%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP251-1 : 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 : n004.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 07:28:28 AM UTC 2026
% Result : Unsatisfiable 13.13s 3.26s
% Output : CNFRefutation 13.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 14
% Syntax : Number of formulae : 132 ( 24 unt; 0 def)
% Number of atoms : 388 ( 387 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 448 ( 192 ~; 256 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 82 ( 0 sgn 12 !; 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_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_19,axiom,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_26,axiom,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_43,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( inverse(VAR_6) != sk_c9
| multiply(VAR_6,sk_c9) != VAR_5
| multiply(sk_c9,VAR_5) != sk_c8
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c9
| inverse(VAR_3) != sk_c10
| multiply(VAR_3,sk_c10) != sk_c9
| multiply(VAR_2,sk_c8) != sk_c9
| inverse(VAR_2) != sk_c9
| inverse(VAR_1) != sk_c9
| multiply(VAR_1,sk_c9) != sk_c8
| inverse(VAR_0) != sk_c10
| multiply(VAR_0,sk_c10) != sk_c9 ),
file('theBenchmark.p',prove_this_43) ).
cnf(c_46,plain,
( inverse(V6) != sk_c9
| multiply(V6,sk_c9) != F
| multiply(sk_c9,F) != sk_c8
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c9
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(clausify,[status(thm)],[prove_this_43]) ).
cnf(c_5308,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_47,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5308]) ).
cnf(c_53,plain,
( inverse(E) != sk_c9
| multiply(E,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_65,plain,
( multiply(B,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_74,plain,
( multiply(B,sk_c9) != C
| multiply(sk_c9,C) != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_65]) ).
cnf(c_5309,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_5310,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_5309]) ).
cnf(c_76,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_5310]) ).
cnf(c_105,plain,
( multiply(sk_c10,sk_c1) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_142,plain,
( multiply(sk_c9,sk_c6) = identity
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_155,plain,
( multiply(sk_c9,sk_c2) = identity
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_158,plain,
( multiply(sk_c9,sk_c2) = identity
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_161,plain,
( multiply(sk_c9,sk_c2) = identity
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_209,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_76]) ).
cnf(c_248,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_22,c_76]) ).
cnf(c_295,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_76,c_76]) ).
cnf(c_296,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_295,c_209]) ).
cnf(c_355,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_296,c_2]) ).
cnf(c_5311,plain,
( multiply(identity,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| identity != sk_c9
| multiply(identity,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_355,c_74]) ).
cnf(c_5312,plain,
( multiply(identity,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_5311]) ).
cnf(c_5313,plain,
( multiply(identity,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| inverse(identity) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_5312]) ).
cnf(c_5314,plain,
( multiply(identity,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_355,c_5313]) ).
cnf(c_5315,plain,
( sk_c9 != B
| multiply(sk_c9,B) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_5314]) ).
cnf(c_5316,plain,
( sk_c9 != B
| multiply(sk_c9,B) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5315]) ).
cnf(c_412,plain,
( sk_c9 != B
| multiply(sk_c9,B) != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5316]) ).
cnf(c_5317,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_105,c_76]) ).
cnf(c_416,plain,
( inverse(sk_c10) = sk_c1
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_296,c_5317]) ).
cnf(c_419,plain,
( multiply(sk_c1,sk_c10) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_416,c_2]) ).
cnf(c_5318,plain,
( sk_c9 != identity
| sk_c9 != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_296,c_412]) ).
cnf(c_5319,plain,
( sk_c9 != identity
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5318]) ).
cnf(c_5320,plain,
( identity != sk_c9
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5319]) ).
cnf(c_5321,plain,
( identity != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5320]) ).
cnf(c_550,plain,
( identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5321]) ).
cnf(c_5322,plain,
( identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| identity != sk_c9 ),
inference(paramod,[status(thm)],[c_2,c_550]) ).
cnf(c_589,plain,
( identity != sk_c8
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_5322]) ).
cnf(c_5323,plain,
( multiply(inverse(sk_c9),identity) = sk_c2
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_161,c_76]) ).
cnf(c_785,plain,
( inverse(sk_c9) = sk_c2
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_296,c_5323]) ).
cnf(c_790,plain,
( multiply(sk_c9,sk_c6) = identity
| inverse(sk_c9) = sk_c2 ),
inference(paramod,[status(thm)],[c_785,c_2]) ).
cnf(c_5324,plain,
( inverse(sk_c4) = sk_c10
| identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_419,c_5]) ).
cnf(c_1161,plain,
( identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(copy,[status(thm)],[c_5324]) ).
cnf(c_1173,plain,
( multiply(sk_c10,sk_c4) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1161,c_2]) ).
cnf(c_5325,plain,
( multiply(inverse(sk_c10),identity) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1173,c_76]) ).
cnf(c_1196,plain,
( inverse(sk_c10) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_296,c_5325]) ).
cnf(c_1250,plain,
( multiply(sk_c4,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1196,c_2]) ).
cnf(c_5326,plain,
( identity = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1250,c_4]) ).
cnf(c_1333,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_5326]) ).
cnf(c_5327,plain,
( identity = sk_c9
| inverse(sk_c1) = sk_c10
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1250,c_11]) ).
cnf(c_1334,plain,
( inverse(sk_c1) = sk_c10
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_5327]) ).
cnf(c_1368,plain,
( multiply(sk_c10,sk_c1) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1334,c_2]) ).
cnf(c_5328,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1368,c_76]) ).
cnf(c_1786,plain,
( inverse(sk_c10) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_296,c_5328]) ).
cnf(c_1815,plain,
( multiply(sk_c1,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1786,c_2]) ).
cnf(c_5329,plain,
( identity = sk_c9
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1815,c_1333]) ).
cnf(c_5330,plain,
( identity = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_5329]) ).
cnf(c_2737,plain,
identity = sk_c9,
inference(copy,[status(thm)],[c_5330]) ).
cnf(c_3296,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| inverse(sk_c9) = sk_c2 ),
inference(paramod,[status(thm)],[c_2737,c_790]) ).
cnf(c_5331,plain,
( identity != sk_c8
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_2737,c_589]) ).
cnf(c_5332,plain,
( sk_c9 != sk_c8
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_2737,c_5331]) ).
cnf(c_5333,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| sk_c9 != sk_c9 ),
inference(copy,[status(thm)],[c_5332]) ).
cnf(c_5334,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(copy,[status(thm)],[c_5333]) ).
cnf(c_3417,plain,
( sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(copy,[status(thm)],[c_5334]) ).
cnf(c_5335,plain,
inverse(sk_c9) = identity,
inference(paramod,[status(thm)],[c_2737,c_355]) ).
cnf(c_3468,plain,
inverse(sk_c9) = sk_c9,
inference(paramod,[status(thm)],[c_2737,c_5335]) ).
cnf(c_3469,plain,
multiply(A,sk_c9) = A,
inference(paramod,[status(thm)],[c_2737,c_296]) ).
cnf(c_5336,plain,
( multiply(sk_c9,sk_c2) = identity
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_3469,c_158]) ).
cnf(c_5337,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_2737,c_5336]) ).
cnf(c_3479,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_5337]) ).
cnf(c_3480,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_2737,c_155]) ).
cnf(c_5338,plain,
( multiply(sk_c9,sk_c6) = identity
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3469,c_142]) ).
cnf(c_3483,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2737,c_5338]) ).
cnf(c_3492,plain,
multiply(sk_c9,A) = A,
inference(paramod,[status(thm)],[c_2737,c_1]) ).
cnf(c_5339,plain,
( multiply(sk_c9,sk_c6) = sk_c9
| sk_c9 = sk_c2 ),
inference(paramod,[status(thm)],[c_3468,c_3296]) ).
cnf(c_5340,plain,
( sk_c6 = sk_c9
| sk_c9 = sk_c2 ),
inference(paramod,[status(thm)],[c_3492,c_5339]) ).
cnf(c_3499,plain,
( sk_c6 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_5340]) ).
cnf(c_5341,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3469,c_248]) ).
cnf(c_5342,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3468,c_5341]) ).
cnf(c_5343,plain,
( sk_c8 = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3492,c_5342]) ).
cnf(c_3530,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_5343]) ).
cnf(c_5344,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3469,c_23]) ).
cnf(c_5345,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3469,c_5344]) ).
cnf(c_3802,plain,
( sk_c7 = sk_c6
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_5345]) ).
cnf(c_3803,plain,
( sk_c6 = sk_c9
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3492,c_3483]) ).
cnf(c_5346,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3492,c_3480]) ).
cnf(c_3805,plain,
( sk_c2 = sk_c9
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3492,c_5346]) ).
cnf(c_3806,plain,
( sk_c2 = sk_c9
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_3492,c_3479]) ).
cnf(c_5347,plain,
( sk_c6 = sk_c8
| sk_c2 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3802,c_3530]) ).
cnf(c_4059,plain,
( sk_c6 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_5347]) ).
cnf(c_5348,plain,
( sk_c2 = sk_c9
| sk_c7 = sk_c9
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_3499,c_3806]) ).
cnf(c_4322,plain,
( sk_c7 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_5348]) ).
cnf(c_5349,plain,
( sk_c8 = sk_c9
| sk_c2 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_4059,c_3803]) ).
cnf(c_4369,plain,
( sk_c8 = sk_c9
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_5349]) ).
cnf(c_5350,plain,
( sk_c2 = sk_c9
| sk_c9 = sk_c8
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_4322,c_3805]) ).
cnf(c_5351,plain,
( sk_c2 = sk_c9
| sk_c8 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_5350]) ).
cnf(c_4507,plain,
( sk_c8 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_5351]) ).
cnf(c_5352,plain,
( sk_c8 = sk_c9
| sk_c9 = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_4507,c_4369]) ).
cnf(c_5353,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_5352]) ).
cnf(c_5354,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_5353]) ).
cnf(c_4638,plain,
sk_c8 = sk_c9,
inference(copy,[status(thm)],[c_5354]) ).
cnf(c_5355,plain,
( sk_c9 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(paramod,[status(thm)],[c_4638,c_3417]) ).
cnf(c_5076,plain,
inverse(inverse(sk_c10)) != sk_c10,
inference(copy,[status(thm)],[c_5355]) ).
cnf(c_5356,plain,
multiply(A,sk_c9) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_295,c_3469]) ).
cnf(c_5357,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_3469,c_5356]) ).
cnf(c_5306,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_5357]) ).
cnf(c_5307,plain,
$false,
inference(resolve,[status(thm)],[c_5306,c_5076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP251-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.41 % Computer : n004.cluster.edu
% 0.07/0.41 % Model : x86_64 x86_64
% 0.07/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.41 % Memory : 8046.5625MB
% 0.07/0.41 % OS : Linux 6.8.0-71-generic
% 0.07/0.41 % CPULimit : 300
% 0.07/0.41 % WCLimit : 300
% 0.07/0.41 % DateTime : Fri Sep 25 14:41:07 UTC 2026
% 0.07/0.41 % CPUTime :
% 0.07/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.41 % Process 3416496 was started by sandbox on n004,
% 0.07/0.41 % Fri Sep 25 14:41:07 2026
% 0.07/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.42
% 0.07/0.42 % From the command line: assign(max_seconds, 300).
% 13.13/3.26
% 13.13/3.26 % SZS status Unsatisfiable for theBenchmark
% 13.13/3.26
% 13.13/3.26 % Proof 1 at 1.34 (+ 0.40) seconds.
% 13.13/3.26 % Length of proof is 68.
% 13.13/3.26 % Level of proof is 22.
% 13.13/3.26 % Maximum clause weight is 63.000.
% 13.13/3.26 % Given clauses 337.
% 13.13/3.26
% 13.13/3.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------