%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP355-1 : 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 : n001.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 07:28:42 AM UTC 2026
% Result : Unsatisfiable 4.12s 1.02s
% Output : CNFRefutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 13
% Syntax : Number of formulae : 176 ( 46 unt; 0 def)
% Number of atoms : 383 ( 382 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 302 ( 95 ~; 207 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 5 ( 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 : 96 ( 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_c2,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_5,axiom,
( multiply(sk_c8,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c8,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_15,axiom,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_22,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != VAR_3
| multiply(sk_c8,VAR_3) != sk_c6
| inverse(VAR_2) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(VAR_1) != sk_c8
| multiply(VAR_1,sk_c8) != sk_c7
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c6
| inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
cnf(c_1789,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_26,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(copy,[status(thm)],[c_1789]) ).
cnf(c_1790,plain,
( inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(factor,[status(thm)],[c_26]) ).
cnf(c_27,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(copy,[status(thm)],[c_1790]) ).
cnf(c_1791,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1792,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1791]) ).
cnf(c_29,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1792]) ).
cnf(c_1793,plain,
( multiply(sk_c7,A) = multiply(sk_c2,multiply(sk_c8,A))
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_32,plain,
( multiply(sk_c2,multiply(sk_c8,A)) = multiply(sk_c7,A)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1793]) ).
cnf(c_1794,plain,
( multiply(multiply(A,sk_c2),sk_c8) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_33,plain,
( multiply(A,multiply(sk_c2,sk_c8)) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_3,c_1794]) ).
cnf(c_34,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_1795,plain,
( multiply(sk_c6,A) = multiply(sk_c8,multiply(sk_c5,A))
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_46,plain,
( multiply(sk_c8,multiply(sk_c5,A)) = multiply(sk_c6,A)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1795]) ).
cnf(c_1796,plain,
( multiply(multiply(A,sk_c8),sk_c5) = multiply(A,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_47,plain,
( multiply(A,multiply(sk_c8,sk_c5)) = multiply(A,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_3,c_1796]) ).
cnf(c_50,plain,
( multiply(sk_c5,A) = multiply(sk_c4,multiply(sk_c8,A))
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_83,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_102,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_29]) ).
cnf(c_107,plain,
( multiply(sk_c8,multiply(sk_c2,A)) = A
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_5,c_29]) ).
cnf(c_117,plain,
( multiply(sk_c8,multiply(sk_c4,A)) = A
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_10,c_29]) ).
cnf(c_146,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_29,c_29]) ).
cnf(c_147,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_146,c_102]) ).
cnf(c_216,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_147,c_2]) ).
cnf(c_1797,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_83,c_29]) ).
cnf(c_287,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_147,c_1797]) ).
cnf(c_290,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_287,c_2]) ).
cnf(c_1798,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8))) = multiply(sk_c7,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_33,c_32]) ).
cnf(c_354,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8))) = multiply(sk_c7,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1798]) ).
cnf(c_362,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_34,c_29]) ).
cnf(c_1799,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_34,c_29]) ).
cnf(c_363,plain,
( inverse(sk_c8) = sk_c2
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_147,c_1799]) ).
cnf(c_1800,plain,
( inverse(sk_c2) = sk_c8
| identity = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_290,c_12]) ).
cnf(c_460,plain,
( identity = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(copy,[status(thm)],[c_1800]) ).
cnf(c_466,plain,
( multiply(sk_c8,sk_c2) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_460,c_2]) ).
cnf(c_1801,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_466,c_29]) ).
cnf(c_480,plain,
( inverse(sk_c8) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_147,c_1801]) ).
cnf(c_493,plain,
( multiply(sk_c2,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_480,c_2]) ).
cnf(c_1802,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_493,c_11]) ).
cnf(c_547,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1802]) ).
cnf(c_1803,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_493,c_18]) ).
cnf(c_548,plain,
( inverse(sk_c1) = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1803]) ).
cnf(c_566,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_548,c_2]) ).
cnf(c_1804,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_566,c_29]) ).
cnf(c_679,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_147,c_1804]) ).
cnf(c_691,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_679,c_2]) ).
cnf(c_747,plain,
( multiply(inverse(sk_c8),multiply(sk_c6,A)) = multiply(sk_c5,A)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_46,c_29]) ).
cnf(c_1805,plain,
( multiply(sk_c2,multiply(sk_c8,sk_c6)) = multiply(sk_c7,multiply(sk_c8,sk_c5))
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_47,c_32]) ).
cnf(c_786,plain,
( multiply(sk_c2,multiply(sk_c8,sk_c6)) = multiply(sk_c7,multiply(sk_c8,sk_c5))
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1805]) ).
cnf(c_1806,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c8,sk_c5))) = multiply(sk_c7,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_47,c_32]) ).
cnf(c_787,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c8,sk_c5))) = multiply(sk_c7,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1806]) ).
cnf(c_1807,plain,
( multiply(sk_c4,multiply(sk_c8,multiply(sk_c2,sk_c8))) = multiply(sk_c5,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_50,c_33]) ).
cnf(c_1808,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1807]) ).
cnf(c_930,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1808]) ).
cnf(c_1809,plain,
( multiply(sk_c5,sk_c2) = multiply(sk_c4,identity)
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_34,c_50]) ).
cnf(c_1810,plain,
( multiply(sk_c5,sk_c2) = sk_c4
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_147,c_1809]) ).
cnf(c_932,plain,
( multiply(sk_c5,sk_c2) = sk_c4
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1810]) ).
cnf(c_1811,plain,
( multiply(sk_c8,multiply(sk_c4,multiply(sk_c8,A))) = multiply(sk_c6,A)
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_50,c_46]) ).
cnf(c_942,plain,
( multiply(sk_c8,multiply(sk_c4,multiply(sk_c8,A))) = multiply(sk_c6,A)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1811]) ).
cnf(c_1812,plain,
( multiply(sk_c5,multiply(sk_c5,A)) = multiply(sk_c4,multiply(sk_c6,A))
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_46,c_50]) ).
cnf(c_943,plain,
( multiply(sk_c5,multiply(sk_c5,A)) = multiply(sk_c4,multiply(sk_c6,A))
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1812]) ).
cnf(c_1813,plain,
( multiply(sk_c4,multiply(sk_c8,multiply(sk_c8,sk_c5))) = multiply(sk_c5,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_50,c_47]) ).
cnf(c_1814,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c8,sk_c5)))
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1813]) ).
cnf(c_945,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c8,sk_c5)))
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_1814]) ).
cnf(c_1815,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_691,c_547]) ).
cnf(c_1816,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1815]) ).
cnf(c_968,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_1816]) ).
cnf(c_1076,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_968,c_362]) ).
cnf(c_1817,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_968,c_216]) ).
cnf(c_1184,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_968,c_1817]) ).
cnf(c_1185,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_968,c_147]) ).
cnf(c_1195,plain,
multiply(inverse(A),A) = sk_c7,
inference(paramod,[status(thm)],[c_968,c_2]) ).
cnf(c_1196,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_968,c_1]) ).
cnf(c_1818,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_1184,c_1076]) ).
cnf(c_1819,plain,
( sk_c8 = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_1196,c_1818]) ).
cnf(c_1205,plain,
( sk_c6 = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(copy,[status(thm)],[c_1819]) ).
cnf(c_1820,plain,
( multiply(sk_c5,sk_c7) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_930]) ).
cnf(c_1821,plain,
( sk_c5 = multiply(sk_c4,multiply(sk_c8,multiply(sk_c2,sk_c8)))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1185,c_1820]) ).
cnf(c_1289,plain,
( multiply(sk_c4,multiply(sk_c8,multiply(sk_c2,sk_c8))) = sk_c5
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1821]) ).
cnf(c_1822,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8))) = multiply(sk_c7,sk_c7)
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_354]) ).
cnf(c_1303,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,sk_c8))) = sk_c7
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1185,c_1822]) ).
cnf(c_1823,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_27]) ).
cnf(c_1824,plain,
( sk_c8 != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_1185,c_1823]) ).
cnf(c_1825,plain,
( sk_c6 != sk_c8
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1824]) ).
cnf(c_1317,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1825]) ).
cnf(c_1350,plain,
( multiply(sk_c5,sk_c6) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c8,sk_c5)))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_945]) ).
cnf(c_1351,plain,
( multiply(sk_c5,multiply(sk_c5,A)) = multiply(sk_c4,multiply(sk_c6,A))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_943]) ).
cnf(c_1352,plain,
( multiply(sk_c8,multiply(sk_c4,multiply(sk_c8,A))) = multiply(sk_c6,A)
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_942]) ).
cnf(c_1356,plain,
( multiply(sk_c5,sk_c2) = sk_c4
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_932]) ).
cnf(c_1826,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c8,sk_c5))) = multiply(sk_c7,sk_c6)
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_787]) ).
cnf(c_1381,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c8,sk_c5))) = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_1826]) ).
cnf(c_1827,plain,
( multiply(sk_c2,multiply(sk_c8,sk_c6)) = multiply(sk_c7,multiply(sk_c8,sk_c5))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_786]) ).
cnf(c_1382,plain,
( multiply(sk_c2,multiply(sk_c8,sk_c6)) = multiply(sk_c8,sk_c5)
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_1827]) ).
cnf(c_1385,plain,
( multiply(inverse(sk_c8),multiply(sk_c6,A)) = multiply(sk_c5,A)
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_747]) ).
cnf(c_1414,plain,
( inverse(sk_c8) = sk_c2
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_363]) ).
cnf(c_1423,plain,
( multiply(sk_c8,multiply(sk_c4,A)) = A
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_117]) ).
cnf(c_1427,plain,
( multiply(sk_c8,multiply(sk_c2,A)) = A
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1196,c_107]) ).
cnf(c_1828,plain,
multiply(inverse(inverse(A)),sk_c7) = A,
inference(paramod,[status(thm)],[c_1195,c_29]) ).
cnf(c_1687,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_1185,c_1828]) ).
cnf(c_1829,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(inverse(sk_c8)) != sk_c8
| sk_c7 != sk_c7
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_1195,c_1317]) ).
cnf(c_1830,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| sk_c8 != sk_c8
| sk_c7 != sk_c7
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_1687,c_1829]) ).
cnf(c_1831,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| sk_c8 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1830]) ).
cnf(c_1692,plain,
( inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1831]) ).
cnf(c_1832,plain,
( inverse(inverse(sk_c6)) != sk_c6
| sk_c6 != sk_c8 ),
inference(resolve,[status(thm)],[c_1692,c_1195]) ).
cnf(c_1833,plain,
( sk_c6 != sk_c6
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_1687,c_1832]) ).
cnf(c_1730,plain,
sk_c6 != sk_c8,
inference(copy,[status(thm)],[c_1833]) ).
cnf(c_1732,plain,
multiply(sk_c8,multiply(sk_c2,A)) = A,
inference(resolve,[status(thm)],[c_1730,c_1427]) ).
cnf(c_1736,plain,
multiply(sk_c8,multiply(sk_c4,A)) = A,
inference(resolve,[status(thm)],[c_1730,c_1423]) ).
cnf(c_1740,plain,
inverse(sk_c8) = sk_c2,
inference(resolve,[status(thm)],[c_1730,c_1414]) ).
cnf(c_1834,plain,
( multiply(sk_c2,multiply(sk_c6,A)) = multiply(sk_c5,A)
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1740,c_1385]) ).
cnf(c_1835,plain,
( multiply(sk_c5,A) = multiply(sk_c2,multiply(sk_c6,A))
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1834]) ).
cnf(c_1745,plain,
multiply(sk_c5,A) = multiply(sk_c2,multiply(sk_c6,A)),
inference(resolve,[status(thm)],[c_1730,c_1835]) ).
cnf(c_1747,plain,
multiply(sk_c2,multiply(sk_c8,sk_c6)) = multiply(sk_c8,sk_c5),
inference(resolve,[status(thm)],[c_1730,c_1382]) ).
cnf(c_1748,plain,
multiply(sk_c2,multiply(sk_c8,multiply(sk_c8,sk_c5))) = sk_c6,
inference(resolve,[status(thm)],[c_1730,c_1381]) ).
cnf(c_1836,plain,
( multiply(sk_c2,multiply(sk_c6,sk_c2)) = sk_c4
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1745,c_1356]) ).
cnf(c_1755,plain,
multiply(sk_c2,multiply(sk_c6,sk_c2)) = sk_c4,
inference(resolve,[status(thm)],[c_1730,c_1836]) ).
cnf(c_1837,plain,
( multiply(sk_c8,A) = multiply(sk_c6,A)
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1736,c_1352]) ).
cnf(c_1838,plain,
( multiply(sk_c6,A) = multiply(sk_c8,A)
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1837]) ).
cnf(c_1759,plain,
multiply(sk_c6,A) = multiply(sk_c8,A),
inference(resolve,[status(thm)],[c_1730,c_1838]) ).
cnf(c_1839,plain,
( multiply(sk_c5,multiply(sk_c2,multiply(sk_c6,A))) = multiply(sk_c4,multiply(sk_c6,A))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1745,c_1351]) ).
cnf(c_1840,plain,
( multiply(sk_c5,multiply(sk_c2,multiply(sk_c8,A))) = multiply(sk_c4,multiply(sk_c6,A))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1759,c_1839]) ).
cnf(c_1841,plain,
( multiply(sk_c2,multiply(sk_c6,multiply(sk_c2,multiply(sk_c8,A)))) = multiply(sk_c4,multiply(sk_c6,A))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1745,c_1840]) ).
cnf(c_1842,plain,
( multiply(sk_c2,multiply(sk_c8,multiply(sk_c2,multiply(sk_c8,A)))) = multiply(sk_c4,multiply(sk_c6,A))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1759,c_1841]) ).
cnf(c_1843,plain,
( multiply(sk_c2,multiply(sk_c8,A)) = multiply(sk_c4,multiply(sk_c6,A))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1732,c_1842]) ).
cnf(c_1844,plain,
( multiply(sk_c2,multiply(sk_c8,A)) = multiply(sk_c4,multiply(sk_c8,A))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1759,c_1843]) ).
cnf(c_1845,plain,
( multiply(sk_c4,multiply(sk_c8,A)) = multiply(sk_c2,multiply(sk_c8,A))
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1844]) ).
cnf(c_1760,plain,
multiply(sk_c4,multiply(sk_c8,A)) = multiply(sk_c2,multiply(sk_c8,A)),
inference(resolve,[status(thm)],[c_1730,c_1845]) ).
cnf(c_1846,plain,
( multiply(sk_c2,multiply(sk_c6,sk_c6)) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c8,sk_c5)))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1745,c_1350]) ).
cnf(c_1847,plain,
( multiply(sk_c2,multiply(sk_c8,sk_c6)) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c8,sk_c5)))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1759,c_1846]) ).
cnf(c_1848,plain,
( multiply(sk_c8,sk_c5) = multiply(sk_c4,multiply(sk_c8,multiply(sk_c8,sk_c5)))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1747,c_1847]) ).
cnf(c_1849,plain,
( multiply(sk_c8,sk_c5) = multiply(sk_c2,multiply(sk_c8,multiply(sk_c8,sk_c5)))
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1760,c_1848]) ).
cnf(c_1850,plain,
( multiply(sk_c8,sk_c5) = sk_c6
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1748,c_1849]) ).
cnf(c_1761,plain,
multiply(sk_c8,sk_c5) = sk_c6,
inference(resolve,[status(thm)],[c_1730,c_1850]) ).
cnf(c_1851,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1732,c_1303]) ).
cnf(c_1765,plain,
multiply(sk_c2,sk_c8) = sk_c7,
inference(resolve,[status(thm)],[c_1730,c_1851]) ).
cnf(c_1852,plain,
( multiply(sk_c4,multiply(sk_c8,sk_c7)) = sk_c5
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1765,c_1289]) ).
cnf(c_1853,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1185,c_1852]) ).
cnf(c_1767,plain,
multiply(sk_c4,sk_c8) = sk_c5,
inference(resolve,[status(thm)],[c_1730,c_1853]) ).
cnf(c_1774,plain,
multiply(sk_c8,sk_c2) = sk_c7,
inference(resolve,[status(thm)],[c_1730,c_1205]) ).
cnf(c_1854,plain,
multiply(sk_c2,multiply(sk_c8,sk_c2)) = sk_c4,
inference(paramod,[status(thm)],[c_1759,c_1755]) ).
cnf(c_1855,plain,
multiply(sk_c2,sk_c7) = sk_c4,
inference(paramod,[status(thm)],[c_1774,c_1854]) ).
cnf(c_1856,plain,
sk_c2 = sk_c4,
inference(paramod,[status(thm)],[c_1185,c_1855]) ).
cnf(c_1776,plain,
sk_c4 = sk_c2,
inference(copy,[status(thm)],[c_1856]) ).
cnf(c_1857,plain,
multiply(sk_c2,sk_c8) = sk_c5,
inference(paramod,[status(thm)],[c_1776,c_1767]) ).
cnf(c_1858,plain,
sk_c7 = sk_c5,
inference(paramod,[status(thm)],[c_1765,c_1857]) ).
cnf(c_1787,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_1858]) ).
cnf(c_1859,plain,
multiply(sk_c8,sk_c7) = sk_c6,
inference(paramod,[status(thm)],[c_1787,c_1761]) ).
cnf(c_1860,plain,
sk_c8 = sk_c6,
inference(paramod,[status(thm)],[c_1185,c_1859]) ).
cnf(c_1861,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_1860]) ).
cnf(c_1788,plain,
$false,
inference(resolve,[status(thm)],[c_1730,c_1861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP355-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:53:56 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3593966 was started by sandbox on n001,
% 0.08/0.36 % Fri Sep 25 14:53:56 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 4.12/1.02
% 4.12/1.02 % SZS status Unsatisfiable for theBenchmark
% 4.12/1.02
% 4.12/1.02 % Proof 1 at 0.42 (+ 0.17) seconds.
% 4.12/1.02 % Length of proof is 90.
% 4.12/1.02 % Level of proof is 24.
% 4.12/1.02 % Maximum clause weight is 50.000.
% 4.12/1.02 % Given clauses 137.
% 4.12/1.02
% 4.12/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------