%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP292-1 : 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 : n010.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 07:28:34 AM UTC 2026
% Result : Unsatisfiable 5.51s 1.74s
% Output : CNFRefutation 5.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 9
% Syntax : Number of formulae : 79 ( 22 unt; 0 def)
% Number of atoms : 230 ( 229 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 288 ( 137 ~; 151 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 91 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(left_identity,axiom,
! [VAR_0] : multiply(identity,VAR_0) = VAR_0,
file('theBenchmark.p',left_identity) ).
cnf(c_1,plain,
multiply(identity,A) = A,
inference(clausify,[status(thm)],[left_identity]) ).
fof(left_inverse,axiom,
! [VAR_0] : multiply(inverse(VAR_0),VAR_0) = identity,
file('theBenchmark.p',left_inverse) ).
cnf(c_2,plain,
multiply(inverse(A),A) = identity,
inference(clausify,[status(thm)],[left_inverse]) ).
fof(associativity,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity) ).
cnf(c_3,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity]) ).
fof(prove_this_1,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_6,axiom,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_21,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( multiply(VAR_3,sk_c5) != sk_c6
| inverse(VAR_2) != VAR_3
| multiply(VAR_2,VAR_3) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(VAR_1) != sk_c5
| multiply(VAR_1,sk_c5) != sk_c6
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(C) != D
| multiply(C,D) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(B) != sk_c5
| multiply(B,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
cnf(c_3396,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3397,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3396]) ).
cnf(c_30,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3397]) ).
cnf(c_42,plain,
( multiply(sk_c4,sk_c3) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_46,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_13,c_2]) ).
cnf(c_47,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_80,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_24]) ).
cnf(c_233,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_30]) ).
cnf(c_234,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_30]) ).
cnf(c_257,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_30,c_30]) ).
cnf(c_258,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_257,c_233]) ).
cnf(c_317,plain,
( multiply(sk_c4,sk_c3) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_47,c_2]) ).
cnf(c_3398,plain,
( multiply(inverse(sk_c4),identity) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_317,c_30]) ).
cnf(c_488,plain,
( inverse(sk_c4) = sk_c3
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_258,c_3398]) ).
cnf(c_491,plain,
( multiply(sk_c3,sk_c4) = identity
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_488,c_2]) ).
cnf(c_3399,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_491,c_46]) ).
cnf(c_821,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_3399]) ).
cnf(c_3400,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_821,c_30]) ).
cnf(c_824,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_258,c_3400]) ).
cnf(c_829,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_824,c_2]) ).
cnf(c_3401,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_829,c_9]) ).
cnf(c_1086,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_3401]) ).
cnf(c_3402,plain,
( multiply(sk_c4,sk_c3) = identity
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_829,c_42]) ).
cnf(c_1089,plain,
( multiply(sk_c4,sk_c3) = identity
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_3402]) ).
cnf(c_3403,plain,
( multiply(inverse(sk_c4),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1089,c_30]) ).
cnf(c_1148,plain,
( inverse(sk_c4) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_258,c_3403]) ).
cnf(c_1152,plain,
( multiply(sk_c3,sk_c4) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1148,c_2]) ).
cnf(c_3404,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_1152,c_1086]) ).
cnf(c_3405,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_3404]) ).
cnf(c_1423,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_3405]) ).
cnf(c_2036,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_1423,c_258]) ).
cnf(c_3406,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_2036,c_80]) ).
cnf(c_3407,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| sk_c6 != sk_c6
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_1423,c_3406]) ).
cnf(c_3408,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| sk_c5 != sk_c7
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| sk_c6 != sk_c6
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_2036,c_3407]) ).
cnf(c_3409,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| sk_c7 != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| sk_c6 != sk_c6
| sk_c7 != sk_c5 ),
inference(copy,[status(thm)],[c_3408]) ).
cnf(c_3410,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| sk_c7 != sk_c5
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| sk_c7 != sk_c5 ),
inference(copy,[status(thm)],[c_3409]) ).
cnf(c_2049,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| sk_c7 != sk_c5 ),
inference(copy,[status(thm)],[c_3410]) ).
cnf(c_2059,plain,
multiply(inverse(A),A) = sk_c6,
inference(paramod,[status(thm)],[c_1423,c_2]) ).
cnf(c_3411,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| sk_c7 = sk_c5 ),
inference(paramod,[status(thm)],[c_2036,c_4]) ).
cnf(c_3412,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c5 ),
inference(paramod,[status(thm)],[c_2036,c_3411]) ).
cnf(c_3413,plain,
( sk_c7 = sk_c5
| sk_c7 = sk_c5 ),
inference(copy,[status(thm)],[c_3412]) ).
cnf(c_2673,plain,
sk_c7 = sk_c5,
inference(copy,[status(thm)],[c_3413]) ).
cnf(c_3414,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c7)) != sk_c7
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_2673,c_2049]) ).
cnf(c_3415,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c5)) != sk_c7
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_2673,c_3414]) ).
cnf(c_3416,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c5)) != sk_c5
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_2673,c_3415]) ).
cnf(c_3109,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(B) != C
| multiply(B,C) != sk_c6
| inverse(A) != sk_c5
| multiply(A,sk_c5) != sk_c6
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(copy,[status(thm)],[c_3416]) ).
cnf(c_3417,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(A) != B
| multiply(A,B) != sk_c6
| multiply(inverse(sk_c5),sk_c5) != sk_c6
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(factor,[status(thm)],[c_3109]) ).
cnf(c_3418,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(A) != B
| multiply(A,B) != sk_c6
| sk_c6 != sk_c6
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(paramod,[status(thm)],[c_2059,c_3417]) ).
cnf(c_3269,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(A) != B
| multiply(A,B) != sk_c6
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(copy,[status(thm)],[c_3418]) ).
cnf(c_3419,plain,
multiply(A,sk_c6) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_257,c_2036]) ).
cnf(c_3420,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_2036,c_3419]) ).
cnf(c_3365,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_3420]) ).
cnf(c_3421,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(A) != B
| multiply(A,B) != sk_c6
| sk_c5 != sk_c5 ),
inference(paramod,[status(thm)],[c_3365,c_3269]) ).
cnf(c_3373,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(A) != B
| multiply(A,B) != sk_c6 ),
inference(copy,[status(thm)],[c_3421]) ).
cnf(c_3422,plain,
( multiply(multiply(A,multiply(B,sk_c6)),sk_c5) != sk_c6
| inverse(inverse(multiply(A,B))) != multiply(A,multiply(B,sk_c6)) ),
inference(resolve,[status(thm)],[c_3373,c_234]) ).
cnf(c_3423,plain,
( multiply(multiply(A,multiply(B,sk_c6)),sk_c5) != sk_c6
| multiply(A,B) != multiply(A,multiply(B,sk_c6)) ),
inference(paramod,[status(thm)],[c_3365,c_3422]) ).
cnf(c_3424,plain,
( multiply(multiply(A,multiply(B,sk_c6)),sk_c5) != sk_c6
| multiply(A,B) != multiply(A,B) ),
inference(paramod,[status(thm)],[c_2036,c_3423]) ).
cnf(c_3425,plain,
( multiply(multiply(A,B),sk_c5) != sk_c6
| multiply(A,B) != multiply(A,B) ),
inference(paramod,[status(thm)],[c_2036,c_3424]) ).
cnf(c_3426,plain,
( multiply(A,multiply(B,sk_c5)) != sk_c6
| multiply(A,B) != multiply(A,B) ),
inference(paramod,[status(thm)],[c_3,c_3425]) ).
cnf(c_3394,plain,
multiply(A,multiply(B,sk_c5)) != sk_c6,
inference(copy,[status(thm)],[c_3426]) ).
cnf(c_3395,plain,
$false,
inference(resolve,[status(thm)],[c_3394,c_2059]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP292-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:44:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 998765 was started by sandbox on n010,
% 0.09/0.36 % Fri Sep 25 14:44:00 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 5.51/1.74
% 5.51/1.74 % SZS status Unsatisfiable for theBenchmark
% 5.51/1.74
% 5.51/1.74 % Proof 1 at 0.59 (+ 0.10) seconds.
% 5.51/1.74 % Length of proof is 39.
% 5.51/1.74 % Level of proof is 19.
% 5.51/1.74 % Maximum clause weight is 61.000.
% 5.51/1.74 % Given clauses 140.
% 5.51/1.74
% 5.51/1.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------