%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP315-1 : 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 : n003.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 07:28:37 AM UTC 2026
% Result : Unsatisfiable 270.94s 35.76s
% Output : CNFRefutation 270.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 63
% Number of leaves : 17
% Syntax : Number of formulae : 178 ( 21 unt; 0 def)
% Number of atoms : 481 ( 480 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 455 ( 152 ~; 303 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 60 ( 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_c6,sk_c7) = sk_c5,
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(clausify,[status(thm)],[prove_this_1]) ).
cnf(c_5,plain,
sk_c5 = multiply(sk_c6,sk_c7),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_6,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_7,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_8,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_9,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
cnf(c_10,plain,
( multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_9]) ).
fof(prove_this_6,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_11,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_12,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_13,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_14,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
cnf(c_15,plain,
( multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_14]) ).
fof(prove_this_12,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_20,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
cnf(c_21,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_20]) ).
fof(prove_this_13,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_22,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
cnf(c_7854,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_22]) ).
cnf(c_23,plain,
( multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6
| multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_7854]) ).
fof(prove_this_16,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_26,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_27,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
cnf(c_28,plain,
( multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_27]) ).
fof(prove_this_18,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( multiply(VAR_3,sk_c5) != sk_c6
| inverse(VAR_3) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(VAR_2) != sk_c7
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c5
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_29,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
cnf(c_7855,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_29]) ).
cnf(c_7856,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != multiply(sk_c6,sk_c7)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_7855]) ).
cnf(c_7857,plain,
( multiply(D,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != multiply(sk_c6,sk_c7)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_7856]) ).
cnf(c_7858,plain,
( multiply(D,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| inverse(B) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(B,sk_c6)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(copy,[status(thm)],[c_7857]) ).
cnf(c_30,plain,
( multiply(D,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| inverse(B) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(B,sk_c6)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_7858]) ).
cnf(c_31,plain,
( multiply(C,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(C) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(B) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(B,sk_c6)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_33,plain,
( multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(B) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(B,sk_c6)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_31]) ).
cnf(c_7859,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_7860,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_7859]) ).
cnf(c_34,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_7860]) ).
cnf(c_38,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_41,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_42,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_43,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_44,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_48,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_53,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_26,c_2]) ).
cnf(c_54,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c4,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_200,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_34]) ).
cnf(c_203,plain,
( multiply(inverse(sk_c3),sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_34]) ).
cnf(c_205,plain,
( multiply(inverse(sk_c4),sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_34]) ).
cnf(c_218,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_34,c_34]) ).
cnf(c_219,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_218,c_200]) ).
cnf(c_220,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_219,c_2]) ).
cnf(c_7861,plain,
( multiply(identity,multiply(sk_c6,sk_c7)) != sk_c6
| multiply(A,sk_c6) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != multiply(identity,sk_c6)
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_220,c_33]) ).
cnf(c_7862,plain,
( multiply(identity,multiply(sk_c6,sk_c7)) != sk_c6
| multiply(A,sk_c6) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_7861]) ).
cnf(c_7863,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_7862]) ).
cnf(c_230,plain,
( multiply(A,sk_c6) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_7863]) ).
cnf(c_239,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_41,c_2]) ).
cnf(c_253,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_43,c_2]) ).
cnf(c_281,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_53,c_2]) ).
cnf(c_7864,plain,
( multiply(identity,sk_c6) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_220,c_230]) ).
cnf(c_7865,plain,
( multiply(identity,sk_c6) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_7864]) ).
cnf(c_7866,plain,
( sk_c6 != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_7865]) ).
cnf(c_7867,plain,
( sk_c7 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_7866]) ).
cnf(c_323,plain,
( identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_7867]) ).
cnf(c_331,plain,
( multiply(inverse(sk_c3),sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_42,c_34]) ).
cnf(c_7868,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_239,c_34]) ).
cnf(c_337,plain,
( inverse(sk_c7) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_219,c_7868]) ).
cnf(c_338,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_337,c_2]) ).
cnf(c_7869,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_253,c_34]) ).
cnf(c_355,plain,
( inverse(sk_c7) = sk_c1
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_219,c_7869]) ).
cnf(c_444,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_355,c_2]) ).
cnf(c_7870,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_281,c_34]) ).
cnf(c_492,plain,
( inverse(sk_c6) = sk_c4
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_219,c_7870]) ).
cnf(c_7871,plain,
( multiply(inverse(sk_c3),identity) = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_338,c_34]) ).
cnf(c_514,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_219,c_7871]) ).
cnf(c_7872,plain,
( multiply(sk_c6,sk_c4) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_444,c_38]) ).
cnf(c_542,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(copy,[status(thm)],[c_7872]) ).
cnf(c_7873,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_542,c_34]) ).
cnf(c_545,plain,
( inverse(sk_c6) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_219,c_7873]) ).
cnf(c_547,plain,
( multiply(sk_c4,sk_c6) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_545,c_2]) ).
cnf(c_7874,plain,
( multiply(inverse(sk_c4),identity) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_547,c_34]) ).
cnf(c_565,plain,
( inverse(sk_c4) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_219,c_7874]) ).
cnf(c_7875,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_6,c_203]) ).
cnf(c_655,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_7875]) ).
cnf(c_658,plain,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_655,c_34]) ).
cnf(c_671,plain,
( multiply(inverse(sk_c4),sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_44,c_34]) ).
cnf(c_7876,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_514,c_331]) ).
cnf(c_733,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_7876]) ).
cnf(c_7877,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_733,c_34]) ).
cnf(c_736,plain,
( inverse(sk_c7) = sk_c1
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_219,c_7877]) ).
cnf(c_738,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_736,c_2]) ).
cnf(c_7878,plain,
( multiply(inverse(sk_c1),identity) = sk_c7
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_738,c_34]) ).
cnf(c_756,plain,
( inverse(sk_c1) = sk_c7
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_219,c_7878]) ).
cnf(c_7879,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_738,c_655]) ).
cnf(c_759,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_7879]) ).
cnf(c_762,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_759,c_34]) ).
cnf(c_7880,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_756,c_658]) ).
cnf(c_842,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_7880]) ).
cnf(c_7881,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_8,c_205]) ).
cnf(c_7882,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_7881]) ).
cnf(c_904,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_7882]) ).
cnf(c_7883,plain,
( multiply(sk_c6,sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_565,c_671]) ).
cnf(c_919,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| multiply(sk_c7,sk_c1) = identity
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_7883]) ).
cnf(c_7884,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_919,c_34]) ).
cnf(c_923,plain,
( inverse(sk_c7) = sk_c1
| multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_219,c_7884]) ).
cnf(c_974,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_923,c_2]) ).
cnf(c_7885,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| identity = sk_c6
| multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_974,c_904]) ).
cnf(c_7886,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_7885]) ).
cnf(c_1004,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6)
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_7886]) ).
cnf(c_7887,plain,
( multiply(inverse(sk_c6),multiply(sk_c6,sk_c6)) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1004,c_34]) ).
cnf(c_7888,plain,
( sk_c6 = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_34,c_7887]) ).
cnf(c_1007,plain,
( sk_c7 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_7888]) ).
cnf(c_1020,plain,
( multiply(sk_c6,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1007,c_1]) ).
cnf(c_1022,plain,
( inverse(sk_c6) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1007,c_220]) ).
cnf(c_1045,plain,
( identity = sk_c4
| multiply(sk_c6,sk_c2) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1022,c_492]) ).
cnf(c_1104,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7)
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1020,c_23]) ).
cnf(c_1112,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c2,sk_c6) = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1020,c_48]) ).
cnf(c_1128,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c4,sk_c7) = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1020,c_54]) ).
cnf(c_7889,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c4
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1045,c_34]) ).
cnf(c_1161,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c4
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_219,c_7889]) ).
cnf(c_1245,plain,
( multiply(sk_c2,sk_c6) = identity
| identity = sk_c4
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1161,c_2]) ).
cnf(c_7890,plain,
( multiply(sk_c2,sk_c6) = sk_c6
| identity = sk_c4
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1007,c_1245]) ).
cnf(c_2006,plain,
( multiply(sk_c2,sk_c6) = sk_c6
| identity = sk_c4
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7890]) ).
cnf(c_7891,plain,
( sk_c7 = sk_c6
| identity = sk_c4
| sk_c7 = sk_c6
| multiply(sk_c6,sk_c4) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1112,c_2006]) ).
cnf(c_7892,plain,
( sk_c7 = sk_c6
| identity = sk_c4
| multiply(sk_c6,sk_c4) = identity
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7891]) ).
cnf(c_3474,plain,
( identity = sk_c4
| multiply(sk_c6,sk_c4) = identity
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7892]) ).
cnf(c_7893,plain,
( identity = sk_c4
| sk_c7 = sk_c6
| identity = sk_c4
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_3474,c_1020]) ).
cnf(c_7894,plain,
( identity = sk_c4
| identity = sk_c4
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7893]) ).
cnf(c_4209,plain,
( identity = sk_c4
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7894]) ).
cnf(c_4210,plain,
( multiply(sk_c4,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_4209,c_1]) ).
cnf(c_7895,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| multiply(sk_c6,sk_c2) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1128,c_4210]) ).
cnf(c_7896,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| multiply(sk_c6,sk_c2) = identity
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7895]) ).
cnf(c_7897,plain,
( sk_c7 = sk_c6
| multiply(sk_c6,sk_c2) = identity
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7896]) ).
cnf(c_5845,plain,
( multiply(sk_c6,sk_c2) = identity
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7897]) ).
cnf(c_7898,plain,
( identity = sk_c2
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_5845,c_1020]) ).
cnf(c_5852,plain,
( identity = sk_c2
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7898]) ).
cnf(c_5882,plain,
( multiply(sk_c2,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_5852,c_1]) ).
cnf(c_7899,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7)
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1104,c_4210]) ).
cnf(c_7900,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7)
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7899]) ).
cnf(c_7901,plain,
( sk_c7 = sk_c6
| multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7)
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7900]) ).
cnf(c_7142,plain,
( multiply(sk_c2,sk_c6) = multiply(sk_c6,sk_c7)
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7901]) ).
cnf(c_7902,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_1020,c_7142]) ).
cnf(c_7146,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7902]) ).
cnf(c_7903,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_7146,c_5882]) ).
cnf(c_7904,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_7903]) ).
cnf(c_7157,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_7904]) ).
cnf(c_7905,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_842]) ).
cnf(c_7906,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_7905]) ).
cnf(c_7907,plain,
( multiply(sk_c6,sk_c6) = sk_c7
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_7906]) ).
cnf(c_7908,plain,
( multiply(sk_c6,sk_c6) = sk_c6
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_7907]) ).
cnf(c_7695,plain,
multiply(sk_c6,sk_c6) = sk_c6,
inference(copy,[status(thm)],[c_7908]) ).
cnf(c_7909,plain,
( multiply(inverse(sk_c6),sk_c6) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_762]) ).
cnf(c_7910,plain,
( identity = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_7909]) ).
cnf(c_7911,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_7910]) ).
cnf(c_7725,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_7911]) ).
cnf(c_7912,plain,
( identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_323]) ).
cnf(c_7913,plain,
( identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| sk_c6 != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_7725,c_7912]) ).
cnf(c_7914,plain,
( identity != sk_c6
| multiply(sk_c6,sk_c7) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_7913]) ).
cnf(c_7915,plain,
( identity != sk_c6
| multiply(sk_c6,sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_7157,c_7914]) ).
cnf(c_7916,plain,
( identity != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_7695,c_7915]) ).
cnf(c_7917,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_7725,c_7916]) ).
cnf(c_7918,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_7917]) ).
cnf(c_7919,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_7918]) ).
cnf(c_7920,plain,
sk_c6 != sk_c6,
inference(copy,[status(thm)],[c_7919]) ).
cnf(c_7853,plain,
$false,
inference(copy,[status(thm)],[c_7920]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP315-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:47:08 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 437028 was started by sandbox on n003,
% 0.11/0.36 % Fri Sep 25 14:47:08 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 270.94/35.76
% 270.94/35.76 % given #500 (W,wt=18): 6720 sk_c7 = sk_c6 | multiply(sk_c7,sk_c6) = sk_c3. [para(6456(b,1),6332(b,1,1)),merge(b)].
% 270.94/35.76
% 270.94/35.76 % SZS status Unsatisfiable for theBenchmark
% 270.94/35.76
% 270.94/35.76 % Proof 1 at 2.64 (+ 0.43) seconds.
% 270.94/35.76 % Length of proof is 94.
% 270.94/35.76 % Level of proof is 28.
% 270.94/35.76 % Maximum clause weight is 60.000.
% 270.94/35.76 % Given clauses 578.
% 270.94/35.76
% 270.94/35.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------