TSTP Solution File: GRP245-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP245-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 2.64s 2.91s
% Output : Refutation 2.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP245-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.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 18:06:47 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.64/2.91 ============================== Prover9 ===============================
% 2.64/2.91 Prover9 (32) version 2009-11A, November 2009.
% 2.64/2.91 Process 16618 was started by sandbox2 on n027.cluster.edu,
% 2.64/2.91 Mon Jun 13 18:06:48 2022
% 2.64/2.91 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16464_n027.cluster.edu".
% 2.64/2.91 ============================== end of head ===========================
% 2.64/2.91
% 2.64/2.91 ============================== INPUT =================================
% 2.64/2.91
% 2.64/2.91 % Reading from file /tmp/Prover9_16464_n027.cluster.edu
% 2.64/2.91
% 2.64/2.91 set(prolog_style_variables).
% 2.64/2.91 set(auto2).
% 2.64/2.91 % set(auto2) -> set(auto).
% 2.64/2.91 % set(auto) -> set(auto_inference).
% 2.64/2.91 % set(auto) -> set(auto_setup).
% 2.64/2.91 % set(auto_setup) -> set(predicate_elim).
% 2.64/2.91 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.64/2.91 % set(auto) -> set(auto_limits).
% 2.64/2.91 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.64/2.91 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.64/2.91 % set(auto) -> set(auto_denials).
% 2.64/2.91 % set(auto) -> set(auto_process).
% 2.64/2.91 % set(auto2) -> assign(new_constants, 1).
% 2.64/2.91 % set(auto2) -> assign(fold_denial_max, 3).
% 2.64/2.91 % set(auto2) -> assign(max_weight, "200.000").
% 2.64/2.91 % set(auto2) -> assign(max_hours, 1).
% 2.64/2.91 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.64/2.91 % set(auto2) -> assign(max_seconds, 0).
% 2.64/2.91 % set(auto2) -> assign(max_minutes, 5).
% 2.64/2.91 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.64/2.91 % set(auto2) -> set(sort_initial_sos).
% 2.64/2.91 % set(auto2) -> assign(sos_limit, -1).
% 2.64/2.91 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.64/2.91 % set(auto2) -> assign(max_megs, 400).
% 2.64/2.91 % set(auto2) -> assign(stats, some).
% 2.64/2.91 % set(auto2) -> clear(echo_input).
% 2.64/2.91 % set(auto2) -> set(quiet).
% 2.64/2.91 % set(auto2) -> clear(print_initial_clauses).
% 2.64/2.91 % set(auto2) -> clear(print_given).
% 2.64/2.91 assign(lrs_ticks,-1).
% 2.64/2.91 assign(sos_limit,10000).
% 2.64/2.91 assign(order,kbo).
% 2.64/2.91 set(lex_order_vars).
% 2.64/2.91 clear(print_given).
% 2.64/2.91
% 2.64/2.91 % formulas(sos). % not echoed (46 formulas)
% 2.64/2.91
% 2.64/2.91 ============================== end of input ==========================
% 2.64/2.91
% 2.64/2.91 % From the command line: assign(max_seconds, 300).
% 2.64/2.91
% 2.64/2.91 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.64/2.91
% 2.64/2.91 % Formulas that are not ordinary clauses:
% 2.64/2.91
% 2.64/2.91 ============================== end of process non-clausal formulas ===
% 2.64/2.91
% 2.64/2.91 ============================== PROCESS INITIAL CLAUSES ===============
% 2.64/2.91
% 2.64/2.91 ============================== PREDICATE ELIMINATION =================
% 2.64/2.91
% 2.64/2.91 ============================== end predicate elimination =============
% 2.64/2.91
% 2.64/2.91 Auto_denials: (non-Horn, no changes).
% 2.64/2.91
% 2.64/2.91 Term ordering decisions:
% 2.64/2.91
% 2.64/2.91 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 2.64/2.91 Function symbol KB weights: sk_c9=1. sk_c10=1. sk_c8=1. sk_c7=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c6=1. identity=1. multiply=1. inverse=0.
% 2.64/2.91
% 2.64/2.91 ============================== end of process initial clauses ========
% 2.64/2.91
% 2.64/2.91 ============================== CLAUSES FOR SEARCH ====================
% 2.64/2.91
% 2.64/2.91 ============================== end of clauses for search =============
% 2.64/2.91
% 2.64/2.91 ============================== SEARCH ================================
% 2.64/2.91
% 2.64/2.91 % Starting search at 0.04 seconds.
% 2.64/2.91
% 2.64/2.91 Low Water (keep): wt=58.000, iters=3616
% 2.64/2.91
% 2.64/2.91 Low Water (keep): wt=54.000, iters=3587
% 2.64/2.91
% 2.64/2.91 Low Water (keep): wt=50.000, iters=3479
% 2.64/2.91
% 2.64/2.91 Low Water (keep): wt=49.000, iters=3435
% 2.64/2.91
% 2.64/2.91 Low Water (keep): wt=44.000, iters=3840
% 2.64/2.91
% 2.64/2.91 Low Water (keep): wt=42.000, iters=3448
% 2.64/2.91
% 2.64/2.91 Low Water (keep): wt=41.000, iters=3366
% 2.64/2.91
% 2.64/2.91 Low Water (keep): wt=40.000, iters=3493
% 2.64/2.91
% 2.64/2.91 ============================== PROOF =================================
% 2.64/2.91 % SZS status Unsatisfiable
% 2.64/2.91 % SZS output start Refutation
% 2.64/2.91
% 2.64/2.91 % Proof 1 at 1.91 (+ 0.03) seconds.
% 2.64/2.91 % Length of proof is 81.
% 2.64/2.91 % Level of proof is 19.
% 2.64/2.91 % Maximum clause weight is 59.000.
% 2.64/2.91 % Given clauses 479.
% 2.64/2.91
% 2.64/2.91 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 2.64/2.91 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 2.64/2.91 5 inverse(sk_c1) = sk_c10 | inverse(sk_c6) = sk_c7 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 2.64/2.91 7 inverse(sk_c2) = sk_c9 | inverse(sk_c5) = sk_c9 # label(prove_this_24) # label(negated_conjecture). [assumption].
% 2.64/2.91 9 inverse(sk_c3) = sk_c10 | inverse(sk_c4) = sk_c10 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 2.64/2.91 14 multiply(sk_c1,sk_c10) = sk_c9 | inverse(sk_c6) = sk_c7 # label(prove_this_6) # label(negated_conjecture). [assumption].
% 2.64/2.91 17 inverse(sk_c1) = sk_c10 | multiply(sk_c6,sk_c7) = sk_c9 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 2.64/2.91 20 multiply(sk_c2,sk_c9) = sk_c8 | inverse(sk_c5) = sk_c9 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 2.64/2.91 23 inverse(sk_c2) = sk_c9 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 2.64/2.91 26 inverse(sk_c3) = sk_c10 | multiply(sk_c4,sk_c9) = sk_c10 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 2.64/2.91 30 multiply(sk_c3,sk_c9) = sk_c10 | inverse(sk_c4) = sk_c10 # label(prove_this_36) # label(negated_conjecture). [assumption].
% 2.64/2.91 35 multiply(sk_c1,sk_c10) = sk_c9 | multiply(sk_c6,sk_c7) = sk_c9 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 2.64/2.91 38 multiply(sk_c2,sk_c9) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c9 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 2.64/2.91 41 multiply(sk_c3,sk_c9) = sk_c10 | multiply(sk_c4,sk_c9) = sk_c10 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 2.64/2.91 45 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 2.64/2.91 46 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c10 | multiply(C,sk_c9) != sk_c10 | inverse(D) != sk_c10 | multiply(D,sk_c9) != sk_c10 | inverse(E) != sk_c9 | multiply(E,sk_c8) != sk_c9 | multiply(F,V6) != sk_c9 | inverse(F) != V6 | multiply(V6,sk_c8) != sk_c9 # label(prove_this_43) # label(negated_conjecture). [assumption].
% 2.64/2.91 48 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(A,sk_c9) != sk_c10 | inverse(C) != sk_c10 | multiply(C,sk_c9) != sk_c10 | inverse(D) != sk_c9 | multiply(D,sk_c8) != sk_c9 | multiply(E,F) != sk_c9 | inverse(E) != F | multiply(F,sk_c8) != sk_c9. [factor(46,b,e)].
% 2.64/2.91 51 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c10 | multiply(C,sk_c9) != sk_c10 | inverse(D) != sk_c9 | multiply(D,sk_c8) != sk_c9 | multiply(E,F) != sk_c9 | inverse(E) != F | multiply(F,sk_c8) != sk_c9. [factor(46,e,g),merge(g)].
% 2.64/2.91 57 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(A,sk_c9) != sk_c10 | inverse(C) != sk_c9 | multiply(C,sk_c8) != sk_c9 | multiply(D,E) != sk_c9 | inverse(D) != E | multiply(E,sk_c8) != sk_c9. [factor(48,b,f),merge(f)].
% 2.64/2.91 66 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c10 | multiply(C,sk_c9) != sk_c10 | inverse(D) != sk_c9 | multiply(D,sk_c8) != sk_c9 | multiply(E,D) != sk_c9 | inverse(E) != D. [factor(51,h,k)].
% 2.64/2.91 77 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(A,sk_c9) != sk_c10 | inverse(C) != sk_c9 | multiply(C,sk_c8) != sk_c9 | multiply(D,C) != sk_c9 | inverse(D) != C. [factor(57,g,j)].
% 2.64/2.91 111 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),45(a,1,1)),rewrite([1(2)]),flip(a)].
% 2.64/2.91 128 inverse(sk_c5) = sk_c9 | multiply(sk_c2,multiply(sk_c9,A)) = multiply(sk_c8,A). [para(20(a,1),45(a,1,1)),flip(b)].
% 2.64/2.91 236 identity != sk_c9 | inverse(inverse(sk_c10)) != sk_c10 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | inverse(B) != sk_c10 | multiply(B,sk_c9) != sk_c10 | inverse(C) != sk_c9 | multiply(C,sk_c8) != sk_c9 | multiply(D,E) != sk_c9 | inverse(D) != E | multiply(E,sk_c8) != sk_c9. [para(2(a,1),51(a,1))].
% 2.64/2.91 551 identity != sk_c9 | inverse(inverse(sk_c10)) != sk_c10 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(inverse(sk_c10),sk_c9) != sk_c10 | inverse(B) != sk_c9 | multiply(B,sk_c8) != sk_c9 | multiply(C,D) != sk_c9 | inverse(C) != D | multiply(D,sk_c8) != sk_c9. [factor(236,b,e)].
% 2.64/2.91 1230 identity != sk_c9 | inverse(inverse(sk_c10)) != sk_c10 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(inverse(sk_c10),sk_c9) != sk_c10 | multiply(A,sk_c8) != sk_c9 | multiply(B,C) != sk_c9 | inverse(B) != C | multiply(C,sk_c8) != sk_c9. [factor(551,d,f)].
% 2.64/2.91 1919 identity != sk_c9 | inverse(inverse(sk_c10)) != sk_c10 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(inverse(sk_c10),sk_c9) != sk_c10 | multiply(A,sk_c8) != sk_c9 | multiply(A,sk_c9) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c9. [factor(1230,d,h)].
% 2.64/2.91 2390 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),111(a,1,2))].
% 2.64/2.91 2410 inverse(sk_c2) = sk_c9 | multiply(inverse(sk_c5),sk_c9) = sk_c8. [para(23(b,1),111(a,1,2))].
% 2.64/2.91 2425 multiply(sk_c2,sk_c9) = sk_c8 | multiply(inverse(sk_c5),sk_c9) = sk_c8. [para(38(b,1),111(a,1,2))].
% 2.64/2.91 2436 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c10 | multiply(C,sk_c9) != sk_c10 | inverse(multiply(D,E)) != sk_c9 | multiply(D,multiply(E,sk_c8)) != sk_c9 | sk_c9 != E | multiply(D,E) != inverse(inverse(D)). [para(111(a,1),66(i,1)),rewrite([45(28)]),flip(i),flip(j)].
% 2.64/2.91 2438 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(A,sk_c9) != sk_c10 | inverse(multiply(C,D)) != sk_c9 | multiply(C,multiply(D,sk_c8)) != sk_c9 | sk_c9 != D | multiply(C,D) != inverse(inverse(C)). [para(111(a,1),77(h,1)),rewrite([45(25)]),flip(h),flip(i)].
% 2.64/2.91 2442 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(111(a,1),111(a,1,2))].
% 2.64/2.91 2443 multiply(A,identity) = A. [back_rewrite(2390),rewrite([2442(4)])].
% 2.64/2.91 2458 inverse(identity) = identity. [para(2443(a,1),2(a,1))].
% 2.64/2.91 2680 multiply(A,inverse(A)) = identity. [para(2442(a,1),2(a,1))].
% 2.64/2.91 2811 inverse(inverse(A)) = A. [para(2442(a,1),2443(a,1)),rewrite([2443(2)]),flip(a)].
% 2.64/2.91 2827 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | multiply(A,sk_c9) != sk_c10 | inverse(multiply(C,D)) != sk_c9 | multiply(C,multiply(D,sk_c8)) != sk_c9 | sk_c9 != D | multiply(C,D) != C. [back_rewrite(2438),rewrite([2811(32)])].
% 2.64/2.91 2829 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(B,sk_c9) != sk_c8 | inverse(B) != sk_c9 | inverse(C) != sk_c10 | multiply(C,sk_c9) != sk_c10 | inverse(multiply(D,E)) != sk_c9 | multiply(D,multiply(E,sk_c8)) != sk_c9 | sk_c9 != E | multiply(D,E) != D. [back_rewrite(2436),rewrite([2811(35)])].
% 2.64/2.91 2871 identity != sk_c9 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(inverse(sk_c10),sk_c9) != sk_c10 | multiply(A,sk_c8) != sk_c9 | multiply(A,sk_c9) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c9. [back_rewrite(1919),rewrite([2811(6)]),xx(b)].
% 2.64/2.91 2932 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(sk_c8,sk_c9) != sk_c8 | inverse(sk_c8) != sk_c9 | multiply(A,sk_c9) != sk_c10 | inverse(multiply(sk_c8,sk_c9)) != sk_c9 | multiply(sk_c8,multiply(sk_c9,sk_c8)) != sk_c9. [factor(2827,c,i),xx(h)].
% 2.64/2.91 2939 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | multiply(sk_c8,sk_c9) != sk_c8 | inverse(sk_c8) != sk_c9 | inverse(B) != sk_c10 | multiply(B,sk_c9) != sk_c10 | inverse(multiply(sk_c8,sk_c9)) != sk_c9 | multiply(sk_c8,multiply(sk_c9,sk_c8)) != sk_c9. [factor(2829,c,j),xx(i)].
% 2.64/2.91 2964 inverse(sk_c1) = sk_c10 | multiply(sk_c6,sk_c7) = identity. [para(5(b,1),2680(a,1,2))].
% 2.64/2.91 3863 inverse(sk_c1) = sk_c10 | identity = sk_c9. [para(2964(b,1),17(b,1)),merge(b)].
% 2.64/2.91 3870 identity = sk_c9 | multiply(sk_c1,sk_c10) = identity. [para(3863(a,1),2680(a,1,2))].
% 2.64/2.91 3944 identity = sk_c9 | inverse(sk_c6) = sk_c7. [para(3870(b,1),14(a,1)),merge(b)].
% 2.64/2.91 3960 identity = sk_c9 | multiply(sk_c6,sk_c7) = identity. [para(3944(b,1),2680(a,1,2))].
% 2.64/2.91 4595 identity = sk_c9 | multiply(sk_c1,sk_c10) = sk_c9. [para(3960(b,1),35(b,1)),merge(c)].
% 2.64/2.91 4783 inverse(sk_c5) = sk_c9 | multiply(sk_c8,inverse(sk_c9)) = sk_c2. [para(2680(a,1),128(b,1,2)),rewrite([2443(7)]),flip(b)].
% 2.64/2.91 5749 identity = sk_c9. [para(4595(b,1),3870(b,1)),flip(c),merge(b),merge(c)].
% 2.64/2.91 7401 multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(inverse(sk_c10),sk_c9) != sk_c10 | multiply(A,sk_c8) != sk_c9 | multiply(A,sk_c9) != sk_c9 | multiply(sk_c9,sk_c8) != sk_c9. [back_rewrite(2871),rewrite([5749(1)]),xx(a)].
% 2.64/2.91 7460 inverse(sk_c9) = sk_c9. [back_rewrite(2458),rewrite([5749(1),5749(3)])].
% 2.64/2.91 7461 multiply(A,sk_c9) = A. [back_rewrite(2443),rewrite([5749(1)])].
% 2.64/2.91 7471 multiply(inverse(A),A) = sk_c9. [back_rewrite(2),rewrite([5749(3)])].
% 2.64/2.91 7472 multiply(sk_c9,A) = A. [back_rewrite(1),rewrite([5749(1)])].
% 2.64/2.91 7581 sk_c8 != sk_c9 | inverse(sk_c10) != sk_c10. [factor(7401,d,f),rewrite([7461(3),7460(5),7461(10),7472(13),7461(16)]),flip(a),xx(b),xx(e),merge(c)].
% 2.64/2.91 7891 inverse(sk_c5) = sk_c9 | sk_c2 = sk_c8. [back_rewrite(4783),rewrite([7460(7),7461(7)]),flip(b)].
% 2.64/2.91 8167 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | inverse(sk_c8) != sk_c9 | inverse(B) != sk_c10 | sk_c10 != B | multiply(sk_c8,sk_c8) != sk_c9. [back_rewrite(2939),rewrite([7461(10),7461(19),7461(22),7472(27)]),flip(f),xx(c),merge(f)].
% 2.64/2.91 8168 multiply(A,sk_c10) != sk_c9 | inverse(A) != sk_c10 | inverse(sk_c8) != sk_c9 | sk_c10 != A | multiply(sk_c8,sk_c8) != sk_c9. [back_rewrite(2932),rewrite([7461(10),7461(16),7461(19),7472(24)]),flip(e),xx(c),merge(e)].
% 2.64/2.91 8180 sk_c2 = sk_c8 | inverse(sk_c5) = sk_c8. [back_rewrite(2425),rewrite([7461(3),7461(7)])].
% 2.64/2.91 8186 inverse(sk_c2) = sk_c9 | inverse(sk_c5) = sk_c8. [back_rewrite(2410),rewrite([7461(8)])].
% 2.64/2.91 9098 sk_c3 = sk_c10 | sk_c4 = sk_c10. [back_rewrite(41),rewrite([7461(3),7461(6)])].
% 2.64/2.91 9105 sk_c3 = sk_c10 | inverse(sk_c4) = sk_c10. [back_rewrite(30),rewrite([7461(3)])].
% 2.64/2.91 9106 inverse(sk_c3) = sk_c10 | sk_c4 = sk_c10. [back_rewrite(26),rewrite([7461(7)])].
% 2.64/2.91 9419 multiply(A,multiply(B,sk_c10)) != sk_c9 | inverse(multiply(A,B)) != sk_c10 | inverse(sk_c8) != sk_c9 | multiply(A,B) != sk_c10 | multiply(sk_c8,sk_c8) != sk_c9. [para(45(a,1),8168(a,1)),flip(d)].
% 2.64/2.91 9579 sk_c2 = sk_c8 | sk_c8 = sk_c9. [para(8180(b,1),7891(a,1)),merge(c)].
% 2.64/2.91 9702 sk_c3 = sk_c10 | inverse(sk_c10) = sk_c10. [para(9098(b,1),9105(b,1,1)),merge(b)].
% 2.64/2.91 10088 inverse(sk_c8) != sk_c9 | inverse(A) != sk_c10 | sk_c10 != A | multiply(sk_c8,sk_c8) != sk_c9. [resolve(8167,a,7471,a),rewrite([2811(3)]),xx(a)].
% 2.64/2.91 10141 inverse(sk_c8) != sk_c9 | sk_c3 != sk_c10 | multiply(sk_c8,sk_c8) != sk_c9 | sk_c4 = sk_c10. [resolve(10088,b,9106,a),flip(b)].
% 2.64/2.91 10154 inverse(sk_c8) != sk_c9 | sk_c4 != sk_c10 | multiply(sk_c8,sk_c8) != sk_c9 | inverse(sk_c3) = sk_c10. [resolve(10088,b,9,b),flip(b)].
% 2.64/2.91 10186 sk_c3 = sk_c10 | sk_c8 != sk_c9. [resolve(9702,b,7581,b)].
% 2.64/2.91 10586 sk_c9 != A | inverse(multiply(A,inverse(sk_c10))) != sk_c10 | inverse(sk_c8) != sk_c9 | multiply(A,inverse(sk_c10)) != sk_c10 | multiply(sk_c8,sk_c8) != sk_c9. [para(7471(a,1),9419(a,1,2)),rewrite([7461(2)]),flip(a)].
% 2.64/2.91 10598 multiply(A,B) != sk_c9 | inverse(multiply(A,multiply(B,inverse(sk_c10)))) != sk_c10 | inverse(sk_c8) != sk_c9 | multiply(A,multiply(B,inverse(sk_c10))) != sk_c10 | multiply(sk_c8,sk_c8) != sk_c9. [para(45(a,1),10586(b,1,1)),rewrite([45(18)]),flip(a)].
% 2.64/2.91 10607 multiply(sk_c8,sk_c8) != sk_c9 | inverse(multiply(sk_c8,multiply(sk_c8,inverse(sk_c10)))) != sk_c10 | inverse(sk_c8) != sk_c9 | multiply(sk_c8,multiply(sk_c8,inverse(sk_c10))) != sk_c10. [factor(10598,a,e)].
% 2.64/2.91 11718 inverse(sk_c2) = sk_c9 | sk_c8 = sk_c9. [para(8186(b,1),7(b,1)),merge(b)].
% 2.64/2.91 11829 sk_c8 = sk_c9 | sk_c2 = sk_c9. [para(11718(a,1),2811(a,1,1)),rewrite([7460(5)]),flip(b)].
% 2.64/2.91 11835 sk_c8 = sk_c9. [para(11829(b,1),9579(a,1)),flip(b),merge(b),merge(c)].
% 2.64/2.91 12131 inverse(sk_c10) != sk_c10. [back_rewrite(10607),rewrite([11835(1),11835(2),7461(3),11835(4),11835(5),7472(8),7472(7),2811(6),11835(7),7460(8),11835(10),11835(11),7472(14),7472(13)]),xx(a),xx(b),xx(c)].
% 2.64/2.91 12244 sk_c3 = sk_c10. [back_rewrite(10186),rewrite([11835(4)]),xx(b)].
% 2.64/2.91 12248 sk_c4 != sk_c10. [back_rewrite(10154),rewrite([11835(1),7460(2),11835(7),11835(8),7461(9),12244(10)]),xx(a),xx(c),unit_del(b,12131)].
% 2.64/2.91 12255 $F. [back_rewrite(10141),rewrite([11835(1),7460(2),12244(4),11835(7),11835(8),7461(9)]),xx(a),xx(b),xx(c),unit_del(a,12248)].
% 2.64/2.91
% 2.64/2.91 % SZS output end Refutation
% 2.64/2.91 ============================== end of proof ==========================
% 2.64/2.91
% 2.64/2.91 ============================== STATISTICS ============================
% 2.64/2.91
% 2.64/2.91 Given=479. Generated=32507. Kept=12254. proofs=1.
% 2.64/2.91 Usable=164. Sos=2118. Demods=20. Limbo=420, Disabled=9598. Hints=0.
% 2.64/2.91 Megabytes=12.49.
% 2.64/2.91 User_CPU=1.91, System_CPU=0.03, Wall_clock=2.
% 2.64/2.91
% 2.64/2.91 ============================== end of statistics =====================
% 2.64/2.91
% 2.64/2.91 ============================== end of search =========================
% 2.64/2.91
% 2.64/2.91 THEOREM PROVED
% 2.64/2.91 % SZS status Unsatisfiable
% 2.64/2.91
% 2.64/2.91 Exiting with 1 proof.
% 2.64/2.91
% 2.64/2.91 Process 16618 exit (max_proofs) Mon Jun 13 18:06:50 2022
% 2.64/2.91 Prover9 interrupted
%------------------------------------------------------------------------------