%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP283-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:32 AM UTC 2026
% Result : Unsatisfiable 34.75s 6.31s
% Output : CNFRefutation 34.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 16
% Syntax : Number of formulae : 171 ( 24 unt; 0 def)
% Number of atoms : 489 ( 488 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 533 ( 215 ~; 318 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_8,axiom,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_11,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_14,axiom,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_16,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_20,axiom,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_26,axiom,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_32,axiom,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_37,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c6
| inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(VAR_2) != sk_c8
| multiply(VAR_2,sk_c8) != VAR_1
| multiply(sk_c8,VAR_1) != sk_c7
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_37) ).
cnf(c_40,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c6
| inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != B
| multiply(sk_c8,B) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_37]) ).
cnf(c_12982,plain,
( inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_42,plain,
( inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_12982]) ).
cnf(c_50,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_12983,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_12984,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_12983]) ).
cnf(c_54,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_12984]) ).
cnf(c_100,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_105,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_106,plain,
( multiply(sk_c7,sk_c4) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_110,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_111,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_12985,plain,
( multiply(sk_c7,A) = multiply(sk_c8,multiply(sk_c3,A))
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_23,c_3]) ).
cnf(c_117,plain,
( multiply(sk_c8,multiply(sk_c3,A)) = multiply(sk_c7,A)
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_12985]) ).
cnf(c_138,plain,
( multiply(sk_c3,A) = multiply(sk_c2,multiply(sk_c8,A))
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_29,c_3]) ).
cnf(c_12986,plain,
( multiply(multiply(A,sk_c2),sk_c8) = multiply(A,sk_c3)
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_29,c_3]) ).
cnf(c_139,plain,
( multiply(A,multiply(sk_c2,sk_c8)) = multiply(A,sk_c3)
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_12986]) ).
cnf(c_157,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_35,c_2]) ).
cnf(c_170,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_54]) ).
cnf(c_173,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_54]) ).
cnf(c_174,plain,
( multiply(inverse(sk_c8),sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_54]) ).
cnf(c_244,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_54,c_54]) ).
cnf(c_245,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_244,c_170]) ).
cnf(c_250,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_245,c_2]) ).
cnf(c_12987,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_100,c_54]) ).
cnf(c_254,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_245,c_12987]) ).
cnf(c_256,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_254,c_2]) ).
cnf(c_12988,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_105,c_54]) ).
cnf(c_279,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_245,c_12988]) ).
cnf(c_12989,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_106,c_54]) ).
cnf(c_286,plain,
( inverse(sk_c7) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_245,c_12989]) ).
cnf(c_12990,plain,
( sk_c4 = sk_c6
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_286,c_17]) ).
cnf(c_291,plain,
( sk_c4 = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_12990]) ).
cnf(c_306,plain,
( multiply(sk_c8,sk_c1) = identity
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_291,c_2]) ).
cnf(c_12991,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_306,c_54]) ).
cnf(c_317,plain,
( inverse(sk_c8) = sk_c1
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_245,c_12991]) ).
cnf(c_12992,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c6) = sk_c7
| inverse(sk_c8) = sk_c1 ),
inference(paramod,[status(thm)],[c_317,c_279]) ).
cnf(c_330,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c8) = sk_c1 ),
inference(copy,[status(thm)],[c_12992]) ).
cnf(c_12993,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_110,c_54]) ).
cnf(c_362,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_245,c_12993]) ).
cnf(c_364,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_362,c_2]) ).
cnf(c_12994,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_111,c_54]) ).
cnf(c_369,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_245,c_12994]) ).
cnf(c_372,plain,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_369,c_2]) ).
cnf(c_12995,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_157,c_54]) ).
cnf(c_378,plain,
( inverse(sk_c8) = sk_c2
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_245,c_12995]) ).
cnf(c_12996,plain,
( inverse(sk_c7) = sk_c6
| identity = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_256,c_11]) ).
cnf(c_731,plain,
( identity = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_12996]) ).
cnf(c_734,plain,
( multiply(sk_c6,sk_c7) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_731,c_2]) ).
cnf(c_12997,plain,
( multiply(inverse(sk_c6),identity) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_734,c_54]) ).
cnf(c_743,plain,
( inverse(sk_c6) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_245,c_12997]) ).
cnf(c_12998,plain,
( inverse(sk_c5) = sk_c8
| identity = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_364,c_15]) ).
cnf(c_2070,plain,
( identity = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_12998]) ).
cnf(c_2077,plain,
( multiply(sk_c8,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2070,c_2]) ).
cnf(c_12999,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2077,c_54]) ).
cnf(c_2106,plain,
( inverse(sk_c8) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_245,c_12999]) ).
cnf(c_2120,plain,
( multiply(sk_c5,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2106,c_2]) ).
cnf(c_13000,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_372,c_20]) ).
cnf(c_2384,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_13000]) ).
cnf(c_2396,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2384,c_2]) ).
cnf(c_13001,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2396,c_54]) ).
cnf(c_2503,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_245,c_13001]) ).
cnf(c_2553,plain,
( inverse(sk_c6) = identity
| inverse(sk_c8) = sk_c1 ),
inference(paramod,[status(thm)],[c_2503,c_250]) ).
cnf(c_13002,plain,
( identity = sk_c7
| inverse(sk_c8) = sk_c1
| inverse(sk_c8) = sk_c1 ),
inference(paramod,[status(thm)],[c_2553,c_330]) ).
cnf(c_3589,plain,
( identity = sk_c7
| inverse(sk_c8) = sk_c1 ),
inference(copy,[status(thm)],[c_13002]) ).
cnf(c_3596,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_3589,c_2]) ).
cnf(c_13003,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c3)) = multiply(sk_c7,multiply(sk_c2,sk_c8))
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_139,c_117]) ).
cnf(c_5015,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c3)) = multiply(sk_c7,multiply(sk_c2,sk_c8))
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_13003]) ).
cnf(c_13004,plain,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_139,c_138]) ).
cnf(c_5019,plain,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_13004]) ).
cnf(c_13005,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_3596,c_14]) ).
cnf(c_5111,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_13005]) ).
cnf(c_13006,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_378,c_174]) ).
cnf(c_9759,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_13006]) ).
cnf(c_13007,plain,
( sk_c6 = identity
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_5111,c_2120]) ).
cnf(c_13008,plain,
( identity = sk_c6
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_13007]) ).
cnf(c_9855,plain,
( identity = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_13008]) ).
cnf(c_9884,plain,
( inverse(sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9855,c_250]) ).
cnf(c_13009,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_9884,c_743]) ).
cnf(c_13010,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_13009]) ).
cnf(c_10485,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_13010]) ).
cnf(c_13011,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_10485,c_250]) ).
cnf(c_11973,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_10485,c_13011]) ).
cnf(c_11974,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_10485,c_245]) ).
cnf(c_11986,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_10485,c_1]) ).
cnf(c_13012,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_11973,c_9759]) ).
cnf(c_12009,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_13012]) ).
cnf(c_13013,plain,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_11973,c_5019]) ).
cnf(c_12050,plain,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_13013]) ).
cnf(c_13014,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c3)) = multiply(sk_c7,multiply(sk_c2,sk_c8))
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_11973,c_5015]) ).
cnf(c_13015,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c3)) = multiply(sk_c2,sk_c8)
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_11986,c_13014]) ).
cnf(c_12052,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c3)) = multiply(sk_c2,sk_c8)
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_13015]) ).
cnf(c_13016,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_11974,c_173]) ).
cnf(c_13017,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_11973,c_13016]) ).
cnf(c_13018,plain,
( sk_c8 = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_11986,c_13017]) ).
cnf(c_13019,plain,
( sk_c8 = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_13018]) ).
cnf(c_13020,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_13019]) ).
cnf(c_12128,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_13020]) ).
cnf(c_13021,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_11974,c_50]) ).
cnf(c_13022,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_12128,c_13021]) ).
cnf(c_13023,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_11974,c_13022]) ).
cnf(c_13024,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c8) != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_12128,c_13023]) ).
cnf(c_13025,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| sk_c8 != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_11986,c_13024]) ).
cnf(c_13026,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| sk_c7 != sk_c6
| sk_c8 != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_11973,c_13025]) ).
cnf(c_13027,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_12128,c_13026]) ).
cnf(c_13028,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(B) != sk_c7
| B != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_11974,c_13027]) ).
cnf(c_13029,plain,
( multiply(A,sk_c8) != sk_c8
| inverse(B) != sk_c7
| B != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_12128,c_13028]) ).
cnf(c_13030,plain,
( multiply(A,sk_c8) != sk_c8
| inverse(B) != sk_c7
| B != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_13029]) ).
cnf(c_13031,plain,
( multiply(A,sk_c8) != sk_c8
| inverse(B) != sk_c7
| sk_c8 != B
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_13030]) ).
cnf(c_13032,plain,
( multiply(A,sk_c8) != sk_c8
| inverse(B) != sk_c7
| sk_c8 != B
| sk_c7 != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_13031]) ).
cnf(c_13033,plain,
( multiply(A,sk_c8) != sk_c8
| inverse(B) != sk_c7
| sk_c8 != B
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_13032]) ).
cnf(c_12134,plain,
( multiply(A,sk_c8) != sk_c8
| inverse(B) != sk_c7
| sk_c8 != B
| sk_c7 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_13033]) ).
cnf(c_13034,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c3)) = multiply(sk_c2,sk_c8)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_12128,c_12052]) ).
cnf(c_12637,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c3)) = multiply(sk_c2,sk_c8)
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_13034]) ).
cnf(c_13035,plain,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_12128,c_12050]) ).
cnf(c_12639,plain,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_13035]) ).
cnf(c_13036,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_12128,c_12009]) ).
cnf(c_13037,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_12128,c_13036]) ).
cnf(c_12646,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_13037]) ).
cnf(c_13038,plain,
( multiply(sk_c7,sk_c8) != sk_c8
| inverse(A) != sk_c7
| sk_c8 != A
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_11973,c_12134]) ).
cnf(c_13039,plain,
( multiply(sk_c7,sk_c8) != sk_c8
| inverse(A) != sk_c7
| sk_c8 != A
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_11986,c_13038]) ).
cnf(c_13040,plain,
( sk_c8 != sk_c8
| inverse(A) != sk_c7
| sk_c8 != A
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_11986,c_13039]) ).
cnf(c_13041,plain,
( sk_c8 != sk_c8
| inverse(A) != sk_c7
| sk_c8 != A
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_13040]) ).
cnf(c_13042,plain,
( inverse(A) != sk_c7
| sk_c8 != A
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_13041]) ).
cnf(c_13043,plain,
( inverse(A) != sk_c7
| sk_c8 != A
| sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_13042]) ).
cnf(c_12932,plain,
( inverse(A) != sk_c7
| sk_c8 != A
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_13043]) ).
cnf(c_13044,plain,
( sk_c8 != sk_c7
| sk_c7 != sk_c8 ),
inference(resolve,[status(thm)],[c_12932,c_11973]) ).
cnf(c_13045,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_13044]) ).
cnf(c_12969,plain,
sk_c7 != sk_c8,
inference(copy,[status(thm)],[c_13045]) ).
cnf(c_12974,plain,
multiply(sk_c2,sk_c8) = sk_c7,
inference(resolve,[status(thm)],[c_12969,c_12646]) ).
cnf(c_13046,plain,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,multiply(sk_c8,sk_c7))
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_12974,c_12639]) ).
cnf(c_13047,plain,
( multiply(sk_c3,sk_c3) = multiply(sk_c2,sk_c8)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_11974,c_13046]) ).
cnf(c_13048,plain,
( multiply(sk_c3,sk_c3) = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_12974,c_13047]) ).
cnf(c_12979,plain,
multiply(sk_c3,sk_c3) = sk_c7,
inference(resolve,[status(thm)],[c_12969,c_13048]) ).
cnf(c_13049,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c2,sk_c8)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_12979,c_12637]) ).
cnf(c_13050,plain,
( sk_c8 = multiply(sk_c2,sk_c8)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_11974,c_13049]) ).
cnf(c_13051,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_12974,c_13050]) ).
cnf(c_13052,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_13051]) ).
cnf(c_13053,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_13052]) ).
cnf(c_12981,plain,
$false,
inference(resolve,[status(thm)],[c_12969,c_13053]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP283-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n014.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 14:42:48 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 463794 was started by sandbox2 on n014,
% 0.16/0.44 % Fri Sep 25 14:42:48 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 34.75/6.31
% 34.75/6.31 % SZS status Unsatisfiable for theBenchmark
% 34.75/6.31
% 34.75/6.31 % Proof 1 at 4.71 (+ 1.07) seconds.
% 34.75/6.31 % Length of proof is 83.
% 34.75/6.31 % Level of proof is 23.
% 34.75/6.31 % Maximum clause weight is 59.000.
% 34.75/6.31 % Given clauses 449.
% 34.75/6.31
% 34.75/6.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------