TSTP Solution File: GRP372-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP372-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 11:18:48 EDT 2022
% Result : Unsatisfiable 1.58s 1.91s
% Output : Refutation 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP372-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 05:22:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.58/1.91 ============================== Prover9 ===============================
% 1.58/1.91 Prover9 (32) version 2009-11A, November 2009.
% 1.58/1.91 Process 23035 was started by sandbox2 on n019.cluster.edu,
% 1.58/1.91 Tue Jun 14 05:22:25 2022
% 1.58/1.91 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22628_n019.cluster.edu".
% 1.58/1.91 ============================== end of head ===========================
% 1.58/1.91
% 1.58/1.91 ============================== INPUT =================================
% 1.58/1.91
% 1.58/1.91 % Reading from file /tmp/Prover9_22628_n019.cluster.edu
% 1.58/1.91
% 1.58/1.91 set(prolog_style_variables).
% 1.58/1.91 set(auto2).
% 1.58/1.91 % set(auto2) -> set(auto).
% 1.58/1.91 % set(auto) -> set(auto_inference).
% 1.58/1.91 % set(auto) -> set(auto_setup).
% 1.58/1.91 % set(auto_setup) -> set(predicate_elim).
% 1.58/1.91 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.58/1.91 % set(auto) -> set(auto_limits).
% 1.58/1.91 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.58/1.91 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.58/1.91 % set(auto) -> set(auto_denials).
% 1.58/1.91 % set(auto) -> set(auto_process).
% 1.58/1.91 % set(auto2) -> assign(new_constants, 1).
% 1.58/1.91 % set(auto2) -> assign(fold_denial_max, 3).
% 1.58/1.91 % set(auto2) -> assign(max_weight, "200.000").
% 1.58/1.91 % set(auto2) -> assign(max_hours, 1).
% 1.58/1.91 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.58/1.91 % set(auto2) -> assign(max_seconds, 0).
% 1.58/1.91 % set(auto2) -> assign(max_minutes, 5).
% 1.58/1.91 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.58/1.91 % set(auto2) -> set(sort_initial_sos).
% 1.58/1.91 % set(auto2) -> assign(sos_limit, -1).
% 1.58/1.91 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.58/1.91 % set(auto2) -> assign(max_megs, 400).
% 1.58/1.91 % set(auto2) -> assign(stats, some).
% 1.58/1.91 % set(auto2) -> clear(echo_input).
% 1.58/1.91 % set(auto2) -> set(quiet).
% 1.58/1.91 % set(auto2) -> clear(print_initial_clauses).
% 1.58/1.91 % set(auto2) -> clear(print_given).
% 1.58/1.91 assign(lrs_ticks,-1).
% 1.58/1.91 assign(sos_limit,10000).
% 1.58/1.91 assign(order,kbo).
% 1.58/1.91 set(lex_order_vars).
% 1.58/1.91 clear(print_given).
% 1.58/1.91
% 1.58/1.91 % formulas(sos). % not echoed (40 formulas)
% 1.58/1.91
% 1.58/1.91 ============================== end of input ==========================
% 1.58/1.91
% 1.58/1.91 % From the command line: assign(max_seconds, 300).
% 1.58/1.91
% 1.58/1.91 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.58/1.91
% 1.58/1.91 % Formulas that are not ordinary clauses:
% 1.58/1.91
% 1.58/1.91 ============================== end of process non-clausal formulas ===
% 1.58/1.91
% 1.58/1.91 ============================== PROCESS INITIAL CLAUSES ===============
% 1.58/1.91
% 1.58/1.91 ============================== PREDICATE ELIMINATION =================
% 1.58/1.91
% 1.58/1.91 ============================== end predicate elimination =============
% 1.58/1.91
% 1.58/1.91 Auto_denials: (non-Horn, no changes).
% 1.58/1.91
% 1.58/1.91 Term ordering decisions:
% 1.58/1.91
% 1.58/1.91 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 1.58/1.91 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.
% 1.58/1.91
% 1.58/1.91 ============================== end of process initial clauses ========
% 1.58/1.91
% 1.58/1.91 ============================== CLAUSES FOR SEARCH ====================
% 1.58/1.91
% 1.58/1.91 ============================== end of clauses for search =============
% 1.58/1.91
% 1.58/1.91 ============================== SEARCH ================================
% 1.58/1.91
% 1.58/1.91 % Starting search at 0.02 seconds.
% 1.58/1.91
% 1.58/1.91 Low Water (keep): wt=36.000, iters=3387
% 1.58/1.91
% 1.58/1.91 Low Water (keep): wt=35.000, iters=3337
% 1.58/1.91
% 1.58/1.91 Low Water (keep): wt=34.000, iters=3346
% 1.58/1.91
% 1.58/1.91 ============================== PROOF =================================
% 1.58/1.91 % SZS status Unsatisfiable
% 1.58/1.91 % SZS output start Refutation
% 1.58/1.91
% 1.58/1.91 % Proof 1 at 0.88 (+ 0.02) seconds.
% 1.58/1.91 % Length of proof is 62.
% 1.58/1.91 % Level of proof is 17.
% 1.58/1.91 % Maximum clause weight is 55.000.
% 1.58/1.91 % Given clauses 392.
% 1.58/1.91
% 1.58/1.91 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 1.58/1.91 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 1.58/1.91 4 inverse(sk_c8) = sk_c7 | inverse(sk_c4) = sk_c8 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 1.58/1.91 5 inverse(sk_c1) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 1.58/1.91 11 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c5) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 1.58/1.91 12 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c8) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 1.58/1.91 13 multiply(sk_c1,sk_c8) = sk_c7 | inverse(sk_c3) = sk_c8 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 1.58/1.91 16 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 1.58/1.91 23 inverse(sk_c2) = sk_c7 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 1.58/1.91 28 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c3,sk_c8) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 1.58/1.91 35 multiply(sk_c2,sk_c7) = sk_c6 | multiply(sk_c8,sk_c7) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 1.58/1.91 39 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 1.58/1.91 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_c7) != sk_c6 | inverse(B) != sk_c7 | 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].
% 1.58/1.91 41 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8 | multiply(sk_c8,C) != sk_c7 | multiply(D,sk_c8) != C | inverse(D) != sk_c8. [factor(40,a,f),merge(f)].
% 1.58/1.91 43 inverse(sk_c8) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,B) != sk_c7 | multiply(C,sk_c8) != B | inverse(C) != sk_c8. [factor(41,b,f),merge(f)].
% 1.58/1.91 55 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c4) = identity. [para(4(b,1),2(a,1,1))].
% 1.58/1.91 60 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),39(a,1,1)),rewrite([1(2)]),flip(a)].
% 1.58/1.91 89 inverse(sk_c2) = sk_c7 | multiply(sk_c8,multiply(sk_c7,A)) = multiply(sk_c6,A). [para(23(b,1),39(a,1,1)),flip(b)].
% 1.58/1.91 142 inverse(sk_c8) != sk_c7 | identity != sk_c7 | inverse(inverse(sk_c8)) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,A) != sk_c7 | multiply(B,sk_c8) != A | inverse(B) != sk_c8. [para(2(a,1),43(b,1))].
% 1.58/1.91 302 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),60(a,1,2))].
% 1.58/1.91 340 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(60(a,1),60(a,1,2))].
% 1.58/1.91 341 multiply(A,identity) = A. [back_rewrite(302),rewrite([340(4)])].
% 1.58/1.91 346 inverse(identity) = identity. [para(341(a,1),2(a,1))].
% 1.58/1.91 368 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c4. [para(55(b,1),60(a,1,2)),rewrite([341(8)])].
% 1.58/1.91 371 inverse(sk_c8) = sk_c7 | multiply(sk_c4,sk_c8) = identity. [para(368(b,1),2(a,1,1))].
% 1.58/1.91 464 multiply(A,inverse(A)) = identity. [para(340(a,1),2(a,1))].
% 1.58/1.91 479 multiply(A,multiply(inverse(A),B)) = B. [para(340(a,1),60(a,1))].
% 1.58/1.91 480 inverse(inverse(A)) = A. [para(340(a,1),341(a,1)),rewrite([341(2)]),flip(a)].
% 1.58/1.91 517 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 | multiply(B,sk_c8) != A | inverse(B) != sk_c8. [back_rewrite(142),rewrite([480(10)]),xx(c)].
% 1.58/1.91 524 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c8) = identity. [para(5(b,1),464(a,1,2))].
% 1.58/1.91 776 inverse(sk_c8) = sk_c7 | identity = sk_c5. [para(371(b,1),12(b,1)),merge(b)].
% 1.58/1.91 847 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 | multiply(B,multiply(C,sk_c8)) != A | inverse(multiply(B,C)) != sk_c8. [para(39(a,1),517(f,1))].
% 1.58/1.91 873 identity = sk_c5 | inverse(sk_c7) = sk_c8. [para(776(a,1),480(a,1,1))].
% 1.58/1.91 993 inverse(sk_c1) = sk_c8 | identity = sk_c7. [para(524(b,1),16(b,1)),merge(b)].
% 1.58/1.91 1002 identity = sk_c7 | multiply(sk_c1,sk_c8) = identity. [para(993(a,1),464(a,1,2))].
% 1.58/1.91 1094 identity = sk_c7 | inverse(sk_c3) = sk_c8. [para(1002(b,1),13(a,1)),merge(b)].
% 1.58/1.91 1168 identity = sk_c7 | multiply(sk_c3,sk_c8) = identity. [para(1094(b,1),464(a,1,2))].
% 1.58/1.91 2389 identity = sk_c7 | multiply(sk_c1,sk_c8) = sk_c7. [para(1168(b,1),28(b,1)),merge(c)].
% 1.58/1.91 4662 inverse(sk_c2) = sk_c7 | multiply(sk_c6,inverse(sk_c7)) = sk_c8. [para(464(a,1),89(b,1,2)),rewrite([341(7)]),flip(b)].
% 1.58/1.91 4711 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 | B != A | inverse(multiply(B,inverse(sk_c8))) != sk_c8. [para(2(a,1),847(f,1,2)),rewrite([341(23)])].
% 1.58/1.91 4765 inverse(sk_c8) != sk_c7 | identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | sk_c7 != A | multiply(inverse(sk_c8),A) != B | inverse(multiply(B,inverse(sk_c8))) != sk_c8. [para(479(a,1),4711(e,1)),flip(e),flip(f)].
% 1.58/1.91 4778 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 | A != B | inverse(multiply(B,inverse(sk_c8))) != sk_c8. [para(60(a,1),4765(f,1)),flip(e)].
% 1.58/1.91 4929 identity = sk_c7. [para(2389(b,1),1002(b,1)),flip(c),merge(b),merge(c)].
% 1.58/1.91 5000 inverse(sk_c8) != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | multiply(sk_c8,sk_c7) != sk_c6 | multiply(sk_c8,A) != sk_c7 | A != B | inverse(multiply(B,inverse(sk_c8))) != sk_c8. [back_rewrite(4778),rewrite([4929(5)]),xx(b)].
% 1.58/1.91 6183 sk_c5 = sk_c7 | inverse(sk_c7) = sk_c8. [back_rewrite(873),rewrite([4929(1)]),flip(a)].
% 1.58/1.91 6339 multiply(A,inverse(A)) = sk_c7. [back_rewrite(464),rewrite([4929(3)])].
% 1.58/1.91 6345 inverse(sk_c7) = sk_c7. [back_rewrite(346),rewrite([4929(1),4929(3)])].
% 1.58/1.91 6346 multiply(A,sk_c7) = A. [back_rewrite(341),rewrite([4929(1)])].
% 1.58/1.91 6354 multiply(sk_c7,A) = A. [back_rewrite(1),rewrite([4929(1)])].
% 1.58/1.91 6359 inverse(sk_c8) != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | sk_c6 != sk_c8. [factor(5000,a,e),rewrite([6346(12),6339(16),6354(19),480(18)]),flip(c),xx(d),xx(e)].
% 1.58/1.91 6360 sk_c5 = sk_c7 | sk_c7 = sk_c8. [back_rewrite(6183),rewrite([6345(5)])].
% 1.58/1.91 6362 inverse(sk_c2) = sk_c7 | sk_c6 = sk_c8. [back_rewrite(4662),rewrite([6345(7),6346(7)])].
% 1.58/1.91 6558 sk_c2 = sk_c6 | sk_c6 = sk_c8. [back_rewrite(35),rewrite([6346(3),6346(6)]),flip(b)].
% 1.58/1.91 6661 sk_c7 = sk_c8 | inverse(sk_c8) = sk_c7. [para(6360(a,1),11(b,1,2)),rewrite([6346(10)]),flip(c),merge(c)].
% 1.58/1.91 6682 sk_c6 = sk_c8 | sk_c2 = sk_c7. [para(6362(a,1),480(a,1,1)),rewrite([6345(5)]),flip(b)].
% 1.58/1.91 6684 sk_c6 = sk_c8 | sk_c6 = sk_c7. [para(6682(b,1),6558(a,1)),flip(b),merge(c)].
% 1.58/1.91 6839 sk_c7 = sk_c8. [para(6661(b,1),480(a,1,1)),rewrite([6345(5)]),merge(b)].
% 1.58/1.91 6926 sk_c6 = sk_c8. [back_rewrite(6684),rewrite([6839(5)]),merge(b)].
% 1.58/1.91 7037 inverse(sk_c8) != sk_c8 | multiply(sk_c8,sk_c8) != sk_c8. [back_rewrite(6359),rewrite([6839(3),6926(6),6839(8),6926(10)]),xx(c)].
% 1.58/1.91 7049 multiply(A,sk_c8) = A. [back_rewrite(6346),rewrite([6839(1)])].
% 1.58/1.91 7050 inverse(sk_c8) = sk_c8. [back_rewrite(6345),rewrite([6839(1),6839(3)])].
% 1.58/1.91 7123 $F. [back_rewrite(7037),rewrite([7050(2),7049(6)]),xx(a),xx(b)].
% 1.58/1.91
% 1.58/1.91 % SZS output end Refutation
% 1.58/1.91 ============================== end of proof ==========================
% 1.58/1.91
% 1.58/1.91 ============================== STATISTICS ============================
% 1.58/1.91
% 1.58/1.91 Given=392. Generated=21507. Kept=7122. proofs=1.
% 1.58/1.91 Usable=24. Sos=258. Demods=15. Limbo=82, Disabled=6798. Hints=0.
% 1.58/1.91 Megabytes=7.39.
% 1.58/1.91 User_CPU=0.88, System_CPU=0.02, Wall_clock=1.
% 1.58/1.91
% 1.58/1.91 ============================== end of statistics =====================
% 1.58/1.91
% 1.58/1.91 ============================== end of search =========================
% 1.58/1.91
% 1.58/1.91 THEOREM PROVED
% 1.58/1.91 % SZS status Unsatisfiable
% 1.58/1.91
% 1.58/1.91 Exiting with 1 proof.
% 1.58/1.91
% 1.58/1.91 Process 23035 exit (max_proofs) Tue Jun 14 05:22:26 2022
% 1.58/1.91 Prover9 interrupted
%------------------------------------------------------------------------------