TSTP Solution File: GRP374-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP374-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:18:49 EDT 2022
% Result : Unsatisfiable 1.72s 2.00s
% Output : Refutation 1.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP374-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n025.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 : Tue Jun 14 03:43:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.72/2.00 ============================== Prover9 ===============================
% 1.72/2.00 Prover9 (32) version 2009-11A, November 2009.
% 1.72/2.00 Process 6340 was started by sandbox2 on n025.cluster.edu,
% 1.72/2.00 Tue Jun 14 03:43:55 2022
% 1.72/2.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6187_n025.cluster.edu".
% 1.72/2.00 ============================== end of head ===========================
% 1.72/2.00
% 1.72/2.00 ============================== INPUT =================================
% 1.72/2.00
% 1.72/2.00 % Reading from file /tmp/Prover9_6187_n025.cluster.edu
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% 1.72/2.00 set(prolog_style_variables).
% 1.72/2.00 set(auto2).
% 1.72/2.00 % set(auto2) -> set(auto).
% 1.72/2.00 % set(auto) -> set(auto_inference).
% 1.72/2.00 % set(auto) -> set(auto_setup).
% 1.72/2.00 % set(auto_setup) -> set(predicate_elim).
% 1.72/2.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.72/2.00 % set(auto) -> set(auto_limits).
% 1.72/2.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.72/2.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.72/2.00 % set(auto) -> set(auto_denials).
% 1.72/2.00 % set(auto) -> set(auto_process).
% 1.72/2.00 % set(auto2) -> assign(new_constants, 1).
% 1.72/2.00 % set(auto2) -> assign(fold_denial_max, 3).
% 1.72/2.00 % set(auto2) -> assign(max_weight, "200.000").
% 1.72/2.00 % set(auto2) -> assign(max_hours, 1).
% 1.72/2.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.72/2.00 % set(auto2) -> assign(max_seconds, 0).
% 1.72/2.00 % set(auto2) -> assign(max_minutes, 5).
% 1.72/2.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.72/2.00 % set(auto2) -> set(sort_initial_sos).
% 1.72/2.00 % set(auto2) -> assign(sos_limit, -1).
% 1.72/2.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.72/2.00 % set(auto2) -> assign(max_megs, 400).
% 1.72/2.00 % set(auto2) -> assign(stats, some).
% 1.72/2.00 % set(auto2) -> clear(echo_input).
% 1.72/2.00 % set(auto2) -> set(quiet).
% 1.72/2.00 % set(auto2) -> clear(print_initial_clauses).
% 1.72/2.00 % set(auto2) -> clear(print_given).
% 1.72/2.00 assign(lrs_ticks,-1).
% 1.72/2.00 assign(sos_limit,10000).
% 1.72/2.00 assign(order,kbo).
% 1.72/2.00 set(lex_order_vars).
% 1.72/2.00 clear(print_given).
% 1.72/2.00
% 1.72/2.00 % formulas(sos). % not echoed (40 formulas)
% 1.72/2.00
% 1.72/2.00 ============================== end of input ==========================
% 1.72/2.00
% 1.72/2.00 % From the command line: assign(max_seconds, 300).
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% 1.72/2.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
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% 1.72/2.00 % Formulas that are not ordinary clauses:
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% 1.72/2.00 ============================== end of process non-clausal formulas ===
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% 1.72/2.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 1.72/2.00 ============================== PREDICATE ELIMINATION =================
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% 1.72/2.00 ============================== end predicate elimination =============
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% 1.72/2.00 Auto_denials: (non-Horn, no changes).
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% 1.72/2.00 Term ordering decisions:
% 1.72/2.00
% 1.72/2.00 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 1.72/2.00 Function symbol KB weights: sk_c8=1. sk_c7=1. sk_c6=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. identity=1. multiply=1. inverse=0.
% 1.72/2.00
% 1.72/2.00 ============================== end of process initial clauses ========
% 1.72/2.00
% 1.72/2.00 ============================== CLAUSES FOR SEARCH ====================
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% 1.72/2.00 ============================== end of clauses for search =============
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% 1.72/2.00 ============================== SEARCH ================================
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% 1.72/2.00 % Starting search at 0.02 seconds.
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% 1.72/2.00 Low Water (keep): wt=44.000, iters=3512
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% 1.72/2.00 Low Water (keep): wt=43.000, iters=3453
% 1.72/2.00
% 1.72/2.00 Low Water (keep): wt=42.000, iters=3394
% 1.72/2.00
% 1.72/2.00 Low Water (keep): wt=41.000, iters=3399
% 1.72/2.00
% 1.72/2.00 Low Water (keep): wt=39.000, iters=3343
% 1.72/2.00
% 1.72/2.00 Low Water (keep): wt=38.000, iters=3368
% 1.72/2.00
% 1.72/2.00 Low Water (keep): wt=37.000, iters=3345
% 1.72/2.00
% 1.72/2.00 ============================== PROOF =================================
% 1.72/2.00 % SZS status Unsatisfiable
% 1.72/2.00 % SZS output start Refutation
% 1.72/2.00
% 1.72/2.00 % Proof 1 at 1.00 (+ 0.01) seconds.
% 1.72/2.00 % Length of proof is 57.
% 1.72/2.00 % Level of proof is 17.
% 1.72/2.00 % Maximum clause weight is 55.000.
% 1.72/2.00 % Given clauses 392.
% 1.72/2.00
% 1.72/2.00 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 1.72/2.00 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 1.72/2.00 4 inverse(sk_c8) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 1.72/2.00 5 inverse(sk_c1) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 1.72/2.00 9 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_1) # label(negated_conjecture). [assumption].
% 1.72/2.00 11 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 1.72/2.00 12 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 1.72/2.00 13 multiply(sk_c1,sk_c8) = sk_c7 | inverse(sk_c3) = sk_c8 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 1.72/2.00 16 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 1.72/2.00 28 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 1.72/2.00 31 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 1.72/2.00 39 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 1.72/2.00 40 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(C,sk_c8) != sk_c7 | inverse(C) != sk_c8 | multiply(sk_c8,D) != sk_c7 | multiply(E,sk_c8) != D | inverse(E) != sk_c8 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 1.72/2.00 41 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,C) != sk_c7 | multiply(D,sk_c8) != C | inverse(D) != sk_c8. [factor(40,b,h),merge(h)].
% 1.72/2.00 58 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 1.72/2.00 63 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),39(a,1,1)),rewrite([1(2)]),flip(a)].
% 1.72/2.00 64 inverse(sk_c8) = sk_c7 | multiply(sk_c8,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(9(b,1),39(a,1,1)),flip(b)].
% 1.72/2.00 149 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8. [para(2(a,1),41(b,1))].
% 1.72/2.00 250 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,B) != sk_c7 | identity != B. [factor(149,c,j),rewrite([2(37)])].
% 1.72/2.00 521 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),63(a,1,2))].
% 1.72/2.00 549 multiply(sk_c8,sk_c7) = sk_c6 | multiply(inverse(sk_c8),sk_c7) = sk_c6. [para(31(a,1),63(a,1,2))].
% 1.72/2.00 559 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(63(a,1),63(a,1,2))].
% 1.72/2.00 560 multiply(A,identity) = A. [back_rewrite(521),rewrite([559(4)])].
% 1.72/2.00 567 inverse(identity) = identity. [para(560(a,1),2(a,1))].
% 1.72/2.00 608 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c4. [para(58(b,1),63(a,1,2)),rewrite([560(8)])].
% 1.72/2.00 611 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c8) = identity. [para(608(b,1),2(a,1,1))].
% 1.72/2.00 726 multiply(A,inverse(A)) = identity. [para(559(a,1),2(a,1))].
% 1.72/2.00 757 inverse(inverse(A)) = A. [para(559(a,1),560(a,1)),rewrite([560(2)]),flip(a)].
% 1.72/2.00 797 inverse(sk_c8) != sk_c7 | identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(A,sk_c6) != sk_c7 | inverse(A) != sk_c6 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,B) != sk_c7 | identity != B. [back_rewrite(250),rewrite([757(10)]),xx(c)].
% 1.72/2.00 807 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = identity. [para(5(b,1),726(a,1,2))].
% 1.72/2.00 820 inverse(sk_c8) = sk_c7 | multiply(sk_c6,inverse(sk_c7)) = sk_c8. [para(726(a,1),64(b,1,2)),rewrite([560(7)]),flip(b)].
% 1.72/2.00 1029 inverse(sk_c8) = sk_c7 | identity = sk_c5. [para(611(b,1),12(b,1)),merge(b)].
% 1.72/2.00 1069 identity = sk_c5 | inverse(sk_c7) = sk_c8. [para(1029(a,1),757(a,1,1))].
% 1.72/2.00 1166 inverse(sk_c8) != sk_c7 | identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,A) != sk_c7 | identity != A. [para(2(a,1),797(d,1)),rewrite([757(18)]),xx(e),merge(d)].
% 1.72/2.00 1191 inverse(sk_c8) != sk_c7 | identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | inverse(sk_c8) != identity. [para(726(a,1),1166(e,1)),flip(f),merge(e)].
% 1.72/2.00 1200 inverse(sk_c1) = sk_c8 | identity = sk_c7. [para(807(b,1),16(b,1)),merge(b)].
% 1.72/2.00 1205 identity = sk_c7 | multiply(sk_c1,sk_c8) = identity. [para(1200(a,1),726(a,1,2))].
% 1.72/2.00 1298 identity = sk_c7 | inverse(sk_c3) = sk_c8. [para(1205(b,1),13(a,1)),merge(b)].
% 1.72/2.00 1370 identity = sk_c7 | multiply(sk_c3,sk_c8) = identity. [para(1298(b,1),726(a,1,2))].
% 1.72/2.00 2458 identity = sk_c7 | multiply(sk_c1,sk_c8) = sk_c7. [para(1370(b,1),28(b,1)),merge(c)].
% 1.72/2.00 5109 identity = sk_c7. [para(2458(b,1),1205(b,1)),flip(c),merge(b),merge(c)].
% 1.72/2.00 6706 inverse(sk_c8) != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6. [back_rewrite(1191),rewrite([5109(5),5109(20)]),xx(b),merge(d)].
% 1.72/2.00 6718 sk_c5 = sk_c7 | inverse(sk_c7) = sk_c8. [back_rewrite(1069),rewrite([5109(1)]),flip(a)].
% 1.72/2.00 6748 inverse(sk_c7) = sk_c7. [back_rewrite(567),rewrite([5109(1),5109(3)])].
% 1.72/2.00 6749 multiply(A,sk_c7) = A. [back_rewrite(560),rewrite([5109(1)])].
% 1.72/2.00 6850 sk_c5 = sk_c7 | sk_c7 = sk_c8. [back_rewrite(6718),rewrite([6748(5)])].
% 1.72/2.00 6864 inverse(sk_c8) = sk_c7 | sk_c6 = sk_c8. [back_rewrite(820),rewrite([6748(7),6749(7)])].
% 1.72/2.00 6869 inverse(sk_c8) != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | sk_c6 != sk_c8. [back_rewrite(6706),rewrite([6749(12)]),flip(c)].
% 1.72/2.00 6987 sk_c6 = sk_c8 | inverse(sk_c8) = sk_c6. [back_rewrite(549),rewrite([6749(3),6749(7)]),flip(a)].
% 1.72/2.00 7134 sk_c7 = sk_c8 | inverse(sk_c8) = sk_c7. [para(6850(a,1),11(b,1,2)),rewrite([6749(10)]),flip(c),merge(c)].
% 1.72/2.00 7249 sk_c6 = sk_c8 | sk_c6 = sk_c7. [para(6987(b,1),6864(a,1)),merge(c)].
% 1.72/2.00 7272 sk_c7 = sk_c8. [para(7134(b,1),757(a,1,1)),rewrite([6748(5)]),merge(b)].
% 1.72/2.00 7291 sk_c6 = sk_c8. [back_rewrite(7249),rewrite([7272(5)]),merge(b)].
% 1.72/2.00 7416 inverse(sk_c8) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c8. [back_rewrite(6869),rewrite([7272(3),7291(6),7272(8),7291(10)]),xx(c)].
% 1.72/2.00 7430 multiply(A,sk_c8) = A. [back_rewrite(6749),rewrite([7272(1)])].
% 1.72/2.00 7431 inverse(sk_c8) = sk_c8. [back_rewrite(6748),rewrite([7272(1),7272(3)])].
% 1.72/2.00 7531 $F. [back_rewrite(7416),rewrite([7431(2),7430(6)]),xx(a),xx(b)].
% 1.72/2.00
% 1.72/2.00 % SZS output end Refutation
% 1.72/2.00 ============================== end of proof ==========================
% 1.72/2.00
% 1.72/2.00 ============================== STATISTICS ============================
% 1.72/2.00
% 1.72/2.00 Given=392. Generated=20223. Kept=7530. proofs=1.
% 1.72/2.00 Usable=24. Sos=206. Demods=15. Limbo=109, Disabled=7231. Hints=0.
% 1.72/2.00 Megabytes=8.19.
% 1.72/2.00 User_CPU=1.00, System_CPU=0.01, Wall_clock=1.
% 1.72/2.00
% 1.72/2.00 ============================== end of statistics =====================
% 1.72/2.00
% 1.72/2.00 ============================== end of search =========================
% 1.72/2.00
% 1.72/2.00 THEOREM PROVED
% 1.72/2.00 % SZS status Unsatisfiable
% 1.72/2.00
% 1.72/2.00 Exiting with 1 proof.
% 1.72/2.00
% 1.72/2.00 Process 6340 exit (max_proofs) Tue Jun 14 03:43:56 2022
% 1.72/2.00 Prover9 interrupted
%------------------------------------------------------------------------------