TSTP Solution File: GRP243-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP243-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 11:18:18 EDT 2022
% Result : Unsatisfiable 4.06s 4.36s
% Output : Refutation 4.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP243-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.35 % Computer : n004.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Mon Jun 13 22:09:09 EDT 2022
% 0.12/0.35 % CPUTime :
% 4.06/4.35 ============================== Prover9 ===============================
% 4.06/4.35 Prover9 (32) version 2009-11A, November 2009.
% 4.06/4.35 Process 25197 was started by sandbox on n004.cluster.edu,
% 4.06/4.35 Mon Jun 13 22:09:09 2022
% 4.06/4.35 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25044_n004.cluster.edu".
% 4.06/4.35 ============================== end of head ===========================
% 4.06/4.35
% 4.06/4.35 ============================== INPUT =================================
% 4.06/4.35
% 4.06/4.35 % Reading from file /tmp/Prover9_25044_n004.cluster.edu
% 4.06/4.35
% 4.06/4.35 set(prolog_style_variables).
% 4.06/4.35 set(auto2).
% 4.06/4.35 % set(auto2) -> set(auto).
% 4.06/4.35 % set(auto) -> set(auto_inference).
% 4.06/4.35 % set(auto) -> set(auto_setup).
% 4.06/4.35 % set(auto_setup) -> set(predicate_elim).
% 4.06/4.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.06/4.35 % set(auto) -> set(auto_limits).
% 4.06/4.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.06/4.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.06/4.35 % set(auto) -> set(auto_denials).
% 4.06/4.35 % set(auto) -> set(auto_process).
% 4.06/4.35 % set(auto2) -> assign(new_constants, 1).
% 4.06/4.35 % set(auto2) -> assign(fold_denial_max, 3).
% 4.06/4.35 % set(auto2) -> assign(max_weight, "200.000").
% 4.06/4.35 % set(auto2) -> assign(max_hours, 1).
% 4.06/4.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.06/4.35 % set(auto2) -> assign(max_seconds, 0).
% 4.06/4.35 % set(auto2) -> assign(max_minutes, 5).
% 4.06/4.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.06/4.35 % set(auto2) -> set(sort_initial_sos).
% 4.06/4.35 % set(auto2) -> assign(sos_limit, -1).
% 4.06/4.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.06/4.35 % set(auto2) -> assign(max_megs, 400).
% 4.06/4.35 % set(auto2) -> assign(stats, some).
% 4.06/4.35 % set(auto2) -> clear(echo_input).
% 4.06/4.35 % set(auto2) -> set(quiet).
% 4.06/4.35 % set(auto2) -> clear(print_initial_clauses).
% 4.06/4.35 % set(auto2) -> clear(print_given).
% 4.06/4.35 assign(lrs_ticks,-1).
% 4.06/4.35 assign(sos_limit,10000).
% 4.06/4.35 assign(order,kbo).
% 4.06/4.35 set(lex_order_vars).
% 4.06/4.35 clear(print_given).
% 4.06/4.35
% 4.06/4.35 % formulas(sos). % not echoed (67 formulas)
% 4.06/4.35
% 4.06/4.35 ============================== end of input ==========================
% 4.06/4.35
% 4.06/4.35 % From the command line: assign(max_seconds, 300).
% 4.06/4.35
% 4.06/4.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.06/4.35
% 4.06/4.35 % Formulas that are not ordinary clauses:
% 4.06/4.35
% 4.06/4.35 ============================== end of process non-clausal formulas ===
% 4.06/4.35
% 4.06/4.35 ============================== PROCESS INITIAL CLAUSES ===============
% 4.06/4.35
% 4.06/4.35 ============================== PREDICATE ELIMINATION =================
% 4.06/4.35
% 4.06/4.35 ============================== end predicate elimination =============
% 4.06/4.35
% 4.06/4.35 Auto_denials: (non-Horn, no changes).
% 4.06/4.35
% 4.06/4.35 Term ordering decisions:
% 4.06/4.35
% 4.06/4.35 % Assigning unary symbol inverse kb_weight 0 and highest precedence (16).
% 4.06/4.35 Function symbol KB weights: sk_c11=1. sk_c12=1. sk_c10=1. sk_c9=1. sk_c5=1. sk_c6=1. sk_c7=1. sk_c8=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 4.06/4.35
% 4.06/4.35 ============================== end of process initial clauses ========
% 4.06/4.35
% 4.06/4.35 ============================== CLAUSES FOR SEARCH ====================
% 4.06/4.35
% 4.06/4.35 ============================== end of clauses for search =============
% 4.06/4.35
% 4.06/4.35 ============================== SEARCH ================================
% 4.06/4.35
% 4.06/4.35 % Starting search at 0.07 seconds.
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=58.000, iters=3438
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=54.000, iters=3431
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=50.000, iters=3370
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=49.000, iters=3337
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=47.000, iters=3481
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=46.000, iters=3436
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=44.000, iters=3504
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=43.000, iters=3363
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=42.000, iters=3368
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=41.000, iters=3400
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=35.000, iters=3483
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=34.000, iters=3426
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=33.000, iters=3369
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=32.000, iters=3367
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=31.000, iters=3426
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=30.000, iters=3345
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=29.000, iters=3336
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=28.000, iters=3348
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=27.000, iters=3373
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=26.000, iters=3344
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=25.000, iters=3395
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=24.000, iters=3336
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=23.000, iters=3364
% 4.06/4.35
% 4.06/4.35 Low Water (keep): wt=22.000, iters=3337
% 4.06/4.35
% 4.06/4.35 ============================== PROOF =================================
% 4.06/4.36 % SZS status Unsatisfiable
% 4.06/4.36 % SZS output start Refutation
% 4.06/4.36
% 4.06/4.36 % Proof 1 at 3.31 (+ 0.05) seconds.
% 4.06/4.36 % Length of proof is 97.
% 4.06/4.36 % Level of proof is 21.
% 4.06/4.36 % Maximum clause weight is 73.000.
% 4.06/4.36 % Given clauses 718.
% 4.06/4.36
% 4.06/4.36 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 4.06/4.36 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 4.06/4.36 3 inverse(sk_c1) = sk_c12 | inverse(sk_c6) = sk_c12 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 4.06/4.36 5 inverse(sk_c1) = sk_c12 | inverse(sk_c8) = sk_c9 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 4.06/4.36 7 inverse(sk_c2) = sk_c11 | inverse(sk_c7) = sk_c11 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 4.06/4.36 9 inverse(sk_c3) = sk_c12 | inverse(sk_c6) = sk_c12 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 4.06/4.36 17 multiply(sk_c1,sk_c12) = sk_c11 | inverse(sk_c8) = sk_c9 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 4.06/4.36 20 inverse(sk_c1) = sk_c12 | multiply(sk_c8,sk_c9) = sk_c11 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 4.06/4.36 23 multiply(sk_c2,sk_c11) = sk_c10 | inverse(sk_c7) = sk_c11 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 4.06/4.36 26 inverse(sk_c2) = sk_c11 | multiply(sk_c7,sk_c10) = sk_c11 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 4.06/4.36 29 inverse(sk_c3) = sk_c12 | multiply(sk_c6,sk_c11) = sk_c12 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 4.06/4.36 33 multiply(sk_c3,sk_c11) = sk_c12 | inverse(sk_c6) = sk_c12 # label(prove_this_36) # label(negated_conjecture). [assumption].
% 4.06/4.36 48 multiply(sk_c1,sk_c12) = sk_c11 | multiply(sk_c8,sk_c9) = sk_c11 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 4.06/4.36 51 multiply(sk_c2,sk_c11) = sk_c10 | multiply(sk_c7,sk_c10) = sk_c11 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 4.06/4.36 54 multiply(sk_c3,sk_c11) = sk_c12 | multiply(sk_c6,sk_c11) = sk_c12 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 4.06/4.36 66 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 4.06/4.36 67 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | inverse(C) != sk_c12 | multiply(C,sk_c11) != sk_c12 | multiply(D,E) != sk_c11 | inverse(D) != E | multiply(E,sk_c10) != sk_c11 | inverse(F) != sk_c12 | multiply(F,sk_c11) != sk_c12 | inverse(V6) != sk_c11 | multiply(V6,sk_c10) != sk_c11 | multiply(V7,V8) != sk_c11 | inverse(V7) != V8 | multiply(V8,sk_c10) != sk_c11 # label(prove_this_64) # label(negated_conjecture). [assumption].
% 4.06/4.36 69 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(A,sk_c11) != sk_c12 | multiply(C,D) != sk_c11 | inverse(C) != D | multiply(D,sk_c10) != sk_c11 | inverse(E) != sk_c12 | multiply(E,sk_c11) != sk_c12 | inverse(F) != sk_c11 | multiply(F,sk_c10) != sk_c11 | multiply(V6,V7) != sk_c11 | inverse(V6) != V7 | multiply(V7,sk_c10) != sk_c11. [factor(67,b,e)].
% 4.06/4.36 72 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | inverse(C) != sk_c12 | multiply(C,sk_c11) != sk_c12 | multiply(D,E) != sk_c11 | inverse(D) != E | multiply(E,sk_c10) != sk_c11 | inverse(F) != sk_c11 | multiply(F,sk_c10) != sk_c11 | multiply(V6,V7) != sk_c11 | inverse(V6) != V7 | multiply(V7,sk_c10) != sk_c11. [factor(67,e,j),merge(j)].
% 4.06/4.36 77 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(A,sk_c11) != sk_c12 | multiply(C,D) != sk_c11 | inverse(C) != D | multiply(D,sk_c10) != sk_c11 | inverse(E) != sk_c11 | multiply(E,sk_c10) != sk_c11 | multiply(F,V6) != sk_c11 | inverse(F) != V6 | multiply(V6,sk_c10) != sk_c11. [factor(69,b,i),merge(i)].
% 4.06/4.36 86 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | inverse(C) != sk_c12 | multiply(C,sk_c11) != sk_c12 | multiply(D,E) != sk_c11 | inverse(D) != E | multiply(E,sk_c10) != sk_c11 | inverse(F) != sk_c11 | multiply(F,sk_c10) != sk_c11. [factor(72,g,l),merge(l),merge(m)].
% 4.06/4.36 97 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(A,sk_c11) != sk_c12 | multiply(C,D) != sk_c11 | inverse(C) != D | multiply(D,sk_c10) != sk_c11 | inverse(E) != sk_c11 | multiply(E,sk_c10) != sk_c11. [factor(77,f,k),merge(k),merge(l)].
% 4.06/4.36 108 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | inverse(C) != sk_c12 | multiply(C,sk_c11) != sk_c12 | multiply(D,E) != sk_c11 | inverse(D) != E | multiply(E,sk_c10) != sk_c11 | inverse(E) != sk_c11. [factor(86,i,k)].
% 4.06/4.36 120 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(A,sk_c11) != sk_c12 | multiply(C,D) != sk_c11 | inverse(C) != D | multiply(D,sk_c10) != sk_c11 | inverse(D) != sk_c11. [factor(97,h,j)].
% 4.06/4.36 144 inverse(sk_c6) = sk_c12 | multiply(sk_c12,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 4.06/4.36 148 inverse(sk_c7) = sk_c11 | multiply(sk_c11,sk_c2) = identity. [para(7(a,1),2(a,1,1))].
% 4.06/4.36 150 inverse(sk_c6) = sk_c12 | multiply(sk_c12,sk_c3) = identity. [para(9(a,1),2(a,1,1))].
% 4.06/4.36 156 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),66(a,1,1)),rewrite([1(2)]),flip(a)].
% 4.06/4.36 173 inverse(sk_c7) = sk_c11 | multiply(sk_c2,multiply(sk_c11,A)) = multiply(sk_c10,A). [para(23(a,1),66(a,1,1)),flip(b)].
% 4.06/4.36 343 identity != sk_c11 | inverse(inverse(sk_c12)) != sk_c12 | multiply(A,sk_c11) != sk_c10 | inverse(A) != sk_c11 | inverse(B) != sk_c12 | multiply(B,sk_c11) != sk_c12 | multiply(C,D) != sk_c11 | inverse(C) != D | multiply(D,sk_c10) != sk_c11 | inverse(E) != sk_c11 | multiply(E,sk_c10) != sk_c11. [para(2(a,1),86(a,1))].
% 4.06/4.36 791 identity != sk_c11 | inverse(inverse(sk_c12)) != sk_c12 | multiply(A,sk_c11) != sk_c10 | inverse(A) != sk_c11 | multiply(inverse(sk_c12),sk_c11) != sk_c12 | multiply(B,C) != sk_c11 | inverse(B) != C | multiply(C,sk_c10) != sk_c11 | inverse(D) != sk_c11 | multiply(D,sk_c10) != sk_c11. [factor(343,b,e)].
% 4.06/4.36 1720 identity != sk_c11 | inverse(inverse(sk_c12)) != sk_c12 | multiply(A,sk_c11) != sk_c10 | inverse(A) != sk_c11 | multiply(inverse(sk_c12),sk_c11) != sk_c12 | multiply(A,sk_c11) != sk_c11 | multiply(sk_c11,sk_c10) != sk_c11 | inverse(B) != sk_c11 | multiply(B,sk_c10) != sk_c11. [factor(791,d,g)].
% 4.06/4.36 2624 identity != sk_c11 | inverse(inverse(sk_c12)) != sk_c12 | multiply(A,sk_c11) != sk_c10 | inverse(A) != sk_c11 | multiply(inverse(sk_c12),sk_c11) != sk_c12 | multiply(A,sk_c11) != sk_c11 | multiply(sk_c11,sk_c10) != sk_c11 | multiply(A,sk_c10) != sk_c11. [factor(1720,d,h)].
% 4.06/4.36 3246 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),156(a,1,2))].
% 4.06/4.36 3313 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | inverse(C) != sk_c12 | multiply(C,sk_c11) != sk_c12 | sk_c11 != D | multiply(E,D) != inverse(inverse(E)) | multiply(E,multiply(D,sk_c10)) != sk_c11 | inverse(multiply(E,D)) != sk_c11. [para(156(a,1),108(g,1)),rewrite([66(30)]),flip(g),flip(h)].
% 4.06/4.36 3315 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(A,sk_c11) != sk_c12 | sk_c11 != C | multiply(D,C) != inverse(inverse(D)) | multiply(D,multiply(C,sk_c10)) != sk_c11 | inverse(multiply(D,C)) != sk_c11. [para(156(a,1),120(f,1)),rewrite([66(27)]),flip(f),flip(g)].
% 4.06/4.36 3318 inverse(sk_c6) = sk_c12 | multiply(inverse(sk_c12),identity) = sk_c1. [para(144(b,1),156(a,1,2))].
% 4.06/4.36 3319 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(156(a,1),156(a,1,2))].
% 4.06/4.36 3320 multiply(A,identity) = A. [back_rewrite(3246),rewrite([3319(4)])].
% 4.06/4.36 3321 inverse(sk_c6) = sk_c12 | inverse(sk_c12) = sk_c1. [back_rewrite(3318),rewrite([3320(8)])].
% 4.06/4.36 3335 inverse(identity) = identity. [para(3320(a,1),2(a,1))].
% 4.06/4.36 3465 inverse(sk_c7) = sk_c11 | inverse(sk_c11) = sk_c2. [para(148(b,1),156(a,1,2)),rewrite([3320(8)])].
% 4.06/4.36 3468 inverse(sk_c11) = sk_c2 | multiply(sk_c11,sk_c7) = identity. [para(3465(a,1),2(a,1,1))].
% 4.06/4.36 3491 inverse(sk_c6) = sk_c12 | inverse(sk_c12) = sk_c3. [para(150(b,1),156(a,1,2)),rewrite([3320(8)])].
% 4.06/4.36 3601 multiply(A,inverse(A)) = identity. [para(3319(a,1),2(a,1))].
% 4.06/4.36 3735 inverse(inverse(A)) = A. [para(3319(a,1),3320(a,1)),rewrite([3320(2)]),flip(a)].
% 4.06/4.36 3755 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | multiply(A,sk_c11) != sk_c12 | sk_c11 != C | multiply(D,C) != D | multiply(D,multiply(C,sk_c10)) != sk_c11 | inverse(multiply(D,C)) != sk_c11. [back_rewrite(3315),rewrite([3735(23)])].
% 4.06/4.36 3757 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(B,sk_c11) != sk_c10 | inverse(B) != sk_c11 | inverse(C) != sk_c12 | multiply(C,sk_c11) != sk_c12 | sk_c11 != D | multiply(E,D) != E | multiply(E,multiply(D,sk_c10)) != sk_c11 | inverse(multiply(E,D)) != sk_c11. [back_rewrite(3313),rewrite([3735(26)])].
% 4.06/4.36 3795 identity != sk_c11 | multiply(A,sk_c11) != sk_c10 | inverse(A) != sk_c11 | multiply(inverse(sk_c12),sk_c11) != sk_c12 | multiply(A,sk_c11) != sk_c11 | multiply(sk_c11,sk_c10) != sk_c11 | multiply(A,sk_c10) != sk_c11. [back_rewrite(2624),rewrite([3735(6)]),xx(b)].
% 4.06/4.36 3856 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(sk_c10,sk_c11) != sk_c10 | inverse(sk_c10) != sk_c11 | multiply(A,sk_c11) != sk_c12 | multiply(sk_c10,multiply(sk_c11,sk_c10)) != sk_c11 | inverse(multiply(sk_c10,sk_c11)) != sk_c11. [factor(3755,c,g),xx(f)].
% 4.06/4.36 3863 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | multiply(sk_c10,sk_c11) != sk_c10 | inverse(sk_c10) != sk_c11 | inverse(B) != sk_c12 | multiply(B,sk_c11) != sk_c12 | multiply(sk_c10,multiply(sk_c11,sk_c10)) != sk_c11 | inverse(multiply(sk_c10,sk_c11)) != sk_c11. [factor(3757,c,h),xx(g)].
% 4.06/4.36 3891 inverse(sk_c8) = sk_c9 | multiply(sk_c1,sk_c12) = identity. [para(5(a,1),3601(a,1,2))].
% 4.06/4.36 5397 inverse(sk_c8) = sk_c9 | identity = sk_c11. [para(3891(b,1),17(a,1)),merge(c)].
% 4.06/4.36 5517 identity = sk_c11 | multiply(sk_c8,sk_c9) = identity. [para(5397(a,1),3601(a,1,2))].
% 4.06/4.36 5521 identity = sk_c11 | inverse(sk_c1) = sk_c12. [para(5517(b,1),20(b,1)),merge(c)].
% 4.06/4.36 5635 identity = sk_c11 | multiply(sk_c1,sk_c12) = identity. [para(5521(b,1),3601(a,1,2))].
% 4.06/4.36 5978 inverse(sk_c7) = sk_c11 | multiply(sk_c10,inverse(sk_c11)) = sk_c2. [para(3601(a,1),173(b,1,2)),rewrite([3320(7)]),flip(b)].
% 4.06/4.36 7021 identity = sk_c11 | multiply(sk_c8,sk_c9) = sk_c11. [para(5635(b,1),48(a,1)),merge(b)].
% 4.06/4.36 8535 identity = sk_c11. [para(7021(b,1),5517(b,1)),flip(c),merge(b),merge(c)].
% 4.06/4.36 11737 multiply(A,sk_c11) != sk_c10 | inverse(A) != sk_c11 | multiply(inverse(sk_c12),sk_c11) != sk_c12 | multiply(A,sk_c11) != sk_c11 | multiply(sk_c11,sk_c10) != sk_c11 | multiply(A,sk_c10) != sk_c11. [back_rewrite(3795),rewrite([8535(1)]),xx(a)].
% 4.06/4.36 11770 inverse(sk_c11) = sk_c2 | multiply(sk_c11,sk_c7) = sk_c11. [back_rewrite(3468),rewrite([8535(8)])].
% 4.06/4.36 11810 inverse(sk_c11) = sk_c11. [back_rewrite(3335),rewrite([8535(1),8535(3)])].
% 4.06/4.36 11811 multiply(A,sk_c11) = A. [back_rewrite(3320),rewrite([8535(1)])].
% 4.06/4.36 11824 multiply(inverse(A),A) = sk_c11. [back_rewrite(2),rewrite([8535(3)])].
% 4.06/4.36 11825 multiply(sk_c11,A) = A. [back_rewrite(1),rewrite([8535(1)])].
% 4.06/4.36 11912 sk_c10 != sk_c11 | inverse(sk_c12) != sk_c12. [factor(11737,e,f),rewrite([11811(3),11810(5),11811(10),11811(13),11825(16)]),flip(a),xx(b),xx(d),merge(c)].
% 4.06/4.36 11927 sk_c2 = sk_c11 | sk_c7 = sk_c11. [back_rewrite(11770),rewrite([11810(2),11825(6)]),flip(a)].
% 4.06/4.36 12434 inverse(sk_c7) = sk_c11 | sk_c2 = sk_c10. [back_rewrite(5978),rewrite([11810(7),11811(7)]),flip(b)].
% 4.06/4.36 12772 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | inverse(sk_c10) != sk_c11 | inverse(B) != sk_c12 | sk_c12 != B | multiply(sk_c10,sk_c10) != sk_c11. [back_rewrite(3863),rewrite([11811(10),11811(19),11825(23),11811(27)]),flip(f),xx(c),merge(g)].
% 4.06/4.36 12773 multiply(A,sk_c12) != sk_c11 | inverse(A) != sk_c12 | inverse(sk_c10) != sk_c11 | sk_c12 != A | multiply(sk_c10,sk_c10) != sk_c11. [back_rewrite(3856),rewrite([11811(10),11811(16),11825(20),11811(24)]),flip(e),xx(c),merge(f)].
% 4.06/4.36 14019 sk_c3 = sk_c12 | sk_c6 = sk_c12. [back_rewrite(54),rewrite([11811(3),11811(6)])].
% 4.06/4.36 14022 sk_c2 = sk_c10 | multiply(sk_c7,sk_c10) = sk_c11. [back_rewrite(51),rewrite([11811(3)])].
% 4.06/4.36 14027 sk_c3 = sk_c12 | inverse(sk_c6) = sk_c12. [back_rewrite(33),rewrite([11811(3)])].
% 4.06/4.36 14028 inverse(sk_c3) = sk_c12 | sk_c6 = sk_c12. [back_rewrite(29),rewrite([11811(7)])].
% 4.06/4.36 14339 sk_c2 = sk_c10 | sk_c7 = sk_c11. [para(12434(a,1),3735(a,1,1)),rewrite([11810(5)]),flip(b)].
% 4.06/4.36 14345 sk_c7 = sk_c11 | sk_c10 = sk_c11. [para(14339(a,1),11927(a,1)),merge(c)].
% 4.06/4.36 14347 sk_c10 = sk_c11 | inverse(sk_c2) = sk_c11. [para(14345(a,1),26(b,1,1)),rewrite([11825(10)]),merge(c)].
% 4.06/4.36 14456 multiply(A,multiply(B,sk_c12)) != sk_c11 | inverse(multiply(A,B)) != sk_c12 | inverse(sk_c10) != sk_c11 | multiply(A,B) != sk_c12 | multiply(sk_c10,sk_c10) != sk_c11. [para(66(a,1),12773(a,1)),flip(d)].
% 4.06/4.36 15129 sk_c6 = sk_c12 | inverse(sk_c12) = sk_c12. [para(14019(a,1),14028(a,1,1)),merge(c)].
% 4.06/4.36 15347 sk_c10 = sk_c11 | sk_c2 = sk_c11. [para(14347(b,1),3735(a,1,1)),rewrite([11810(5)]),flip(b)].
% 4.06/4.36 15364 inverse(sk_c10) != sk_c11 | inverse(A) != sk_c12 | sk_c12 != A | multiply(sk_c10,sk_c10) != sk_c11. [resolve(12772,a,11824,a),rewrite([3735(3)]),xx(a)].
% 4.06/4.36 15403 inverse(sk_c10) != sk_c11 | sk_c6 != sk_c12 | multiply(sk_c10,sk_c10) != sk_c11 | sk_c3 = sk_c12. [resolve(15364,b,14027,b),flip(b)].
% 4.06/4.36 15414 inverse(sk_c10) != sk_c11 | sk_c6 != sk_c12 | multiply(sk_c10,sk_c10) != sk_c11 | inverse(sk_c12) = sk_c3. [resolve(15364,b,3491,a),flip(b)].
% 4.06/4.36 15415 inverse(sk_c10) != sk_c11 | sk_c6 != sk_c12 | multiply(sk_c10,sk_c10) != sk_c11 | inverse(sk_c12) = sk_c1. [resolve(15364,b,3321,a),flip(b)].
% 4.06/4.36 15421 inverse(sk_c10) != sk_c11 | sk_c1 != sk_c12 | multiply(sk_c10,sk_c10) != sk_c11 | inverse(sk_c6) = sk_c12. [resolve(15364,b,3,a),flip(b)].
% 4.06/4.36 15889 sk_c6 = sk_c12 | sk_c10 != sk_c11. [resolve(15129,b,11912,b)].
% 4.06/4.36 15920 sk_c11 != A | inverse(multiply(A,inverse(sk_c12))) != sk_c12 | inverse(sk_c10) != sk_c11 | multiply(A,inverse(sk_c12)) != sk_c12 | multiply(sk_c10,sk_c10) != sk_c11. [para(11824(a,1),14456(a,1,2)),rewrite([11811(2)]),flip(a)].
% 4.06/4.36 15925 multiply(A,B) != sk_c11 | inverse(multiply(A,multiply(B,inverse(sk_c12)))) != sk_c12 | inverse(sk_c10) != sk_c11 | multiply(A,multiply(B,inverse(sk_c12))) != sk_c12 | multiply(sk_c10,sk_c10) != sk_c11. [para(66(a,1),15920(b,1,1)),rewrite([66(18)]),flip(a)].
% 4.06/4.36 15934 multiply(sk_c10,sk_c10) != sk_c11 | inverse(multiply(sk_c10,multiply(sk_c10,inverse(sk_c12)))) != sk_c12 | inverse(sk_c10) != sk_c11 | multiply(sk_c10,multiply(sk_c10,inverse(sk_c12))) != sk_c12. [factor(15925,a,e)].
% 4.06/4.36 19004 sk_c10 = sk_c11 | sk_c2 = sk_c10. [para(14345(a,1),14022(b,1,1)),rewrite([11825(9)]),merge(c)].
% 4.06/4.36 19018 sk_c10 = sk_c11. [para(19004(b,1),15347(b,1)),merge(b),merge(c)].
% 4.06/4.36 19701 inverse(sk_c12) != sk_c12. [back_rewrite(15934),rewrite([19018(1),19018(2),11811(3),19018(4),19018(5),11825(8),11825(7),3735(6),19018(7),11810(8),19018(10),19018(11),11825(14),11825(13)]),xx(a),xx(b),xx(c)].
% 4.06/4.36 19726 sk_c6 = sk_c12. [back_rewrite(15889),rewrite([19018(4)]),xx(b)].
% 4.06/4.36 19742 sk_c1 != sk_c12. [back_rewrite(15421),rewrite([19018(1),11810(2),19018(7),19018(8),11811(9),19726(10)]),xx(a),xx(c),unit_del(b,19701)].
% 4.06/4.36 19744 inverse(sk_c12) = sk_c1. [back_rewrite(15415),rewrite([19018(1),11810(2),19726(4),19018(7),19018(8),11811(9)]),xx(a),xx(b),xx(c)].
% 4.06/4.36 19745 sk_c3 = sk_c1. [back_rewrite(15414),rewrite([19018(1),11810(2),19726(4),19018(7),19018(8),11811(9),19744(11)]),flip(d),xx(a),xx(b),xx(c)].
% 4.06/4.36 19748 $F. [back_rewrite(15403),rewrite([19018(1),11810(2),19726(4),19018(7),19018(8),11811(9),19745(10)]),xx(a),xx(b),xx(c),unit_del(a,19742)].
% 4.06/4.36
% 4.06/4.36 % SZS output end Refutation
% 4.06/4.36 ============================== end of proof ==========================
% 4.06/4.36
% 4.06/4.36 ============================== STATISTICS ============================
% 4.06/4.36
% 4.06/4.36 Given=718. Generated=60333. Kept=19747. proofs=1.
% 4.06/4.36 Usable=228. Sos=2710. Demods=21. Limbo=730, Disabled=16146. Hints=0.
% 4.06/4.36 Megabytes=19.25.
% 4.06/4.36 User_CPU=3.31, System_CPU=0.05, Wall_clock=4.
% 4.06/4.36
% 4.06/4.36 ============================== end of statistics =====================
% 4.06/4.36
% 4.06/4.36 ============================== end of search =========================
% 4.06/4.36
% 4.06/4.36 THEOREM PROVED
% 4.06/4.36 % SZS status Unsatisfiable
% 4.06/4.36
% 4.06/4.36 Exiting with 1 proof.
% 4.06/4.36
% 4.06/4.36 Process 25197 exit (max_proofs) Mon Jun 13 22:09:13 2022
% 4.06/4.36 Prover9 interrupted
%------------------------------------------------------------------------------