%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP353-1 : 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 07:28:42 AM UTC 2026
% Result : Unsatisfiable 4.30s 1.11s
% Output : CNFRefutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 12
% Syntax : Number of formulae : 108 ( 24 unt; 0 def)
% Number of atoms : 291 ( 290 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 323 ( 140 ~; 183 |; 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 : 37 ( 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
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_3,axiom,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_10,axiom,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c3) = sk_c4
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_16,axiom,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c3,sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c3) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_20,axiom,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_25,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( multiply(VAR_3,sk_c7) != sk_c6
| inverse(VAR_2) != VAR_3
| multiply(VAR_2,VAR_3) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| inverse(VAR_1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(D,sk_c7) != sk_c6
| inverse(C) != D
| multiply(C,D) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
cnf(c_30,plain,
( inverse(C) != A
| multiply(C,A) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_35,plain,
( inverse(B) != A
| multiply(B,A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_39,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(factor,[status(thm)],[c_35]) ).
cnf(c_1079,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1080,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1079]) ).
cnf(c_40,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1080]) ).
cnf(c_1081,plain,
( multiply(sk_c7,A) = multiply(sk_c6,multiply(sk_c5,A))
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_48,plain,
( multiply(sk_c6,multiply(sk_c5,A)) = multiply(sk_c7,A)
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_1081]) ).
cnf(c_96,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_105,plain,
( multiply(sk_c7,sk_c2) = identity
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_124,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_40]) ).
cnf(c_127,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_4,c_40]) ).
cnf(c_164,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_40]) ).
cnf(c_166,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_40]) ).
cnf(c_174,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_40,c_40]) ).
cnf(c_175,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_174,c_124]) ).
cnf(c_182,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_175,c_2]) ).
cnf(c_1082,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_96,c_40]) ).
cnf(c_252,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_175,c_1082]) ).
cnf(c_255,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_252,c_2]) ).
cnf(c_1083,plain,
( multiply(sk_c6,multiply(sk_c5,sk_c5)) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_48]) ).
cnf(c_353,plain,
( multiply(sk_c6,multiply(sk_c5,sk_c5)) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_1083]) ).
cnf(c_1084,plain,
( inverse(sk_c3) = sk_c4
| identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference(paramod,[status(thm)],[c_255,c_14]) ).
cnf(c_418,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c4 ),
inference(copy,[status(thm)],[c_1084]) ).
cnf(c_424,plain,
( multiply(sk_c4,sk_c3) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_418,c_2]) ).
cnf(c_1085,plain,
( multiply(inverse(sk_c4),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_424,c_40]) ).
cnf(c_434,plain,
( inverse(sk_c4) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_175,c_1085]) ).
cnf(c_440,plain,
( multiply(sk_c3,sk_c4) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_434,c_2]) ).
cnf(c_1086,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_440,c_13]) ).
cnf(c_472,plain,
( multiply(sk_c1,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1086]) ).
cnf(c_1087,plain,
( identity = sk_c6
| inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_440,c_19]) ).
cnf(c_473,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1087]) ).
cnf(c_483,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_473,c_2]) ).
cnf(c_1088,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_483,c_40]) ).
cnf(c_548,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_175,c_1088]) ).
cnf(c_559,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_548,c_2]) ).
cnf(c_1089,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_559,c_472]) ).
cnf(c_1090,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_1089]) ).
cnf(c_630,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_1090]) ).
cnf(c_1091,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_630,c_182]) ).
cnf(c_760,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_630,c_1091]) ).
cnf(c_761,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_630,c_175]) ).
cnf(c_763,plain,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_630,c_105]) ).
cnf(c_769,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_630,c_1]) ).
cnf(c_1092,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_769,c_127]) ).
cnf(c_1093,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_760,c_1092]) ).
cnf(c_1094,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_769,c_1093]) ).
cnf(c_790,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_1094]) ).
cnf(c_1095,plain,
( multiply(sk_c6,multiply(sk_c5,sk_c5)) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_761,c_353]) ).
cnf(c_1096,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c5)) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1095]) ).
cnf(c_1097,plain,
( multiply(sk_c6,multiply(sk_c7,sk_c7)) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1096]) ).
cnf(c_794,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_769,c_1097]) ).
cnf(c_1098,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_761,c_166]) ).
cnf(c_1099,plain,
( inverse(sk_c7) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_761,c_1098]) ).
cnf(c_800,plain,
( inverse(sk_c7) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1099]) ).
cnf(c_1100,plain,
( inverse(sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_761,c_164]) ).
cnf(c_801,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1100]) ).
cnf(c_1101,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_39]) ).
cnf(c_1102,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_769,c_1101]) ).
cnf(c_1103,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c5) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1102]) ).
cnf(c_1104,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1103]) ).
cnf(c_1105,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1104]) ).
cnf(c_1106,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| sk_c7 != sk_c5
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_769,c_1105]) ).
cnf(c_1107,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c5,sk_c6) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1106]) ).
cnf(c_1108,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1107]) ).
cnf(c_1109,plain,
( inverse(sk_c7) != sk_c5
| sk_c7 != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_761,c_1108]) ).
cnf(c_1110,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_790,c_1109]) ).
cnf(c_1111,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1110]) ).
cnf(c_1112,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1111]) ).
cnf(c_1113,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1112]) ).
cnf(c_1114,plain,
( inverse(sk_c7) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1113]) ).
cnf(c_825,plain,
( inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1114]) ).
cnf(c_850,plain,
( multiply(sk_c7,sk_c2) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_790,c_763]) ).
cnf(c_1032,plain,
( inverse(sk_c7) != sk_c7
| sk_c2 = sk_c7 ),
inference(resolve,[status(thm)],[c_794,c_825]) ).
cnf(c_1115,plain,
( sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(resolve,[status(thm)],[c_1032,c_800]) ).
cnf(c_1034,plain,
sk_c2 = sk_c7,
inference(copy,[status(thm)],[c_1115]) ).
cnf(c_1116,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1034,c_850]) ).
cnf(c_1062,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(copy,[status(thm)],[c_1116]) ).
cnf(c_1117,plain,
( inverse(sk_c7) = sk_c7
| inverse(sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_1034,c_801]) ).
cnf(c_1065,plain,
inverse(sk_c7) = sk_c7,
inference(copy,[status(thm)],[c_1117]) ).
cnf(c_1118,plain,
( inverse(sk_c7) != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_1062,c_825]) ).
cnf(c_1119,plain,
( sk_c7 != sk_c7
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_1065,c_1118]) ).
cnf(c_1120,plain,
sk_c7 != sk_c7,
inference(copy,[status(thm)],[c_1119]) ).
cnf(c_1078,plain,
$false,
inference(copy,[status(thm)],[c_1120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP353-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n002.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 14:50:34 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3550804 was started by sandbox2 on n002,
% 0.19/0.45 % Fri Sep 25 14:50:34 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 4.30/1.11
% 4.30/1.11 % SZS status Unsatisfiable for theBenchmark
% 4.30/1.11
% 4.30/1.11 % Proof 1 at 0.45 (+ 0.17) seconds.
% 4.30/1.11 % Length of proof is 54.
% 4.30/1.11 % Level of proof is 21.
% 4.30/1.11 % Maximum clause weight is 51.000.
% 4.30/1.11 % Given clauses 135.
% 4.30/1.11
% 4.30/1.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------