TSTP Solution File: GRP728-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP728-1 : 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 11:20:49 EDT 2022
% Result : Unsatisfiable 1.79s 2.08s
% Output : Refutation 1.79s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP728-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 04:39:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.79/2.08 ============================== Prover9 ===============================
% 1.79/2.08 Prover9 (32) version 2009-11A, November 2009.
% 1.79/2.08 Process 12922 was started by sandbox on n020.cluster.edu,
% 1.79/2.08 Tue Jun 14 04:39:20 2022
% 1.79/2.08 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12769_n020.cluster.edu".
% 1.79/2.08 ============================== end of head ===========================
% 1.79/2.08
% 1.79/2.08 ============================== INPUT =================================
% 1.79/2.08
% 1.79/2.08 % Reading from file /tmp/Prover9_12769_n020.cluster.edu
% 1.79/2.08
% 1.79/2.08 set(prolog_style_variables).
% 1.79/2.08 set(auto2).
% 1.79/2.08 % set(auto2) -> set(auto).
% 1.79/2.08 % set(auto) -> set(auto_inference).
% 1.79/2.08 % set(auto) -> set(auto_setup).
% 1.79/2.08 % set(auto_setup) -> set(predicate_elim).
% 1.79/2.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.79/2.08 % set(auto) -> set(auto_limits).
% 1.79/2.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.79/2.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.79/2.08 % set(auto) -> set(auto_denials).
% 1.79/2.08 % set(auto) -> set(auto_process).
% 1.79/2.08 % set(auto2) -> assign(new_constants, 1).
% 1.79/2.08 % set(auto2) -> assign(fold_denial_max, 3).
% 1.79/2.08 % set(auto2) -> assign(max_weight, "200.000").
% 1.79/2.08 % set(auto2) -> assign(max_hours, 1).
% 1.79/2.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.79/2.08 % set(auto2) -> assign(max_seconds, 0).
% 1.79/2.08 % set(auto2) -> assign(max_minutes, 5).
% 1.79/2.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.79/2.08 % set(auto2) -> set(sort_initial_sos).
% 1.79/2.08 % set(auto2) -> assign(sos_limit, -1).
% 1.79/2.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.79/2.08 % set(auto2) -> assign(max_megs, 400).
% 1.79/2.08 % set(auto2) -> assign(stats, some).
% 1.79/2.08 % set(auto2) -> clear(echo_input).
% 1.79/2.08 % set(auto2) -> set(quiet).
% 1.79/2.08 % set(auto2) -> clear(print_initial_clauses).
% 1.79/2.08 % set(auto2) -> clear(print_given).
% 1.79/2.08 assign(lrs_ticks,-1).
% 1.79/2.08 assign(sos_limit,10000).
% 1.79/2.08 assign(order,kbo).
% 1.79/2.08 set(lex_order_vars).
% 1.79/2.08 clear(print_given).
% 1.79/2.08
% 1.79/2.08 % formulas(sos). % not echoed (23 formulas)
% 1.79/2.08
% 1.79/2.08 ============================== end of input ==========================
% 1.79/2.08
% 1.79/2.08 % From the command line: assign(max_seconds, 300).
% 1.79/2.08
% 1.79/2.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.79/2.08
% 1.79/2.08 % Formulas that are not ordinary clauses:
% 1.79/2.08
% 1.79/2.08 ============================== end of process non-clausal formulas ===
% 1.79/2.08
% 1.79/2.08 ============================== PROCESS INITIAL CLAUSES ===============
% 1.79/2.08
% 1.79/2.08 ============================== PREDICATE ELIMINATION =================
% 1.79/2.08
% 1.79/2.08 ============================== end predicate elimination =============
% 1.79/2.08
% 1.79/2.08 Auto_denials:
% 1.79/2.08 % copying label goals to answer in negative clause
% 1.79/2.08
% 1.79/2.08 Term ordering decisions:
% 1.79/2.08
% 1.79/2.08 % Assigning unary symbol i kb_weight 0 and highest precedence (13).
% 1.79/2.08 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. op_t=1. rd=1. op_k=1. op_l=1. op_r=1. asoc=1. i=0.
% 1.79/2.08
% 1.79/2.08 ============================== end of process initial clauses ========
% 1.79/2.08
% 1.79/2.08 ============================== CLAUSES FOR SEARCH ====================
% 1.79/2.08
% 1.79/2.08 ============================== end of clauses for search =============
% 1.79/2.08
% 1.79/2.08 ============================== SEARCH ================================
% 1.79/2.08
% 1.79/2.08 % Starting search at 0.01 seconds.
% 1.79/2.08
% 1.79/2.08 ============================== PROOF =================================
% 1.79/2.08 % SZS status Unsatisfiable
% 1.79/2.08 % SZS output start Refutation
% 1.79/2.08
% 1.79/2.08 % Proof 1 at 1.07 (+ 0.01) seconds: goals.
% 1.79/2.08 % Length of proof is 57.
% 1.79/2.08 % Level of proof is 14.
% 1.79/2.08 % Maximum clause weight is 23.000.
% 1.79/2.08 % Given clauses 191.
% 1.79/2.08
% 1.79/2.08 1 mult(unit,A) = A # label(c01) # label(axiom). [assumption].
% 1.79/2.08 2 mult(A,unit) = A # label(c02) # label(axiom). [assumption].
% 1.79/2.08 3 mult(A,i(A)) = unit # label(c03) # label(axiom). [assumption].
% 1.79/2.08 4 mult(i(A),A) = unit # label(c04) # label(axiom). [assumption].
% 1.79/2.08 5 rd(mult(A,B),B) = A # label(c07) # label(axiom). [assumption].
% 1.79/2.08 6 mult(rd(A,B),B) = A # label(c08) # label(axiom). [assumption].
% 1.79/2.08 7 mult(i(A),mult(A,B)) = B # label(c06) # label(axiom). [assumption].
% 1.79/2.08 8 asoc(asoc(A,B,C),D,E) = unit # label(c21) # label(axiom). [assumption].
% 1.79/2.08 10 i(mult(A,B)) = mult(i(A),i(B)) # label(c05) # label(axiom). [assumption].
% 1.79/2.08 12 mult(A,B) = mult(mult(B,A),op_k(A,B)) # label(c11) # label(axiom). [assumption].
% 1.79/2.08 13 mult(mult(A,B),op_k(B,A)) = mult(B,A). [copy(12),flip(a)].
% 1.79/2.08 21 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))) # label(c09) # label(axiom). [assumption].
% 1.79/2.08 30 mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) # label(c10) # label(axiom). [assumption].
% 1.79/2.08 31 mult(mult(A,mult(B,C)),asoc(A,B,C)) = mult(mult(A,B),C). [copy(30),flip(a)].
% 1.79/2.08 32 op_k(op_k(a,b),c) != unit # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 1.79/2.08 38 rd(unit,i(A)) = A. [para(3(a,1),5(a,1,1))].
% 1.79/2.08 39 rd(unit,A) = i(A). [para(4(a,1),5(a,1,1))].
% 1.79/2.08 40 i(i(A)) = A. [back_rewrite(38),rewrite([39(3)])].
% 1.79/2.08 41 rd(A,mult(B,A)) = i(B). [para(7(a,1),5(a,1,1))].
% 1.79/2.08 45 mult(mult(A,B),mult(i(A),i(B))) = unit. [para(10(a,1),3(a,1,2))].
% 1.79/2.08 47 mult(i(rd(A,B)),i(B)) = i(A). [para(6(a,1),10(a,1,1)),flip(a)].
% 1.79/2.08 54 rd(mult(A,B),op_k(A,B)) = mult(B,A). [para(13(a,1),5(a,1,1))].
% 1.79/2.08 56 mult(mult(i(A),i(B)),mult(B,A)) = op_k(B,A). [para(13(a,1),7(a,1,2)),rewrite([10(2)])].
% 1.79/2.08 81 rd(mult(A,mult(B,mult(A,C))),C) = mult(A,mult(B,A)). [para(21(a,1),5(a,1,1))].
% 1.79/2.08 206 mult(mult(mult(i(A),i(B)),A),B) = asoc(mult(i(A),i(B)),A,B). [para(4(a,1),31(a,1,1)),rewrite([10(3),1(6),10(6)]),flip(a)].
% 1.79/2.09 211 mult(mult(i(A),mult(i(B),i(C))),mult(mult(A,B),C)) = asoc(A,B,C). [para(31(a,1),7(a,1,2)),rewrite([10(3),10(3)])].
% 1.79/2.09 392 mult(A,mult(i(A),B)) = B. [para(40(a,1),7(a,1,1))].
% 1.79/2.09 402 i(rd(A,B)) = rd(B,A). [para(6(a,1),41(a,1,2)),flip(a)].
% 1.79/2.09 424 mult(rd(A,B),i(A)) = i(B). [back_rewrite(47),rewrite([402(2)])].
% 1.79/2.09 472 mult(mult(A,B),mult(mult(i(A),i(B)),C)) = C. [para(10(a,1),392(a,1,2,1))].
% 1.79/2.09 547 rd(i(A),i(B)) = rd(B,A). [para(424(a,1),5(a,1,1))].
% 1.79/2.09 596 mult(mult(A,B),mult(i(B),i(A))) = i(op_k(B,A)). [para(54(a,1),424(a,1,1)),rewrite([10(3)])].
% 1.79/2.09 610 rd(A,i(B)) = rd(B,i(A)). [para(40(a,1),547(a,1,1))].
% 1.79/2.09 874 mult(mult(i(A),rd(A,B)),B) = op_k(rd(B,A),A). [para(6(a,1),56(a,1,2)),rewrite([402(3)])].
% 1.79/2.09 875 asoc(mult(i(A),i(B)),A,B) = op_k(i(A),mult(A,B)). [para(7(a,1),56(a,1,2)),rewrite([10(2),40(5),206(5)])].
% 1.79/2.09 910 mult(mult(mult(i(A),i(B)),A),B) = op_k(i(A),mult(A,B)). [back_rewrite(206),rewrite([875(9)])].
% 1.79/2.09 1506 i(op_k(A,B)) = op_k(i(A),i(B)). [para(13(a,1),472(a,1,2)),rewrite([596(5)])].
% 1.79/2.09 1522 mult(op_k(A,B),mult(op_k(i(A),i(B)),C)) = C. [para(56(a,1),472(a,1,1)),rewrite([10(5),40(3),40(3),10(4),596(6),1506(3)])].
% 1.79/2.09 1611 mult(op_k(A,B),op_k(i(A),i(B))) = unit. [para(1506(a,1),3(a,1,2))].
% 1.79/2.09 1612 mult(op_k(i(A),i(B)),op_k(A,B)) = unit. [para(1506(a,1),4(a,1,1))].
% 1.79/2.09 1681 mult(op_k(A,i(B)),op_k(i(A),B)) = unit. [para(40(a,1),1611(a,1,2,2))].
% 1.79/2.09 1698 mult(op_k(op_k(i(A),i(B)),i(C)),op_k(op_k(A,B),C)) = unit. [para(1506(a,1),1612(a,1,1,1))].
% 1.79/2.09 1809 mult(op_k(op_k(A,B),i(C)),op_k(op_k(i(A),i(B)),C)) = unit. [para(1506(a,1),1681(a,1,2,1))].
% 1.79/2.09 2827 mult(op_k(i(A),B),mult(op_k(A,i(B)),C)) = C. [para(40(a,1),1522(a,1,2,1,1))].
% 1.79/2.09 2927 mult(i(A),mult(mult(A,B),i(A))) = rd(B,A). [para(45(a,1),81(a,1,1,2)),rewrite([2(3),610(3),40(2)]),flip(a)].
% 1.79/2.09 2960 rd(mult(op_k(A,i(B)),C),op_k(i(A),B)) = mult(op_k(A,i(B)),mult(C,op_k(A,i(B)))). [para(1681(a,1),81(a,1,1,2,2)),rewrite([2(4)])].
% 1.79/2.09 3069 mult(mult(A,B),i(A)) = mult(A,rd(B,A)). [para(2927(a,1),7(a,1,2)),rewrite([40(2)]),flip(a)].
% 1.79/2.09 3259 mult(mult(i(A),B),A) = mult(i(A),rd(A,i(B))). [para(40(a,1),3069(a,1,2)),rewrite([610(6)])].
% 1.79/2.09 3311 op_k(rd(A,B),B) = op_k(i(B),mult(B,A)). [back_rewrite(910),rewrite([3259(4),40(3),874(4)])].
% 1.79/2.09 4292 op_k(mult(op_k(A,i(B)),mult(C,op_k(A,i(B)))),op_k(i(A),B)) = op_k(op_k(A,i(B)),C). [para(2827(a,1),3311(a,2,2)),rewrite([2960(6),1506(12),40(11)])].
% 1.79/2.09 6853 asoc(i(A),i(B),mult(B,A)) = op_k(B,A). [para(56(a,1),211(a,1,2)),rewrite([40(2),40(2),10(2),392(4),3(2),1(3)]),flip(a)].
% 1.79/2.09 6973 asoc(op_k(A,B),C,D) = unit. [para(6853(a,1),8(a,1,1))].
% 1.79/2.09 6992 op_k(A,op_k(B,C)) = unit. [para(1506(a,1),6853(a,1,1)),rewrite([6973(7)]),flip(a)].
% 1.79/2.09 7108 op_k(op_k(A,i(B)),C) = unit. [back_rewrite(4292),rewrite([6992(9)]),flip(a)].
% 1.79/2.09 7368 op_k(op_k(A,B),i(C)) = unit. [back_rewrite(1809),rewrite([7108(7),2(5)])].
% 1.79/2.09 7369 op_k(op_k(A,B),C) = unit. [back_rewrite(1698),rewrite([7368(5),1(4)])].
% 1.79/2.09 7370 $F # answer(goals). [resolve(7369,a,32,a)].
% 1.79/2.09
% 1.79/2.09 % SZS output end Refutation
% 1.79/2.09 ============================== end of proof ==========================
% 1.79/2.09
% 1.79/2.09 ============================== STATISTICS ============================
% 1.79/2.09
% 1.79/2.09 Given=191. Generated=20078. Kept=7360. proofs=1.
% 1.79/2.09 Usable=137. Sos=4395. Demods=3893. Limbo=262, Disabled=2588. Hints=0.
% 1.79/2.09 Megabytes=17.12.
% 1.79/2.09 User_CPU=1.07, System_CPU=0.01, Wall_clock=1.
% 1.79/2.09
% 1.79/2.09 ============================== end of statistics =====================
% 1.79/2.09
% 1.79/2.09 ============================== end of search =========================
% 1.79/2.09
% 1.79/2.09 THEOREM PROVED
% 1.79/2.09 % SZS status Unsatisfiable
% 1.79/2.09
% 1.79/2.09 Exiting with 1 proof.
% 1.79/2.09
% 1.79/2.09 Process 12922 exit (max_proofs) Tue Jun 14 04:39:21 2022
% 1.79/2.09 Prover9 interrupted
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