%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP301-1 : 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 : n009.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 52.69s 7.19s
% Output : CNFRefutation 52.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 22
% Syntax : Number of formulae : 178 ( 34 unt; 0 def)
% Number of atoms : 453 ( 452 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 425 ( 150 ~; 275 |; 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 : 52 ( 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
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_6,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_21,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_24,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_29,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,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_c6
| multiply(VAR_1,sk_c6) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,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_c6
| multiply(B,sk_c6) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_35,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_38,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(factor,[status(thm)],[c_35]) ).
cnf(c_42,plain,
multiply(multiply(A,identity),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_43,plain,
multiply(multiply(identity,A),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_22035,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_44,plain,
multiply(inverse(A),multiply(A,B)) = multiply(identity,B),
inference(copy,[status(thm)],[c_22035]) ).
cnf(c_50,plain,
( multiply(sk_c5,A) = multiply(sk_c7,multiply(sk_c6,A))
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_51,plain,
( multiply(multiply(A,sk_c7),sk_c6) = multiply(A,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_59,plain,
( multiply(multiply(A,sk_c1),sk_c7) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_66,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_71,plain,
( multiply(sk_c5,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_77,plain,
( multiply(multiply(A,sk_c2),sk_c6) = multiply(A,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_24,c_3]) ).
cnf(c_84,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_437,plain,
multiply(multiply(identity,identity),A) = A,
inference(paramod,[status(thm)],[c_1,c_42]) ).
cnf(c_22036,plain,
multiply(identity,A) = multiply(inverse(identity),A),
inference(paramod,[status(thm)],[c_2,c_42]) ).
cnf(c_438,plain,
multiply(inverse(identity),A) = multiply(identity,A),
inference(copy,[status(thm)],[c_22036]) ).
cnf(c_439,plain,
multiply(multiply(inverse(A),identity),A) = identity,
inference(paramod,[status(thm)],[c_2,c_42]) ).
cnf(c_613,plain,
multiply(inverse(inverse(A)),identity) = multiply(identity,A),
inference(paramod,[status(thm)],[c_2,c_44]) ).
cnf(c_22037,plain,
( multiply(identity,sk_c6) = multiply(sk_c5,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_71,c_51]) ).
cnf(c_1209,plain,
( multiply(identity,sk_c6) = multiply(sk_c5,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22037]) ).
cnf(c_1370,plain,
( multiply(sk_c5,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1209,c_1]) ).
cnf(c_1538,plain,
multiply(inverse(identity),A) = A,
inference(paramod,[status(thm)],[c_1,c_438]) ).
cnf(c_22038,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_66,c_59]) ).
cnf(c_1732,plain,
( multiply(identity,sk_c7) = multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22038]) ).
cnf(c_1794,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1732,c_1]) ).
cnf(c_22039,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_84,c_77]) ).
cnf(c_2264,plain,
( multiply(identity,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22039]) ).
cnf(c_2609,plain,
( multiply(sk_c6,sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_2264,c_1]) ).
cnf(c_22040,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c5,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_2264,c_1209]) ).
cnf(c_22041,plain,
( multiply(sk_c5,sk_c5) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22040]) ).
cnf(c_2624,plain,
( multiply(sk_c5,sk_c5) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22041]) ).
cnf(c_22042,plain,
( multiply(sk_c5,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_2609,c_50]) ).
cnf(c_2645,plain,
( multiply(sk_c5,sk_c5) = multiply(sk_c7,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22042]) ).
cnf(c_22043,plain,
( multiply(sk_c5,sk_c5) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_2645]) ).
cnf(c_3068,plain,
( multiply(sk_c5,sk_c5) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22043]) ).
cnf(c_22044,plain,
( multiply(sk_c7,sk_c6) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_2645,c_1370]) ).
cnf(c_3083,plain,
( multiply(sk_c7,sk_c6) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22044]) ).
cnf(c_22045,plain,
( multiply(sk_c5,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1794,c_2645]) ).
cnf(c_3085,plain,
( multiply(sk_c5,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22045]) ).
cnf(c_22046,plain,
( multiply(identity,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3083,c_1732]) ).
cnf(c_3238,plain,
( multiply(identity,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22046]) ).
cnf(c_22047,plain,
( 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_3085,c_2624]) ).
cnf(c_22048,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22047]) ).
cnf(c_3285,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22048]) ).
cnf(c_22049,plain,
( multiply(sk_c6,A) = multiply(sk_c7,A)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3238,c_43]) ).
cnf(c_3441,plain,
( multiply(sk_c7,A) = multiply(sk_c6,A)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22049]) ).
cnf(c_22050,plain,
( multiply(sk_c5,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_3285,c_50]) ).
cnf(c_3742,plain,
( multiply(sk_c5,sk_c5) = multiply(sk_c7,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22050]) ).
cnf(c_22051,plain,
( multiply(sk_c7,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3742,c_3068]) ).
cnf(c_4675,plain,
( multiply(sk_c7,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22051]) ).
cnf(c_22052,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_4675,c_3441]) ).
cnf(c_22053,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_22052]) ).
cnf(c_22054,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22053]) ).
cnf(c_4851,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(copy,[status(thm)],[c_22054]) ).
cnf(c_5759,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(resolve,[status(thm)],[c_4851,c_38]) ).
cnf(c_5765,plain,
multiply(multiply(A,sk_c6),sk_c7) = multiply(A,sk_c5),
inference(paramod,[status(thm)],[c_4851,c_3]) ).
cnf(c_11876,plain,
multiply(multiply(identity,A),inverse(A)) = identity,
inference(paramod,[status(thm)],[c_613,c_439]) ).
cnf(c_12941,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_1,c_11876]) ).
cnf(c_22055,plain,
identity = inverse(identity),
inference(paramod,[status(thm)],[c_11876,c_437]) ).
cnf(c_12983,plain,
inverse(identity) = identity,
inference(copy,[status(thm)],[c_22055]) ).
cnf(c_13079,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_12941]) ).
cnf(c_13080,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_12,c_12941]) ).
cnf(c_13081,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_12941]) ).
cnf(c_13082,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_16,c_12941]) ).
cnf(c_13083,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_12941]) ).
cnf(c_13084,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_18,c_12941]) ).
cnf(c_13090,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_27,c_12941]) ).
cnf(c_13093,plain,
( multiply(sk_c2,sk_c6) = identity
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_32,c_12941]) ).
cnf(c_13094,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_33,c_12941]) ).
cnf(c_22056,plain,
identity = inverse(inverse(identity)),
inference(paramod,[status(thm)],[c_12941,c_1538]) ).
cnf(c_13119,plain,
inverse(inverse(identity)) = identity,
inference(copy,[status(thm)],[c_22056]) ).
cnf(c_13781,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_13081,c_12941]) ).
cnf(c_13794,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_13083,c_12941]) ).
cnf(c_13913,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c2,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_13093,c_12941]) ).
cnf(c_22057,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| identity = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_13082,c_11]) ).
cnf(c_14133,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_22057]) ).
cnf(c_22058,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| identity = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_13084,c_13]) ).
cnf(c_14207,plain,
( identity = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_22058]) ).
cnf(c_22059,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| identity = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_13094,c_28]) ).
cnf(c_14566,plain,
( identity = sk_c5
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_22059]) ).
cnf(c_14879,plain,
( multiply(inverse(identity),sk_c5) != sk_c6
| identity != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_13119,c_5759]) ).
cnf(c_22060,plain,
( multiply(sk_c3,sk_c7) = identity
| identity = sk_c6
| multiply(sk_c3,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_13781,c_13079]) ).
cnf(c_15437,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c7) = identity ),
inference(copy,[status(thm)],[c_22060]) ).
cnf(c_22061,plain,
( multiply(sk_c4,sk_c6) = identity
| identity = sk_c6
| multiply(sk_c4,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_13794,c_13080]) ).
cnf(c_15570,plain,
( identity = sk_c6
| multiply(sk_c4,sk_c6) = identity ),
inference(copy,[status(thm)],[c_22061]) ).
cnf(c_15726,plain,
( multiply(identity,sk_c7) = multiply(sk_c4,sk_c5)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15570,c_5765]) ).
cnf(c_22062,plain,
( multiply(sk_c4,sk_c6) = identity
| identity = sk_c5
| multiply(sk_c4,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_13913,c_13090]) ).
cnf(c_16217,plain,
( identity = sk_c5
| multiply(sk_c4,sk_c6) = identity ),
inference(copy,[status(thm)],[c_22062]) ).
cnf(c_16314,plain,
( multiply(identity,sk_c7) = multiply(sk_c4,sk_c5)
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_16217,c_5765]) ).
cnf(c_16736,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15726,c_1]) ).
cnf(c_22063,plain,
( identity = sk_c6
| sk_c7 = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_16736,c_14207]) ).
cnf(c_16987,plain,
( sk_c7 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_22063]) ).
cnf(c_16988,plain,
( multiply(sk_c6,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_16987,c_1]) ).
cnf(c_22064,plain,
( sk_c7 = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_16988,c_4851]) ).
cnf(c_17402,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_22064]) ).
cnf(c_19518,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_1538,c_14879]) ).
cnf(c_19524,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(inverse(identity),sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| identity != sk_c7
| multiply(inverse(identity),sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_13119,c_19518]) ).
cnf(c_19800,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| multiply(inverse(identity),sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_1538,c_19524]) ).
cnf(c_22065,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_1538,c_19800]) ).
cnf(c_22066,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| sk_c7 != sk_c6
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_22065]) ).
cnf(c_19803,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| identity != sk_c7
| sk_c7 != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_22066]) ).
cnf(c_20016,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_16314,c_1]) ).
cnf(c_22067,plain,
( identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_20016,c_14566]) ).
cnf(c_20100,plain,
( sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_22067]) ).
cnf(c_22068,plain,
( sk_c7 = sk_c6
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_20100,c_16987]) ).
cnf(c_20268,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_22068]) ).
cnf(c_22069,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_20268,c_17402]) ).
cnf(c_22070,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_22069]) ).
cnf(c_22071,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_22070]) ).
cnf(c_20383,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_22071]) ).
cnf(c_20384,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| inverse(sk_c7) != sk_c6
| inverse(sk_c7) != sk_c5
| identity != sk_c7
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(resolve,[status(thm)],[c_20383,c_19803]) ).
cnf(c_20442,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(paramod,[status(thm)],[c_20383,c_4851]) ).
cnf(c_20562,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_20383,c_14133]) ).
cnf(c_20593,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_20383,c_15437]) ).
cnf(c_20791,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| inverse(sk_c7) != sk_c6
| inverse(sk_c6) != sk_c5
| identity != sk_c7
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_20383,c_20384]) ).
cnf(c_21092,plain,
( sk_c5 != sk_c6
| identity != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(sk_c6) != sk_c5
| identity != sk_c7
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_20383,c_20791]) ).
cnf(c_22072,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_20593,c_20562]) ).
cnf(c_22073,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_22072]) ).
cnf(c_21406,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_22073]) ).
cnf(c_21411,plain,
( sk_c5 != sk_c6
| inverse(sk_c6) != sk_c6
| inverse(sk_c6) != sk_c5
| identity != sk_c7
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(resolve,[status(thm)],[c_21406,c_21092]) ).
cnf(c_21542,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_21406,c_1]) ).
cnf(c_21684,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_21406,c_12983]) ).
cnf(c_21819,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_21406,c_21684]) ).
cnf(c_21825,plain,
( sk_c5 != sk_c6
| inverse(sk_c6) != sk_c5
| identity != sk_c7
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(resolve,[status(thm)],[c_21819,c_21411]) ).
cnf(c_22074,plain,
( sk_c5 != sk_c6
| sk_c6 != sk_c5
| identity != sk_c7
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_21819,c_21825]) ).
cnf(c_22075,plain,
( sk_c5 != sk_c6
| sk_c5 != sk_c6
| identity != sk_c7
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_22074]) ).
cnf(c_21912,plain,
( sk_c5 != sk_c6
| identity != sk_c7
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(copy,[status(thm)],[c_22075]) ).
cnf(c_22076,plain,
( sk_c5 != sk_c6
| identity != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_20383,c_21912]) ).
cnf(c_21948,plain,
( sk_c5 != sk_c6
| identity != sk_c7 ),
inference(resolve,[status(thm)],[c_20442,c_22076]) ).
cnf(c_22077,plain,
( sk_c5 != sk_c6
| identity != sk_c6 ),
inference(paramod,[status(thm)],[c_20383,c_21948]) ).
cnf(c_21949,plain,
sk_c5 != sk_c6,
inference(resolve,[status(thm)],[c_21406,c_22077]) ).
cnf(c_22078,plain,
sk_c6 = sk_c5,
inference(paramod,[status(thm)],[c_21542,c_20442]) ).
cnf(c_22079,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_22078]) ).
cnf(c_22034,plain,
$false,
inference(resolve,[status(thm)],[c_21949,c_22079]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP301-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n009.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 14:43:59 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 1852289 was started by sandbox2 on n009,
% 0.19/0.46 % Fri Sep 25 14:43:59 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 52.69/7.19
% 52.69/7.19 % given #500 (F,wt=49): 16281 multiply(sk_c7,sk_c6) != sk_c5 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | inverse(sk_c7) != sk_c5 | multiply(identity,sk_c6) != sk_c5 | identity != sk_c6 | identity != sk_c7 | multiply(identity,sk_c6) != sk_c7 | multiply(identity,sk_c5) != sk_c6. [para(12983(a,1),13067(g,1))].
% 52.69/7.19
% 52.69/7.19 % SZS status Unsatisfiable for theBenchmark
% 52.69/7.19
% 52.69/7.19 % Proof 1 at 5.68 (+ 1.01) seconds.
% 52.69/7.19 % Length of proof is 111.
% 52.69/7.19 % Level of proof is 25.
% 52.69/7.19 % Maximum clause weight is 60.000.
% 52.69/7.19 % Given clauses 648.
% 52.69/7.19
% 52.69/7.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------