TSTP Solution File: GRP670-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP670-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:20:30 EDT 2022
% Result : Unsatisfiable 38.91s 39.21s
% Output : Refutation 38.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP670-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 16:05:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 7.16/7.43 ============================== Prover9 ===============================
% 7.16/7.43 Prover9 (32) version 2009-11A, November 2009.
% 7.16/7.43 Process 21860 was started by sandbox on n009.cluster.edu,
% 7.16/7.43 Mon Jun 13 16:05:23 2022
% 7.16/7.43 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21707_n009.cluster.edu".
% 7.16/7.43 ============================== end of head ===========================
% 7.16/7.43
% 7.16/7.43 ============================== INPUT =================================
% 7.16/7.43
% 7.16/7.43 % Reading from file /tmp/Prover9_21707_n009.cluster.edu
% 7.16/7.43
% 7.16/7.43 set(prolog_style_variables).
% 7.16/7.43 set(auto2).
% 7.16/7.43 % set(auto2) -> set(auto).
% 7.16/7.43 % set(auto) -> set(auto_inference).
% 7.16/7.43 % set(auto) -> set(auto_setup).
% 7.16/7.43 % set(auto_setup) -> set(predicate_elim).
% 7.16/7.43 % set(auto_setup) -> assign(eq_defs, unfold).
% 7.16/7.43 % set(auto) -> set(auto_limits).
% 7.16/7.43 % set(auto_limits) -> assign(max_weight, "100.000").
% 7.16/7.43 % set(auto_limits) -> assign(sos_limit, 20000).
% 7.16/7.43 % set(auto) -> set(auto_denials).
% 7.16/7.43 % set(auto) -> set(auto_process).
% 7.16/7.43 % set(auto2) -> assign(new_constants, 1).
% 7.16/7.43 % set(auto2) -> assign(fold_denial_max, 3).
% 7.16/7.43 % set(auto2) -> assign(max_weight, "200.000").
% 7.16/7.43 % set(auto2) -> assign(max_hours, 1).
% 7.16/7.43 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 7.16/7.43 % set(auto2) -> assign(max_seconds, 0).
% 7.16/7.43 % set(auto2) -> assign(max_minutes, 5).
% 7.16/7.43 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 7.16/7.43 % set(auto2) -> set(sort_initial_sos).
% 7.16/7.43 % set(auto2) -> assign(sos_limit, -1).
% 7.16/7.43 % set(auto2) -> assign(lrs_ticks, 3000).
% 7.16/7.43 % set(auto2) -> assign(max_megs, 400).
% 7.16/7.43 % set(auto2) -> assign(stats, some).
% 7.16/7.43 % set(auto2) -> clear(echo_input).
% 7.16/7.43 % set(auto2) -> set(quiet).
% 7.16/7.43 % set(auto2) -> clear(print_initial_clauses).
% 7.16/7.43 % set(auto2) -> clear(print_given).
% 7.16/7.43 assign(lrs_ticks,-1).
% 7.16/7.43 assign(sos_limit,10000).
% 7.16/7.43 assign(order,kbo).
% 7.16/7.43 set(lex_order_vars).
% 7.16/7.43 clear(print_given).
% 7.16/7.43
% 7.16/7.43 % formulas(sos). % not echoed (10 formulas)
% 7.16/7.43
% 7.16/7.43 ============================== end of input ==========================
% 7.16/7.43
% 7.16/7.43 % From the command line: assign(max_seconds, 300).
% 7.16/7.43
% 7.16/7.43 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 7.16/7.43
% 7.16/7.43 % Formulas that are not ordinary clauses:
% 7.16/7.43
% 7.16/7.43 ============================== end of process non-clausal formulas ===
% 7.16/7.43
% 7.16/7.43 ============================== PROCESS INITIAL CLAUSES ===============
% 7.16/7.43
% 7.16/7.43 ============================== PREDICATE ELIMINATION =================
% 7.16/7.43
% 7.16/7.43 ============================== end predicate elimination =============
% 7.16/7.43
% 7.16/7.43 Auto_denials:
% 7.16/7.43 % copying label goals to answer in negative clause
% 7.16/7.43
% 7.16/7.43 Term ordering decisions:
% 7.16/7.43
% 7.16/7.43 % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 7.16/7.43 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. i=0.
% 7.16/7.43
% 7.16/7.43 ============================== end of process initial clauses ========
% 7.16/7.43
% 7.16/7.43 ============================== CLAUSES FOR SEARCH ====================
% 7.16/7.43
% 7.16/7.43 ============================== end of clauses for search =============
% 7.16/7.43
% 7.16/7.43 ============================== SEARCH ================================
% 7.16/7.43
% 7.16/7.43 % Starting search at 0.01 seconds.
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=107.000, iters=3357
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=81.000, iters=3377
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=69.000, iters=3405
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=58.000, iters=3362
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=56.000, iters=3333
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=54.000, iters=3363
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=53.000, iters=3353
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=51.000, iters=3357
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=50.000, iters=3387
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=49.000, iters=3357
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=47.000, iters=3361
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=46.000, iters=3388
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=45.000, iters=3381
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=44.000, iters=3431
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=43.000, iters=3358
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=42.000, iters=3335
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=41.000, iters=3398
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=40.000, iters=3397
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=39.000, iters=3414
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=38.000, iters=3400
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=37.000, iters=3355
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=36.000, iters=3342
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=35.000, iters=3340
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=34.000, iters=3405
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=33.000, iters=3348
% 7.16/7.43
% 7.16/7.43 Low Water (keep): wt=32.000, iters=3345
% 7.16/7.43
% 7.16/7.43 Low Water (displace): id=14282, wt=28.000
% 7.16/7.43
% 38.91/39.21 Low Water (displace): id=14288, wt=26.000
% 38.91/39.21
% 38.91/39.21 Low Water (displace): id=14364, wt=24.000
% 38.91/39.21
% 38.91/39.21 Low Water (displace): id=14376, wt=23.000
% 38.91/39.21
% 38.91/39.21 Low Water (keep): wt=31.000, iters=3333
% 38.91/39.21
% 38.91/39.21 Low Water (displace): id=15094, wt=22.000
% 38.91/39.21
% 38.91/39.21 Low Water (keep): wt=30.000, iters=3333
% 38.91/39.21
% 38.91/39.21 Low Water (displace): id=18616, wt=21.000
% 38.91/39.21
% 38.91/39.21 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 17.12 sec).
% 38.91/39.21
% 38.91/39.21 Low Water (keep): wt=29.000, iters=3342
% 38.91/39.21
% 38.91/39.21 ============================== PROOF =================================
% 38.91/39.21 % SZS status Unsatisfiable
% 38.91/39.21 % SZS output start Refutation
% 38.91/39.21
% 38.91/39.21 % Proof 1 at 37.70 (+ 0.56) seconds: goals.
% 38.91/39.21 % Length of proof is 52.
% 38.91/39.21 % Level of proof is 14.
% 38.91/39.21 % Maximum clause weight is 35.000.
% 38.91/39.21 % Given clauses 802.
% 38.91/39.21
% 38.91/39.21 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 38.91/39.21 2 mult(unit,A) = A # label(c06) # label(axiom). [assumption].
% 38.91/39.21 3 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 38.91/39.21 5 mult(rd(A,B),B) = A # label(c03) # label(axiom). [assumption].
% 38.91/39.21 6 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 38.91/39.21 7 mult(i(A),mult(A,B)) = B # label(c07) # label(axiom). [assumption].
% 38.91/39.21 8 mult(mult(A,B),i(B)) = A # label(c08) # label(axiom). [assumption].
% 38.91/39.21 9 mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) # label(c09) # label(axiom). [assumption].
% 38.91/39.21 10 mult(mult(mult(A,mult(B,C)),A),B) = mult(mult(A,B),mult(C,mult(A,B))). [copy(9),flip(a)].
% 38.91/39.21 11 mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 38.91/39.21 12 mult(mult(a,mult(mult(b,c),b)),c) != mult(mult(a,b),mult(mult(c,b),c)) # answer(goals). [copy(11),flip(a)].
% 38.91/39.21 18 rd(A,ld(B,A)) = B. [para(3(a,1),6(a,1,1))].
% 38.91/39.21 21 ld(A,B) = mult(i(A),B). [para(3(a,1),7(a,1,2)),flip(a)].
% 38.91/39.21 24 rd(A,mult(B,A)) = i(B). [para(7(a,1),6(a,1,1))].
% 38.91/39.21 25 i(i(A)) = A. [back_rewrite(18),rewrite([21(1),24(3)])].
% 38.91/39.21 29 rd(A,B) = mult(A,i(B)). [para(5(a,1),8(a,1,1)),flip(a)].
% 38.91/39.21 30 mult(i(mult(A,B)),A) = i(B). [para(8(a,1),7(a,1,2))].
% 38.91/39.21 32 mult(mult(A,i(B)),B) = A. [back_rewrite(5),rewrite([29(1)])].
% 38.91/39.21 33 mult(mult(A,B),A) = mult(A,mult(B,A)). [para(10(a,1),1(a,1)),rewrite([1(2),1(2),2(4)]),flip(a)].
% 38.91/39.21 34 mult(mult(A,mult(B,A)),B) = mult(mult(A,B),mult(A,B)). [para(1(a,1),10(a,1,1,1,2)),rewrite([33(2),2(7)])].
% 38.91/39.21 36 mult(mult(A,i(B)),mult(mult(B,C),mult(A,i(B)))) = mult(mult(A,mult(C,A)),i(B)). [para(7(a,1),10(a,1,1,1,2)),rewrite([33(2)]),flip(a)].
% 38.91/39.21 45 mult(mult(a,mult(b,mult(c,b))),c) != mult(mult(a,b),mult(c,mult(b,c))) # answer(goals). [back_rewrite(12),rewrite([33(6),33(17)])].
% 38.91/39.21 46 mult(mult(A,mult(mult(B,C),A)),B) = mult(mult(A,B),mult(C,mult(A,B))). [back_rewrite(10),rewrite([33(3)])].
% 38.91/39.21 48 i(mult(A,B)) = mult(i(B),i(A)). [para(7(a,1),30(a,1,1,1)),flip(a)].
% 38.91/39.21 50 mult(mult(i(A),i(B)),mult(mult(B,A),C)) = C. [para(48(a,1),7(a,1,1))].
% 38.91/39.21 51 mult(mult(A,mult(B,C)),mult(i(C),i(B))) = A. [para(48(a,1),8(a,1,2))].
% 38.91/39.21 57 mult(i(A),mult(mult(A,B),i(A))) = mult(B,i(A)). [para(7(a,1),33(a,1,1)),flip(a)].
% 38.91/39.21 58 mult(mult(A,mult(B,A)),i(A)) = mult(A,B). [para(33(a,1),8(a,1,1))].
% 38.91/39.21 59 mult(mult(A,B),mult(i(B),mult(A,B))) = mult(A,mult(A,B)). [para(8(a,1),33(a,1,1)),flip(a)].
% 38.91/39.21 80 mult(mult(A,i(B)),mult(B,A)) = mult(A,A). [para(7(a,1),34(a,2,1)),rewrite([57(5),7(7)])].
% 38.91/39.21 83 mult(mult(A,mult(A,B)),i(B)) = mult(A,A). [para(8(a,1),34(a,2,1)),rewrite([59(5),8(7)])].
% 38.91/39.21 101 mult(mult(A,B),i(A)) = mult(A,mult(B,i(A))). [para(32(a,1),58(a,1,1,2))].
% 38.91/39.21 105 mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))). [para(58(a,1),34(a,1,1,2)),rewrite([7(3),7(7),7(8)]),flip(a)].
% 38.91/39.21 124 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [back_rewrite(34),rewrite([105(6)])].
% 38.91/39.21 125 mult(mult(A,i(B)),mult(B,B)) = mult(A,B). [para(80(a,1),7(a,1,2)),rewrite([48(3),25(2)])].
% 38.91/39.21 132 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(83(a,1),8(a,1,1)),rewrite([25(3)])].
% 38.91/39.21 144 mult(mult(A,B),mult(A,mult(B,A))) = mult(A,mult(B,mult(A,mult(B,A)))). [para(33(a,1),132(a,2,2)),rewrite([105(3),33(4),124(3)]),flip(a)].
% 38.91/39.21 163 mult(mult(A,i(B)),mult(mult(B,mult(C,B)),i(A))) = mult(mult(A,C),mult(B,i(A))). [para(36(a,1),7(a,1,2)),rewrite([48(3),25(2)])].
% 38.91/39.21 203 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(8(a,1),125(a,1,1)),flip(a)].
% 38.91/39.21 242 mult(mult(mult(A,mult(B,A)),i(C)),mult(mult(C,B),mult(A,i(C)))) = mult(mult(A,i(C)),mult(mult(C,B),mult(mult(A,mult(B,A)),i(C)))). [para(36(a,1),203(a,1,1)),rewrite([105(20),36(19)])].
% 38.91/39.21 310 mult(mult(A,i(B)),mult(mult(B,i(A)),C)) = C. [para(25(a,1),50(a,1,1,1))].
% 38.91/39.21 323 mult(mult(A,mult(B,i(C))),mult(C,i(B))) = A. [para(25(a,1),51(a,1,2,1))].
% 38.91/39.21 486 mult(mult(mult(A,mult(B,A)),i(C)),mult(C,i(A))) = mult(mult(A,i(C)),mult(C,B)). [para(36(a,1),101(a,1,1)),rewrite([48(7),25(6),48(16),25(15),323(16)])].
% 38.91/39.21 1001 mult(mult(A,mult(B,mult(A,B))),C) = mult(mult(A,B),mult(mult(A,B),C)). [para(105(a,1),132(a,1,1))].
% 38.91/39.21 9943 mult(mult(A,i(B)),mult(mult(B,C),mult(mult(A,mult(C,A)),i(B)))) = mult(mult(A,mult(C,mult(A,mult(C,A)))),i(B)). [para(163(a,1),36(a,1,2)),rewrite([242(9),7(15),203(13),105(12)])].
% 38.91/39.21 10138 mult(mult(mult(A,mult(B,A)),i(C)),mult(mult(C,B),mult(A,i(C)))) = mult(mult(A,mult(B,mult(A,mult(B,A)))),i(C)). [back_rewrite(242),rewrite([9943(18)])].
% 38.91/39.21 26964 mult(mult(mult(A,B),i(C)),mult(C,i(A))) = mult(mult(A,i(C)),mult(C,mult(B,i(A)))). [para(32(a,1),486(a,1,1,1,2))].
% 38.91/39.21 26974 mult(mult(mult(A,mult(B,A)),i(C)),mult(C,B)) = mult(mult(A,i(C)),mult(C,mult(B,mult(A,B)))). [para(486(a,1),124(a,2,2,2)),rewrite([163(11),10138(9),26964(9),1001(7),8(6),33(4),310(17)]),flip(a)].
% 38.91/39.21 26987 mult(mult(A,B),mult(mult(C,i(A)),mult(A,B))) = mult(A,mult(B,mult(C,B))). [para(486(a,1),144(a,1,2,2)),rewrite([163(7),310(11),33(6),26964(21),8(19),310(19),26974(14),310(15)])].
% 38.91/39.21 27033 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))). [para(8(a,1),26987(a,1,2,1))].
% 38.91/39.21 27049 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [para(26987(a,1),46(a,1,1)),rewrite([27033(11),7(8)])].
% 38.91/39.21 27050 $F # answer(goals). [resolve(27049,a,45,a)].
% 38.91/39.21
% 38.91/39.21 % SZS output end Refutation
% 38.91/39.21 ============================== end of proof ==========================
% 38.91/39.21
% 38.91/39.21 ============================== STATISTICS ============================
% 38.91/39.21
% 38.91/39.21 Given=802. Generated=1003044. Kept=27047. proofs=1.
% 38.91/39.21 Usable=771. Sos=9999. Demods=10737. Limbo=20, Disabled=16266. Hints=0.
% 38.91/39.21 Megabytes=29.53.
% 38.91/39.21 User_CPU=37.70, System_CPU=0.56, Wall_clock=38.
% 38.91/39.21
% 38.91/39.21 ============================== end of statistics =====================
% 38.91/39.21
% 38.91/39.21 ============================== end of search =========================
% 38.91/39.21
% 38.91/39.21 THEOREM PROVED
% 38.91/39.21 % SZS status Unsatisfiable
% 38.91/39.21
% 38.91/39.21 Exiting with 1 proof.
% 38.91/39.21
% 38.91/39.21 Process 21860 exit (max_proofs) Mon Jun 13 16:06:01 2022
% 38.91/39.21 Prover9 interrupted
%------------------------------------------------------------------------------