%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP345-1 : 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 : n007.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 07:28:40 AM UTC 2026
% Result : Unsatisfiable 59.39s 8.05s
% Output : CNFRefutation 59.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 22
% Syntax : Number of formulae : 200 ( 43 unt; 0 def)
% Number of atoms : 497 ( 496 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 452 ( 155 ~; 297 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 65 ( 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_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_14,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_20,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_23,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_26,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_29,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(VAR_3) != sk_c6
| multiply(VAR_3,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| inverse(VAR_2) != sk_c7
| multiply(VAR_2,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(VAR_1,sk_c5) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_36,plain,
( multiply(B,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_38,plain,
multiply(multiply(A,identity),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_25954,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_40,plain,
multiply(inverse(A),multiply(A,B)) = multiply(identity,B),
inference(copy,[status(thm)],[c_25954]) ).
cnf(c_41,plain,
multiply(multiply(A,inverse(B)),B) = multiply(A,identity),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_25955,plain,
( multiply(sk_c7,A) = multiply(sk_c6,multiply(sk_c5,A))
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_46,plain,
( multiply(sk_c6,multiply(sk_c5,A)) = multiply(sk_c7,A)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25955]) ).
cnf(c_47,plain,
( multiply(multiply(A,sk_c6),sk_c5) = multiply(A,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_49,plain,
( multiply(multiply(A,sk_c3),sk_c7) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_50,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_51,plain,
( multiply(sk_c5,sk_c6) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_53,plain,
( multiply(multiply(A,sk_c4),sk_c6) = multiply(A,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_54,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_293,plain,
multiply(multiply(identity,identity),A) = A,
inference(paramod,[status(thm)],[c_1,c_38]) ).
cnf(c_25956,plain,
multiply(identity,A) = multiply(inverse(identity),A),
inference(paramod,[status(thm)],[c_2,c_38]) ).
cnf(c_294,plain,
multiply(inverse(identity),A) = multiply(identity,A),
inference(copy,[status(thm)],[c_25956]) ).
cnf(c_295,plain,
multiply(multiply(inverse(A),identity),A) = identity,
inference(paramod,[status(thm)],[c_2,c_38]) ).
cnf(c_25957,plain,
multiply(A,B) = multiply(A,multiply(identity,B)),
inference(paramod,[status(thm)],[c_38,c_3]) ).
cnf(c_297,plain,
multiply(A,multiply(identity,B)) = multiply(A,B),
inference(copy,[status(thm)],[c_25957]) ).
cnf(c_416,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(paramod,[status(thm)],[c_1,c_40]) ).
cnf(c_417,plain,
multiply(inverse(inverse(A)),identity) = multiply(identity,A),
inference(paramod,[status(thm)],[c_2,c_40]) ).
cnf(c_463,plain,
multiply(inverse(A),A) = multiply(identity,identity),
inference(paramod,[status(thm)],[c_1,c_41]) ).
cnf(c_25958,plain,
( multiply(sk_c6,identity) = multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_51,c_46]) ).
cnf(c_25959,plain,
( multiply(sk_c7,sk_c6) = multiply(sk_c6,identity)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25958]) ).
cnf(c_973,plain,
( multiply(sk_c7,sk_c6) = multiply(sk_c6,identity)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25959]) ).
cnf(c_25960,plain,
( multiply(sk_c6,sk_c5) = multiply(identity,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1,c_47]) ).
cnf(c_986,plain,
( multiply(identity,sk_c7) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25960]) ).
cnf(c_25961,plain,
( multiply(identity,sk_c5) = multiply(sk_c5,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_51,c_47]) ).
cnf(c_999,plain,
( multiply(identity,sk_c5) = multiply(sk_c5,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25961]) ).
cnf(c_25962,plain,
A = multiply(identity,multiply(identity,A)),
inference(paramod,[status(thm)],[c_293,c_3]) ).
cnf(c_1055,plain,
multiply(identity,multiply(identity,A)) = A,
inference(copy,[status(thm)],[c_25962]) ).
cnf(c_25963,plain,
( multiply(identity,sk_c7) = multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_50,c_49]) ).
cnf(c_1139,plain,
( multiply(identity,sk_c7) = multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25963]) ).
cnf(c_1177,plain,
( multiply(sk_c5,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_999,c_1]) ).
cnf(c_25964,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c7,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1177,c_46]) ).
cnf(c_25965,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25964]) ).
cnf(c_1205,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25965]) ).
cnf(c_25966,plain,
( multiply(identity,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_54,c_53]) ).
cnf(c_1285,plain,
( multiply(identity,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25966]) ).
cnf(c_1310,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1139,c_1]) ).
cnf(c_25967,plain,
( multiply(sk_c7,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1139,c_986]) ).
cnf(c_1327,plain,
( multiply(sk_c7,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25967]) ).
cnf(c_25968,plain,
( sk_c7 = multiply(sk_c6,identity)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1310,c_973]) ).
cnf(c_25969,plain,
( multiply(sk_c6,identity) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25968]) ).
cnf(c_1344,plain,
( multiply(sk_c6,identity) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25969]) ).
cnf(c_1349,plain,
( multiply(sk_c7,A) = multiply(sk_c6,A)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1344,c_38]) ).
cnf(c_25970,plain,
( multiply(identity,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_1285]) ).
cnf(c_1481,plain,
( multiply(identity,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25970]) ).
cnf(c_25971,plain,
( multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1349,c_1205]) ).
cnf(c_25972,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25971]) ).
cnf(c_1955,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25972]) ).
cnf(c_25973,plain,
( multiply(sk_c7,sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1955,c_1327]) ).
cnf(c_2829,plain,
( multiply(sk_c7,sk_c6) = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25973]) ).
cnf(c_4128,plain,
multiply(inverse(identity),A) = A,
inference(paramod,[status(thm)],[c_1,c_294]) ).
cnf(c_25974,plain,
( multiply(sk_c5,sk_c6) = multiply(identity,identity)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_7,c_463]) ).
cnf(c_4450,plain,
( multiply(identity,identity) = multiply(sk_c5,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25974]) ).
cnf(c_6026,plain,
( multiply(A,sk_c7) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1481,c_297]) ).
cnf(c_25975,plain,
( multiply(sk_c5,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6026,c_1177]) ).
cnf(c_6285,plain,
( multiply(sk_c5,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25975]) ).
cnf(c_25976,plain,
( multiply(identity,identity) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6285,c_4450]) ).
cnf(c_6369,plain,
( multiply(identity,identity) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25976]) ).
cnf(c_6510,plain,
( multiply(sk_c5,A) = A
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6369,c_293]) ).
cnf(c_25977,plain,
( multiply(identity,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6510,c_999]) ).
cnf(c_6630,plain,
( multiply(identity,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25977]) ).
cnf(c_6793,plain,
( multiply(identity,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6630,c_1055]) ).
cnf(c_25978,plain,
( sk_c5 = multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6793,c_1139]) ).
cnf(c_25979,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25978]) ).
cnf(c_7188,plain,
( multiply(sk_c7,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25979]) ).
cnf(c_25980,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_7188,c_2829]) ).
cnf(c_25981,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25980]) ).
cnf(c_25982,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_25981]) ).
cnf(c_7751,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(copy,[status(thm)],[c_25982]) ).
cnf(c_8821,plain,
( multiply(B,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7 ),
inference(resolve,[status(thm)],[c_7751,c_36]) ).
cnf(c_8825,plain,
multiply(multiply(A,sk_c6),sk_c7) = multiply(A,sk_c5),
inference(paramod,[status(thm)],[c_7751,c_3]) ).
cnf(c_8844,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(paramod,[status(thm)],[c_7751,c_416]) ).
cnf(c_16245,plain,
multiply(multiply(identity,A),inverse(A)) = identity,
inference(paramod,[status(thm)],[c_417,c_295]) ).
cnf(c_16763,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_1,c_16245]) ).
cnf(c_25983,plain,
identity = inverse(identity),
inference(paramod,[status(thm)],[c_16245,c_293]) ).
cnf(c_16806,plain,
inverse(identity) = identity,
inference(copy,[status(thm)],[c_25983]) ).
cnf(c_16903,plain,
( multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_16806,c_8821]) ).
cnf(c_16915,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_11,c_16763]) ).
cnf(c_16916,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_16763]) ).
cnf(c_16920,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_16763]) ).
cnf(c_16924,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_23,c_16763]) ).
cnf(c_16925,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_24,c_16763]) ).
cnf(c_16927,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_26,c_16763]) ).
cnf(c_16928,plain,
( multiply(sk_c4,sk_c6) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_27,c_16763]) ).
cnf(c_16929,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_30,c_16763]) ).
cnf(c_16931,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_33,c_16763]) ).
cnf(c_25984,plain,
identity = inverse(inverse(identity)),
inference(paramod,[status(thm)],[c_16763,c_4128]) ).
cnf(c_16962,plain,
inverse(inverse(identity)) = identity,
inference(copy,[status(thm)],[c_25984]) ).
cnf(c_17473,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_16916,c_16763]) ).
cnf(c_17528,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c3,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_16925,c_16763]) ).
cnf(c_17737,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c4,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_16928,c_16763]) ).
cnf(c_25985,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_16920,c_17]) ).
cnf(c_17832,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_25985]) ).
cnf(c_25986,plain,
( identity = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_16929,c_29]) ).
cnf(c_18461,plain,
( identity = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_25986]) ).
cnf(c_25987,plain,
( identity = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_16931,c_32]) ).
cnf(c_18557,plain,
( identity = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_25987]) ).
cnf(c_25988,plain,
( multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| identity != sk_c7
| multiply(inverse(identity),sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_16962,c_16903]) ).
cnf(c_18897,plain,
( multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(inverse(identity),sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_25988]) ).
cnf(c_25989,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_17473,c_16915]) ).
cnf(c_19206,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference(copy,[status(thm)],[c_25989]) ).
cnf(c_25990,plain,
( multiply(sk_c2,sk_c6) = identity
| identity = sk_c6
| multiply(sk_c2,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_17528,c_16924]) ).
cnf(c_19691,plain,
( identity = sk_c6
| multiply(sk_c2,sk_c6) = identity ),
inference(copy,[status(thm)],[c_25990]) ).
cnf(c_19712,plain,
( multiply(identity,sk_c7) = multiply(sk_c2,sk_c5)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_19691,c_8825]) ).
cnf(c_25991,plain,
( multiply(sk_c2,sk_c6) = identity
| identity = sk_c5
| multiply(sk_c2,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_17737,c_16927]) ).
cnf(c_19982,plain,
( identity = sk_c5
| multiply(sk_c2,sk_c6) = identity ),
inference(copy,[status(thm)],[c_25991]) ).
cnf(c_20003,plain,
( multiply(identity,sk_c7) = multiply(sk_c2,sk_c5)
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_19982,c_8825]) ).
cnf(c_20504,plain,
( multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_19712,c_1]) ).
cnf(c_25992,plain,
( identity = sk_c6
| sk_c7 = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_20504,c_18461]) ).
cnf(c_20603,plain,
( sk_c7 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_25992]) ).
cnf(c_20604,plain,
( multiply(sk_c6,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_20603,c_1]) ).
cnf(c_20900,plain,
( multiply(A,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_4128,c_18897]) ).
cnf(c_20905,plain,
( multiply(inverse(identity),sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(inverse(identity),sk_c5) != sk_c6
| identity != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_16962,c_20900]) ).
cnf(c_20907,plain,
( multiply(inverse(identity),sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_4128,c_20905]) ).
cnf(c_25993,plain,
( sk_c7 = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_20604,c_7751]) ).
cnf(c_21043,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_25993]) ).
cnf(c_25994,plain,
( sk_c6 != sk_c5
| inverse(sk_c6) != sk_c5
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_4128,c_20907]) ).
cnf(c_25995,plain,
( sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_25994]) ).
cnf(c_21273,plain,
( inverse(sk_c6) != sk_c5
| sk_c7 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_25995]) ).
cnf(c_23374,plain,
( multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_20003,c_1]) ).
cnf(c_25996,plain,
( identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_23374,c_18557]) ).
cnf(c_23467,plain,
( sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_25996]) ).
cnf(c_25997,plain,
( sk_c7 = sk_c6
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_23467,c_20603]) ).
cnf(c_23669,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_25997]) ).
cnf(c_25998,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_23669,c_21043]) ).
cnf(c_25999,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_25998]) ).
cnf(c_26000,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_25999]) ).
cnf(c_23829,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_26000]) ).
cnf(c_23862,plain,
( inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(resolve,[status(thm)],[c_23829,c_21273]) ).
cnf(c_23935,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(paramod,[status(thm)],[c_23829,c_7751]) ).
cnf(c_24027,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_23829,c_17832]) ).
cnf(c_24054,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_23829,c_19206]) ).
cnf(c_26001,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_24054,c_24027]) ).
cnf(c_26002,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_26001]) ).
cnf(c_24608,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_26002]) ).
cnf(c_24630,plain,
( inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(resolve,[status(thm)],[c_24608,c_23862]) ).
cnf(c_24694,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_24608,c_1]) ).
cnf(c_24894,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_24608,c_16806]) ).
cnf(c_25029,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_24608,c_24894]) ).
cnf(c_25098,plain,
( identity != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_24894,c_24630]) ).
cnf(c_26003,plain,
( identity != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_25098]) ).
cnf(c_26004,plain,
( identity != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| sk_c7 != sk_c6
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_26003]) ).
cnf(c_25099,plain,
( identity != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7
| sk_c5 != sk_c6
| identity != sk_c7 ),
inference(resolve,[status(thm)],[c_23829,c_26004]) ).
cnf(c_25157,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(paramod,[status(thm)],[c_25029,c_8844]) ).
cnf(c_25194,plain,
( identity != sk_c5
| sk_c5 != sk_c6
| identity != sk_c7 ),
inference(resolve,[status(thm)],[c_25157,c_25099]) ).
cnf(c_26005,plain,
sk_c6 = sk_c5,
inference(paramod,[status(thm)],[c_24694,c_23935]) ).
cnf(c_25421,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_26005]) ).
cnf(c_25437,plain,
( identity != sk_c5
| identity != sk_c7 ),
inference(resolve,[status(thm)],[c_25421,c_25194]) ).
cnf(c_26006,plain,
( sk_c6 != sk_c5
| identity != sk_c7 ),
inference(paramod,[status(thm)],[c_24608,c_25437]) ).
cnf(c_26007,plain,
( sk_c5 != sk_c6
| identity != sk_c7 ),
inference(copy,[status(thm)],[c_26006]) ).
cnf(c_25952,plain,
identity != sk_c7,
inference(resolve,[status(thm)],[c_25421,c_26007]) ).
cnf(c_26008,plain,
identity != sk_c6,
inference(paramod,[status(thm)],[c_23829,c_25952]) ).
cnf(c_25953,plain,
$false,
inference(resolve,[status(thm)],[c_24608,c_26008]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP345-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:44:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1254215 was started by sandbox2 on n007,
% 0.10/0.37 % Fri Sep 25 14:44:55 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 59.39/8.05
% 59.39/8.05 % given #500 (T,wt=24): 12482 multiply(sk_c5,sk_c6) = multiply(sk_c6,sk_c4) | multiply(sk_c1,sk_c5) = multiply(sk_c7,sk_c7). [para(5051(a,1),8825(a,1,1)),flip(b)].
% 59.39/8.05
% 59.39/8.05 % SZS status Unsatisfiable for theBenchmark
% 59.39/8.05
% 59.39/8.05 % Proof 1 at 6.44 (+ 1.11) seconds.
% 59.39/8.05 % Length of proof is 123.
% 59.39/8.05 % Level of proof is 27.
% 59.39/8.05 % Maximum clause weight is 60.000.
% 59.39/8.05 % Given clauses 809.
% 59.39/8.05
% 59.39/8.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------