C),B)). [back_rewrite(549),rewrite([615(5)]),flip(a)].
% 0.79/1.10 710 $F # answer(goals). [back_rewrite(15),rewrite([639(9),28(7),323(9)]),xx(a)].
% 0.79/1.10
% 0.79/1.10 % SZS output end Refutation
% 0.79/1.10 ============================== end of proof ==========================
% 0.79/1.10
% 0.79/1.10 ============================== STATISTICS ============================
% 0.79/1.10
% 0.79/1.10 Given=66. Generated=2109. Kept=706. proofs=1.
% 0.79/1.10 Usable=35. Sos=246. Demods=349. Limbo=71, Disabled=366. Hints=0.
% 0.79/1.10 Megabytes=0.72.
% 0.79/1.10 User_CPU=0.09, System_CPU=0.01, Wall_clock=0.
% 0.79/1.10
% 0.79/1.10 ============================== end of statistics =====================
% 0.79/1.10
% 0.79/1.10 ============================== end of search =========================
% 0.79/1.10
% 0.79/1.10 THEOREM PROVED
% 0.79/1.10 % SZS status Unsatisfiable
% 0.79/1.10
% 0.79/1.10 Exiting with 1 proof.
% 0.79/1.10
% 0.79/1.10 Process 3462 exit (max_proofs) Mon Jun 13 18:41:35 2022
% 0.79/1.10 Prover9 interrupted
%------------------------------------------------------------------------------