TSTP Solution File: GRP317-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP317-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 11:18:36 EDT 2022
% Result : Unsatisfiable 3.12s 3.38s
% Output : Refutation 3.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : GRP317-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n007.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 03:00:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.12/3.38 ============================== Prover9 ===============================
% 3.12/3.38 Prover9 (32) version 2009-11A, November 2009.
% 3.12/3.38 Process 3925 was started by sandbox on n007.cluster.edu,
% 3.12/3.38 Tue Jun 14 03:00:10 2022
% 3.12/3.38 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3769_n007.cluster.edu".
% 3.12/3.38 ============================== end of head ===========================
% 3.12/3.38
% 3.12/3.38 ============================== INPUT =================================
% 3.12/3.38
% 3.12/3.38 % Reading from file /tmp/Prover9_3769_n007.cluster.edu
% 3.12/3.38
% 3.12/3.38 set(prolog_style_variables).
% 3.12/3.38 set(auto2).
% 3.12/3.38 % set(auto2) -> set(auto).
% 3.12/3.38 % set(auto) -> set(auto_inference).
% 3.12/3.38 % set(auto) -> set(auto_setup).
% 3.12/3.38 % set(auto_setup) -> set(predicate_elim).
% 3.12/3.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.12/3.38 % set(auto) -> set(auto_limits).
% 3.12/3.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.12/3.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.12/3.38 % set(auto) -> set(auto_denials).
% 3.12/3.38 % set(auto) -> set(auto_process).
% 3.12/3.38 % set(auto2) -> assign(new_constants, 1).
% 3.12/3.38 % set(auto2) -> assign(fold_denial_max, 3).
% 3.12/3.38 % set(auto2) -> assign(max_weight, "200.000").
% 3.12/3.38 % set(auto2) -> assign(max_hours, 1).
% 3.12/3.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.12/3.38 % set(auto2) -> assign(max_seconds, 0).
% 3.12/3.38 % set(auto2) -> assign(max_minutes, 5).
% 3.12/3.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.12/3.38 % set(auto2) -> set(sort_initial_sos).
% 3.12/3.38 % set(auto2) -> assign(sos_limit, -1).
% 3.12/3.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.12/3.38 % set(auto2) -> assign(max_megs, 400).
% 3.12/3.38 % set(auto2) -> assign(stats, some).
% 3.12/3.38 % set(auto2) -> clear(echo_input).
% 3.12/3.38 % set(auto2) -> set(quiet).
% 3.12/3.38 % set(auto2) -> clear(print_initial_clauses).
% 3.12/3.38 % set(auto2) -> clear(print_given).
% 3.12/3.38 assign(lrs_ticks,-1).
% 3.12/3.38 assign(sos_limit,10000).
% 3.12/3.38 assign(order,kbo).
% 3.12/3.38 set(lex_order_vars).
% 3.12/3.38 clear(print_given).
% 3.12/3.38
% 3.12/3.38 % formulas(sos). % not echoed (58 formulas)
% 3.12/3.38
% 3.12/3.38 ============================== end of input ==========================
% 3.12/3.38
% 3.12/3.38 % From the command line: assign(max_seconds, 300).
% 3.12/3.38
% 3.12/3.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.12/3.38
% 3.12/3.38 % Formulas that are not ordinary clauses:
% 3.12/3.38
% 3.12/3.38 ============================== end of process non-clausal formulas ===
% 3.12/3.38
% 3.12/3.38 ============================== PROCESS INITIAL CLAUSES ===============
% 3.12/3.38
% 3.12/3.38 ============================== PREDICATE ELIMINATION =================
% 3.12/3.38
% 3.12/3.38 ============================== end predicate elimination =============
% 3.12/3.38
% 3.12/3.38 Auto_denials: (non-Horn, no changes).
% 3.12/3.38
% 3.12/3.38 Term ordering decisions:
% 3.12/3.38
% 3.12/3.38 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 3.12/3.38 Function symbol KB weights: sk_c9=1. sk_c8=1. sk_c7=1. sk_c3=1. sk_c5=1. sk_c6=1. sk_c1=1. sk_c2=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 3.12/3.38
% 3.12/3.38 ============================== end of process initial clauses ========
% 3.12/3.38
% 3.12/3.38 ============================== CLAUSES FOR SEARCH ====================
% 3.12/3.38
% 3.12/3.38 ============================== end of clauses for search =============
% 3.12/3.38
% 3.12/3.38 ============================== SEARCH ================================
% 3.12/3.38
% 3.12/3.38 % Starting search at 0.05 seconds.
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=58.000, iters=3376
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=57.000, iters=3350
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=56.000, iters=3335
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=54.000, iters=3354
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=52.000, iters=3393
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=49.000, iters=3399
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=48.000, iters=3344
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=46.000, iters=3334
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=45.000, iters=3379
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=44.000, iters=3357
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=43.000, iters=3390
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=42.000, iters=3343
% 3.12/3.38
% 3.12/3.38 Low Water (keep): wt=41.000, iters=3552
% 3.12/3.38
% 3.12/3.38 ============================== PROOF =================================
% 3.12/3.38 % SZS status Unsatisfiable
% 3.12/3.38 % SZS output start Refutation
% 3.12/3.38
% 3.12/3.38 % Proof 1 at 2.36 (+ 0.03) seconds.
% 3.12/3.38 % Length of proof is 97.
% 3.12/3.38 % Level of proof is 21.
% 3.12/3.38 % Maximum clause weight is 68.000.
% 3.12/3.38 % Given clauses 546.
% 3.12/3.38
% 3.12/3.38 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 3.12/3.38 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 3.12/3.38 3 inverse(sk_c1) = sk_c9 | inverse(sk_c8) = sk_c7 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 3.12/3.38 4 inverse(sk_c1) = sk_c9 | inverse(sk_c5) = sk_c8 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 3.12/3.38 5 inverse(sk_c1) = sk_c9 | inverse(sk_c6) = sk_c9 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 3.12/3.38 6 inverse(sk_c2) = sk_c8 | inverse(sk_c8) = sk_c7 # label(prove_this_32) # label(negated_conjecture). [assumption].
% 3.12/3.38 15 multiply(sk_c8,sk_c9) = sk_c7 | inverse(sk_c8) = sk_c7 # label(prove_this_2) # label(negated_conjecture). [assumption].
% 3.12/3.38 18 multiply(sk_c1,sk_c9) = sk_c8 | inverse(sk_c8) = sk_c7 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 3.12/3.38 19 multiply(sk_c1,sk_c9) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 3.12/3.38 20 multiply(sk_c1,sk_c9) = sk_c8 | inverse(sk_c6) = sk_c9 # label(prove_this_12) # label(negated_conjecture). [assumption].
% 3.12/3.38 23 inverse(sk_c1) = sk_c9 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 3.12/3.38 27 multiply(sk_c2,sk_c8) = sk_c9 | inverse(sk_c8) = sk_c7 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 3.12/3.38 28 multiply(sk_c2,sk_c8) = sk_c9 | inverse(sk_c5) = sk_c8 # label(prove_this_28) # label(negated_conjecture). [assumption].
% 3.12/3.38 30 inverse(sk_c2) = sk_c8 | multiply(sk_c8,sk_c7) = sk_c9 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 3.12/3.38 47 multiply(sk_c1,sk_c9) = sk_c8 | multiply(sk_c6,sk_c9) = sk_c7 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 3.12/3.38 51 multiply(sk_c2,sk_c8) = sk_c9 | multiply(sk_c8,sk_c7) = sk_c9 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 3.12/3.38 57 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 3.12/3.38 58 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,sk_c7) != sk_c8 | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | inverse(C) != D | inverse(D) != sk_c9 | multiply(C,sk_c9) != D | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7 | multiply(E,sk_c8) != sk_c9 | inverse(E) != sk_c8 | multiply(F,sk_c9) != sk_c7 | inverse(F) != sk_c9 # label(prove_this_55) # label(negated_conjecture). [assumption].
% 3.12/3.38 64 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,sk_c7) != sk_c8 | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | inverse(C) != D | inverse(D) != sk_c9 | multiply(C,sk_c9) != D | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7 | multiply(E,sk_c9) != sk_c7 | inverse(E) != sk_c9. [factor(58,e,l),merge(l)].
% 3.12/3.38 127 inverse(sk_c8) = sk_c7 | multiply(sk_c9,sk_c1) = identity. [para(3(a,1),2(a,1,1))].
% 3.12/3.38 128 inverse(sk_c5) = sk_c8 | multiply(sk_c9,sk_c1) = identity. [para(4(a,1),2(a,1,1))].
% 3.12/3.38 129 inverse(sk_c6) = sk_c9 | multiply(sk_c9,sk_c1) = identity. [para(5(a,1),2(a,1,1))].
% 3.12/3.38 130 inverse(sk_c8) = sk_c7 | multiply(sk_c8,sk_c2) = identity. [para(6(a,1),2(a,1,1))].
% 3.12/3.38 139 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),57(a,1,1)),rewrite([1(2)]),flip(a)].
% 3.12/3.38 140 inverse(sk_c8) = sk_c7 | multiply(sk_c8,multiply(sk_c9,A)) = multiply(sk_c7,A). [para(15(a,1),57(a,1,1)),flip(b)].
% 3.12/3.38 146 inverse(sk_c8) = sk_c7 | multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c8,A). [para(18(a,1),57(a,1,1)),flip(b)].
% 3.12/3.38 148 inverse(sk_c5) = sk_c8 | multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c8,A). [para(19(a,1),57(a,1,1)),flip(b)].
% 3.12/3.38 150 inverse(sk_c6) = sk_c9 | multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c8,A). [para(20(a,1),57(a,1,1)),flip(b)].
% 3.12/3.38 156 inverse(sk_c1) = sk_c9 | multiply(sk_c6,multiply(sk_c9,A)) = multiply(sk_c7,A). [para(23(b,1),57(a,1,1)),flip(b)].
% 3.12/3.38 264 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,sk_c7) != sk_c8 | identity != sk_c9 | inverse(inverse(sk_c8)) != sk_c8 | inverse(B) != C | inverse(C) != sk_c9 | multiply(B,sk_c9) != C | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7 | multiply(D,sk_c9) != sk_c7 | inverse(D) != sk_c9. [para(2(a,1),64(e,1))].
% 3.12/3.38 561 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,sk_c7) != sk_c8 | identity != sk_c9 | inverse(inverse(sk_c8)) != sk_c8 | inverse(sk_c9) != sk_c9 | multiply(A,sk_c9) != sk_c9 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7 | multiply(B,sk_c9) != sk_c7 | inverse(B) != sk_c9. [factor(264,c,g)].
% 3.12/3.38 1877 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),139(a,1,2))].
% 3.12/3.38 1932 inverse(sk_c8) = sk_c7 | multiply(inverse(sk_c9),identity) = sk_c1. [para(127(b,1),139(a,1,2))].
% 3.12/3.38 1933 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(139(a,1),139(a,1,2))].
% 3.12/3.38 1934 multiply(A,identity) = A. [back_rewrite(1877),rewrite([1933(4)])].
% 3.12/3.38 1935 inverse(sk_c8) = sk_c7 | inverse(sk_c9) = sk_c1. [back_rewrite(1932),rewrite([1934(8)])].
% 3.12/3.38 1937 inverse(identity) = identity. [para(1934(a,1),2(a,1))].
% 3.12/3.38 2056 inverse(sk_c5) = sk_c8 | inverse(sk_c9) = sk_c1. [para(128(b,1),139(a,1,2)),rewrite([1934(8)])].
% 3.12/3.38 2064 inverse(sk_c6) = sk_c9 | inverse(sk_c9) = sk_c1. [para(129(b,1),139(a,1,2)),rewrite([1934(8)])].
% 3.12/3.38 2069 inverse(sk_c9) = sk_c1 | multiply(sk_c9,sk_c6) = identity. [para(2064(a,1),2(a,1,1))].
% 3.12/3.38 2072 inverse(sk_c8) = sk_c7 | inverse(sk_c8) = sk_c2. [para(130(b,1),139(a,1,2)),rewrite([1934(8)])].
% 3.12/3.38 2083 inverse(sk_c8) = sk_c7 | multiply(sk_c2,sk_c8) = identity. [para(2072(b,1),2(a,1,1))].
% 3.12/3.38 2382 multiply(A,inverse(A)) = identity. [para(1933(a,1),2(a,1))].
% 3.12/3.38 2480 inverse(inverse(A)) = A. [para(1933(a,1),1934(a,1)),rewrite([1934(2)]),flip(a)].
% 3.12/3.38 2595 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,sk_c7) != sk_c8 | identity != sk_c9 | inverse(sk_c9) != sk_c9 | multiply(A,sk_c9) != sk_c9 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7 | multiply(B,sk_c9) != sk_c7 | inverse(B) != sk_c9. [back_rewrite(561),rewrite([2480(23)]),xx(f)].
% 3.12/3.38 2617 inverse(sk_c9) = sk_c1 | inverse(sk_c7) = sk_c8. [para(1935(a,1),2480(a,1,1))].
% 3.12/3.38 2618 inverse(sk_c9) = sk_c1 | inverse(sk_c8) = sk_c5. [para(2056(a,1),2480(a,1,1))].
% 3.12/3.38 2647 inverse(sk_c8) = sk_c7 | multiply(sk_c7,inverse(sk_c9)) = sk_c8. [para(2382(a,1),140(b,1,2)),rewrite([1934(7)]),flip(b)].
% 3.12/3.38 2689 inverse(sk_c9) = sk_c1 | sk_c5 = sk_c7. [para(2618(b,1),1935(a,1)),merge(c)].
% 3.12/3.38 3054 inverse(sk_c8) = sk_c7 | multiply(sk_c8,inverse(sk_c9)) = sk_c1. [para(2382(a,1),146(b,1,2)),rewrite([1934(7)]),flip(b)].
% 3.12/3.38 3194 inverse(sk_c5) = sk_c8 | multiply(sk_c8,inverse(sk_c9)) = sk_c1. [para(2382(a,1),148(b,1,2)),rewrite([1934(7)]),flip(b)].
% 3.12/3.38 3353 inverse(sk_c6) = sk_c9 | multiply(sk_c8,inverse(sk_c9)) = sk_c1. [para(2382(a,1),150(b,1,2)),rewrite([1934(7)]),flip(b)].
% 3.12/3.38 3418 inverse(sk_c8) = sk_c7 | identity = sk_c9. [para(2083(b,1),27(a,1)),merge(c)].
% 3.12/3.38 3483 identity = sk_c9 | multiply(sk_c8,sk_c7) = identity. [para(3418(a,1),2382(a,1,2))].
% 3.12/3.38 3508 identity = sk_c9 | inverse(sk_c2) = sk_c8. [para(3483(b,1),30(b,1)),merge(c)].
% 3.12/3.38 3623 identity = sk_c9 | multiply(sk_c2,sk_c8) = identity. [para(3508(b,1),2382(a,1,2))].
% 3.12/3.38 4170 inverse(sk_c1) = sk_c9 | multiply(sk_c7,inverse(sk_c9)) = sk_c6. [para(2382(a,1),156(b,1,2)),rewrite([1934(7)]),flip(b)].
% 3.12/3.38 4777 identity = sk_c9 | inverse(sk_c5) = sk_c8. [para(3623(b,1),28(a,1)),merge(b)].
% 3.12/3.38 4779 identity = sk_c9 | multiply(sk_c8,sk_c7) = sk_c9. [para(3623(b,1),51(a,1)),merge(b)].
% 3.12/3.38 4785 identity = sk_c9 | inverse(sk_c8) = sk_c5. [para(4777(b,1),2480(a,1,1))].
% 3.12/3.38 4900 identity = sk_c9 | sk_c5 = sk_c7. [para(4785(b,1),3418(a,1)),merge(c)].
% 3.12/3.38 4906 sk_c5 = sk_c7 | inverse(sk_c9) = identity. [para(4900(a,1),1937(a,1,1))].
% 3.12/3.38 5340 sk_c5 = sk_c7 | identity = sk_c1. [para(4906(b,1),2689(a,1)),merge(c)].
% 3.12/3.38 5417 sk_c5 = sk_c7 | sk_c1 = sk_c9. [para(5340(b,1),4900(a,1)),merge(c)].
% 3.12/3.38 7599 identity = sk_c9. [para(4779(b,1),3483(b,1)),flip(c),merge(b),merge(c)].
% 3.12/3.38 10365 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(sk_c9,sk_c7) != sk_c8 | inverse(sk_c9) != sk_c9 | multiply(A,sk_c9) != sk_c9 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7 | multiply(B,sk_c9) != sk_c7 | inverse(B) != sk_c9. [back_rewrite(2595),rewrite([7599(18)]),xx(e)].
% 3.12/3.38 10411 inverse(sk_c9) = sk_c1 | multiply(sk_c9,sk_c6) = sk_c9. [back_rewrite(2069),rewrite([7599(8)])].
% 3.12/3.38 10414 inverse(sk_c9) = sk_c9. [back_rewrite(1937),rewrite([7599(1),7599(3)])].
% 3.12/3.38 10415 multiply(A,sk_c9) = A. [back_rewrite(1934),rewrite([7599(1)])].
% 3.12/3.38 10428 multiply(inverse(A),A) = sk_c9. [back_rewrite(2),rewrite([7599(3)])].
% 3.12/3.38 10429 multiply(sk_c9,A) = A. [back_rewrite(1),rewrite([7599(1)])].
% 3.12/3.38 10500 sk_c7 != sk_c8 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7 | sk_c7 != A | inverse(A) != sk_c9. [factor(10365,c,e),rewrite([10415(3),10415(6),10414(8),10429(12),10415(15),10415(26)]),flip(a),flip(b),flip(h),xx(c),xx(e),merge(c)].
% 3.12/3.38 10521 sk_c1 = sk_c9 | sk_c6 = sk_c9. [back_rewrite(10411),rewrite([10414(2),10429(6)]),flip(a)].
% 3.12/3.38 10875 inverse(sk_c1) = sk_c9 | sk_c6 = sk_c7. [back_rewrite(4170),rewrite([10414(7),10415(7)]),flip(b)].
% 3.12/3.38 10888 inverse(sk_c6) = sk_c9 | sk_c1 = sk_c8. [back_rewrite(3353),rewrite([10414(7),10415(7)]),flip(b)].
% 3.12/3.38 10890 inverse(sk_c5) = sk_c8 | sk_c1 = sk_c8. [back_rewrite(3194),rewrite([10414(7),10415(7)]),flip(b)].
% 3.12/3.38 10894 inverse(sk_c8) = sk_c7 | sk_c1 = sk_c8. [back_rewrite(3054),rewrite([10414(7),10415(7)]),flip(b)].
% 3.12/3.38 10913 inverse(sk_c8) = sk_c7 | sk_c7 = sk_c8. [back_rewrite(2647),rewrite([10414(7),10415(7)])].
% 3.12/3.38 10919 sk_c1 = sk_c9 | inverse(sk_c7) = sk_c8. [back_rewrite(2617),rewrite([10414(2)]),flip(a)].
% 3.12/3.38 12158 sk_c1 = sk_c8 | sk_c6 = sk_c7. [back_rewrite(47),rewrite([10415(3),10415(6)])].
% 3.12/3.38 12277 sk_c7 != sk_c8 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7 | inverse(A) != sk_c7 | sk_c9 != A. [para(2480(a,1),10500(f,1)),flip(e),flip(f)].
% 3.12/3.38 12281 sk_c7 != sk_c8 | sk_c8 != sk_c9 | multiply(sk_c8,sk_c7) != sk_c9 | inverse(sk_c8) != sk_c7. [factor(12277,d,e),flip(e),merge(e)].
% 3.12/3.38 12473 sk_c6 = sk_c7 | sk_c1 = sk_c9. [para(10875(a,1),2480(a,1,1)),rewrite([10414(5)]),flip(b)].
% 3.12/3.38 12476 sk_c6 = sk_c7 | sk_c8 = sk_c9. [para(12473(b,1),12158(a,1)),flip(b),merge(c)].
% 3.12/3.38 12600 sk_c1 = sk_c8 | sk_c6 = sk_c9. [para(10888(a,1),2480(a,1,1)),rewrite([10414(5)]),flip(b)].
% 3.12/3.38 12617 sk_c6 = sk_c9 | sk_c8 = sk_c9. [para(12600(a,1),10521(a,1)),merge(c)].
% 3.12/3.38 12620 sk_c8 = sk_c9 | sk_c7 = sk_c9. [para(12617(a,1),12476(a,1)),flip(b),merge(c)].
% 3.12/3.38 12844 sk_c1 = sk_c8 | inverse(sk_c8) = sk_c5. [para(10890(a,1),2480(a,1,1))].
% 3.12/3.38 13071 sk_c7 = sk_c8 | multiply(sk_c7,sk_c8) = sk_c9. [para(10913(a,1),10428(a,1,1))].
% 3.12/3.38 13102 sk_c8 = sk_c9 | sk_c1 = sk_c9. [para(12620(b,1),10919(b,1,1)),rewrite([10414(8)]),flip(c),merge(c)].
% 3.12/3.38 13410 sk_c1 = sk_c8 | sk_c5 = sk_c7. [para(12844(b,1),10894(a,1)),merge(c)].
% 3.12/3.38 13420 sk_c5 = sk_c7 | sk_c8 = sk_c9. [para(13410(a,1),5417(b,1)),merge(b)].
% 3.12/3.38 13449 sk_c8 = sk_c9 | sk_c5 = sk_c9. [para(12620(b,1),13420(a,2)),merge(c)].
% 3.12/3.38 13450 sk_c8 = sk_c9 | sk_c1 = sk_c8. [para(13449(b,1),10890(a,1,1)),rewrite([10414(5)]),flip(b),merge(b)].
% 3.12/3.38 13458 sk_c8 = sk_c9. [para(13450(b,1),13102(b,1)),merge(b),merge(c)].
% 3.12/3.38 13552 sk_c7 = sk_c9. [back_rewrite(13071),rewrite([13458(2),13458(5),10415(6)]),merge(b)].
% 3.12/3.38 13653 $F. [back_rewrite(12281),rewrite([13552(1),13458(2),13458(4),13458(7),13552(8),10415(9),13458(10),10414(11),13552(11)]),xx(a),xx(b),xx(c),xx(d)].
% 3.12/3.38
% 3.12/3.38 % SZS output end Refutation
% 3.12/3.38 ============================== end of proof ==========================
% 3.12/3.38
% 3.12/3.38 ============================== STATISTICS ============================
% 3.12/3.38
% 3.12/3.38 Given=546. Generated=40111. Kept=13652. proofs=1.
% 3.12/3.38 Usable=139. Sos=1044. Demods=23. Limbo=195, Disabled=12332. Hints=0.
% 3.12/3.38 Megabytes=16.76.
% 3.12/3.38 User_CPU=2.36, System_CPU=0.03, Wall_clock=2.
% 3.12/3.38
% 3.12/3.38 ============================== end of statistics =====================
% 3.12/3.38
% 3.12/3.38 ============================== end of search =========================
% 3.12/3.38
% 3.12/3.38 THEOREM PROVED
% 3.12/3.38 % SZS status Unsatisfiable
% 3.12/3.38
% 3.12/3.38 Exiting with 1 proof.
% 3.12/3.38
% 3.12/3.38 Process 3925 exit (max_proofs) Tue Jun 14 03:00:12 2022
% 3.12/3.38 Prover9 interrupted
%------------------------------------------------------------------------------