%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP304-1 : 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 07:28:36 AM UTC 2026
% Result : Unsatisfiable 61.38s 16.98s
% Output : CNFRefutation 61.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 18
% Syntax : Number of formulae : 164 ( 31 unt; 0 def)
% Number of atoms : 444 ( 443 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 468 ( 188 ~; 280 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 74 ( 0 sgn 9 !; 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_c5,
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
multiply(sk_c7,sk_c6) = sk_c5,
inference(clausify,[status(thm)],[prove_this_1]) ).
cnf(c_5,plain,
sk_c5 = multiply(sk_c7,sk_c6),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_this_9,axiom,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_20,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
cnf(c_21,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c7) = multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_5,c_20]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_22,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
cnf(c_23,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c7) = multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_5,c_22]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_24,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
cnf(c_25,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_5,c_24]) ).
fof(prove_this_12,axiom,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_26,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_27,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_28,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c3,sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_29,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_30,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_31,plain,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c2) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_32,plain,
( inverse(sk_c2) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_33,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_34,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_35,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != VAR_2
| multiply(sk_c7,VAR_2) != sk_c6
| inverse(VAR_1) != sk_c7
| multiply(VAR_1,sk_c7) != sk_c6
| inverse(VAR_0) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_36,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
cnf(c_15634,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_5,c_36]) ).
cnf(c_15635,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c7,sk_c6) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_5,c_15634]) ).
cnf(c_15636,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c7,sk_c6) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_5,c_15635]) ).
cnf(c_37,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(copy,[status(thm)],[c_15636]) ).
cnf(c_15637,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_15638,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_15637]) ).
cnf(c_44,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_15638]) ).
cnf(c_15639,plain,
( multiply(multiply(sk_c7,sk_c6),sk_c7) = identity
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_55,plain,
( multiply(sk_c7,multiply(sk_c6,sk_c7)) = identity
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_15639]) ).
cnf(c_65,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_66,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_69,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c3,sk_c7) = sk_c4 ),
inference(paramod,[status(thm)],[c_34,c_2]) ).
cnf(c_70,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_35,c_2]) ).
cnf(c_275,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_44]) ).
cnf(c_297,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_44,c_44]) ).
cnf(c_298,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_297,c_275]) ).
cnf(c_336,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_298,c_2]) ).
cnf(c_432,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_297,c_2]) ).
cnf(c_449,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_297,c_44]) ).
cnf(c_15640,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_297,c_298]) ).
cnf(c_15641,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_298,c_15640]) ).
cnf(c_450,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_15641]) ).
cnf(c_15642,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != B
| multiply(sk_c7,B) != sk_c6
| multiply(inverse(sk_c7),sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(resolve,[status(thm)],[c_450,c_37]) ).
cnf(c_474,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != B
| multiply(sk_c7,B) != sk_c6
| identity != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_2,c_15642]) ).
cnf(c_512,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c7) = multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_25,c_432]) ).
cnf(c_513,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_27,c_432]) ).
cnf(c_514,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_432]) ).
cnf(c_516,plain,
( multiply(sk_c2,sk_c7) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_32,c_432]) ).
cnf(c_517,plain,
( multiply(sk_c1,sk_c6) = identity
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_33,c_432]) ).
cnf(c_519,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_35,c_432]) ).
cnf(c_523,plain,
( multiply(sk_c1,sk_c6) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_70,c_432]) ).
cnf(c_917,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c2,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_516,c_2]) ).
cnf(c_937,plain,
( multiply(sk_c6,sk_c1) = identity
| multiply(sk_c3,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_519,c_2]) ).
cnf(c_15643,plain,
( multiply(inverse(sk_c7),identity) = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_55,c_44]) ).
cnf(c_2046,plain,
( inverse(sk_c7) = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_298,c_15643]) ).
cnf(c_15644,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_513,c_26]) ).
cnf(c_3269,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_15644]) ).
cnf(c_15645,plain,
( identity = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_514,c_29]) ).
cnf(c_3423,plain,
( identity = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_15645]) ).
cnf(c_15646,plain,
( multiply(sk_c7,sk_c4) = sk_c6
| identity = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_517,c_28]) ).
cnf(c_3748,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c4) = sk_c6 ),
inference(copy,[status(thm)],[c_15646]) ).
cnf(c_3755,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_3748,c_44]) ).
cnf(c_15647,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c7
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_523,c_65]) ).
cnf(c_4503,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c3) = identity ),
inference(copy,[status(thm)],[c_15647]) ).
cnf(c_15648,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_4503,c_44]) ).
cnf(c_4508,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_298,c_15648]) ).
cnf(c_15649,plain,
( multiply(sk_c3,sk_c6) = sk_c4
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_4508,c_3755]) ).
cnf(c_4583,plain,
( multiply(sk_c3,sk_c6) = sk_c4
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15649]) ).
cnf(c_15650,plain,
( multiply(sk_c6,sk_c1) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_917,c_66]) ).
cnf(c_5582,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_15650]) ).
cnf(c_15651,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5582,c_44]) ).
cnf(c_5591,plain,
( inverse(sk_c6) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_298,c_15651]) ).
cnf(c_5594,plain,
( multiply(sk_c1,sk_c6) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5591,c_2]) ).
cnf(c_15652,plain,
( identity = sk_c6
| identity = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_5594,c_3269]) ).
cnf(c_6099,plain,
( identity = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_15652]) ).
cnf(c_6101,plain,
( multiply(A,sk_c6) = A
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6099,c_298]) ).
cnf(c_15653,plain,
( inverse(sk_c7) = sk_c4
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6101,c_3755]) ).
cnf(c_6455,plain,
( inverse(sk_c7) = sk_c4
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15653]) ).
cnf(c_15654,plain,
( sk_c3 = sk_c4
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6101,c_4583]) ).
cnf(c_15655,plain,
( sk_c4 = sk_c3
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15654]) ).
cnf(c_6463,plain,
( sk_c4 = sk_c3
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15655]) ).
cnf(c_6857,plain,
( multiply(sk_c7,A) = A
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_6463,c_1]) ).
cnf(c_6903,plain,
( inverse(sk_c4) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6455,c_450]) ).
cnf(c_15656,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6
| multiply(inverse(sk_c6),sk_c6) != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(resolve,[status(thm)],[c_474,c_450]) ).
cnf(c_7416,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6
| identity != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_2,c_15656]) ).
cnf(c_15657,plain,
( inverse(identity) != sk_c7
| sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6
| identity != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_1,c_7416]) ).
cnf(c_15658,plain,
( identity != sk_c7
| sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6
| identity != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_336,c_15657]) ).
cnf(c_7577,plain,
( sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| identity != sk_c6
| identity != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(copy,[status(thm)],[c_15658]) ).
cnf(c_15659,plain,
( sk_c7 != multiply(inverse(sk_c7),A)
| A != sk_c6
| identity != sk_c6
| identity != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_449,c_7577]) ).
cnf(c_15660,plain,
( sk_c7 != multiply(inverse(sk_c7),A)
| sk_c6 != A
| identity != sk_c6
| identity != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(copy,[status(thm)],[c_15659]) ).
cnf(c_7658,plain,
( multiply(inverse(sk_c7),A) != sk_c7
| sk_c6 != A
| identity != sk_c6
| identity != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(copy,[status(thm)],[c_15660]) ).
cnf(c_8623,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c7) = sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_6857,c_23]) ).
cnf(c_15661,plain,
( multiply(sk_c6,sk_c1) = identity
| identity = sk_c4
| multiply(sk_c6,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_937,c_69]) ).
cnf(c_10710,plain,
( identity = sk_c4
| multiply(sk_c6,sk_c1) = identity ),
inference(copy,[status(thm)],[c_15661]) ).
cnf(c_15662,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10710,c_44]) ).
cnf(c_10727,plain,
( inverse(sk_c6) = sk_c1
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_298,c_15662]) ).
cnf(c_10736,plain,
( multiply(sk_c1,sk_c6) = identity
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10727,c_2]) ).
cnf(c_15663,plain,
( identity = sk_c4
| identity = sk_c7
| identity = sk_c4 ),
inference(paramod,[status(thm)],[c_10736,c_3423]) ).
cnf(c_10989,plain,
( identity = sk_c7
| identity = sk_c4 ),
inference(copy,[status(thm)],[c_15663]) ).
cnf(c_10992,plain,
( inverse(sk_c4) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10989,c_336]) ).
cnf(c_15664,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10992,c_6903]) ).
cnf(c_15665,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15664]) ).
cnf(c_11046,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_15665]) ).
cnf(c_15666,plain,
( multiply(inverse(sk_c7),A) != sk_c7
| sk_c6 != A
| identity != sk_c6
| sk_c7 != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_11046,c_7658]) ).
cnf(c_15667,plain,
( multiply(inverse(sk_c7),A) != sk_c7
| sk_c6 != A
| sk_c7 != sk_c6
| sk_c7 != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_11046,c_15666]) ).
cnf(c_15668,plain,
( multiply(inverse(sk_c7),A) != sk_c7
| sk_c6 != A
| sk_c6 != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(copy,[status(thm)],[c_15667]) ).
cnf(c_13056,plain,
( multiply(inverse(sk_c7),A) != sk_c7
| sk_c6 != A
| sk_c6 != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(copy,[status(thm)],[c_15668]) ).
cnf(c_15485,plain,
( multiply(sk_c3,sk_c7) = sk_c7
| inverse(sk_c7) = multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_11046,c_512]) ).
cnf(c_15669,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_11046,c_336]) ).
cnf(c_15506,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_11046,c_15669]) ).
cnf(c_15507,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_11046,c_298]) ).
cnf(c_15520,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_11046,c_1]) ).
cnf(c_15670,plain,
( multiply(inverse(sk_c7),sk_c7) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) != multiply(sk_c7,sk_c6) ),
inference(factor,[status(thm)],[c_13056]) ).
cnf(c_15671,plain,
( multiply(inverse(sk_c7),sk_c7) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| sk_c6 != multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_15507,c_15670]) ).
cnf(c_15672,plain,
( multiply(inverse(sk_c7),sk_c7) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != multiply(sk_c7,sk_c6)
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_15520,c_15671]) ).
cnf(c_15673,plain,
( multiply(inverse(sk_c7),sk_c7) != sk_c7
| sk_c6 != sk_c7
| sk_c7 != multiply(sk_c7,sk_c6)
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_15506,c_15672]) ).
cnf(c_15674,plain,
( multiply(inverse(sk_c7),sk_c7) != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_15520,c_15673]) ).
cnf(c_15675,plain,
( multiply(sk_c7,sk_c7) != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_15506,c_15674]) ).
cnf(c_15676,plain,
( sk_c7 != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_15507,c_15675]) ).
cnf(c_15677,plain,
( sk_c7 != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_15676]) ).
cnf(c_15678,plain,
( sk_c7 != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_15677]) ).
cnf(c_15679,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_15678]) ).
cnf(c_15586,plain,
sk_c6 != sk_c7,
inference(copy,[status(thm)],[c_15679]) ).
cnf(c_15680,plain,
( multiply(sk_c3,sk_c7) = sk_c7
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(paramod,[status(thm)],[c_15506,c_15485]) ).
cnf(c_15681,plain,
( multiply(sk_c3,sk_c7) = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_15520,c_15680]) ).
cnf(c_15682,plain,
( sk_c3 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_15507,c_15681]) ).
cnf(c_15683,plain,
( sk_c3 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_15682]) ).
cnf(c_15622,plain,
sk_c3 = sk_c7,
inference(resolve,[status(thm)],[c_15586,c_15683]) ).
cnf(c_15684,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| inverse(sk_c7) = sk_c6
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_15622,c_8623]) ).
cnf(c_15685,plain,
( multiply(sk_c3,sk_c7) = sk_c4
| sk_c7 = sk_c6
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_15506,c_15684]) ).
cnf(c_15686,plain,
( multiply(sk_c7,sk_c7) = sk_c4
| sk_c7 = sk_c6
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_15622,c_15685]) ).
cnf(c_15687,plain,
( sk_c7 = sk_c4
| sk_c7 = sk_c6
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_15507,c_15686]) ).
cnf(c_15688,plain,
( sk_c7 = sk_c4
| sk_c6 = sk_c7
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_15687]) ).
cnf(c_15689,plain,
( sk_c4 = sk_c7
| sk_c6 = sk_c7
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_15688]) ).
cnf(c_15690,plain,
( sk_c6 = sk_c7
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_15689]) ).
cnf(c_15625,plain,
sk_c4 = sk_c7,
inference(resolve,[status(thm)],[c_15586,c_15690]) ).
cnf(c_15691,plain,
( inverse(sk_c7) = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_15625,c_2046]) ).
cnf(c_15692,plain,
( inverse(sk_c7) = multiply(sk_c6,sk_c7)
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_15507,c_15691]) ).
cnf(c_15693,plain,
( sk_c7 = multiply(sk_c6,sk_c7)
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_15506,c_15692]) ).
cnf(c_15694,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_15507,c_15693]) ).
cnf(c_15695,plain,
( sk_c7 = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_15694]) ).
cnf(c_15696,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_15695]) ).
cnf(c_15697,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_15696]) ).
cnf(c_15633,plain,
$false,
inference(resolve,[status(thm)],[c_15586,c_15697]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP304-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 14:39:32 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 2515919 was started by sandbox on n017,
% 0.11/0.36 % Fri Sep 25 14:39:32 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 61.38/16.98
% 61.38/16.98 % SZS status Unsatisfiable for theBenchmark
% 61.38/16.98
% 61.38/16.98 % Proof 1 at 6.95 (+ 0.81) seconds.
% 61.38/16.98 % Length of proof is 82.
% 61.38/16.98 % Level of proof is 18.
% 61.38/16.98 % Maximum clause weight is 45.000.
% 61.38/16.98 % Given clauses 373.
% 61.38/16.98
% 61.38/16.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------