TSTP Solution File: GRP275-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP275-1 : 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 11:18:27 EDT 2022
% Result : Unsatisfiable 0.82s 1.63s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP275-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 01:14:39 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.82/1.63 ============================== Prover9 ===============================
% 0.82/1.63 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.63 Process 19681 was started by sandbox on n019.cluster.edu,
% 0.82/1.63 Tue Jun 14 01:14:40 2022
% 0.82/1.63 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19527_n019.cluster.edu".
% 0.82/1.63 ============================== end of head ===========================
% 0.82/1.63
% 0.82/1.63 ============================== INPUT =================================
% 0.82/1.63
% 0.82/1.63 % Reading from file /tmp/Prover9_19527_n019.cluster.edu
% 0.82/1.63
% 0.82/1.63 set(prolog_style_variables).
% 0.82/1.63 set(auto2).
% 0.82/1.63 % set(auto2) -> set(auto).
% 0.82/1.63 % set(auto) -> set(auto_inference).
% 0.82/1.63 % set(auto) -> set(auto_setup).
% 0.82/1.63 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.63 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.63 % set(auto) -> set(auto_limits).
% 0.82/1.63 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.63 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.63 % set(auto) -> set(auto_denials).
% 0.82/1.63 % set(auto) -> set(auto_process).
% 0.82/1.63 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.63 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.63 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.63 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.63 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.63 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.63 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.63 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.63 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.63 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.63 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.63 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.63 % set(auto2) -> assign(stats, some).
% 0.82/1.63 % set(auto2) -> clear(echo_input).
% 0.82/1.63 % set(auto2) -> set(quiet).
% 0.82/1.63 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.63 % set(auto2) -> clear(print_given).
% 0.82/1.63 assign(lrs_ticks,-1).
% 0.82/1.63 assign(sos_limit,10000).
% 0.82/1.63 assign(order,kbo).
% 0.82/1.63 set(lex_order_vars).
% 0.82/1.63 clear(print_given).
% 0.82/1.63
% 0.82/1.63 % formulas(sos). % not echoed (34 formulas)
% 0.82/1.63
% 0.82/1.63 ============================== end of input ==========================
% 0.82/1.63
% 0.82/1.63 % From the command line: assign(max_seconds, 300).
% 0.82/1.63
% 0.82/1.63 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.63
% 0.82/1.63 % Formulas that are not ordinary clauses:
% 0.82/1.63
% 0.82/1.63 ============================== end of process non-clausal formulas ===
% 0.82/1.63
% 0.82/1.63 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.63
% 0.82/1.63 ============================== PREDICATE ELIMINATION =================
% 0.82/1.63
% 0.82/1.63 ============================== end predicate elimination =============
% 0.82/1.63
% 0.82/1.63 Auto_denials: (non-Horn, no changes).
% 0.82/1.63
% 0.82/1.63 Term ordering decisions:
% 0.82/1.63
% 0.82/1.63 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 0.82/1.63 Function symbol KB weights: sk_c8=1. sk_c7=1. sk_c5=1. sk_c1=1. sk_c2=1. sk_c6=1. sk_c3=1. sk_c4=1. identity=1. multiply=1. inverse=0.
% 0.82/1.63
% 0.82/1.63 ============================== end of process initial clauses ========
% 0.82/1.63
% 0.82/1.63 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.63
% 0.82/1.63 ============================== end of clauses for search =============
% 0.82/1.63
% 0.82/1.63 ============================== SEARCH ================================
% 0.82/1.63
% 0.82/1.63 % Starting search at 0.02 seconds.
% 0.82/1.63
% 0.82/1.63 ============================== PROOF =================================
% 0.82/1.63 % SZS status Unsatisfiable
% 0.82/1.63 % SZS output start Refutation
% 0.82/1.63
% 0.82/1.63 % Proof 1 at 0.55 (+ 0.01) seconds.
% 0.82/1.63 % Length of proof is 121.
% 0.82/1.63 % Level of proof is 21.
% 0.82/1.63 % Maximum clause weight is 51.000.
% 0.82/1.63 % Given clauses 431.
% 0.82/1.63
% 0.82/1.63 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.82/1.63 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.82/1.63 3 inverse(sk_c1) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 0.82/1.63 4 inverse(sk_c1) = sk_c8 | inverse(sk_c4) = sk_c5 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 0.82/1.63 5 inverse(sk_c2) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_20) # label(negated_conjecture). [assumption].
% 0.82/1.63 8 multiply(sk_c1,sk_c8) = sk_c7 | inverse(sk_c4) = sk_c5 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 0.82/1.63 10 inverse(sk_c1) = sk_c8 | multiply(sk_c3,sk_c7) = sk_c8 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 0.82/1.63 11 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c5) = sk_c7 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 0.82/1.63 13 multiply(sk_c8,sk_c6) = sk_c7 | inverse(sk_c3) = sk_c8 # label(prove_this_14) # label(negated_conjecture). [assumption].
% 0.82/1.63 14 multiply(sk_c8,sk_c6) = sk_c7 | inverse(sk_c4) = sk_c5 # label(prove_this_17) # label(negated_conjecture). [assumption].
% 0.82/1.63 15 inverse(sk_c2) = sk_c8 | multiply(sk_c7,sk_c8) = sk_c6 # label(prove_this_19) # label(negated_conjecture). [assumption].
% 0.82/1.63 16 inverse(sk_c2) = sk_c8 | multiply(sk_c3,sk_c7) = sk_c8 # label(prove_this_21) # label(negated_conjecture). [assumption].
% 0.82/1.63 19 multiply(sk_c2,sk_c7) = sk_c8 | inverse(sk_c3) = sk_c8 # label(prove_this_26) # label(negated_conjecture). [assumption].
% 0.82/1.63 23 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c4,sk_c5) = sk_c7 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 0.82/1.63 25 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c7,sk_c8) = sk_c6 # label(prove_this_13) # label(negated_conjecture). [assumption].
% 0.82/1.63 26 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c3,sk_c7) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 0.82/1.63 28 multiply(sk_c8,sk_c6) = sk_c7 | multiply(sk_c5,sk_c8) = sk_c7 # label(prove_this_18) # label(negated_conjecture). [assumption].
% 0.82/1.63 29 multiply(sk_c2,sk_c7) = sk_c8 | multiply(sk_c7,sk_c8) = sk_c6 # label(prove_this_25) # label(negated_conjecture). [assumption].
% 0.82/1.63 30 multiply(sk_c2,sk_c7) = sk_c8 | multiply(sk_c3,sk_c7) = sk_c8 # label(prove_this_27) # label(negated_conjecture). [assumption].
% 0.82/1.63 33 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.82/1.63 34 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6 | inverse(C) != sk_c8 | multiply(C,sk_c7) != sk_c8 | multiply(D,E) != sk_c7 | inverse(D) != E | multiply(E,sk_c8) != sk_c7 # label(prove_this_31) # label(negated_conjecture). [assumption].
% 0.82/1.63 39 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6 | multiply(C,D) != sk_c7 | inverse(C) != D | multiply(D,sk_c8) != sk_c7. [factor(34,d,g),merge(g)].
% 0.82/1.63 54 inverse(sk_c1) = sk_c8 | multiply(sk_c8,sk_c3) = identity. [para(3(b,1),2(a,1,1))].
% 0.82/1.63 56 inverse(sk_c2) = sk_c8 | multiply(sk_c8,sk_c3) = identity. [para(5(b,1),2(a,1,1))].
% 0.82/1.63 58 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),33(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.82/1.63 65 inverse(sk_c1) = sk_c8 | multiply(sk_c3,multiply(sk_c7,A)) = multiply(sk_c8,A). [para(10(b,1),33(a,1,1)),flip(b)].
% 0.82/1.63 141 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c7 | inverse(inverse(C)) != C | multiply(C,sk_c8) != sk_c7. [para(2(a,1),39(g,1))].
% 0.82/1.63 231 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c7 | inverse(inverse(A)) != A. [factor(141,a,i)].
% 0.82/1.63 407 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),58(a,1,2))].
% 0.82/1.63 417 inverse(sk_c3) = sk_c8 | multiply(inverse(sk_c8),sk_c7) = sk_c6. [para(13(a,1),58(a,1,2))].
% 0.82/1.63 418 inverse(sk_c4) = sk_c5 | multiply(inverse(sk_c8),sk_c7) = sk_c6. [para(14(a,1),58(a,1,2))].
% 0.82/1.63 419 inverse(sk_c2) = sk_c8 | multiply(inverse(sk_c7),sk_c6) = sk_c8. [para(15(b,1),58(a,1,2))].
% 0.82/1.63 429 multiply(sk_c8,sk_c6) = sk_c7 | multiply(inverse(sk_c7),sk_c6) = sk_c8. [para(25(b,1),58(a,1,2))].
% 0.82/1.63 432 multiply(sk_c8,sk_c6) = sk_c7 | multiply(inverse(sk_c5),sk_c7) = sk_c8. [para(28(b,1),58(a,1,2))].
% 0.82/1.63 433 multiply(sk_c7,sk_c8) = sk_c6 | multiply(inverse(sk_c2),sk_c8) = sk_c7. [para(29(a,1),58(a,1,2))].
% 0.82/1.63 442 inverse(sk_c1) = sk_c8 | multiply(inverse(sk_c8),identity) = sk_c3. [para(54(b,1),58(a,1,2))].
% 0.82/1.63 443 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(58(a,1),58(a,1,2))].
% 0.82/1.63 444 multiply(A,identity) = A. [back_rewrite(407),rewrite([443(4)])].
% 0.82/1.63 445 inverse(sk_c1) = sk_c8 | inverse(sk_c8) = sk_c3. [back_rewrite(442),rewrite([444(8)])].
% 0.82/1.63 462 inverse(identity) = identity. [para(444(a,1),2(a,1))].
% 0.82/1.63 506 inverse(sk_c2) = sk_c8 | inverse(sk_c8) = sk_c3. [para(56(b,1),58(a,1,2)),rewrite([444(8)])].
% 0.82/1.63 507 inverse(sk_c8) = sk_c3 | multiply(sk_c8,sk_c2) = identity. [para(506(a,1),2(a,1,1))].
% 0.82/1.63 536 multiply(A,inverse(A)) = identity. [para(443(a,1),2(a,1))].
% 0.82/1.63 561 multiply(A,multiply(inverse(A),B)) = B. [para(443(a,1),58(a,1))].
% 0.82/1.63 562 inverse(inverse(A)) = A. [para(443(a,1),444(a,1)),rewrite([444(2)]),flip(a)].
% 0.82/1.63 581 multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(B) != sk_c8 | multiply(B,sk_c7) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6 | identity != sk_c7. [back_rewrite(231),rewrite([562(29)]),xx(h)].
% 0.82/1.63 597 inverse(sk_c1) = sk_c8 | multiply(sk_c4,sk_c5) = identity. [para(4(b,1),536(a,1,2))].
% 0.82/1.63 652 inverse(sk_c8) = sk_c3 | multiply(sk_c1,multiply(sk_c8,A)) = A. [para(445(a,1),561(a,1,2,1))].
% 0.82/1.63 859 inverse(sk_c1) = sk_c8 | identity = sk_c7. [para(597(b,1),11(b,1)),merge(b)].
% 0.82/1.63 866 identity = sk_c7 | multiply(sk_c1,sk_c8) = identity. [para(859(a,1),536(a,1,2))].
% 0.82/1.63 919 identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(A) != sk_c8 | multiply(A,sk_c7) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6. [para(2(a,1),581(a,1)),rewrite([562(6)]),xx(b),merge(f)].
% 0.82/1.63 929 identity = sk_c7 | inverse(sk_c4) = sk_c5. [para(866(b,1),8(a,1)),merge(b)].
% 0.82/1.63 949 inverse(sk_c1) = sk_c8 | multiply(sk_c8,inverse(sk_c7)) = sk_c3. [para(536(a,1),65(b,1,2)),rewrite([444(7)]),flip(b)].
% 0.82/1.63 972 identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(multiply(A,B)) != sk_c8 | multiply(A,multiply(B,sk_c7)) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6. [para(33(a,1),919(d,1))].
% 0.82/1.63 973 identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(multiply(A,inverse(sk_c7))) != sk_c8 | sk_c8 != A | multiply(sk_c7,sk_c8) != sk_c6. [para(2(a,1),972(d,1,2)),rewrite([444(16)]),flip(d)].
% 0.82/1.63 989 identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(multiply(A,multiply(B,inverse(sk_c7)))) != sk_c8 | multiply(A,B) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6. [para(33(a,1),973(c,1,1)),flip(d)].
% 0.82/1.63 1005 identity = sk_c7 | multiply(sk_c4,sk_c5) = identity. [para(929(b,1),536(a,1,2))].
% 0.82/1.63 1045 identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(multiply(A,multiply(B,multiply(C,inverse(sk_c7))))) != sk_c8 | multiply(A,multiply(B,C)) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6. [para(33(a,1),989(c,1,1,2))].
% 0.82/1.63 1275 identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(A) != sk_c8 | multiply(A,multiply(inverse(multiply(B,inverse(sk_c7))),B)) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6. [para(2(a,1),1045(c,1,1,2)),rewrite([444(10)])].
% 0.82/1.63 1299 identity = sk_c7 | multiply(sk_c1,sk_c8) = sk_c7. [para(1005(b,1),23(b,1)),merge(c)].
% 0.82/1.63 1324 identity != sk_c7 | multiply(sk_c8,sk_c6) != sk_c7 | inverse(multiply(sk_c8,inverse(sk_c7))) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6. [resolve(1275,d,561,a)].
% 0.82/1.63 1835 identity = sk_c7. [para(1299(b,1),866(b,1)),flip(c),merge(b),merge(c)].
% 0.82/1.63 2098 multiply(sk_c8,sk_c6) != sk_c7 | inverse(multiply(sk_c8,inverse(sk_c7))) != sk_c8 | multiply(sk_c7,sk_c8) != sk_c6. [back_rewrite(1324),rewrite([1835(1)]),xx(a)].
% 0.82/1.63 2462 multiply(A,inverse(A)) = sk_c7. [back_rewrite(536),rewrite([1835(3)])].
% 0.82/1.63 2464 inverse(sk_c8) = sk_c3 | multiply(sk_c8,sk_c2) = sk_c7. [back_rewrite(507),rewrite([1835(8)])].
% 0.82/1.63 2477 inverse(sk_c7) = sk_c7. [back_rewrite(462),rewrite([1835(1),1835(3)])].
% 0.82/1.63 2478 multiply(A,sk_c7) = A. [back_rewrite(444),rewrite([1835(1)])].
% 0.82/1.63 2484 multiply(sk_c7,A) = A. [back_rewrite(1),rewrite([1835(1)])].
% 0.82/1.63 2505 multiply(sk_c8,sk_c6) != sk_c7 | inverse(sk_c8) != sk_c8 | sk_c6 != sk_c8. [back_rewrite(2098),rewrite([2477(8),2478(8),2484(12)]),flip(c)].
% 0.82/1.63 2544 inverse(sk_c1) = sk_c8 | sk_c3 = sk_c8. [back_rewrite(949),rewrite([2477(7),2478(7)]),flip(b)].
% 0.82/1.63 2548 multiply(sk_c8,sk_c6) = sk_c7 | sk_c6 = sk_c8. [back_rewrite(429),rewrite([2477(7),2484(8)])].
% 0.82/1.63 2549 inverse(sk_c2) = sk_c8 | sk_c6 = sk_c8. [back_rewrite(419),rewrite([2477(6),2484(7)])].
% 0.82/1.63 2685 multiply(sk_c8,sk_c6) = sk_c7 | inverse(sk_c5) = sk_c8. [back_rewrite(432),rewrite([2478(9)])].
% 0.82/1.63 2687 inverse(sk_c4) = sk_c5 | inverse(sk_c8) = sk_c6. [back_rewrite(418),rewrite([2478(8)])].
% 0.82/1.63 2688 inverse(sk_c3) = sk_c8 | inverse(sk_c8) = sk_c6. [back_rewrite(417),rewrite([2478(8)])].
% 0.82/1.63 2716 sk_c2 = sk_c8 | sk_c3 = sk_c8. [back_rewrite(30),rewrite([2478(3),2478(6)])].
% 0.82/1.63 2718 multiply(sk_c8,sk_c6) = sk_c7 | sk_c3 = sk_c8. [back_rewrite(26),rewrite([2478(8)])].
% 0.82/1.63 2720 sk_c2 = sk_c8 | inverse(sk_c3) = sk_c8. [back_rewrite(19),rewrite([2478(3)])].
% 0.82/1.63 2721 inverse(sk_c2) = sk_c8 | sk_c3 = sk_c8. [back_rewrite(16),rewrite([2478(7)])].
% 0.82/1.63 2804 sk_c6 = sk_c8 | multiply(inverse(sk_c2),sk_c8) = sk_c7. [back_rewrite(433),rewrite([2484(3)]),flip(a)].
% 0.82/1.63 2830 inverse(sk_c8) != sk_c8 | sk_c6 != sk_c8 | inverse(sk_c4) = sk_c5. [resolve(2505,a,14,a)].
% 0.82/1.63 2864 sk_c3 = sk_c8 | inverse(sk_c8) = sk_c1. [para(2544(a,1),562(a,1,1))].
% 0.82/1.63 2915 sk_c2 = sk_c8 | inverse(sk_c8) = sk_c8. [para(2716(b,1),2720(b,1,1)),merge(b)].
% 0.82/1.63 2918 sk_c3 = sk_c8 | inverse(sk_c8) = sk_c2. [para(2721(a,1),562(a,1,1))].
% 0.82/1.63 2962 sk_c2 = sk_c8 | multiply(sk_c8,sk_c8) = sk_c7. [para(2915(b,1),2462(a,1,2))].
% 0.82/1.63 2965 sk_c3 = sk_c8 | sk_c2 = sk_c1. [para(2918(b,1),2864(b,1)),merge(b)].
% 0.82/1.63 2985 sk_c6 = sk_c8 | inverse(sk_c8) = sk_c6. [para(2548(a,1),58(a,1,2)),rewrite([2478(7)])].
% 0.82/1.63 3006 inverse(sk_c8) = sk_c6 | inverse(sk_c5) = sk_c4. [para(2687(a,1),562(a,1,1))].
% 0.82/1.63 3095 sk_c3 = sk_c8 | inverse(sk_c8) != sk_c8 | sk_c6 != sk_c8. [resolve(2718,a,2505,a)].
% 0.82/1.63 3100 sk_c3 = sk_c8 | inverse(sk_c8) = sk_c6. [para(2718(a,1),58(a,1,2)),rewrite([2478(7)])].
% 0.82/1.63 3103 sk_c3 = sk_c8 | inverse(sk_c6) = sk_c8. [para(3100(b,1),562(a,1,1))].
% 0.82/1.63 3509 inverse(sk_c8) = sk_c3 | sk_c2 = sk_c1. [para(2464(b,1),652(b,1,2)),rewrite([2478(11)]),flip(c),merge(b)].
% 0.82/1.63 3517 sk_c2 = sk_c1 | inverse(sk_c8) = sk_c8. [para(2965(a,1),3509(a,2)),merge(c)].
% 0.82/1.63 3558 sk_c2 = sk_c1 | multiply(sk_c8,sk_c8) = sk_c7. [para(3517(b,1),2462(a,1,2))].
% 0.82/1.63 3604 inverse(sk_c5) = sk_c8 | inverse(sk_c8) = sk_c6. [para(2685(a,1),58(a,1,2)),rewrite([2478(8)])].
% 0.82/1.63 3614 inverse(sk_c8) = sk_c6 | sk_c4 = sk_c8. [para(3604(a,1),3006(b,1)),flip(c),merge(b)].
% 0.82/1.63 3619 sk_c4 = sk_c8 | inverse(sk_c6) = sk_c8. [para(3614(a,1),562(a,1,1))].
% 0.82/1.63 3622 sk_c4 = sk_c8 | multiply(sk_c8,sk_c6) = sk_c7. [para(3614(a,1),2462(a,1,2))].
% 0.82/1.63 3725 sk_c4 = sk_c8 | inverse(sk_c8) != sk_c8 | sk_c6 != sk_c8. [resolve(3622,b,2505,a)].
% 0.82/1.63 3745 sk_c6 = sk_c8 | multiply(sk_c8,sk_c8) = sk_c7. [para(2549(a,1),2804(b,1,1)),merge(b)].
% 0.82/1.63 3752 sk_c6 = sk_c8 | inverse(sk_c8) = sk_c8. [para(3745(b,1),58(a,1,2)),rewrite([2478(7)])].
% 0.82/1.63 3757 sk_c6 = sk_c8. [para(3752(b,1),2985(b,1)),flip(c),merge(b),merge(c)].
% 0.82/1.63 3765 sk_c4 = sk_c8 | inverse(sk_c8) != sk_c8. [back_rewrite(3725),rewrite([3757(8)]),xx(c)].
% 0.82/1.63 3818 sk_c4 = sk_c8 | inverse(sk_c8) = sk_c8. [back_rewrite(3619),rewrite([3757(4)])].
% 0.82/1.63 3886 sk_c3 = sk_c8 | inverse(sk_c8) = sk_c8. [back_rewrite(3103),rewrite([3757(4)])].
% 0.82/1.63 3890 sk_c3 = sk_c8 | inverse(sk_c8) != sk_c8. [back_rewrite(3095),rewrite([3757(8)]),xx(c)].
% 0.82/1.63 3940 inverse(sk_c8) != sk_c8 | inverse(sk_c4) = sk_c5. [back_rewrite(2830),rewrite([3757(5)]),xx(b)].
% 0.82/1.63 3994 inverse(sk_c3) = sk_c8 | inverse(sk_c8) = sk_c8. [back_rewrite(2688),rewrite([3757(7)])].
% 0.82/1.63 4082 multiply(sk_c8,sk_c8) != sk_c7 | inverse(sk_c8) != sk_c8. [back_rewrite(2505),rewrite([3757(2),3757(10)]),xx(c)].
% 0.82/1.63 4100 inverse(sk_c8) != sk_c8 | sk_c2 = sk_c1. [resolve(4082,a,3558,b)].
% 0.82/1.63 4101 inverse(sk_c8) != sk_c8 | sk_c2 = sk_c8. [resolve(4082,a,2962,b)].
% 0.82/1.63 4188 sk_c4 = sk_c8. [resolve(3818,b,3765,b),merge(b)].
% 0.82/1.63 4228 inverse(sk_c8) != sk_c8 | inverse(sk_c8) = sk_c5. [back_rewrite(3940),rewrite([4188(5)])].
% 0.82/1.63 4358 multiply(sk_c1,sk_c8) = sk_c7 | multiply(sk_c8,sk_c5) = sk_c7. [back_rewrite(23),rewrite([4188(6)])].
% 0.82/1.63 4373 sk_c3 = sk_c8. [resolve(3890,b,3886,b),merge(b)].
% 0.82/1.63 4427 inverse(sk_c8) = sk_c8. [back_rewrite(3994),rewrite([4373(1)]),merge(b)].
% 0.82/1.63 4497 sk_c5 = sk_c8. [back_rewrite(4228),rewrite([4427(2),4427(5)]),flip(b),xx(a)].
% 0.82/1.63 4498 sk_c2 = sk_c8. [back_rewrite(4101),rewrite([4427(2)]),xx(a)].
% 0.82/1.63 4499 sk_c1 = sk_c8. [back_rewrite(4100),rewrite([4427(2),4498(4)]),flip(b),xx(a)].
% 0.82/1.63 4500 multiply(sk_c8,sk_c8) != sk_c7. [back_rewrite(4082),rewrite([4427(7)]),xx(b)].
% 0.82/1.63 4501 $F. [back_rewrite(4358),rewrite([4499(1),4497(7)]),merge(b),unit_del(a,4500)].
% 0.82/1.63
% 0.82/1.63 % SZS output end Refutation
% 0.82/1.63 ============================== end of proof ==========================
% 0.82/1.63
% 0.82/1.63 ============================== STATISTICS ============================
% 0.82/1.63
% 0.82/1.63 Given=431. Generated=13313. Kept=4500. proofs=1.
% 0.82/1.63 Usable=33. Sos=187. Demods=23. Limbo=4, Disabled=4310. Hints=0.
% 0.82/1.63 Megabytes=3.71.
% 0.82/1.63 User_CPU=0.55, System_CPU=0.01, Wall_clock=1.
% 0.82/1.63
% 0.82/1.63 ============================== end of statistics =====================
% 0.82/1.63
% 0.82/1.63 ============================== end of search =========================
% 0.82/1.63
% 0.82/1.63 THEOREM PROVED
% 0.82/1.63 % SZS status Unsatisfiable
% 0.82/1.63
% 0.82/1.63 Exiting with 1 proof.
% 0.82/1.63
% 0.82/1.63 Process 19681 exit (max_proofs) Tue Jun 14 01:14:41 2022
% 0.82/1.63 Prover9 interrupted
%------------------------------------------------------------------------------