%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP259-1 : 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 07:28:29 AM UTC 2026
% Result : Unsatisfiable 58.77s 11.29s
% Output : CNFRefutation 58.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 22
% Syntax : Number of formulae : 177 ( 27 unt; 0 def)
% Number of atoms : 494 ( 493 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 519 ( 202 ~; 317 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_14,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_19,axiom,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_26,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_31,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
fof(prove_this_36,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( multiply(VAR_4,sk_c6) != sk_c7
| inverse(VAR_4) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(VAR_2) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(VAR_1) != sk_c7
| multiply(VAR_1,sk_c7) != sk_c6
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_36) ).
cnf(c_39,plain,
( multiply(E,sk_c6) != sk_c7
| inverse(E) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(D) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_36]) ).
cnf(c_41,plain,
( multiply(D,sk_c6) != sk_c7
| inverse(D) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_39]) ).
cnf(c_17824,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_17825,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_17824]) ).
cnf(c_47,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_17825]) ).
cnf(c_50,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_53,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_17826,plain,
( multiply(sk_c6,A) = multiply(sk_c2,multiply(sk_c7,A))
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_61,plain,
( multiply(sk_c2,multiply(sk_c7,A)) = multiply(sk_c6,A)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_17826]) ).
cnf(c_66,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_600,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_47]) ).
cnf(c_637,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_47,c_47]) ).
cnf(c_638,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_637,c_600]) ).
cnf(c_639,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_638,c_2]) ).
cnf(c_17827,plain,
( multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(identity,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| multiply(identity,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_639,c_41]) ).
cnf(c_17828,plain,
( multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(identity,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_17827]) ).
cnf(c_17829,plain,
( multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| sk_c7 != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_17828]) ).
cnf(c_17830,plain,
( multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| sk_c8 != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_17829]) ).
cnf(c_649,plain,
( multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_17830]) ).
cnf(c_1053,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_637,c_2]) ).
cnf(c_17831,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_637,c_638]) ).
cnf(c_17832,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_638,c_17831]) ).
cnf(c_1078,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_17832]) ).
cnf(c_1129,plain,
( inverse(sk_c7) = sk_c2
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_1078]) ).
cnf(c_1187,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_9,c_1053]) ).
cnf(c_1188,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_10,c_1053]) ).
cnf(c_1189,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_11,c_1053]) ).
cnf(c_1190,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_1053]) ).
cnf(c_1191,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_13,c_1053]) ).
cnf(c_1194,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_1053]) ).
cnf(c_1197,plain,
( multiply(sk_c2,sk_c7) = identity
| inverse(sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_1053]) ).
cnf(c_1198,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_1053]) ).
cnf(c_1203,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_34,c_1053]) ).
cnf(c_17833,plain,
( multiply(sk_c2,identity) = multiply(sk_c6,inverse(sk_c7))
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1053,c_61]) ).
cnf(c_17834,plain,
( sk_c2 = multiply(sk_c6,inverse(sk_c7))
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_638,c_17833]) ).
cnf(c_3445,plain,
( multiply(sk_c6,inverse(sk_c7)) = sk_c2
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_17834]) ).
cnf(c_4005,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c1,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_1188,c_2]) ).
cnf(c_4069,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c1,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_1190,c_2]) ).
cnf(c_4205,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c2,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_1197,c_2]) ).
cnf(c_17835,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c6),sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7 ),
inference(resolve,[status(thm)],[c_649,c_1078]) ).
cnf(c_17836,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| identity != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_17835]) ).
cnf(c_9819,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_17836]) ).
cnf(c_9876,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c8 != sk_c7 ),
inference(resolve,[status(thm)],[c_9819,c_1078]) ).
cnf(c_17837,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1187,c_4]) ).
cnf(c_10041,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_17837]) ).
cnf(c_10045,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10041,c_47]) ).
cnf(c_17838,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| identity = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_1189,c_6]) ).
cnf(c_10316,plain,
( identity = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_17838]) ).
cnf(c_10320,plain,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10316,c_47]) ).
cnf(c_17839,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| identity = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1191,c_8]) ).
cnf(c_10341,plain,
( identity = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_17839]) ).
cnf(c_17840,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1194,c_14]) ).
cnf(c_10944,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_17840]) ).
cnf(c_10950,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_10944,c_47]) ).
cnf(c_17841,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| identity = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1198,c_18]) ).
cnf(c_11228,plain,
( identity = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_17841]) ).
cnf(c_17842,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1203,c_29]) ).
cnf(c_11519,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_17842]) ).
cnf(c_11524,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11519,c_47]) ).
cnf(c_17843,plain,
( multiply(sk_c8,sk_c4) = identity
| identity = sk_c7
| multiply(sk_c8,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_4005,c_50]) ).
cnf(c_12033,plain,
( identity = sk_c7
| multiply(sk_c8,sk_c4) = identity ),
inference(copy,[status(thm)],[c_17843]) ).
cnf(c_17844,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12033,c_47]) ).
cnf(c_12036,plain,
( inverse(sk_c8) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_638,c_17844]) ).
cnf(c_12040,plain,
( inverse(sk_c4) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12036,c_1078]) ).
cnf(c_17845,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12040,c_10320]) ).
cnf(c_12350,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_17845]) ).
cnf(c_12354,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12350,c_47]) ).
cnf(c_17846,plain,
( multiply(sk_c7,sk_c5) = identity
| identity = sk_c7
| multiply(sk_c7,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_4069,c_53]) ).
cnf(c_12553,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c5) = identity ),
inference(copy,[status(thm)],[c_17846]) ).
cnf(c_17847,plain,
( multiply(inverse(sk_c7),identity) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12553,c_47]) ).
cnf(c_12556,plain,
( inverse(sk_c7) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_638,c_17847]) ).
cnf(c_17848,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12556,c_10045]) ).
cnf(c_12595,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_17848]) ).
cnf(c_17849,plain,
( identity = sk_c7
| sk_c8 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12595,c_10341]) ).
cnf(c_12714,plain,
( sk_c8 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_17849]) ).
cnf(c_12717,plain,
( inverse(sk_c7) = identity
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_12714,c_639]) ).
cnf(c_17850,plain,
( multiply(identity,sk_c6) = sk_c8
| identity = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_12717,c_11524]) ).
cnf(c_13107,plain,
( sk_c6 = sk_c8
| identity = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_17850]) ).
cnf(c_17851,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7
| sk_c6 = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_13107,c_12714]) ).
cnf(c_17852,plain,
( sk_c8 = sk_c7
| sk_c6 = sk_c8
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_17851]) ).
cnf(c_13582,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_17852]) ).
cnf(c_17853,plain,
( multiply(sk_c7,sk_c5) = identity
| identity = sk_c6
| multiply(sk_c7,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_4205,c_66]) ).
cnf(c_13977,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c5) = identity ),
inference(copy,[status(thm)],[c_17853]) ).
cnf(c_17854,plain,
( multiply(inverse(sk_c7),identity) = sk_c5
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_13977,c_47]) ).
cnf(c_13980,plain,
( inverse(sk_c7) = sk_c5
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_638,c_17854]) ).
cnf(c_17855,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_13980,c_10950]) ).
cnf(c_14000,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_17855]) ).
cnf(c_17856,plain,
( identity = sk_c6
| sk_c8 = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_14000,c_11228]) ).
cnf(c_14166,plain,
( sk_c8 = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_17856]) ).
cnf(c_17857,plain,
( sk_c8 = sk_c7
| sk_c6 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_14166,c_12714]) ).
cnf(c_14196,plain,
( sk_c6 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_17857]) ).
cnf(c_17858,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_14196,c_13582]) ).
cnf(c_17859,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_17858]) ).
cnf(c_17860,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_17859]) ).
cnf(c_14292,plain,
sk_c8 = sk_c7,
inference(copy,[status(thm)],[c_17860]) ).
cnf(c_17861,plain,
( multiply(inverse(sk_c7),sk_c7) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_14292,c_12354]) ).
cnf(c_17862,plain,
( identity = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_17861]) ).
cnf(c_17863,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_14292,c_17862]) ).
cnf(c_15215,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_17863]) ).
cnf(c_17864,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| identity != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14292,c_9876]) ).
cnf(c_17865,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| sk_c7 != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_15215,c_17864]) ).
cnf(c_17866,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14292,c_17865]) ).
cnf(c_17867,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14292,c_17866]) ).
cnf(c_17868,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| sk_c7 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_14292,c_17867]) ).
cnf(c_17869,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(copy,[status(thm)],[c_17868]) ).
cnf(c_16704,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_17869]) ).
cnf(c_17342,plain,
( multiply(sk_c6,inverse(sk_c7)) = sk_c2
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_14292,c_3445]) ).
cnf(c_17506,plain,
( inverse(sk_c7) = sk_c2
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_14292,c_1129]) ).
cnf(c_17870,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_15215,c_639]) ).
cnf(c_17729,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_15215,c_17870]) ).
cnf(c_17730,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_15215,c_638]) ).
cnf(c_17737,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_15215,c_1]) ).
cnf(c_17871,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_16704]) ).
cnf(c_17872,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_17730,c_17871]) ).
cnf(c_17873,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_17729,c_17872]) ).
cnf(c_17874,plain,
( multiply(inverse(sk_c7),sk_c6) != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_17730,c_17873]) ).
cnf(c_17875,plain,
( multiply(sk_c7,sk_c6) != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_17729,c_17874]) ).
cnf(c_17876,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_17737,c_17875]) ).
cnf(c_17877,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c7 != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_17876]) ).
cnf(c_17878,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_17877]) ).
cnf(c_17879,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_17878]) ).
cnf(c_17809,plain,
sk_c6 != sk_c7,
inference(copy,[status(thm)],[c_17879]) ).
cnf(c_17880,plain,
( inverse(sk_c7) = sk_c2
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_17730,c_17506]) ).
cnf(c_17881,plain,
( sk_c7 = sk_c2
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_17729,c_17880]) ).
cnf(c_17882,plain,
( sk_c7 = sk_c2
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_17881]) ).
cnf(c_17883,plain,
( sk_c2 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_17882]) ).
cnf(c_17822,plain,
sk_c2 = sk_c7,
inference(resolve,[status(thm)],[c_17809,c_17883]) ).
cnf(c_17884,plain,
( multiply(sk_c6,inverse(sk_c7)) = sk_c2
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_17730,c_17342]) ).
cnf(c_17885,plain,
( multiply(sk_c6,sk_c7) = sk_c2
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_17729,c_17884]) ).
cnf(c_17886,plain,
( sk_c6 = sk_c2
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_17730,c_17885]) ).
cnf(c_17887,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_17822,c_17886]) ).
cnf(c_17888,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_17887]) ).
cnf(c_17889,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_17888]) ).
cnf(c_17823,plain,
$false,
inference(resolve,[status(thm)],[c_17809,c_17889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP259-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41 % Computer : n003.cluster.edu
% 0.08/0.41 % Model : x86_64 x86_64
% 0.08/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.41 % Memory : 8046.5625MB
% 0.08/0.41 % OS : Linux 6.8.0-71-generic
% 0.08/0.41 % CPULimit : 300
% 0.08/0.41 % WCLimit : 300
% 0.08/0.41 % DateTime : Fri Sep 25 14:43:07 UTC 2026
% 0.08/0.41 % CPUTime :
% 0.08/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.41 % Process 421719 was started by sandbox on n003,
% 0.08/0.41 % Fri Sep 25 14:43:07 2026
% 0.08/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.42
% 0.08/0.42 % From the command line: assign(max_seconds, 300).
% 58.77/11.29
% 58.77/11.29 % SZS status Unsatisfiable for theBenchmark
% 58.77/11.29
% 58.77/11.29 % Proof 1 at 6.74 (+ 0.80) seconds.
% 58.77/11.29 % Length of proof is 89.
% 58.77/11.29 % Level of proof is 18.
% 58.77/11.29 % Maximum clause weight is 55.000.
% 58.77/11.29 % Given clauses 474.
% 58.77/11.29
% 58.77/11.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------