%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP370-1 : 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 : n002.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 07:28:43 AM UTC 2026
% Result : Unsatisfiable 36.40s 5.72s
% Output : CNFRefutation 36.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 13
% Syntax : Number of formulae : 121 ( 26 unt; 0 def)
% Number of atoms : 343 ( 342 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 391 ( 169 ~; 222 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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 : 109 ( 2 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_c9) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_5,axiom,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c5) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_15,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_29,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( inverse(VAR_5) != sk_c9
| multiply(VAR_5,sk_c9) != VAR_4
| multiply(sk_c9,VAR_4) != sk_c7
| inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_2) != sk_c9
| multiply(VAR_2,sk_c9) != sk_c8
| multiply(VAR_1,sk_c7) != sk_c8
| inverse(VAR_0) != VAR_1
| multiply(VAR_0,VAR_1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c7
| inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
cnf(c_7135,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_7136,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_7135]) ).
cnf(c_53,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_7136]) ).
cnf(c_7137,plain,
( multiply(multiply(A,sk_c3),sk_c9) = multiply(A,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_55,plain,
( multiply(A,multiply(sk_c3,sk_c9)) = multiply(A,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_3,c_7137]) ).
cnf(c_56,plain,
( multiply(sk_c9,sk_c3) = identity
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_64,plain,
( multiply(sk_c9,sk_c5) = identity
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_67,plain,
( multiply(sk_c9,sk_c3) = identity
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_76,plain,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_77,plain,
( multiply(sk_c9,sk_c3) = identity
| inverse(sk_c1) = sk_c2 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_139,plain,
( inverse(E) != sk_c9
| multiply(E,sk_c9) != D
| multiply(sk_c9,D) != sk_c7
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(paramod,[status(thm)],[c_2,c_32]) ).
cnf(c_7138,plain,
( inverse(C) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(factor,[status(thm)],[c_139]) ).
cnf(c_356,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(copy,[status(thm)],[c_7138]) ).
cnf(c_1207,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_53]) ).
cnf(c_1208,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_53]) ).
cnf(c_1243,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_53,c_53]) ).
cnf(c_1244,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_1243,c_1207]) ).
cnf(c_1266,plain,
( multiply(inverse(sk_c8),multiply(sk_c3,sk_c9)) = identity
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_2,c_55]) ).
cnf(c_1280,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_1244,c_2]) ).
cnf(c_1372,plain,
( multiply(sk_c2,sk_c1) = identity
| multiply(sk_c9,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_77,c_2]) ).
cnf(c_7139,plain,
( multiply(inverse(sk_c2),identity) = sk_c1
| multiply(sk_c9,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_1372,c_53]) ).
cnf(c_2053,plain,
( inverse(sk_c2) = sk_c1
| multiply(sk_c9,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_1244,c_7139]) ).
cnf(c_2060,plain,
( multiply(sk_c1,sk_c2) = identity
| multiply(sk_c9,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_2053,c_2]) ).
cnf(c_7140,plain,
( multiply(sk_c9,sk_c3) = identity
| identity = sk_c8
| multiply(sk_c9,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_2060,c_67]) ).
cnf(c_2734,plain,
( identity = sk_c8
| multiply(sk_c9,sk_c3) = identity ),
inference(copy,[status(thm)],[c_7140]) ).
cnf(c_7141,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2734,c_53]) ).
cnf(c_2749,plain,
( inverse(sk_c9) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1244,c_7141]) ).
cnf(c_2760,plain,
( multiply(sk_c3,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2749,c_2]) ).
cnf(c_7142,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2760,c_11]) ).
cnf(c_2818,plain,
( multiply(sk_c1,sk_c2) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_7142]) ).
cnf(c_7143,plain,
( multiply(sk_c2,sk_c1) = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2760,c_76]) ).
cnf(c_2833,plain,
( multiply(sk_c2,sk_c1) = identity
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_7143]) ).
cnf(c_7144,plain,
( multiply(inverse(sk_c2),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2833,c_53]) ).
cnf(c_3117,plain,
( inverse(sk_c2) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1244,c_7144]) ).
cnf(c_3124,plain,
( multiply(sk_c1,sk_c2) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_3117,c_2]) ).
cnf(c_7145,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_3124,c_2818]) ).
cnf(c_7146,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_7145]) ).
cnf(c_3181,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_7146]) ).
cnf(c_7147,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_3181,c_1280]) ).
cnf(c_4228,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_3181,c_7147]) ).
cnf(c_7148,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c9)) = identity
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_4228,c_1266]) ).
cnf(c_4229,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c9)) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_3181,c_7148]) ).
cnf(c_4237,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_3181,c_1244]) ).
cnf(c_7149,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_356]) ).
cnf(c_7150,plain,
( multiply(sk_c9,sk_c8) != sk_c7
| inverse(inverse(sk_c7)) != sk_c7
| sk_c8 != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_3181,c_7149]) ).
cnf(c_7151,plain,
( sk_c9 != sk_c7
| inverse(inverse(sk_c7)) != sk_c7
| sk_c8 != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_7150]) ).
cnf(c_7152,plain,
( sk_c7 != sk_c9
| inverse(inverse(sk_c7)) != sk_c7
| sk_c8 != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c7 != sk_c9 ),
inference(copy,[status(thm)],[c_7151]) ).
cnf(c_7153,plain,
( sk_c7 != sk_c9
| inverse(inverse(sk_c7)) != sk_c7
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c7 != sk_c9 ),
inference(copy,[status(thm)],[c_7152]) ).
cnf(c_4253,plain,
( inverse(inverse(sk_c7)) != sk_c7
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c7 != sk_c9 ),
inference(copy,[status(thm)],[c_7153]) ).
cnf(c_7154,plain,
( multiply(sk_c9,sk_c5) = identity
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_64]) ).
cnf(c_4268,plain,
( multiply(sk_c9,sk_c5) = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_3181,c_7154]) ).
cnf(c_7155,plain,
( multiply(sk_c9,sk_c3) = identity
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_56]) ).
cnf(c_4270,plain,
( multiply(sk_c9,sk_c3) = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_3181,c_7155]) ).
cnf(c_4271,plain,
multiply(inverse(A),A) = sk_c8,
inference(paramod,[status(thm)],[c_3181,c_2]) ).
cnf(c_4272,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_3181,c_1]) ).
cnf(c_7156,plain,
( multiply(sk_c8,multiply(sk_c3,sk_c9)) = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_4229]) ).
cnf(c_4571,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4272,c_7156]) ).
cnf(c_5259,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_9]) ).
cnf(c_5260,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_8]) ).
cnf(c_7157,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c5
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4268,c_53]) ).
cnf(c_5555,plain,
( inverse(sk_c9) = sk_c5
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_7157]) ).
cnf(c_7158,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c3
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4270,c_53]) ).
cnf(c_5560,plain,
( inverse(sk_c9) = sk_c3
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_7158]) ).
cnf(c_7159,plain,
( sk_c3 = sk_c5
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5560,c_5555]) ).
cnf(c_7160,plain,
( sk_c5 = sk_c3
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_7159]) ).
cnf(c_5563,plain,
( sk_c5 = sk_c3
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_7160]) ).
cnf(c_7161,plain,
( multiply(sk_c3,sk_c9) = sk_c6
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5563,c_5259]) ).
cnf(c_5735,plain,
( multiply(sk_c3,sk_c9) = sk_c6
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_7161]) ).
cnf(c_7162,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5735,c_4571]) ).
cnf(c_5748,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_7162]) ).
cnf(c_7163,plain,
( multiply(sk_c9,sk_c8) = sk_c7
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_5748,c_5260]) ).
cnf(c_7164,plain,
( sk_c9 = sk_c7
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4237,c_7163]) ).
cnf(c_7165,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_7164]) ).
cnf(c_7166,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_7165]) ).
cnf(c_5759,plain,
sk_c7 = sk_c9,
inference(copy,[status(thm)],[c_7166]) ).
cnf(c_7167,plain,
( inverse(inverse(sk_c7)) != sk_c7
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_5759,c_4253]) ).
cnf(c_7168,plain,
( inverse(inverse(sk_c7)) != sk_c7
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_5759,c_7167]) ).
cnf(c_7169,plain,
( inverse(inverse(sk_c9)) != sk_c7
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_5759,c_7168]) ).
cnf(c_7170,plain,
( inverse(inverse(sk_c9)) != sk_c9
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_5759,c_7169]) ).
cnf(c_6426,plain,
( inverse(inverse(sk_c9)) != sk_c9
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(copy,[status(thm)],[c_7170]) ).
cnf(c_7171,plain,
( inverse(inverse(sk_c9)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8
| multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(factor,[status(thm)],[c_6426]) ).
cnf(c_7172,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8
| multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(paramod,[status(thm)],[c_4271,c_7171]) ).
cnf(c_6758,plain,
( inverse(inverse(sk_c9)) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(copy,[status(thm)],[c_7172]) ).
cnf(c_7173,plain,
multiply(A,sk_c8) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1243,c_4237]) ).
cnf(c_7174,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_4237,c_7173]) ).
cnf(c_7088,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_7174]) ).
cnf(c_7175,plain,
( sk_c9 != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(paramod,[status(thm)],[c_7088,c_6758]) ).
cnf(c_7128,plain,
( multiply(B,sk_c9) != sk_c8
| inverse(A) != B
| multiply(A,B) != sk_c8 ),
inference(copy,[status(thm)],[c_7175]) ).
cnf(c_7176,plain,
( multiply(multiply(A,multiply(B,sk_c8)),sk_c9) != sk_c8
| inverse(inverse(multiply(A,B))) != multiply(A,multiply(B,sk_c8)) ),
inference(resolve,[status(thm)],[c_7128,c_1208]) ).
cnf(c_7177,plain,
( multiply(multiply(A,multiply(B,sk_c8)),sk_c9) != sk_c8
| multiply(A,B) != multiply(A,multiply(B,sk_c8)) ),
inference(paramod,[status(thm)],[c_7088,c_7176]) ).
cnf(c_7178,plain,
( multiply(multiply(A,multiply(B,sk_c8)),sk_c9) != sk_c8
| multiply(A,B) != multiply(A,B) ),
inference(paramod,[status(thm)],[c_4237,c_7177]) ).
cnf(c_7179,plain,
( multiply(multiply(A,B),sk_c9) != sk_c8
| multiply(A,B) != multiply(A,B) ),
inference(paramod,[status(thm)],[c_4237,c_7178]) ).
cnf(c_7180,plain,
( multiply(A,multiply(B,sk_c9)) != sk_c8
| multiply(A,B) != multiply(A,B) ),
inference(paramod,[status(thm)],[c_3,c_7179]) ).
cnf(c_7133,plain,
multiply(A,multiply(B,sk_c9)) != sk_c8,
inference(copy,[status(thm)],[c_7180]) ).
cnf(c_7134,plain,
$false,
inference(resolve,[status(thm)],[c_7133,c_4271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP370-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n002.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Fri Sep 25 14:51:34 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 3554572 was started by sandbox2 on n002,
% 0.20/0.45 % Fri Sep 25 14:51:34 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 36.40/5.72
% 36.40/5.72 % SZS status Unsatisfiable for theBenchmark
% 36.40/5.72
% 36.40/5.72 % Proof 1 at 4.60 (+ 0.63) seconds.
% 36.40/5.72 % Length of proof is 62.
% 36.40/5.72 % Level of proof is 24.
% 36.40/5.72 % Maximum clause weight is 70.000.
% 36.40/5.72 % Given clauses 224.
% 36.40/5.72
% 36.40/5.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------