%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP230-1 : 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 : 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 07:28:25 AM UTC 2026
% Result : Unsatisfiable 19.30s 12.83s
% Output : CNFRefutation 19.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 16
% Syntax : Number of formulae : 149 ( 24 unt; 0 def)
% Number of atoms : 360 ( 359 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 330 ( 119 ~; 211 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 59 ( 0 sgn 11 !; 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_c3,sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_4,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_10,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( inverse(sk_c3) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_19,axiom,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c3,sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( inverse(sk_c3) = sk_c4
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_25,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( inverse(VAR_5) != sk_c8
| multiply(VAR_5,sk_c8) != VAR_4
| multiply(sk_c8,VAR_4) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_2) != VAR_3
| multiply(VAR_2,VAR_3) != sk_c8
| inverse(VAR_1) != sk_c7
| multiply(VAR_1,sk_c7) != sk_c8
| multiply(VAR_0,sk_c7) != sk_c8
| inverse(VAR_0) != sk_c8 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(C) != D
| multiply(C,D) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
cnf(c_30,plain,
( multiply(A,sk_c8) != E
| multiply(sk_c8,E) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(C) != D
| multiply(C,D) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_42,plain,
( multiply(A,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(B) != C
| multiply(B,C) != sk_c8
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_64,plain,
( multiply(A,sk_c8) != C
| multiply(sk_c8,C) != sk_c7
| inverse(B) != A
| multiply(B,A) != sk_c8
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_3881,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3882,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3881]) ).
cnf(c_73,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3882]) ).
cnf(c_78,plain,
( multiply(sk_c4,sk_c3) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_82,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_85,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_89,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_3883,plain,
( multiply(sk_c7,A) = multiply(sk_c8,multiply(sk_c6,A))
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_13,c_3]) ).
cnf(c_103,plain,
( multiply(sk_c8,multiply(sk_c6,A)) = multiply(sk_c7,A)
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_3883]) ).
cnf(c_3884,plain,
( multiply(sk_c8,A) = multiply(sk_c1,multiply(sk_c7,A))
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_105,plain,
( multiply(sk_c1,multiply(sk_c7,A)) = multiply(sk_c8,A)
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_3884]) ).
cnf(c_3885,plain,
( multiply(multiply(A,sk_c5),sk_c8) = multiply(A,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_108,plain,
( multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_3,c_3885]) ).
cnf(c_109,plain,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_137,plain,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_177,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_73]) ).
cnf(c_227,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_73,c_73]) ).
cnf(c_228,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_227,c_177]) ).
cnf(c_237,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_228,c_2]) ).
cnf(c_3886,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(identity,identity) != sk_c8
| inverse(identity) != sk_c7
| multiply(identity,sk_c7) != sk_c8
| inverse(identity) != sk_c8 ),
inference(resolve,[status(thm)],[c_237,c_64]) ).
cnf(c_3887,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(identity,identity) != sk_c8
| inverse(identity) != sk_c7
| multiply(identity,sk_c7) != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_237,c_3886]) ).
cnf(c_3888,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(identity,identity) != sk_c8
| inverse(identity) != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_3887]) ).
cnf(c_3889,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(identity,identity) != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_237,c_3888]) ).
cnf(c_3890,plain,
( multiply(identity,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| identity != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_228,c_3889]) ).
cnf(c_3891,plain,
( sk_c8 != A
| multiply(sk_c8,A) != sk_c7
| identity != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_3890]) ).
cnf(c_264,plain,
( sk_c8 != A
| multiply(sk_c8,A) != sk_c7
| identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_3891]) ).
cnf(c_3892,plain,
( multiply(inverse(sk_c4),identity) = sk_c3
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_78,c_73]) ).
cnf(c_283,plain,
( inverse(sk_c4) = sk_c3
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_228,c_3892]) ).
cnf(c_3893,plain,
( sk_c8 != identity
| sk_c8 != sk_c7
| identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_228,c_264]) ).
cnf(c_3894,plain,
( sk_c8 != identity
| sk_c7 != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_3893]) ).
cnf(c_3895,plain,
( identity != sk_c8
| sk_c7 != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_3894]) ).
cnf(c_3896,plain,
( identity != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_3895]) ).
cnf(c_333,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_3896]) ).
cnf(c_336,plain,
( multiply(sk_c3,sk_c4) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_283,c_2]) ).
cnf(c_3897,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_89,c_73]) ).
cnf(c_354,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_228,c_3897]) ).
cnf(c_357,plain,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_354,c_2]) ).
cnf(c_3898,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_137,c_73]) ).
cnf(c_438,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_228,c_3898]) ).
cnf(c_440,plain,
( multiply(sk_c2,sk_c7) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_438,c_2]) ).
cnf(c_3899,plain,
( identity = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_336,c_4]) ).
cnf(c_737,plain,
( identity = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_3899]) ).
cnf(c_3900,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_357,c_8]) ).
cnf(c_1444,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_3900]) ).
cnf(c_3901,plain,
( sk_c6 = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_1444,c_737]) ).
cnf(c_1487,plain,
( sk_c6 = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_3901]) ).
cnf(c_1503,plain,
( multiply(sk_c8,sk_c1) = identity
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1487,c_2]) ).
cnf(c_3902,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_1503,c_82]) ).
cnf(c_1701,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c1) = identity ),
inference(copy,[status(thm)],[c_3902]) ).
cnf(c_3903,plain,
( multiply(sk_c1,multiply(sk_c7,sk_c1)) = identity
| multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_85,c_105]) ).
cnf(c_1869,plain,
( multiply(sk_c1,multiply(sk_c7,sk_c1)) = identity
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_3903]) ).
cnf(c_3904,plain,
( multiply(sk_c8,multiply(sk_c6,multiply(sk_c5,sk_c8))) = multiply(sk_c7,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_108,c_103]) ).
cnf(c_1990,plain,
( multiply(sk_c8,multiply(sk_c6,multiply(sk_c5,sk_c8))) = multiply(sk_c7,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_3904]) ).
cnf(c_3905,plain,
( inverse(sk_c3) = sk_c4
| identity = sk_c8
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_440,c_17]) ).
cnf(c_2036,plain,
( identity = sk_c8
| inverse(sk_c3) = sk_c4 ),
inference(copy,[status(thm)],[c_3905]) ).
cnf(c_2051,plain,
( multiply(sk_c4,sk_c3) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2036,c_2]) ).
cnf(c_3906,plain,
( multiply(inverse(sk_c4),identity) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2051,c_73]) ).
cnf(c_2076,plain,
( inverse(sk_c4) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_228,c_3906]) ).
cnf(c_2111,plain,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_109,c_73]) ).
cnf(c_2142,plain,
( multiply(sk_c3,sk_c4) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2076,c_2]) ).
cnf(c_3907,plain,
( identity = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2142,c_16]) ).
cnf(c_2209,plain,
( multiply(sk_c2,sk_c7) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3907]) ).
cnf(c_3908,plain,
( identity = sk_c8
| inverse(sk_c2) = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2142,c_22]) ).
cnf(c_2210,plain,
( inverse(sk_c2) = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3908]) ).
cnf(c_2271,plain,
( multiply(sk_c7,sk_c2) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2210,c_2]) ).
cnf(c_3909,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2271,c_73]) ).
cnf(c_2564,plain,
( inverse(sk_c7) = sk_c2
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_228,c_3909]) ).
cnf(c_2599,plain,
( multiply(sk_c2,sk_c7) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2564,c_2]) ).
cnf(c_3910,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2599,c_2209]) ).
cnf(c_3911,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3910]) ).
cnf(c_2863,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_3911]) ).
cnf(c_3092,plain,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_2863,c_2111]) ).
cnf(c_3178,plain,
( multiply(sk_c1,multiply(sk_c7,sk_c1)) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_2863,c_1869]) ).
cnf(c_3260,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_2863,c_1701]) ).
cnf(c_3912,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_2863,c_333]) ).
cnf(c_3913,plain,
( sk_c8 != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_2863,c_3912]) ).
cnf(c_3914,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_3913]) ).
cnf(c_3915,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8 ),
inference(copy,[status(thm)],[c_3914]) ).
cnf(c_3736,plain,
sk_c7 != sk_c8,
inference(copy,[status(thm)],[c_3915]) ).
cnf(c_3916,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_2863,c_237]) ).
cnf(c_3748,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_2863,c_3916]) ).
cnf(c_3752,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_2863,c_228]) ).
cnf(c_3762,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_2863,c_1]) ).
cnf(c_3917,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_3762,c_3260]) ).
cnf(c_3918,plain,
( sk_c8 = sk_c7
| sk_c1 = sk_c8 ),
inference(paramod,[status(thm)],[c_3752,c_3917]) ).
cnf(c_3919,plain,
( sk_c7 = sk_c8
| sk_c1 = sk_c8 ),
inference(copy,[status(thm)],[c_3918]) ).
cnf(c_3838,plain,
sk_c1 = sk_c8,
inference(resolve,[status(thm)],[c_3736,c_3919]) ).
cnf(c_3920,plain,
( multiply(sk_c1,multiply(sk_c7,sk_c1)) = sk_c8
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_3752,c_3178]) ).
cnf(c_3921,plain,
( multiply(sk_c8,multiply(sk_c7,sk_c1)) = sk_c8
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_3838,c_3920]) ).
cnf(c_3922,plain,
( multiply(sk_c8,multiply(sk_c7,sk_c8)) = sk_c8
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_3838,c_3921]) ).
cnf(c_3923,plain,
( multiply(sk_c8,sk_c7) = sk_c8
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_3752,c_3922]) ).
cnf(c_3924,plain,
( sk_c7 = sk_c8
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_3762,c_3923]) ).
cnf(c_3925,plain,
( sk_c7 = sk_c8
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_3924]) ).
cnf(c_3839,plain,
sk_c6 = sk_c5,
inference(resolve,[status(thm)],[c_3736,c_3925]) ).
cnf(c_3926,plain,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_3762,c_3092]) ).
cnf(c_3927,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_3838,c_3926]) ).
cnf(c_3928,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_3748,c_3927]) ).
cnf(c_3929,plain,
( sk_c8 = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_3752,c_3928]) ).
cnf(c_3930,plain,
( sk_c7 = sk_c8
| sk_c5 = sk_c8 ),
inference(copy,[status(thm)],[c_3929]) ).
cnf(c_3841,plain,
sk_c5 = sk_c8,
inference(resolve,[status(thm)],[c_3736,c_3930]) ).
cnf(c_3931,plain,
( multiply(sk_c8,multiply(sk_c6,multiply(sk_c5,sk_c8))) = multiply(sk_c7,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_3838,c_1990]) ).
cnf(c_3932,plain,
( multiply(sk_c8,multiply(sk_c6,multiply(sk_c5,sk_c8))) = multiply(sk_c7,sk_c6)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3762,c_3931]) ).
cnf(c_3933,plain,
( multiply(sk_c8,multiply(sk_c5,multiply(sk_c5,sk_c8))) = multiply(sk_c7,sk_c6)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3839,c_3932]) ).
cnf(c_3934,plain,
( multiply(sk_c8,multiply(sk_c8,multiply(sk_c5,sk_c8))) = multiply(sk_c7,sk_c6)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3841,c_3933]) ).
cnf(c_3935,plain,
( multiply(sk_c8,multiply(sk_c8,multiply(sk_c8,sk_c8))) = multiply(sk_c7,sk_c6)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3841,c_3934]) ).
cnf(c_3936,plain,
( multiply(sk_c8,multiply(sk_c8,sk_c8)) = multiply(sk_c7,sk_c6)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3752,c_3935]) ).
cnf(c_3937,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c7,sk_c6)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3752,c_3936]) ).
cnf(c_3938,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3752,c_3937]) ).
cnf(c_3939,plain,
( sk_c8 = multiply(sk_c7,sk_c5)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3839,c_3938]) ).
cnf(c_3940,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3841,c_3939]) ).
cnf(c_3941,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_3752,c_3940]) ).
cnf(c_3942,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_3941]) ).
cnf(c_3943,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_3942]) ).
cnf(c_3880,plain,
$false,
inference(resolve,[status(thm)],[c_3736,c_3943]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP230-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n009.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Fri Sep 25 14:39:55 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/10.38 % Process 1838825 was started by sandbox on n009,
% 0.09/10.38 % Fri Sep 25 14:39:55 2026
% 0.09/10.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/10.38
% 0.09/10.38 % From the command line: assign(max_seconds, 300).
% 19.30/12.83
% 19.30/12.83 % SZS status Unsatisfiable for theBenchmark
% 19.30/12.83
% 19.30/12.83 % Proof 1 at 1.80 (+ 0.62) seconds.
% 19.30/12.83 % Length of proof is 70.
% 19.30/12.83 % Level of proof is 18.
% 19.30/12.83 % Maximum clause weight is 50.000.
% 19.30/12.83 % Given clauses 258.
% 19.30/12.83
% 19.30/12.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------