%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP268-1 : 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 : n020.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 07:28:30 AM UTC 2026
% Result : Unsatisfiable 13.86s 2.30s
% Output : CNFRefutation 13.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 163 ( 29 unt; 0 def)
% Number of atoms : 386 ( 385 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 334 ( 111 ~; 223 |; 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 56 ( 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_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_4,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_9,axiom,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_12,axiom,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_15,axiom,
( inverse(sk_c6) = sk_c7
| multiply(sk_c6,sk_c4) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c6,sk_c4) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_18,axiom,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_21,axiom,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(sk_c6) != sk_c7
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c7
| inverse(VAR_3) != sk_c6
| multiply(VAR_3,sk_c6) != VAR_2
| multiply(sk_c6,VAR_2) != sk_c7
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c6) != sk_c7
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c7
| inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
cnf(c_3334,plain,
( inverse(sk_c6) != sk_c7
| inverse(A) != sk_c8
| inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_27,plain,
( inverse(sk_c6) != sk_c7
| inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_3334]) ).
cnf(c_3335,plain,
( inverse(sk_c6) != sk_c7
| inverse(B) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_27]) ).
cnf(c_32,plain,
( inverse(sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_3335]) ).
cnf(c_3336,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3337,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3336]) ).
cnf(c_36,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3337]) ).
cnf(c_47,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_50,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_3338,plain,
( multiply(sk_c7,A) = multiply(sk_c2,multiply(sk_c6,A))
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_3]) ).
cnf(c_62,plain,
( multiply(sk_c2,multiply(sk_c6,A)) = multiply(sk_c7,A)
| inverse(sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_3338]) ).
cnf(c_69,plain,
( multiply(sk_c6,sk_c2) = identity
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_70,plain,
( multiply(sk_c7,sk_c6) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_88,plain,
( multiply(sk_c7,sk_c6) = identity
| multiply(sk_c3,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_96,plain,
( multiply(sk_c6,sk_c3) = identity
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_105,plain,
( inverse(sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| inverse(identity) != sk_c6
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_32]) ).
cnf(c_115,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_36]) ).
cnf(c_159,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_36,c_36]) ).
cnf(c_160,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_159,c_115]) ).
cnf(c_221,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_160,c_2]) ).
cnf(c_281,plain,
( inverse(sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| identity != sk_c6
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_221,c_105]) ).
cnf(c_3339,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_50,c_36]) ).
cnf(c_287,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_160,c_3339]) ).
cnf(c_290,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_287,c_2]) ).
cnf(c_3340,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_69,c_36]) ).
cnf(c_488,plain,
( inverse(sk_c6) = sk_c2
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_160,c_3340]) ).
cnf(c_519,plain,
( multiply(sk_c7,sk_c6) = identity
| inverse(sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_488,c_2]) ).
cnf(c_3341,plain,
( multiply(inverse(sk_c7),identity) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_70,c_36]) ).
cnf(c_531,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_160,c_3341]) ).
cnf(c_3342,plain,
( multiply(inverse(sk_c6),identity) = sk_c3
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_96,c_36]) ).
cnf(c_649,plain,
( inverse(sk_c6) = sk_c3
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_160,c_3342]) ).
cnf(c_3343,plain,
( sk_c3 = sk_c2
| inverse(sk_c6) = sk_c7
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_649,c_488]) ).
cnf(c_669,plain,
( sk_c3 = sk_c2
| inverse(sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_3343]) ).
cnf(c_682,plain,
( multiply(sk_c7,sk_c6) = identity
| sk_c3 = sk_c2 ),
inference(paramod,[status(thm)],[c_669,c_2]) ).
cnf(c_3344,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_669,c_21]) ).
cnf(c_684,plain,
( multiply(sk_c2,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_3344]) ).
cnf(c_3345,plain,
( multiply(inverse(sk_c7),identity) = sk_c6
| sk_c3 = sk_c2 ),
inference(paramod,[status(thm)],[c_682,c_36]) ).
cnf(c_693,plain,
( inverse(sk_c7) = sk_c6
| sk_c3 = sk_c2 ),
inference(paramod,[status(thm)],[c_160,c_3345]) ).
cnf(c_3346,plain,
( inverse(sk_c5) = sk_c8
| identity = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_290,c_5]) ).
cnf(c_771,plain,
( identity = sk_c7
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_3346]) ).
cnf(c_781,plain,
( multiply(sk_c8,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_771,c_2]) ).
cnf(c_3347,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_781,c_36]) ).
cnf(c_800,plain,
( inverse(sk_c8) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_160,c_3347]) ).
cnf(c_820,plain,
( multiply(sk_c5,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_800,c_2]) ).
cnf(c_3348,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_820,c_4]) ).
cnf(c_866,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3348]) ).
cnf(c_3349,plain,
( identity = sk_c7
| inverse(sk_c2) = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_820,c_13]) ).
cnf(c_869,plain,
( inverse(sk_c2) = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3349]) ).
cnf(c_3350,plain,
( identity = sk_c7
| inverse(sk_c3) = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_820,c_22]) ).
cnf(c_872,plain,
( inverse(sk_c3) = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3350]) ).
cnf(c_3351,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_820,c_47]) ).
cnf(c_892,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3351]) ).
cnf(c_923,plain,
( multiply(sk_c6,sk_c2) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_869,c_2]) ).
cnf(c_926,plain,
( inverse(sk_c7) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_869,c_221]) ).
cnf(c_947,plain,
( multiply(sk_c6,sk_c3) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_872,c_2]) ).
cnf(c_3352,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_892,c_36]) ).
cnf(c_1101,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_160,c_3352]) ).
cnf(c_1119,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1101,c_2]) ).
cnf(c_3353,plain,
( multiply(sk_c2,sk_c7) = multiply(sk_c7,sk_c4)
| inverse(sk_c6) = sk_c7
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_62]) ).
cnf(c_1187,plain,
( multiply(sk_c2,sk_c7) = multiply(sk_c7,sk_c4)
| inverse(sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_3353]) ).
cnf(c_3354,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_923,c_36]) ).
cnf(c_1295,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_160,c_3354]) ).
cnf(c_3355,plain,
( identity = sk_c6
| inverse(sk_c2) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_926,c_531]) ).
cnf(c_1364,plain,
( identity = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(copy,[status(thm)],[c_3355]) ).
cnf(c_3356,plain,
( inverse(sk_c2) = sk_c6
| sk_c6 = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_1364,c_869]) ).
cnf(c_1396,plain,
( sk_c6 = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(copy,[status(thm)],[c_3356]) ).
cnf(c_3357,plain,
( multiply(inverse(sk_c6),identity) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_947,c_36]) ).
cnf(c_1417,plain,
( inverse(sk_c6) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_160,c_3357]) ).
cnf(c_3358,plain,
( sk_c3 = sk_c2
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1417,c_1295]) ).
cnf(c_1469,plain,
( sk_c3 = sk_c2
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3358]) ).
cnf(c_1472,plain,
( inverse(sk_c7) = identity
| sk_c3 = sk_c2 ),
inference(paramod,[status(thm)],[c_1469,c_221]) ).
cnf(c_3359,plain,
( identity = sk_c6
| sk_c3 = sk_c2
| sk_c3 = sk_c2 ),
inference(paramod,[status(thm)],[c_1472,c_693]) ).
cnf(c_1506,plain,
( identity = sk_c6
| sk_c3 = sk_c2 ),
inference(copy,[status(thm)],[c_3359]) ).
cnf(c_3360,plain,
( sk_c3 = sk_c2
| sk_c6 = sk_c7
| sk_c3 = sk_c2 ),
inference(paramod,[status(thm)],[c_1506,c_1469]) ).
cnf(c_1537,plain,
( sk_c6 = sk_c7
| sk_c3 = sk_c2 ),
inference(copy,[status(thm)],[c_3360]) ).
cnf(c_3361,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1119,c_866]) ).
cnf(c_3362,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_3361]) ).
cnf(c_1663,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_3362]) ).
cnf(c_1967,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| inverse(sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_1663,c_519]) ).
cnf(c_3363,plain,
( inverse(sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| sk_c7 != sk_c6
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1663,c_281]) ).
cnf(c_3364,plain,
( inverse(sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_3363]) ).
cnf(c_2141,plain,
( inverse(sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c7
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_3364]) ).
cnf(c_3365,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_1663,c_221]) ).
cnf(c_2200,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_1663,c_3365]) ).
cnf(c_2201,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_1663,c_160]) ).
cnf(c_2204,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_1663,c_88]) ).
cnf(c_2209,plain,
multiply(inverse(A),A) = sk_c7,
inference(paramod,[status(thm)],[c_1663,c_2]) ).
cnf(c_2210,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_1663,c_1]) ).
cnf(c_3366,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_2201,c_2141]) ).
cnf(c_2248,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_3366]) ).
cnf(c_3367,plain,
( sk_c2 = multiply(sk_c7,sk_c4)
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_2201,c_1187]) ).
cnf(c_3368,plain,
( sk_c2 = sk_c4
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_2210,c_3367]) ).
cnf(c_2338,plain,
( sk_c4 = sk_c2
| inverse(sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_3368]) ).
cnf(c_2383,plain,
( sk_c6 = sk_c7
| multiply(sk_c3,sk_c6) = sk_c4 ),
inference(paramod,[status(thm)],[c_2210,c_2204]) ).
cnf(c_2387,plain,
( sk_c6 = sk_c7
| inverse(sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_2210,c_1967]) ).
cnf(c_2603,plain,
( sk_c4 = sk_c2
| sk_c2 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_2387,c_2338]) ).
cnf(c_3369,plain,
( sk_c6 = sk_c7
| inverse(sk_c7) = sk_c6
| sk_c4 = sk_c2
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_2603,c_1396]) ).
cnf(c_3370,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| sk_c4 = sk_c2
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_2200,c_3369]) ).
cnf(c_3371,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c4 = sk_c2
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_3370]) ).
cnf(c_3372,plain,
( sk_c6 = sk_c7
| sk_c4 = sk_c2
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_3371]) ).
cnf(c_2632,plain,
( sk_c4 = sk_c2
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_3372]) ).
cnf(c_3373,plain,
multiply(inverse(inverse(A)),sk_c7) = A,
inference(paramod,[status(thm)],[c_2209,c_36]) ).
cnf(c_2781,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_2201,c_3373]) ).
cnf(c_3374,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_2209,c_2248]) ).
cnf(c_3375,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != sk_c7
| sk_c8 != sk_c8
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_2781,c_3374]) ).
cnf(c_3376,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != sk_c7
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_3375]) ).
cnf(c_2784,plain,
( inverse(sk_c6) != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_3376]) ).
cnf(c_2819,plain,
( sk_c4 = sk_c2
| sk_c6 != sk_c7 ),
inference(resolve,[status(thm)],[c_2784,c_2338]) ).
cnf(c_2820,plain,
( sk_c3 = sk_c2
| sk_c6 != sk_c7 ),
inference(resolve,[status(thm)],[c_2784,c_669]) ).
cnf(c_2822,plain,
( inverse(sk_c6) = sk_c2
| sk_c6 != sk_c7 ),
inference(resolve,[status(thm)],[c_2784,c_488]) ).
cnf(c_3377,plain,
( sk_c4 = sk_c2
| sk_c4 = sk_c2 ),
inference(resolve,[status(thm)],[c_2819,c_2632]) ).
cnf(c_2959,plain,
sk_c4 = sk_c2,
inference(copy,[status(thm)],[c_3377]) ).
cnf(c_3045,plain,
( sk_c6 = sk_c7
| multiply(sk_c3,sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_2959,c_2383]) ).
cnf(c_3078,plain,
( multiply(sk_c2,sk_c6) = sk_c2
| inverse(sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_2959,c_684]) ).
cnf(c_3378,plain,
( sk_c3 = sk_c2
| sk_c3 = sk_c2 ),
inference(resolve,[status(thm)],[c_2820,c_1537]) ).
cnf(c_3096,plain,
sk_c3 = sk_c2,
inference(copy,[status(thm)],[c_3378]) ).
cnf(c_3104,plain,
( sk_c6 = sk_c7
| multiply(sk_c2,sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_3096,c_3045]) ).
cnf(c_3379,plain,
( inverse(sk_c6) = sk_c2
| inverse(sk_c6) = sk_c2 ),
inference(resolve,[status(thm)],[c_2822,c_2387]) ).
cnf(c_3159,plain,
inverse(sk_c6) = sk_c2,
inference(copy,[status(thm)],[c_3379]) ).
cnf(c_3181,plain,
( multiply(sk_c2,sk_c6) = sk_c2
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_3159,c_3078]) ).
cnf(c_3217,plain,
( sk_c2 != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_3159,c_2784]) ).
cnf(c_3282,plain,
multiply(sk_c2,sk_c6) = sk_c7,
inference(paramod,[status(thm)],[c_3159,c_2209]) ).
cnf(c_3380,plain,
( sk_c7 = sk_c2
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_3282,c_3181]) ).
cnf(c_3381,plain,
( sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_3380]) ).
cnf(c_3302,plain,
sk_c2 = sk_c7,
inference(copy,[status(thm)],[c_3381]) ).
cnf(c_3382,plain,
( sk_c6 = sk_c7
| multiply(sk_c7,sk_c6) = sk_c2 ),
inference(paramod,[status(thm)],[c_3302,c_3104]) ).
cnf(c_3383,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c2 ),
inference(paramod,[status(thm)],[c_2210,c_3382]) ).
cnf(c_3384,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_3302,c_3383]) ).
cnf(c_3322,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_3384]) ).
cnf(c_3385,plain,
( sk_c2 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_3322,c_3217]) ).
cnf(c_3386,plain,
( sk_c7 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_3302,c_3385]) ).
cnf(c_3387,plain,
sk_c7 != sk_c7,
inference(copy,[status(thm)],[c_3386]) ).
cnf(c_3333,plain,
$false,
inference(copy,[status(thm)],[c_3387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP268-1 : 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 : n020.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 14:42:48 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3157073 was started by sandbox2 on n020,
% 0.19/0.45 % Fri Sep 25 14:42:48 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 13.86/2.30
% 13.86/2.30 % SZS status Unsatisfiable for theBenchmark
% 13.86/2.30
% 13.86/2.30 % Proof 1 at 1.19 (+ 0.41) seconds.
% 13.86/2.30 % Length of proof is 94.
% 13.86/2.30 % Level of proof is 23.
% 13.86/2.30 % Maximum clause weight is 49.000.
% 13.86/2.30 % Given clauses 220.
% 13.86/2.30
% 13.86/2.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------