%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP274-1 : 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 : n006.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 07:28:31 AM UTC 2026
% Result : Unsatisfiable 283.25s 37.53s
% Output : CNFRefutation 283.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 19
% Syntax : Number of formulae : 180 ( 22 unt; 0 def)
% Number of atoms : 502 ( 501 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 493 ( 171 ~; 322 |; 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 : 64 ( 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_2,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,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_6,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_7,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_11,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_16,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,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
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(VAR_1) != sk_c5
| multiply(VAR_1,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(B) != sk_c5
| multiply(B,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
cnf(c_30,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(B) != sk_c5
| multiply(B,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_9145,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_9146,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_9145]) ).
cnf(c_33,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_9146]) ).
cnf(c_36,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_43,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_44,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_57,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_9147,plain,
( multiply(sk_c7,A) = multiply(sk_c3,multiply(sk_c6,A))
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_21,c_3]) ).
cnf(c_58,plain,
( multiply(sk_c3,multiply(sk_c6,A)) = multiply(sk_c7,A)
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_9147]) ).
cnf(c_60,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_2]) ).
cnf(c_63,plain,
( multiply(sk_c5,sk_c2) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_64,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c2) = sk_c5 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_65,plain,
( multiply(sk_c5,sk_c2) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_26,c_2]) ).
cnf(c_66,plain,
( multiply(sk_c6,sk_c4) = identity
| inverse(sk_c2) = sk_c5 ),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_67,plain,
( multiply(sk_c5,sk_c2) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_213,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_33]) ).
cnf(c_225,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_33]) ).
cnf(c_240,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_33,c_33]) ).
cnf(c_241,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_240,c_213]) ).
cnf(c_242,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_241,c_2]) ).
cnf(c_9148,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_242,c_30]) ).
cnf(c_9149,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_9148]) ).
cnf(c_9150,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| sk_c6 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_9149]) ).
cnf(c_9151,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| sk_c6 != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_9150]) ).
cnf(c_247,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_9151]) ).
cnf(c_261,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_43,c_2]) ).
cnf(c_287,plain,
( multiply(sk_c5,sk_c2) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_64,c_2]) ).
cnf(c_301,plain,
( multiply(sk_c5,sk_c2) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_66,c_2]) ).
cnf(c_9152,plain,
( multiply(inverse(sk_c5),identity) = sk_c2
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_63,c_33]) ).
cnf(c_481,plain,
( inverse(sk_c5) = sk_c2
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_241,c_9152]) ).
cnf(c_618,plain,
( multiply(sk_c2,sk_c5) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_481,c_2]) ).
cnf(c_9153,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_261,c_33]) ).
cnf(c_628,plain,
( inverse(sk_c7) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_241,c_9153]) ).
cnf(c_9154,plain,
( multiply(inverse(sk_c5),identity) = sk_c2
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_287,c_33]) ).
cnf(c_792,plain,
( inverse(sk_c5) = sk_c2
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_241,c_9154]) ).
cnf(c_793,plain,
( multiply(sk_c2,sk_c5) = identity
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_792,c_2]) ).
cnf(c_9155,plain,
( multiply(inverse(sk_c5),identity) = sk_c2
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_301,c_33]) ).
cnf(c_829,plain,
( inverse(sk_c5) = sk_c2
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_241,c_9155]) ).
cnf(c_830,plain,
( multiply(sk_c2,sk_c5) = identity
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_829,c_2]) ).
cnf(c_9156,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_618,c_19]) ).
cnf(c_877,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_9156]) ).
cnf(c_880,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_877,c_33]) ).
cnf(c_9157,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c7
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_793,c_57]) ).
cnf(c_966,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c3) = identity ),
inference(copy,[status(thm)],[c_9157]) ).
cnf(c_9158,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_966,c_33]) ).
cnf(c_969,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_241,c_9158]) ).
cnf(c_971,plain,
( multiply(sk_c3,sk_c7) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_969,c_2]) ).
cnf(c_9159,plain,
( multiply(inverse(sk_c3),identity) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_971,c_33]) ).
cnf(c_1002,plain,
( inverse(sk_c3) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_241,c_9159]) ).
cnf(c_9160,plain,
( multiply(sk_c6,sk_c4) = identity
| identity = sk_c7
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_830,c_60]) ).
cnf(c_1041,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c4) = identity ),
inference(copy,[status(thm)],[c_9160]) ).
cnf(c_9161,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1041,c_33]) ).
cnf(c_1044,plain,
( inverse(sk_c6) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_241,c_9161]) ).
cnf(c_9162,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1044,c_880]) ).
cnf(c_1130,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9162]) ).
cnf(c_9163,plain,
( sk_c7 = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1130,c_23]) ).
cnf(c_1135,plain,
( sk_c6 = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9163]) ).
cnf(c_9164,plain,
( multiply(sk_c5,sk_c2) = identity
| sk_c7 = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1130,c_67]) ).
cnf(c_1138,plain,
( multiply(sk_c5,sk_c2) = identity
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9164]) ).
cnf(c_9165,plain,
( multiply(inverse(sk_c5),identity) = sk_c2
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1138,c_33]) ).
cnf(c_1278,plain,
( inverse(sk_c5) = sk_c2
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_241,c_9165]) ).
cnf(c_1279,plain,
( multiply(sk_c2,sk_c5) = identity
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1278,c_2]) ).
cnf(c_9166,plain,
( sk_c6 = sk_c7
| identity = sk_c7
| identity = sk_c7
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1279,c_1135]) ).
cnf(c_9167,plain,
( sk_c6 = sk_c7
| identity = sk_c7
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9166]) ).
cnf(c_9168,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9167]) ).
cnf(c_1610,plain,
( sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9168]) ).
cnf(c_1611,plain,
( multiply(sk_c7,A) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1610,c_1]) ).
cnf(c_1613,plain,
( inverse(sk_c7) = identity
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1610,c_242]) ).
cnf(c_1649,plain,
( identity = sk_c3
| multiply(sk_c7,sk_c1) = identity
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1613,c_628]) ).
cnf(c_9169,plain,
( multiply(sk_c3,identity) = multiply(sk_c7,sk_c4)
| multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1041,c_58]) ).
cnf(c_9170,plain,
( sk_c3 = multiply(sk_c7,sk_c4)
| multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_241,c_9169]) ).
cnf(c_1774,plain,
( multiply(sk_c7,sk_c4) = sk_c3
| multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9170]) ).
cnf(c_9171,plain,
( identity = sk_c1
| sk_c6 = sk_c7
| identity = sk_c3
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1649,c_1611]) ).
cnf(c_1895,plain,
( identity = sk_c1
| identity = sk_c3
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9171]) ).
cnf(c_1897,plain,
( multiply(sk_c3,A) = A
| identity = sk_c1
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1895,c_1]) ).
cnf(c_9172,plain,
( multiply(sk_c7,sk_c1) = identity
| sk_c6 = sk_c7
| identity = sk_c1
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1897,c_44]) ).
cnf(c_2852,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c1
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9172]) ).
cnf(c_9173,plain,
( identity = sk_c1
| sk_c6 = sk_c7
| identity = sk_c1
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_2852,c_1611]) ).
cnf(c_9174,plain,
( identity = sk_c1
| identity = sk_c1
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9173]) ).
cnf(c_3804,plain,
( identity = sk_c1
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9174]) ).
cnf(c_3805,plain,
( multiply(sk_c1,A) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_3804,c_1]) ).
cnf(c_9175,plain,
( multiply(sk_c7,sk_c3) = identity
| sk_c7 = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_3805,c_36]) ).
cnf(c_9176,plain,
( multiply(sk_c7,sk_c3) = identity
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9175]) ).
cnf(c_4064,plain,
( multiply(sk_c7,sk_c3) = identity
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9176]) ).
cnf(c_9177,plain,
( identity = sk_c3
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_4064,c_1611]) ).
cnf(c_4170,plain,
( identity = sk_c3
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9177]) ).
cnf(c_4173,plain,
( multiply(sk_c3,A) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_4170,c_1]) ).
cnf(c_9178,plain,
( sk_c6 = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_4173,c_6]) ).
cnf(c_4667,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9178]) ).
cnf(c_9179,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_4667,c_3805]) ).
cnf(c_9180,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_9179]) ).
cnf(c_4819,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_9180]) ).
cnf(c_5201,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_4819,c_1041]) ).
cnf(c_9181,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| identity != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_4819,c_247]) ).
cnf(c_9182,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| identity != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_4819,c_9181]) ).
cnf(c_9183,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| identity != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_4819,c_9182]) ).
cnf(c_9184,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| identity != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_4819,c_9183]) ).
cnf(c_9185,plain,
( multiply(B,sk_c5) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| identity != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_4819,c_9184]) ).
cnf(c_5688,plain,
( multiply(B,sk_c5) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_9185]) ).
cnf(c_9186,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_4819,c_225]) ).
cnf(c_5701,plain,
( multiply(inverse(sk_c7),sk_c5) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_4819,c_9186]) ).
cnf(c_5763,plain,
( multiply(sk_c5,sk_c2) = identity
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_4819,c_65]) ).
cnf(c_6227,plain,
( inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| identity != sk_c7 ),
inference(factor,[status(thm)],[c_5688]) ).
cnf(c_9187,plain,
( sk_c7 = identity
| identity = sk_c7
| multiply(sk_c5,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_5763,c_971]) ).
cnf(c_9188,plain,
( identity = sk_c7
| identity = sk_c7
| multiply(sk_c5,sk_c2) = identity ),
inference(copy,[status(thm)],[c_9187]) ).
cnf(c_6942,plain,
( identity = sk_c7
| multiply(sk_c5,sk_c2) = identity ),
inference(copy,[status(thm)],[c_9188]) ).
cnf(c_9189,plain,
( multiply(inverse(sk_c5),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6942,c_33]) ).
cnf(c_6952,plain,
( inverse(sk_c5) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_241,c_9189]) ).
cnf(c_6954,plain,
( multiply(sk_c2,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_6952,c_2]) ).
cnf(c_9190,plain,
( sk_c7 = identity
| identity = sk_c7
| multiply(sk_c7,sk_c4) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1774,c_6954]) ).
cnf(c_9191,plain,
( identity = sk_c7
| identity = sk_c7
| multiply(sk_c7,sk_c4) = sk_c3
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9190]) ).
cnf(c_9192,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c4) = sk_c3
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9191]) ).
cnf(c_7863,plain,
( multiply(sk_c7,sk_c4) = sk_c3
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9192]) ).
cnf(c_9193,plain,
( identity = sk_c7
| sk_c3 = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_7863,c_5201]) ).
cnf(c_9194,plain,
( identity = sk_c7
| identity = sk_c3
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9193]) ).
cnf(c_8238,plain,
( identity = sk_c3
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9194]) ).
cnf(c_8255,plain,
( inverse(sk_c3) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_8238,c_242]) ).
cnf(c_9195,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_8255,c_1002]) ).
cnf(c_9196,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_9195]) ).
cnf(c_8360,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_9196]) ).
cnf(c_9197,plain,
( inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_8360,c_6227]) ).
cnf(c_8845,plain,
( inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_9197]) ).
cnf(c_9198,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_8360,c_242]) ).
cnf(c_9115,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_8360,c_9198]) ).
cnf(c_9116,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_8360,c_241]) ).
cnf(c_9120,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_8360,c_1]) ).
cnf(c_9199,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7 ),
inference(factor,[status(thm)],[c_8845]) ).
cnf(c_9200,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c5
| sk_c5 != sk_c7 ),
inference(paramod,[status(thm)],[c_9120,c_9199]) ).
cnf(c_9201,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5
| sk_c7 != sk_c5
| sk_c5 != sk_c7 ),
inference(paramod,[status(thm)],[c_9115,c_9200]) ).
cnf(c_9202,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c5
| sk_c7 != sk_c5
| sk_c5 != sk_c7 ),
inference(paramod,[status(thm)],[c_9116,c_9201]) ).
cnf(c_9203,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c5
| sk_c7 != sk_c5
| sk_c5 != sk_c7 ),
inference(paramod,[status(thm)],[c_9115,c_9202]) ).
cnf(c_9204,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_9203]) ).
cnf(c_9205,plain,
( sk_c7 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_9204]) ).
cnf(c_9206,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_9205]) ).
cnf(c_9207,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_9206]) ).
cnf(c_9134,plain,
sk_c5 != sk_c7,
inference(copy,[status(thm)],[c_9207]) ).
cnf(c_9208,plain,
( multiply(inverse(sk_c7),sk_c5) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_9120,c_5701]) ).
cnf(c_9209,plain,
( multiply(sk_c7,sk_c5) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_9115,c_9208]) ).
cnf(c_9210,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_9120,c_9209]) ).
cnf(c_9211,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_9210]) ).
cnf(c_9144,plain,
$false,
inference(resolve,[status(thm)],[c_9134,c_9211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP274-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n006.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Fri Sep 25 14:42:14 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.53 % Process 3138035 was started by sandbox2 on n006,
% 0.10/0.53 % Fri Sep 25 14:42:14 2026
% 0.10/0.53 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.53
% 0.10/0.53 % From the command line: assign(max_seconds, 300).
% 283.25/37.53
% 283.25/37.53 % given #500 (T,wt=17): 7639 sk_c3 = sk_c7 | inverse(sk_c5) = sk_c7. [para(7577(a,1),7593(b,2)),merge(b)].
% 283.25/37.53
% 283.25/37.53 % SZS status Unsatisfiable for theBenchmark
% 283.25/37.53
% 283.25/37.53 % Proof 1 at 3.81 (+ 0.77) seconds.
% 283.25/37.53 % Length of proof is 94.
% 283.25/37.53 % Level of proof is 35.
% 283.25/37.53 % Maximum clause weight is 56.000.
% 283.25/37.53 % Given clauses 569.
% 283.25/37.53
% 283.25/37.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------