%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP334-1 : 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 07:28:39 AM UTC 2026
% Result : Unsatisfiable 8.32s 1.58s
% Output : CNFRefutation 8.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 16
% Syntax : Number of formulae : 172 ( 37 unt; 0 def)
% Number of atoms : 466 ( 465 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 518 ( 224 ~; 294 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 0 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_c6,sk_c7) = sk_c5,
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(clausify,[status(thm)],[prove_this_1]) ).
cnf(c_5,plain,
sk_c5 = multiply(sk_c6,sk_c7),
inference(copy,[status(thm)],[c_4]) ).
fof(prove_this_4,axiom,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_10,plain,
( multiply(sk_c6,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
cnf(c_11,plain,
( multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c7)
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_10]) ).
fof(prove_this_5,axiom,
( multiply(sk_c3,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_12,plain,
( multiply(sk_c3,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_13,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_14,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
cnf(c_15,plain,
( inverse(sk_c6) = multiply(sk_c6,sk_c7)
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_14]) ).
fof(prove_this_8,axiom,
( inverse(sk_c7) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_16,plain,
( inverse(sk_c7) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
cnf(c_17,plain,
( inverse(sk_c7) = multiply(sk_c6,sk_c7)
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_16]) ).
fof(prove_this_9,axiom,
( multiply(sk_c6,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_18,plain,
( multiply(sk_c6,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
cnf(c_19,plain,
( multiply(sk_c6,sk_c4) = multiply(sk_c6,sk_c7)
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_18]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_20,plain,
( multiply(sk_c3,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_21,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_22,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
cnf(c_23,plain,
( inverse(sk_c6) = multiply(sk_c6,sk_c7)
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_22]) ).
fof(prove_this_13,axiom,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_24,plain,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
cnf(c_25,plain,
( inverse(sk_c7) = multiply(sk_c6,sk_c7)
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_24]) ).
fof(prove_this_18,axiom,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_32,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
cnf(c_2169,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_32]) ).
cnf(c_33,plain,
( inverse(sk_c7) = multiply(sk_c6,sk_c7)
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_2169]) ).
fof(prove_this_22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(VAR_3) != sk_c6
| multiply(VAR_3,sk_c6) != VAR_2
| multiply(sk_c6,VAR_2) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(VAR_1,sk_c5) != sk_c6
| inverse(VAR_1) != sk_c6
| inverse(VAR_0) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_40,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
cnf(c_2170,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_40]) ).
cnf(c_2171,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(sk_c6) != sk_c5
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_2170]) ).
cnf(c_2172,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_2171]) ).
cnf(c_2173,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != sk_c5
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_2172]) ).
cnf(c_2174,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,C) != multiply(sk_c6,sk_c7)
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(paramod,[status(thm)],[c_5,c_2173]) ).
cnf(c_2175,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,sk_c7) != multiply(sk_c6,C)
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7) ),
inference(copy,[status(thm)],[c_2174]) ).
cnf(c_41,plain,
( inverse(D) != sk_c6
| multiply(D,sk_c6) != C
| multiply(sk_c6,sk_c7) != multiply(sk_c6,C)
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_2175]) ).
cnf(c_2176,plain,
( inverse(A) != sk_c6
| multiply(sk_c6,sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(factor,[status(thm)],[c_41]) ).
cnf(c_2177,plain,
( inverse(A) != sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_2176]) ).
cnf(c_42,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(B,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(copy,[status(thm)],[c_2177]) ).
cnf(c_43,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(A,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7 ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_2178,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_2179,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_2178]) ).
cnf(c_44,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_2179]) ).
cnf(c_2180,plain,
( multiply(multiply(sk_c6,sk_c7),sk_c7) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_65,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c7)) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_2180]) ).
cnf(c_72,plain,
( multiply(sk_c6,sk_c1) = identity
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_2181,plain,
( multiply(multiply(sk_c6,sk_c7),sk_c7) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_77,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c7)) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_2181]) ).
cnf(c_2182,plain,
( multiply(multiply(sk_c6,sk_c7),sk_c7) = identity
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_33,c_2]) ).
cnf(c_89,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c7)) = identity
| multiply(sk_c2,multiply(sk_c6,sk_c7)) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_2182]) ).
cnf(c_2183,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(identity,multiply(sk_c6,sk_c7)) != sk_c6
| inverse(identity) != sk_c6
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_43]) ).
cnf(c_2184,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_2183]) ).
cnf(c_105,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2184]) ).
cnf(c_107,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_44]) ).
cnf(c_2185,plain,
( multiply(inverse(sk_c6),multiply(sk_c6,sk_c7)) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_11,c_44]) ).
cnf(c_2186,plain,
( sk_c7 = sk_c4
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_44,c_2185]) ).
cnf(c_114,plain,
( sk_c4 = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_2186]) ).
cnf(c_2187,plain,
( multiply(inverse(sk_c6),multiply(sk_c6,sk_c7)) = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_44]) ).
cnf(c_2188,plain,
( sk_c7 = sk_c4
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_44,c_2187]) ).
cnf(c_124,plain,
( sk_c4 = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_2188]) ).
cnf(c_149,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_44,c_44]) ).
cnf(c_150,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_149,c_107]) ).
cnf(c_156,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c7 != sk_c6 ),
inference(resolve,[status(thm)],[c_105,c_23]) ).
cnf(c_157,plain,
( inverse(sk_c1) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| inverse(identity) != sk_c6
| sk_c7 != sk_c6 ),
inference(resolve,[status(thm)],[c_105,c_15]) ).
cnf(c_162,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_150,c_2]) ).
cnf(c_167,plain,
( inverse(sk_c1) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_162,c_157]) ).
cnf(c_168,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_162,c_156]) ).
cnf(c_169,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| identity != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_162,c_105]) ).
cnf(c_170,plain,
( multiply(sk_c6,sk_c1) = identity
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_124,c_2]) ).
cnf(c_2189,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_124,c_20]) ).
cnf(c_172,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_2189]) ).
cnf(c_2190,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_170,c_44]) ).
cnf(c_189,plain,
( inverse(sk_c6) = sk_c1
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_150,c_2190]) ).
cnf(c_191,plain,
( multiply(sk_c1,sk_c6) = identity
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_189,c_2]) ).
cnf(c_2191,plain,
( sk_c4 = sk_c7
| identity = sk_c7
| sk_c4 = sk_c7 ),
inference(paramod,[status(thm)],[c_191,c_114]) ).
cnf(c_226,plain,
( identity = sk_c7
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_2191]) ).
cnf(c_2192,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_72,c_44]) ).
cnf(c_304,plain,
( inverse(sk_c6) = sk_c1
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_150,c_2192]) ).
cnf(c_309,plain,
( multiply(sk_c1,sk_c6) = identity
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_304,c_2]) ).
cnf(c_2193,plain,
( inverse(sk_c3) = sk_c6
| identity = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(paramod,[status(thm)],[c_309,c_13]) ).
cnf(c_503,plain,
( identity = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(copy,[status(thm)],[c_2193]) ).
cnf(c_510,plain,
( multiply(sk_c6,sk_c3) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_503,c_2]) ).
cnf(c_2194,plain,
( multiply(inverse(sk_c6),identity) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_510,c_44]) ).
cnf(c_519,plain,
( inverse(sk_c6) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_150,c_2194]) ).
cnf(c_542,plain,
( multiply(sk_c3,sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_519,c_2]) ).
cnf(c_2195,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_542,c_172]) ).
cnf(c_568,plain,
( inverse(sk_c1) = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2195]) ).
cnf(c_573,plain,
( multiply(sk_c6,sk_c1) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_568,c_2]) ).
cnf(c_2196,plain,
( multiply(inverse(sk_c6),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_573,c_44]) ).
cnf(c_626,plain,
( inverse(sk_c6) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_150,c_2196]) ).
cnf(c_640,plain,
( multiply(sk_c1,sk_c6) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_626,c_2]) ).
cnf(c_2197,plain,
( multiply(sk_c3,sk_c6) = sk_c4
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_640,c_12]) ).
cnf(c_933,plain,
( multiply(sk_c3,sk_c6) = sk_c4
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2197]) ).
cnf(c_2198,plain,
( sk_c4 = identity
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_933,c_542]) ).
cnf(c_2199,plain,
( identity = sk_c4
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2198]) ).
cnf(c_1464,plain,
( identity = sk_c4
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2199]) ).
cnf(c_2200,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_226,c_1464]) ).
cnf(c_2201,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2200]) ).
cnf(c_1486,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_2201]) ).
cnf(c_2202,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1486,c_169]) ).
cnf(c_1685,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2202]) ).
cnf(c_2203,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1486,c_168]) ).
cnf(c_1686,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2203]) ).
cnf(c_2204,plain,
( inverse(sk_c1) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1486,c_167]) ).
cnf(c_1687,plain,
( inverse(sk_c1) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2204]) ).
cnf(c_2205,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_1486,c_162]) ).
cnf(c_1692,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_1486,c_2205]) ).
cnf(c_1696,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_1486,c_150]) ).
cnf(c_2206,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c7)) = identity
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_89]) ).
cnf(c_2207,plain,
( multiply(sk_c6,sk_c7) = identity
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_2206]) ).
cnf(c_2208,plain,
( sk_c6 = identity
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_2207]) ).
cnf(c_2209,plain,
( sk_c6 = sk_c7
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_1486,c_2208]) ).
cnf(c_1698,plain,
( sk_c7 = sk_c6
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(copy,[status(thm)],[c_2209]) ).
cnf(c_2210,plain,
( multiply(sk_c6,sk_c7) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_77]) ).
cnf(c_2211,plain,
( sk_c6 = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_2210]) ).
cnf(c_2212,plain,
( sk_c6 = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_1486,c_2211]) ).
cnf(c_1702,plain,
( sk_c7 = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(copy,[status(thm)],[c_2212]) ).
cnf(c_2213,plain,
( multiply(sk_c6,sk_c7) = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_65]) ).
cnf(c_2214,plain,
( sk_c6 = identity
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_2213]) ).
cnf(c_2215,plain,
( sk_c6 = sk_c7
| inverse(sk_c1) = sk_c6 ),
inference(paramod,[status(thm)],[c_1486,c_2214]) ).
cnf(c_1706,plain,
( sk_c7 = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(copy,[status(thm)],[c_2215]) ).
cnf(c_1710,plain,
multiply(inverse(A),A) = sk_c7,
inference(paramod,[status(thm)],[c_1486,c_2]) ).
cnf(c_2216,plain,
( inverse(sk_c1) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_1687]) ).
cnf(c_2217,plain,
( inverse(sk_c1) = sk_c6
| sk_c7 != multiply(sk_c6,sk_c7)
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1692,c_2216]) ).
cnf(c_2218,plain,
( inverse(sk_c1) = sk_c6
| sk_c7 != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_2217]) ).
cnf(c_2219,plain,
( inverse(sk_c1) = sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2218]) ).
cnf(c_1713,plain,
( inverse(sk_c1) = sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2219]) ).
cnf(c_2220,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c7) != multiply(sk_c6,sk_c7)
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_1686]) ).
cnf(c_2221,plain,
( inverse(sk_c2) = sk_c6
| sk_c7 != multiply(sk_c6,sk_c7)
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1692,c_2220]) ).
cnf(c_2222,plain,
( inverse(sk_c2) = sk_c6
| sk_c7 != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_2221]) ).
cnf(c_2223,plain,
( inverse(sk_c2) = sk_c6
| sk_c7 != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2222]) ).
cnf(c_1714,plain,
( inverse(sk_c2) = sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2223]) ).
cnf(c_2224,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != multiply(sk_c6,sk_c7)
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_1685]) ).
cnf(c_2225,plain,
( inverse(sk_c7) != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_2224]) ).
cnf(c_2226,plain,
( sk_c7 != multiply(sk_c6,sk_c7)
| inverse(sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1692,c_2225]) ).
cnf(c_2227,plain,
( sk_c7 != sk_c6
| inverse(sk_c6) != sk_c6
| sk_c6 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1696,c_2226]) ).
cnf(c_2228,plain,
( sk_c7 != sk_c6
| inverse(sk_c6) != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2227]) ).
cnf(c_1715,plain,
( inverse(sk_c6) != sk_c6
| sk_c7 != sk_c6 ),
inference(copy,[status(thm)],[c_2228]) ).
cnf(c_2229,plain,
( inverse(sk_c1) = sk_c6
| inverse(sk_c1) = sk_c6 ),
inference(resolve,[status(thm)],[c_1713,c_1706]) ).
cnf(c_1992,plain,
inverse(sk_c1) = sk_c6,
inference(copy,[status(thm)],[c_2229]) ).
cnf(c_2230,plain,
( inverse(sk_c2) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(resolve,[status(thm)],[c_1714,c_1702]) ).
cnf(c_2007,plain,
inverse(sk_c2) = sk_c6,
inference(copy,[status(thm)],[c_2230]) ).
cnf(c_2022,plain,
multiply(inverse(sk_c6),A) = multiply(sk_c1,A),
inference(paramod,[status(thm)],[c_1992,c_149]) ).
cnf(c_2231,plain,
multiply(inverse(sk_c6),A) = multiply(sk_c2,A),
inference(paramod,[status(thm)],[c_2007,c_149]) ).
cnf(c_2232,plain,
multiply(sk_c1,A) = multiply(sk_c2,A),
inference(paramod,[status(thm)],[c_2022,c_2231]) ).
cnf(c_2023,plain,
multiply(sk_c2,A) = multiply(sk_c1,A),
inference(copy,[status(thm)],[c_2232]) ).
cnf(c_2057,plain,
( sk_c7 = sk_c6
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_2023,c_1698]) ).
cnf(c_2115,plain,
multiply(sk_c6,sk_c1) = sk_c7,
inference(paramod,[status(thm)],[c_1992,c_1710]) ).
cnf(c_2233,plain,
multiply(inverse(sk_c6),sk_c7) = sk_c1,
inference(paramod,[status(thm)],[c_2115,c_44]) ).
cnf(c_2117,plain,
inverse(sk_c6) = sk_c1,
inference(paramod,[status(thm)],[c_1696,c_2233]) ).
cnf(c_2132,plain,
( sk_c1 != sk_c6
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_2117,c_1715]) ).
cnf(c_2136,plain,
multiply(sk_c1,sk_c6) = sk_c7,
inference(paramod,[status(thm)],[c_2117,c_1710]) ).
cnf(c_2234,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_2136,c_2057]) ).
cnf(c_2145,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_2234]) ).
cnf(c_2235,plain,
( sk_c1 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_2145,c_2132]) ).
cnf(c_2160,plain,
sk_c1 != sk_c6,
inference(copy,[status(thm)],[c_2235]) ).
cnf(c_2236,plain,
inverse(sk_c6) = sk_c7,
inference(paramod,[status(thm)],[c_2145,c_1692]) ).
cnf(c_2237,plain,
sk_c1 = sk_c7,
inference(paramod,[status(thm)],[c_2117,c_2236]) ).
cnf(c_2238,plain,
sk_c1 = sk_c6,
inference(paramod,[status(thm)],[c_2145,c_2237]) ).
cnf(c_2168,plain,
$false,
inference(resolve,[status(thm)],[c_2160,c_2238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP334-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.44 % Computer : n015.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Fri Sep 25 14:49:43 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.44 % Process 1638432 was started by sandbox2 on n015,
% 0.15/0.44 % Fri Sep 25 14:49:43 2026
% 0.15/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.45
% 0.15/0.45 % From the command line: assign(max_seconds, 300).
% 8.32/1.58
% 8.32/1.58 % SZS status Unsatisfiable for theBenchmark
% 8.32/1.58
% 8.32/1.58 % Proof 1 at 0.71 (+ 0.22) seconds.
% 8.32/1.58 % Length of proof is 86.
% 8.32/1.58 % Level of proof is 25.
% 8.32/1.58 % Maximum clause weight is 56.000.
% 8.32/1.58 % Given clauses 188.
% 8.32/1.58
% 8.32/1.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------