TSTP Solution File: GRP774+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP774+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 11:21:00 EDT 2022
% Result : Theorem 10.81s 11.15s
% Output : Refutation 10.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP774+1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n015.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 04:35:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.32/2.62 ============================== Prover9 ===============================
% 2.32/2.62 Prover9 (32) version 2009-11A, November 2009.
% 2.32/2.62 Process 9679 was started by sandbox on n015.cluster.edu,
% 2.32/2.62 Mon Jun 13 04:35:08 2022
% 2.32/2.62 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9525_n015.cluster.edu".
% 2.32/2.62 ============================== end of head ===========================
% 2.32/2.62
% 2.32/2.62 ============================== INPUT =================================
% 2.32/2.62
% 2.32/2.62 % Reading from file /tmp/Prover9_9525_n015.cluster.edu
% 2.32/2.62
% 2.32/2.62 set(prolog_style_variables).
% 2.32/2.62 set(auto2).
% 2.32/2.62 % set(auto2) -> set(auto).
% 2.32/2.62 % set(auto) -> set(auto_inference).
% 2.32/2.62 % set(auto) -> set(auto_setup).
% 2.32/2.62 % set(auto_setup) -> set(predicate_elim).
% 2.32/2.62 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.32/2.62 % set(auto) -> set(auto_limits).
% 2.32/2.62 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.32/2.62 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.32/2.62 % set(auto) -> set(auto_denials).
% 2.32/2.62 % set(auto) -> set(auto_process).
% 2.32/2.62 % set(auto2) -> assign(new_constants, 1).
% 2.32/2.62 % set(auto2) -> assign(fold_denial_max, 3).
% 2.32/2.62 % set(auto2) -> assign(max_weight, "200.000").
% 2.32/2.62 % set(auto2) -> assign(max_hours, 1).
% 2.32/2.62 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.32/2.62 % set(auto2) -> assign(max_seconds, 0).
% 2.32/2.62 % set(auto2) -> assign(max_minutes, 5).
% 2.32/2.62 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.32/2.62 % set(auto2) -> set(sort_initial_sos).
% 2.32/2.62 % set(auto2) -> assign(sos_limit, -1).
% 2.32/2.62 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.32/2.62 % set(auto2) -> assign(max_megs, 400).
% 2.32/2.62 % set(auto2) -> assign(stats, some).
% 2.32/2.62 % set(auto2) -> clear(echo_input).
% 2.32/2.62 % set(auto2) -> set(quiet).
% 2.32/2.62 % set(auto2) -> clear(print_initial_clauses).
% 2.32/2.62 % set(auto2) -> clear(print_given).
% 2.32/2.62 assign(lrs_ticks,-1).
% 2.32/2.62 assign(sos_limit,10000).
% 2.32/2.62 assign(order,kbo).
% 2.32/2.62 set(lex_order_vars).
% 2.32/2.62 clear(print_given).
% 2.32/2.62
% 2.32/2.62 % formulas(sos). % not echoed (4 formulas)
% 2.32/2.62
% 2.32/2.62 ============================== end of input ==========================
% 2.32/2.62
% 2.32/2.62 % From the command line: assign(max_seconds, 300).
% 2.32/2.62
% 2.32/2.62 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.32/2.62
% 2.32/2.62 % Formulas that are not ordinary clauses:
% 2.32/2.62 1 (all C all B all A product(product(A,B),C) = product(A,product(B,C))) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.62 2 (all A product(A,A) = A) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.62 3 (all X0 all X1 (d(X0,X1) <-> product(X0,product(X1,X0)) = X0 & product(X1,product(X0,X1)) = X1)) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 2.32/2.62 4 -(all X2 all X3 all X4 all X5 (d(X2,X3) & d(X4,X5) -> d(product(X2,X4),product(X3,X5)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 2.32/2.62
% 2.32/2.62 ============================== end of process non-clausal formulas ===
% 2.32/2.62
% 2.32/2.62 ============================== PROCESS INITIAL CLAUSES ===============
% 2.32/2.62
% 2.32/2.62 ============================== PREDICATE ELIMINATION =================
% 2.32/2.62
% 2.32/2.62 ============================== end predicate elimination =============
% 2.32/2.62
% 2.32/2.62 Auto_denials:
% 2.32/2.62 % copying label goals to answer in negative clause
% 2.32/2.62
% 2.32/2.62 Term ordering decisions:
% 2.32/2.62 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. product=1.
% 2.32/2.62
% 2.32/2.62 ============================== end of process initial clauses ========
% 2.32/2.62
% 2.32/2.62 ============================== CLAUSES FOR SEARCH ====================
% 2.32/2.62
% 2.32/2.62 ============================== end of clauses for search =============
% 2.32/2.62
% 2.32/2.62 ============================== SEARCH ================================
% 2.32/2.62
% 2.32/2.62 % Starting search at 0.01 seconds.
% 2.32/2.62
% 2.32/2.62 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 0.53 sec).
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=107.000, iters=3370
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=91.000, iters=3336
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=89.000, iters=3336
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=71.000, iters=3388
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=65.000, iters=3383
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=61.000, iters=3348
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=60.000, iters=3421
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=59.000, iters=3405
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=58.000, iters=3373
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=57.000, iters=3356
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=56.000, iters=3350
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=55.000, iters=3445
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=49.000, iters=3353
% 2.32/2.62
% 2.32/2.62 Low Water (keep): wt=48.000, iters=3343
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=46.000, iters=3338
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=45.000, iters=3396
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=43.000, iters=3336
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=40.000, iters=3376
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=37.000, iters=3463
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=35.000, iters=3343
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=33.000, iters=3477
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=32.000, iters=3390
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=31.000, iters=3437
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=29.000, iters=3353
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=28.000, iters=3384
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=27.000, iters=3341
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=26.000, iters=3366
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=25.000, iters=3335
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=24.000, iters=3338
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=4513, wt=121.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=4509, wt=115.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=4550, wt=111.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=4344, wt=109.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=6215, wt=107.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=6677, wt=105.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=6664, wt=99.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=12604, wt=23.000
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=23.000, iters=3353
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=12707, wt=21.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=12711, wt=19.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=12879, wt=17.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=13549, wt=15.000
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=22.000, iters=3338
% 10.81/11.15
% 10.81/11.15 Low Water (keep): wt=21.000, iters=3336
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=18450, wt=13.000
% 10.81/11.15
% 10.81/11.15 Low Water (displace): id=18460, wt=11.000
% 10.81/11.15
% 10.81/11.15 ============================== PROOF =================================
% 10.81/11.15 % SZS status Theorem
% 10.81/11.15 % SZS output start Refutation
% 10.81/11.15
% 10.81/11.15 % Proof 1 at 9.94 (+ 0.23) seconds: goals.
% 10.81/11.15 % Length of proof is 40.
% 10.81/11.15 % Level of proof is 10.
% 10.81/11.15 % Maximum clause weight is 59.000.
% 10.81/11.15 % Given clauses 5231.
% 10.81/11.15
% 10.81/11.15 1 (all C all B all A product(product(A,B),C) = product(A,product(B,C))) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 10.81/11.15 2 (all A product(A,A) = A) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 10.81/11.15 3 (all X0 all X1 (d(X0,X1) <-> product(X0,product(X1,X0)) = X0 & product(X1,product(X0,X1)) = X1)) # label(sos03) # label(axiom) # label(non_clause). [assumption].
% 10.81/11.15 4 -(all X2 all X3 all X4 all X5 (d(X2,X3) & d(X4,X5) -> d(product(X2,X4),product(X3,X5)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 10.81/11.15 5 d(c1,c2) # label(goals) # label(negated_conjecture). [clausify(4)].
% 10.81/11.15 6 d(c3,c4) # label(goals) # label(negated_conjecture). [clausify(4)].
% 10.81/11.15 7 product(A,A) = A # label(sos02) # label(axiom). [clausify(2)].
% 10.81/11.15 8 product(product(A,B),C) = product(A,product(B,C)) # label(sos01) # label(axiom). [clausify(1)].
% 10.81/11.15 9 -d(product(c1,c3),product(c2,c4)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(4)].
% 10.81/11.15 10 -d(A,B) | product(A,product(B,A)) = A # label(sos03) # label(axiom). [clausify(3)].
% 10.81/11.15 11 -d(A,B) | product(B,product(A,B)) = B # label(sos03) # label(axiom). [clausify(3)].
% 10.81/11.15 12 d(A,B) | product(A,product(B,A)) != A | product(B,product(A,B)) != B # label(sos03) # label(axiom). [clausify(3)].
% 10.81/11.15 13 product(A,product(B,product(A,B))) = product(A,B). [para(8(a,1),7(a,1))].
% 10.81/11.15 15 product(c3,product(c4,c3)) = c3. [hyper(10,a,6,a)].
% 10.81/11.15 16 product(c1,product(c2,c1)) = c1. [hyper(10,a,5,a)].
% 10.81/11.15 17 product(c4,product(c3,c4)) = c4. [hyper(11,a,6,a)].
% 10.81/11.15 18 product(c2,product(c1,c2)) = c2. [hyper(11,a,5,a)].
% 10.81/11.15 20 d(A,product(B,C)) | product(A,product(B,product(C,A))) != A | product(B,product(C,product(A,product(B,C)))) != product(B,C). [para(8(a,1),12(b,1,2)),rewrite([8(10)])].
% 10.81/11.15 21 d(product(A,B),C) | product(A,product(B,product(C,product(A,B)))) != product(A,B) | product(C,product(A,product(B,C))) != C. [para(8(a,1),12(b,1)),rewrite([8(10)])].
% 10.81/11.15 22 product(A,product(B,product(A,product(B,C)))) = product(A,product(B,C)). [para(13(a,1),8(a,1,1)),rewrite([8(2),8(5),8(4)]),flip(a)].
% 10.81/11.15 23 product(A,product(B,product(C,product(A,product(B,C))))) = product(A,product(B,C)). [para(13(a,1),8(a,1)),rewrite([8(2),8(4)]),flip(a)].
% 10.81/11.15 32 product(c1,product(c2,product(c1,A))) = product(c1,A). [para(16(a,1),8(a,1,1)),rewrite([8(7)]),flip(a)].
% 10.81/11.15 39 product(c2,product(c1,product(c2,A))) = product(c2,A). [para(18(a,1),8(a,1,1)),rewrite([8(7)]),flip(a)].
% 10.81/11.15 43 d(A,product(B,product(C,D))) | product(A,product(B,product(C,product(D,A)))) != A | product(B,product(C,product(D,product(A,product(B,product(C,D)))))) != product(B,product(C,D)). [para(8(a,1),20(b,1,2,2)),rewrite([8(13)])].
% 10.81/11.15 67 product(A,product(B,product(C,product(A,product(B,product(C,D)))))) = product(A,product(B,product(C,D))). [para(22(a,1),8(a,1)),rewrite([8(3),8(6)]),flip(a)].
% 10.81/11.15 86 product(A,product(B,product(C,product(D,product(A,product(B,product(C,D))))))) = product(A,product(B,product(C,D))). [para(23(a,1),8(a,1)),rewrite([8(3),8(6)]),flip(a)].
% 10.81/11.15 91 d(product(A,B),product(C,product(D,product(B,product(C,D))))) | product(A,product(B,product(C,product(D,product(A,B))))) != product(A,B) | product(C,product(D,product(B,product(C,product(D,product(A,product(B,product(C,D)))))))) != product(C,product(D,product(B,product(C,D)))). [para(23(a,1),21(c,1,2,2)),rewrite([8(12),8(11),8(10),8(9),67(13),8(21),8(20),8(19),8(18)])].
% 10.81/11.15 94 product(c1,product(A,product(c2,product(c1,A)))) = product(c1,A). [para(23(a,1),32(a,1,2)),rewrite([32(6)]),flip(a)].
% 10.81/11.15 193 d(product(A,product(B,product(A,C))),product(D,product(E,B))) | product(A,product(B,product(A,product(C,product(D,product(E,product(B,product(A,C)))))))) != product(A,product(B,product(A,C))) | product(D,product(E,product(B,product(A,product(C,product(D,product(E,B))))))) != product(D,product(E,B)). [para(22(a,1),43(b,1,2,2,2)),rewrite([8(14),8(13),8(12),8(24),8(23),8(22),22(25)])].
% 10.81/11.15 419 product(c1,product(A,product(c2,product(c1,product(A,B))))) = product(c1,product(A,B)). [para(94(a,1),8(a,1,1)),rewrite([8(3),8(10),8(9),8(8)]),flip(a)].
% 10.81/11.15 420 product(c1,product(A,product(B,product(c2,product(c1,product(A,B)))))) = product(c1,product(A,B)). [para(8(a,1),94(a,1,2))].
% 10.81/11.15 543 product(A,product(c3,product(c4,product(A,c3)))) = product(A,c3). [para(15(a,1),67(a,1,2,2,2,2)),rewrite([15(12)])].
% 10.81/11.15 545 product(A,product(c4,product(c3,product(A,c4)))) = product(A,c4). [para(17(a,1),67(a,1,2,2,2,2)),rewrite([17(12)])].
% 10.81/11.15 555 product(A,product(c2,product(c1,product(A,product(c2,B))))) = product(A,product(c2,B)). [para(39(a,1),67(a,1,2,2,2,2)),rewrite([39(14)])].
% 10.81/11.15 1408 d(product(c1,A),product(B,product(C,product(A,product(c2,product(c1,product(A,product(B,C)))))))) | product(c1,product(A,product(B,product(C,product(c1,A))))) != product(c1,A). [para(94(a,1),91(b,1,2,2,2,2)),rewrite([94(7),8(9),8(8),8(7),8(23),8(22),8(21),419(24),94(26),8(35),8(34),8(33),419(36),8(34),8(33),8(32),86(32),8(38),8(37),8(36)]),xx(c)].
% 10.81/11.15 5915 d(product(c2,product(A,product(c2,product(c1,product(B,A))))),product(c1,product(B,A))). [para(420(a,1),193(b,1,2,2,2,2)),rewrite([7(21),7(38),420(38)]),xx(b),xx(c)].
% 10.81/11.15 19381 d(product(c2,product(c4,product(c1,c3))),product(c1,c3)). [para(543(a,1),5915(a,1,2,2,2)),rewrite([8(12),8(11),94(11),543(16)])].
% 10.81/11.15 19390 product(c1,product(c3,product(c2,product(c4,product(c1,c3))))) = product(c1,c3). [hyper(11,a,19381,a),rewrite([8(14),8(13),7(12),8(11)])].
% 10.81/11.15 19404 d(product(c1,c3),product(c2,c4)). [hyper(1408,b,19390,a),rewrite([555(16),545(12)])].
% 10.81/11.15 19405 $F # answer(goals). [resolve(19404,a,9,a)].
% 10.81/11.15
% 10.81/11.15 % SZS output end Refutation
% 10.81/11.15 ============================== end of proof ==========================
% 10.81/11.15
% 10.81/11.15 ============================== STATISTICS ============================
% 10.81/11.15
% 10.81/11.15 Given=5231. Generated=447663. Kept=19400. proofs=1.
% 10.81/11.15 Usable=5074. Sos=9857. Demods=243. Limbo=0, Disabled=4476. Hints=0.
% 10.81/11.15 Megabytes=19.08.
% 10.81/11.15 User_CPU=9.94, System_CPU=0.23, Wall_clock=10.
% 10.81/11.15
% 10.81/11.15 ============================== end of statistics =====================
% 10.81/11.15
% 10.81/11.15 ============================== end of search =========================
% 10.81/11.15
% 10.81/11.15 THEOREM PROVED
% 10.81/11.15 % SZS status Theorem
% 10.81/11.15
% 10.81/11.15 Exiting with 1 proof.
% 10.81/11.15
% 10.81/11.15 Process 9679 exit (max_proofs) Mon Jun 13 04:35:18 2022
% 10.81/11.15 Prover9 interrupted
%------------------------------------------------------------------------------