%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:28:39 AM UTC 2026
% Result : Unsatisfiable 14.31s 9.16s
% Output : CNFRefutation 14.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 14
% Syntax : Number of formulae : 164 ( 24 unt; 0 def)
% Number of atoms : 445 ( 444 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 446 ( 165 ~; 281 |; 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 43 ( 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_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_16,axiom,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_20,axiom,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_26,axiom,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_37,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != sk_c6
| multiply(VAR_4,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c6
| inverse(VAR_3) != sk_c8
| multiply(VAR_3,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(VAR_2,sk_c8) != sk_c7
| inverse(VAR_1) != VAR_2
| multiply(VAR_1,VAR_2) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c8
| inverse(VAR_0) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('theBenchmark.p',prove_this_37) ).
cnf(c_40,plain,
( inverse(E) != sk_c6
| multiply(E,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c6
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(C,sk_c8) != sk_c7
| inverse(B) != C
| multiply(B,C) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_37]) ).
cnf(c_42,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(C,sk_c8) != sk_c7
| inverse(B) != C
| multiply(B,C) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_3642,plain,
( inverse(B) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_50,plain,
( inverse(sk_c8) != sk_c6
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_3642]) ).
cnf(c_61,plain,
( multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_50]) ).
cnf(c_67,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8
| inverse(sk_c6) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_61]) ).
cnf(c_3643,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3644,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3643]) ).
cnf(c_68,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3644]) ).
cnf(c_96,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_97,plain,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_98,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_116,plain,
( multiply(sk_c6,sk_c8) = identity
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_3645,plain,
( multiply(sk_c8,A) = multiply(sk_c1,multiply(sk_c7,A))
| inverse(sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_117,plain,
( multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c8,A)
| inverse(sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_3645]) ).
cnf(c_153,plain,
( multiply(sk_c3,sk_c2) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_154,plain,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c2) = sk_c3 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_184,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_68]) ).
cnf(c_187,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_68]) ).
cnf(c_258,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_68,c_68]) ).
cnf(c_259,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_258,c_184]) ).
cnf(c_264,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_259,c_2]) ).
cnf(c_3646,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_96,c_68]) ).
cnf(c_268,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_259,c_3646]) ).
cnf(c_3647,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_97,c_68]) ).
cnf(c_276,plain,
( inverse(sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_259,c_3647]) ).
cnf(c_288,plain,
( multiply(sk_c4,sk_c8) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_276,c_2]) ).
cnf(c_3648,plain,
( sk_c4 = sk_c6
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_276,c_13]) ).
cnf(c_290,plain,
( sk_c4 = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_3648]) ).
cnf(c_293,plain,
( multiply(sk_c8,sk_c1) = identity
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_290,c_2]) ).
cnf(c_3649,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_293,c_68]) ).
cnf(c_311,plain,
( inverse(sk_c8) = sk_c1
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_259,c_3649]) ).
cnf(c_3650,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c6) = sk_c8
| inverse(sk_c8) = sk_c1 ),
inference(paramod,[status(thm)],[c_311,c_268]) ).
cnf(c_332,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c8) = sk_c1 ),
inference(copy,[status(thm)],[c_3650]) ).
cnf(c_363,plain,
( multiply(sk_c8,sk_c6) = identity
| inverse(sk_c8) = sk_c1 ),
inference(paramod,[status(thm)],[c_332,c_2]) ).
cnf(c_3651,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_98,c_68]) ).
cnf(c_374,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_259,c_3651]) ).
cnf(c_3652,plain,
( multiply(inverse(sk_c3),identity) = sk_c2
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_153,c_68]) ).
cnf(c_483,plain,
( inverse(sk_c3) = sk_c2
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_259,c_3652]) ).
cnf(c_485,plain,
( multiply(sk_c2,sk_c3) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_483,c_2]) ).
cnf(c_3653,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| inverse(sk_c2) = sk_c3 ),
inference(paramod,[status(thm)],[c_154,c_68]) ).
cnf(c_498,plain,
( inverse(sk_c8) = sk_c4
| inverse(sk_c2) = sk_c3 ),
inference(paramod,[status(thm)],[c_259,c_3653]) ).
cnf(c_3654,plain,
( sk_c4 = sk_c6
| inverse(sk_c2) = sk_c3
| inverse(sk_c2) = sk_c3 ),
inference(paramod,[status(thm)],[c_498,c_31]) ).
cnf(c_506,plain,
( sk_c4 = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(copy,[status(thm)],[c_3654]) ).
cnf(c_511,plain,
( multiply(sk_c3,sk_c2) = identity
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_506,c_2]) ).
cnf(c_3655,plain,
( multiply(inverse(sk_c3),identity) = sk_c2
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_511,c_68]) ).
cnf(c_534,plain,
( inverse(sk_c3) = sk_c2
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_259,c_3655]) ).
cnf(c_541,plain,
( multiply(sk_c2,sk_c3) = identity
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_534,c_2]) ).
cnf(c_3656,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_288,c_11]) ).
cnf(c_762,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_3656]) ).
cnf(c_767,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_762,c_2]) ).
cnf(c_3657,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_767,c_68]) ).
cnf(c_784,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_259,c_3657]) ).
cnf(c_911,plain,
( sk_c1 = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_363,c_19]) ).
cnf(c_3658,plain,
( inverse(sk_c4) = sk_c8
| identity = sk_c7
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_485,c_24]) ).
cnf(c_1034,plain,
( identity = sk_c7
| inverse(sk_c4) = sk_c8 ),
inference(copy,[status(thm)],[c_3658]) ).
cnf(c_1062,plain,
( multiply(sk_c8,sk_c4) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1034,c_2]) ).
cnf(c_3659,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1062,c_68]) ).
cnf(c_1073,plain,
( inverse(sk_c8) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_259,c_3659]) ).
cnf(c_1104,plain,
( multiply(sk_c4,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1073,c_2]) ).
cnf(c_3660,plain,
( sk_c4 = sk_c1
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1073,c_784]) ).
cnf(c_1129,plain,
( sk_c4 = sk_c1
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3660]) ).
cnf(c_3661,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1104,c_23]) ).
cnf(c_1238,plain,
( multiply(sk_c2,sk_c3) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3661]) ).
cnf(c_3662,plain,
( identity = sk_c7
| inverse(sk_c2) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1104,c_29]) ).
cnf(c_1239,plain,
( inverse(sk_c2) = sk_c3
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3662]) ).
cnf(c_1268,plain,
( multiply(sk_c3,sk_c2) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1239,c_2]) ).
cnf(c_3663,plain,
( sk_c7 = identity
| sk_c4 = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1238,c_541]) ).
cnf(c_3664,plain,
( identity = sk_c7
| sk_c4 = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3663]) ).
cnf(c_1596,plain,
( sk_c4 = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3664]) ).
cnf(c_3665,plain,
( sk_c6 = sk_c1
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1596,c_1129]) ).
cnf(c_3666,plain,
( sk_c1 = sk_c6
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3665]) ).
cnf(c_1613,plain,
( sk_c1 = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3666]) ).
cnf(c_1667,plain,
( inverse(sk_c7) = identity
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_1613,c_264]) ).
cnf(c_3667,plain,
( inverse(sk_c7) = sk_c7
| sk_c1 = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_1613,c_1667]) ).
cnf(c_1768,plain,
( inverse(sk_c7) = sk_c7
| sk_c1 = sk_c6 ),
inference(copy,[status(thm)],[c_3667]) ).
cnf(c_1797,plain,
( multiply(sk_c7,sk_c7) = identity
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_1768,c_2]) ).
cnf(c_1831,plain,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_116,c_68]) ).
cnf(c_3668,plain,
( multiply(inverse(sk_c3),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1268,c_68]) ).
cnf(c_1862,plain,
( inverse(sk_c3) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_259,c_3668]) ).
cnf(c_1867,plain,
( multiply(sk_c2,sk_c3) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1862,c_2]) ).
cnf(c_3669,plain,
( multiply(sk_c1,identity) = multiply(sk_c8,sk_c7)
| inverse(sk_c8) = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_1797,c_117]) ).
cnf(c_3670,plain,
( sk_c1 = multiply(sk_c8,sk_c7)
| inverse(sk_c8) = sk_c6
| sk_c1 = sk_c6 ),
inference(paramod,[status(thm)],[c_259,c_3669]) ).
cnf(c_2861,plain,
( multiply(sk_c8,sk_c7) = sk_c1
| inverse(sk_c8) = sk_c6
| sk_c1 = sk_c6 ),
inference(copy,[status(thm)],[c_3670]) ).
cnf(c_3671,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1867,c_1238]) ).
cnf(c_3672,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3671]) ).
cnf(c_2890,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_3672]) ).
cnf(c_2967,plain,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_2890,c_1831]) ).
cnf(c_3047,plain,
( sk_c1 = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_2890,c_911]) ).
cnf(c_3673,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_2890,c_264]) ).
cnf(c_3126,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_2890,c_3673]) ).
cnf(c_3127,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_2890,c_259]) ).
cnf(c_3142,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_2890,c_1]) ).
cnf(c_3674,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_3142,c_187]) ).
cnf(c_3675,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_3126,c_3674]) ).
cnf(c_3676,plain,
( sk_c8 = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_3142,c_3675]) ).
cnf(c_3677,plain,
( sk_c8 = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_3676]) ).
cnf(c_3678,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_3677]) ).
cnf(c_3172,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_3678]) ).
cnf(c_3679,plain,
( sk_c1 = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3172,c_3047]) ).
cnf(c_3680,plain,
( sk_c1 = sk_c6
| sk_c1 = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3127,c_3679]) ).
cnf(c_3681,plain,
( sk_c1 = sk_c8
| sk_c1 = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3172,c_3680]) ).
cnf(c_3174,plain,
( sk_c1 = sk_c8
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_3681]) ).
cnf(c_3682,plain,
( multiply(sk_c8,sk_c7) = sk_c1
| inverse(sk_c8) = sk_c6
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_2861]) ).
cnf(c_3683,plain,
( multiply(sk_c8,sk_c7) = sk_c1
| inverse(sk_c8) = sk_c8
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_3682]) ).
cnf(c_3684,plain,
( sk_c8 = sk_c1
| inverse(sk_c8) = sk_c8
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_3127,c_3683]) ).
cnf(c_3685,plain,
( sk_c1 = sk_c8
| inverse(sk_c8) = sk_c8
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_3684]) ).
cnf(c_3198,plain,
( inverse(sk_c8) = sk_c8
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_3685]) ).
cnf(c_3686,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8
| inverse(sk_c6) != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_3142,c_67]) ).
cnf(c_3687,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8
| inverse(sk_c6) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_3686]) ).
cnf(c_3688,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_3687]) ).
cnf(c_3689,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_3688]) ).
cnf(c_3690,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3127,c_3689]) ).
cnf(c_3691,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_3690]) ).
cnf(c_3692,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_3691]) ).
cnf(c_3693,plain,
( multiply(sk_c7,sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_3692]) ).
cnf(c_3694,plain,
( multiply(sk_c7,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_3693]) ).
cnf(c_3695,plain,
( sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3142,c_3694]) ).
cnf(c_3696,plain,
( sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_3695]) ).
cnf(c_3697,plain,
( sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_3696]) ).
cnf(c_3698,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_3697]) ).
cnf(c_3699,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_3698]) ).
cnf(c_3335,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_3699]) ).
cnf(c_3418,plain,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3172,c_2967]) ).
cnf(c_3468,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_3172,c_374]) ).
cnf(c_3600,plain,
( inverse(sk_c8) != sk_c8
| sk_c1 = sk_c8 ),
inference(resolve,[status(thm)],[c_3174,c_3335]) ).
cnf(c_3700,plain,
( sk_c1 = sk_c8
| sk_c1 = sk_c8 ),
inference(resolve,[status(thm)],[c_3600,c_3198]) ).
cnf(c_3602,plain,
sk_c1 = sk_c8,
inference(copy,[status(thm)],[c_3700]) ).
cnf(c_3701,plain,
( inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_3602,c_3468]) ).
cnf(c_3627,plain,
inverse(sk_c8) = sk_c8,
inference(copy,[status(thm)],[c_3701]) ).
cnf(c_3702,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3602,c_3418]) ).
cnf(c_3703,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3627,c_3702]) ).
cnf(c_3633,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(copy,[status(thm)],[c_3703]) ).
cnf(c_3704,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3627,c_3335]) ).
cnf(c_3705,plain,
( sk_c7 != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3633,c_3704]) ).
cnf(c_3706,plain,
sk_c7 != sk_c7,
inference(copy,[status(thm)],[c_3705]) ).
cnf(c_3641,plain,
$false,
inference(copy,[status(thm)],[c_3706]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/5.34 % Computer : n017.cluster.edu
% 0.06/5.34 % Model : x86_64 x86_64
% 0.06/5.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/5.34 % Memory : 8046.5625MB
% 0.06/5.34 % OS : Linux 6.8.0-71-generic
% 0.06/5.34 % CPULimit : 300
% 0.06/5.34 % WCLimit : 300
% 0.06/5.34 % DateTime : Fri Sep 25 14:42:10 UTC 2026
% 0.06/5.35 % CPUTime :
% 0.06/5.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/5.35 % Process 2527857 was started by sandbox on n017,
% 0.06/5.35 % Fri Sep 25 14:42:10 2026
% 0.06/5.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/5.35
% 0.06/5.35 % From the command line: assign(max_seconds, 300).
% 14.31/9.16
% 14.31/9.16 % SZS status Unsatisfiable for theBenchmark
% 14.31/9.16
% 14.31/9.16 % Proof 1 at 1.44 (+ 0.39) seconds.
% 14.31/9.16 % Length of proof is 85.
% 14.31/9.16 % Level of proof is 22.
% 14.31/9.16 % Maximum clause weight is 59.000.
% 14.31/9.16 % Given clauses 287.
% 14.31/9.16
% 14.31/9.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------