%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP261-1 : 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 : n003.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 07:28:29 AM UTC 2026
% Result : Unsatisfiable 4.14s 0.95s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 16
% Syntax : Number of formulae : 149 ( 29 unt; 0 def)
% Number of atoms : 384 ( 383 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 398 ( 163 ~; 235 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 62 ( 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_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_5,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_7,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_11,axiom,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_21,axiom,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_29,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( multiply(VAR_4,sk_c8) != sk_c6
| inverse(VAR_4) != sk_c6
| inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c6
| inverse(VAR_2) != sk_c8
| multiply(VAR_2,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(VAR_1) != sk_c7
| multiply(VAR_1,sk_c7) != sk_c6
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(E,sk_c8) != sk_c6
| inverse(E) != sk_c6
| inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c6
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_35,plain,
( multiply(D,sk_c8) != sk_c6
| inverse(D) != sk_c6
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_2054,plain,
( multiply(C,sk_c8) != sk_c6
| inverse(C) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(sk_c6) != sk_c8
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_35]) ).
cnf(c_38,plain,
( multiply(C,sk_c8) != sk_c6
| inverse(C) != sk_c6
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2054]) ).
cnf(c_2055,plain,
( multiply(B,sk_c8) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_38]) ).
cnf(c_41,plain,
( multiply(B,sk_c8) != sk_c6
| inverse(B) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2055]) ).
cnf(c_2056,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_2057,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_2056]) ).
cnf(c_42,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_2057]) ).
cnf(c_67,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_90,plain,
( multiply(sk_c7,sk_c4) = identity
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_105,plain,
( multiply(sk_c7,sk_c2) = identity
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_108,plain,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_2058,plain,
( multiply(multiply(A,sk_c5),sk_c8) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_33,c_3]) ).
cnf(c_135,plain,
( multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_2058]) ).
cnf(c_2059,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(A) != sk_c6
| inverse(identity) != sk_c7
| sk_c7 != sk_c6
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_41]) ).
cnf(c_146,plain,
( multiply(A,sk_c8) != sk_c6
| inverse(A) != sk_c6
| inverse(identity) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2059]) ).
cnf(c_149,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_42]) ).
cnf(c_208,plain,
( multiply(sk_c6,multiply(sk_c5,A)) = A
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_32,c_42]) ).
cnf(c_210,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_33,c_42]) ).
cnf(c_211,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_42,c_42]) ).
cnf(c_212,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_211,c_149]) ).
cnf(c_2060,plain,
( sk_c8 != sk_c6
| inverse(identity) != sk_c6
| inverse(identity) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_146]) ).
cnf(c_231,plain,
( sk_c6 != sk_c8
| inverse(identity) != sk_c6
| inverse(identity) != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2060]) ).
cnf(c_290,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_212,c_2]) ).
cnf(c_2061,plain,
( sk_c6 != sk_c8
| inverse(identity) != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_290,c_231]) ).
cnf(c_349,plain,
( sk_c6 != sk_c8
| identity != sk_c6
| identity != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_290,c_2061]) ).
cnf(c_2062,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_67,c_42]) ).
cnf(c_369,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_212,c_2062]) ).
cnf(c_372,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_369,c_2]) ).
cnf(c_2063,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_108,c_42]) ).
cnf(c_487,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_212,c_2063]) ).
cnf(c_491,plain,
( multiply(sk_c7,sk_c4) = identity
| inverse(sk_c7) = sk_c2 ),
inference(paramod,[status(thm)],[c_487,c_2]) ).
cnf(c_2064,plain,
( inverse(sk_c3) = sk_c8
| identity = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_372,c_5]) ).
cnf(c_574,plain,
( identity = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_2064]) ).
cnf(c_581,plain,
( multiply(sk_c8,sk_c3) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_574,c_2]) ).
cnf(c_2065,plain,
( multiply(inverse(sk_c8),identity) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_581,c_42]) ).
cnf(c_604,plain,
( inverse(sk_c8) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_212,c_2065]) ).
cnf(c_618,plain,
( multiply(sk_c3,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_604,c_2]) ).
cnf(c_2066,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_618,c_4]) ).
cnf(c_668,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2066]) ).
cnf(c_2067,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_618,c_10]) ).
cnf(c_669,plain,
( inverse(sk_c1) = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2067]) ).
cnf(c_688,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_669,c_2]) ).
cnf(c_2068,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_688,c_42]) ).
cnf(c_844,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_212,c_2068]) ).
cnf(c_857,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_844,c_2]) ).
cnf(c_2069,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_857,c_668]) ).
cnf(c_2070,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2069]) ).
cnf(c_1129,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_2070]) ).
cnf(c_1284,plain,
( multiply(sk_c7,sk_c4) = sk_c7
| inverse(sk_c7) = sk_c2 ),
inference(paramod,[status(thm)],[c_1129,c_491]) ).
cnf(c_2071,plain,
( sk_c6 != sk_c8
| identity != sk_c6
| sk_c7 != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1129,c_349]) ).
cnf(c_2072,plain,
( sk_c6 != sk_c8
| sk_c7 != sk_c6
| sk_c7 != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1129,c_2071]) ).
cnf(c_2073,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c7
| sk_c7 != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2072]) ).
cnf(c_2074,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2073]) ).
cnf(c_1347,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2074]) ).
cnf(c_2075,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_1129,c_290]) ).
cnf(c_1380,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_1129,c_2075]) ).
cnf(c_1381,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_1129,c_212]) ).
cnf(c_2076,plain,
( multiply(sk_c7,sk_c2) = identity
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_1381,c_105]) ).
cnf(c_1388,plain,
( multiply(sk_c7,sk_c2) = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_1129,c_2076]) ).
cnf(c_2077,plain,
( multiply(sk_c7,sk_c4) = identity
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_1381,c_90]) ).
cnf(c_1390,plain,
( multiply(sk_c7,sk_c4) = sk_c7
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_1129,c_2077]) ).
cnf(c_1397,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_1129,c_1]) ).
cnf(c_2078,plain,
( multiply(sk_c7,sk_c4) = sk_c7
| sk_c7 = sk_c2 ),
inference(paramod,[status(thm)],[c_1380,c_1284]) ).
cnf(c_2079,plain,
( sk_c4 = sk_c7
| sk_c7 = sk_c2 ),
inference(paramod,[status(thm)],[c_1397,c_2078]) ).
cnf(c_1398,plain,
( sk_c4 = sk_c7
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_2079]) ).
cnf(c_2080,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_1381,c_18]) ).
cnf(c_1554,plain,
( sk_c4 = sk_c6
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_1381,c_2080]) ).
cnf(c_1556,plain,
( sk_c4 = sk_c7
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_1397,c_1390]) ).
cnf(c_1557,plain,
( sk_c2 = sk_c7
| sk_c4 = sk_c6 ),
inference(paramod,[status(thm)],[c_1397,c_1388]) ).
cnf(c_2081,plain,
( sk_c7 = sk_c6
| sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(paramod,[status(thm)],[c_1556,c_1554]) ).
cnf(c_2082,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c6
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_2081]) ).
cnf(c_1733,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c6 ),
inference(copy,[status(thm)],[c_2082]) ).
cnf(c_2083,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_1557,c_1398]) ).
cnf(c_1740,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_2083]) ).
cnf(c_2084,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1740,c_1733]) ).
cnf(c_2085,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_2084]) ).
cnf(c_2086,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_2085]) ).
cnf(c_1845,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_2086]) ).
cnf(c_2087,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_1347]) ).
cnf(c_2088,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c7
| inverse(sk_c6) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1397,c_2087]) ).
cnf(c_2089,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_2088]) ).
cnf(c_2090,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1380,c_2089]) ).
cnf(c_2091,plain,
( sk_c6 != sk_c8
| sk_c7 != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_2090]) ).
cnf(c_2092,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c7
| sk_c7 != sk_c8
| sk_c8 != sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_2091]) ).
cnf(c_2093,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c7
| sk_c8 != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_2092]) ).
cnf(c_2094,plain,
( sk_c8 != sk_c7
| sk_c7 != sk_c7
| sk_c8 != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_2093]) ).
cnf(c_2095,plain,
( sk_c8 != sk_c7
| sk_c8 != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_2094]) ).
cnf(c_2096,plain,
( sk_c8 != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_2095]) ).
cnf(c_1998,plain,
sk_c8 != sk_c7,
inference(copy,[status(thm)],[c_2096]) ).
cnf(c_2097,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_210]) ).
cnf(c_2098,plain,
( multiply(inverse(sk_c5),sk_c6) = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1397,c_2097]) ).
cnf(c_2099,plain,
( multiply(inverse(sk_c5),sk_c7) = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_2098]) ).
cnf(c_2100,plain,
( inverse(sk_c5) = sk_c8
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1381,c_2099]) ).
cnf(c_2032,plain,
inverse(sk_c5) = sk_c8,
inference(resolve,[status(thm)],[c_1998,c_2100]) ).
cnf(c_2101,plain,
( multiply(sk_c6,multiply(sk_c5,A)) = A
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_208]) ).
cnf(c_2102,plain,
( multiply(sk_c6,multiply(sk_c5,A)) = A
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1397,c_2101]) ).
cnf(c_2103,plain,
( multiply(sk_c7,multiply(sk_c5,A)) = A
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_2102]) ).
cnf(c_2104,plain,
( multiply(sk_c5,A) = A
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1397,c_2103]) ).
cnf(c_2033,plain,
multiply(sk_c5,A) = A,
inference(resolve,[status(thm)],[c_1998,c_2104]) ).
cnf(c_2105,plain,
( multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_135]) ).
cnf(c_2106,plain,
( multiply(A,multiply(sk_c5,sk_c8)) = multiply(A,sk_c6)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1397,c_2105]) ).
cnf(c_2107,plain,
( multiply(A,sk_c8) = multiply(A,sk_c6)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_2033,c_2106]) ).
cnf(c_2108,plain,
( multiply(A,sk_c8) = multiply(A,sk_c7)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_2107]) ).
cnf(c_2109,plain,
( multiply(A,sk_c8) = A
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_1381,c_2108]) ).
cnf(c_2038,plain,
multiply(A,sk_c8) = A,
inference(resolve,[status(thm)],[c_1998,c_2109]) ).
cnf(c_2110,plain,
( sk_c8 = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_2032,c_14]) ).
cnf(c_2111,plain,
( sk_c8 = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_1845,c_2110]) ).
cnf(c_2042,plain,
inverse(sk_c1) = sk_c8,
inference(resolve,[status(thm)],[c_1998,c_2111]) ).
cnf(c_2112,plain,
( inverse(sk_c5) = sk_c6
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_2038,c_8]) ).
cnf(c_2113,plain,
( sk_c8 = sk_c6
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_2032,c_2112]) ).
cnf(c_2114,plain,
( sk_c8 = sk_c7
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_1845,c_2113]) ).
cnf(c_2044,plain,
sk_c1 = sk_c7,
inference(resolve,[status(thm)],[c_1998,c_2114]) ).
cnf(c_2115,plain,
inverse(sk_c7) = sk_c8,
inference(paramod,[status(thm)],[c_2044,c_2042]) ).
cnf(c_2116,plain,
sk_c7 = sk_c8,
inference(paramod,[status(thm)],[c_1380,c_2115]) ).
cnf(c_2117,plain,
sk_c8 = sk_c7,
inference(copy,[status(thm)],[c_2116]) ).
cnf(c_2053,plain,
$false,
inference(resolve,[status(thm)],[c_1998,c_2117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP261-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:43:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 422938 was started by sandbox on n003,
% 0.09/0.36 % Fri Sep 25 14:43:22 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 4.14/0.95
% 4.14/0.95 % SZS status Unsatisfiable for theBenchmark
% 4.14/0.95
% 4.14/0.95 % Proof 1 at 0.36 (+ 0.13) seconds.
% 4.14/0.95 % Length of proof is 69.
% 4.14/0.95 % Level of proof is 24.
% 4.14/0.95 % Maximum clause weight is 54.000.
% 4.14/0.95 % Given clauses 155.
% 4.14/0.95
% 4.14/0.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------