%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP302-1 : 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 : n015.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 07:28:36 AM UTC 2026
% Result : Unsatisfiable 17.20s 2.65s
% Output : CNFRefutation 17.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 14
% Syntax : Number of formulae : 119 ( 37 unt; 0 def)
% Number of atoms : 393 ( 392 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 525 ( 251 ~; 274 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 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 : 93 ( 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_c8,sk_c7) = sk_c6,
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(clausify,[status(thm)],[prove_this_1]) ).
cnf(c_5,plain,
sk_c6 = multiply(sk_c8,sk_c7),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_this_3,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_7,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_8,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c5) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_9,plain,
( inverse(sk_c5) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_10,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( multiply(sk_c5,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_11,plain,
( multiply(sk_c5,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_9,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_13,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_14,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_14,axiom,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_18,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
cnf(c_19,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_18]) ).
fof(prove_this_20,axiom,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_30,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_26,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( multiply(VAR_3,sk_c8) != VAR_4
| inverse(VAR_4) != sk_c8
| inverse(VAR_3) != VAR_4
| multiply(VAR_2,sk_c7) != sk_c8
| inverse(VAR_2) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(VAR_1) != sk_c8
| multiply(VAR_1,sk_c8) != sk_c6
| multiply(VAR_0,sk_c7) != sk_c8
| inverse(VAR_0) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_36,plain,
( multiply(D,sk_c8) != E
| inverse(E) != sk_c8
| inverse(D) != E
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c6
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
cnf(c_4940,plain,
( multiply(D,sk_c8) != E
| inverse(E) != sk_c8
| inverse(D) != E
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c6
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_36]) ).
cnf(c_4941,plain,
( multiply(D,sk_c8) != E
| inverse(E) != sk_c8
| inverse(D) != E
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != multiply(sk_c8,sk_c7)
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(sk_c8,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_4940]) ).
cnf(c_4942,plain,
( multiply(D,sk_c8) != E
| inverse(E) != sk_c8
| inverse(D) != E
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(B,sk_c8)
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(sk_c8,sk_c7) ),
inference(copy,[status(thm)],[c_4941]) ).
cnf(c_37,plain,
( multiply(D,sk_c8) != E
| inverse(E) != sk_c8
| inverse(D) != E
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(B,sk_c8)
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(copy,[status(thm)],[c_4942]) ).
cnf(c_4943,plain,
( multiply(C,sk_c8) != D
| inverse(D) != sk_c8
| inverse(C) != D
| multiply(A,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(B,sk_c8)
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(factor,[status(thm)],[c_37]) ).
cnf(c_39,plain,
( multiply(C,sk_c8) != D
| inverse(D) != sk_c8
| inverse(C) != D
| inverse(sk_c8) != sk_c7
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(B,sk_c8)
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(copy,[status(thm)],[c_4943]) ).
cnf(c_4944,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4945,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_4944]) ).
cnf(c_59,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_4945]) ).
cnf(c_92,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_105,plain,
( inverse(sk_c3) = sk_c8
| multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| inverse(sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(A,sk_c8)
| inverse(sk_c1) != sk_c8 ),
inference(resolve,[status(thm)],[c_39,c_13]) ).
cnf(c_129,plain,
( multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| inverse(sk_c8) != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_39]) ).
cnf(c_186,plain,
( inverse(sk_c3) = sk_c8
| multiply(B,sk_c8) != A
| inverse(B) != A
| inverse(sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(A,sk_c8)
| inverse(sk_c1) != sk_c8 ),
inference(factor,[status(thm)],[c_105]) ).
cnf(c_276,plain,
( multiply(B,sk_c8) != A
| inverse(B) != A
| inverse(sk_c8) != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(factor,[status(thm)],[c_129]) ).
cnf(c_4946,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != multiply(sk_c7,sk_c8)
| inverse(sk_c1) != sk_c8 ),
inference(factor,[status(thm)],[c_186]) ).
cnf(c_419,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != multiply(sk_c8,sk_c7)
| inverse(sk_c1) != sk_c8 ),
inference(copy,[status(thm)],[c_4946]) ).
cnf(c_483,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(sk_c7,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8 ),
inference(factor,[status(thm)],[c_276]) ).
cnf(c_560,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_59]) ).
cnf(c_569,plain,
( multiply(inverse(sk_c1),sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_13,c_59]) ).
cnf(c_586,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_59,c_59]) ).
cnf(c_587,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_586,c_560]) ).
cnf(c_4947,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_92,c_59]) ).
cnf(c_753,plain,
( inverse(sk_c8) = sk_c2
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_587,c_4947]) ).
cnf(c_754,plain,
( multiply(sk_c2,sk_c8) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_753,c_2]) ).
cnf(c_4948,plain,
( inverse(sk_c8) = sk_c7
| identity = multiply(sk_c8,sk_c7)
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_754,c_19]) ).
cnf(c_4949,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = identity
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_4948]) ).
cnf(c_1413,plain,
( multiply(sk_c8,sk_c7) = identity
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_4949]) ).
cnf(c_4950,plain,
( multiply(inverse(sk_c8),identity) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1413,c_59]) ).
cnf(c_4951,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_587,c_4950]) ).
cnf(c_1796,plain,
inverse(sk_c8) = sk_c7,
inference(copy,[status(thm)],[c_4951]) ).
cnf(c_4952,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(sk_c7,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_1796,c_483]) ).
cnf(c_4953,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(sk_c7,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_1796,c_4952]) ).
cnf(c_4954,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(sk_c7,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_4953]) ).
cnf(c_2736,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != identity
| multiply(sk_c7,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_4954]) ).
cnf(c_4955,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != multiply(sk_c8,sk_c7)
| inverse(sk_c1) != sk_c8 ),
inference(paramod,[status(thm)],[c_1796,c_419]) ).
cnf(c_2779,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != multiply(sk_c8,sk_c7)
| inverse(sk_c1) != sk_c8 ),
inference(copy,[status(thm)],[c_4955]) ).
cnf(c_4956,plain,
( multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| inverse(sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(paramod,[status(thm)],[c_1796,c_129]) ).
cnf(c_4957,plain,
( multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(paramod,[status(thm)],[c_1796,c_4956]) ).
cnf(c_3035,plain,
( multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(copy,[status(thm)],[c_4957]) ).
cnf(c_3189,plain,
multiply(sk_c7,sk_c8) = identity,
inference(paramod,[status(thm)],[c_1796,c_2]) ).
cnf(c_4958,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| identity != multiply(sk_c8,sk_c7)
| inverse(sk_c1) != sk_c8 ),
inference(paramod,[status(thm)],[c_3189,c_2779]) ).
cnf(c_3199,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != identity
| inverse(sk_c1) != sk_c8 ),
inference(copy,[status(thm)],[c_4958]) ).
cnf(c_4959,plain,
multiply(inverse(sk_c7),identity) = sk_c8,
inference(paramod,[status(thm)],[c_3189,c_59]) ).
cnf(c_3242,plain,
inverse(sk_c7) = sk_c8,
inference(paramod,[status(thm)],[c_587,c_4959]) ).
cnf(c_4960,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c7) != identity
| inverse(sk_c1) != sk_c8 ),
inference(paramod,[status(thm)],[c_3242,c_3199]) ).
cnf(c_3251,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != identity
| inverse(sk_c1) != sk_c8 ),
inference(copy,[status(thm)],[c_4960]) ).
cnf(c_4961,plain,
( multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c7) != identity
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(paramod,[status(thm)],[c_3242,c_3035]) ).
cnf(c_3261,plain,
( multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| multiply(sk_c8,sk_c7) != identity
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(copy,[status(thm)],[c_4961]) ).
cnf(c_4962,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != identity
| multiply(sk_c7,sk_c7) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_3242,c_2736]) ).
cnf(c_3300,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != identity
| multiply(sk_c7,sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_4962]) ).
cnf(c_3353,plain,
multiply(sk_c8,sk_c7) = identity,
inference(paramod,[status(thm)],[c_3242,c_2]) ).
cnf(c_4963,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| identity != identity
| multiply(sk_c7,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_3353,c_3300]) ).
cnf(c_3394,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_4963]) ).
cnf(c_4964,plain,
( multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| identity != identity
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(paramod,[status(thm)],[c_3353,c_3261]) ).
cnf(c_3423,plain,
( multiply(B,sk_c8) != C
| inverse(C) != sk_c8
| inverse(B) != C
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8 ),
inference(copy,[status(thm)],[c_4964]) ).
cnf(c_4965,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| identity != identity
| inverse(sk_c1) != sk_c8 ),
inference(paramod,[status(thm)],[c_3353,c_3251]) ).
cnf(c_3429,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c1) != sk_c8 ),
inference(copy,[status(thm)],[c_4965]) ).
cnf(c_4966,plain,
( inverse(sk_c1) = sk_c8
| multiply(A,sk_c8) != B
| inverse(B) != sk_c8
| inverse(A) != B
| multiply(sk_c3,sk_c7) != sk_c8 ),
inference(resolve,[status(thm)],[c_3423,c_7]) ).
cnf(c_4967,plain,
( inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| multiply(A,sk_c8) != B
| inverse(B) != sk_c8
| inverse(A) != B ),
inference(resolve,[status(thm)],[c_4966,c_8]) ).
cnf(c_4968,plain,
( inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) != sk_c4
| inverse(sk_c4) != sk_c8 ),
inference(resolve,[status(thm)],[c_4967,c_9]) ).
cnf(c_4969,plain,
( inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c8) != sk_c4 ),
inference(resolve,[status(thm)],[c_4968,c_10]) ).
cnf(c_4970,plain,
( inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(resolve,[status(thm)],[c_4969,c_11]) ).
cnf(c_4971,plain,
( inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_4970]) ).
cnf(c_4972,plain,
( inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_4971]) ).
cnf(c_4973,plain,
( inverse(sk_c1) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_4972]) ).
cnf(c_4567,plain,
inverse(sk_c1) = sk_c8,
inference(copy,[status(thm)],[c_4973]) ).
cnf(c_4974,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_4567,c_3429]) ).
cnf(c_4631,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_4974]) ).
cnf(c_4641,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_4567,c_569]) ).
cnf(c_4668,plain,
multiply(sk_c8,sk_c1) = identity,
inference(paramod,[status(thm)],[c_4567,c_2]) ).
cnf(c_4975,plain,
multiply(inverse(sk_c8),identity) = sk_c1,
inference(paramod,[status(thm)],[c_4668,c_59]) ).
cnf(c_4976,plain,
multiply(sk_c7,identity) = sk_c1,
inference(paramod,[status(thm)],[c_1796,c_4975]) ).
cnf(c_4977,plain,
sk_c7 = sk_c1,
inference(paramod,[status(thm)],[c_587,c_4976]) ).
cnf(c_4672,plain,
sk_c1 = sk_c7,
inference(copy,[status(thm)],[c_4977]) ).
cnf(c_4785,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_4672,c_14]) ).
cnf(c_4978,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(resolve,[status(thm)],[c_4641,c_4631]) ).
cnf(c_4875,plain,
inverse(sk_c3) = sk_c8,
inference(copy,[status(thm)],[c_4978]) ).
cnf(c_4904,plain,
multiply(sk_c8,sk_c3) = identity,
inference(paramod,[status(thm)],[c_4875,c_2]) ).
cnf(c_4979,plain,
multiply(inverse(sk_c8),identity) = sk_c3,
inference(paramod,[status(thm)],[c_4904,c_59]) ).
cnf(c_4980,plain,
multiply(sk_c7,identity) = sk_c3,
inference(paramod,[status(thm)],[c_1796,c_4979]) ).
cnf(c_4981,plain,
sk_c7 = sk_c3,
inference(paramod,[status(thm)],[c_587,c_4980]) ).
cnf(c_4908,plain,
sk_c3 = sk_c7,
inference(copy,[status(thm)],[c_4981]) ).
cnf(c_4982,plain,
( multiply(sk_c7,sk_c7) = sk_c8
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_4908,c_4785]) ).
cnf(c_4914,plain,
multiply(sk_c7,sk_c7) = sk_c8,
inference(copy,[status(thm)],[c_4982]) ).
cnf(c_4983,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_4914,c_3394]) ).
cnf(c_4929,plain,
multiply(sk_c8,sk_c8) != sk_c7,
inference(copy,[status(thm)],[c_4983]) ).
cnf(c_4984,plain,
multiply(inverse(sk_c7),sk_c8) = sk_c7,
inference(paramod,[status(thm)],[c_4914,c_59]) ).
cnf(c_4985,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(paramod,[status(thm)],[c_3242,c_4984]) ).
cnf(c_4939,plain,
$false,
inference(resolve,[status(thm)],[c_4929,c_4985]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP302-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:47:27 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1635578 was started by sandbox2 on n015,
% 0.10/0.36 % Fri Sep 25 14:47:27 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 17.20/2.65
% 17.20/2.65 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 17.20/2.65
% 17.20/2.65 % SZS status Unsatisfiable for theBenchmark
% 17.20/2.65
% 17.20/2.65 % Proof 1 at 1.84 (+ 0.36) seconds.
% 17.20/2.65 % Length of proof is 59.
% 17.20/2.65 % Level of proof is 19.
% 17.20/2.65 % Maximum clause weight is 56.000.
% 17.20/2.65 % Given clauses 296.
% 17.20/2.65
% 17.20/2.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------