%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP252-1 : 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 : n026.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 07:28:28 AM UTC 2026
% Result : Unsatisfiable 46.42s 6.36s
% Output : CNFRefutation 46.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 17
% Syntax : Number of formulae : 142 ( 25 unt; 0 def)
% Number of atoms : 408 ( 407 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 453 ( 187 ~; 266 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 12 !; 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_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_17,axiom,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_25,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_43,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( inverse(VAR_6) != sk_c8
| multiply(VAR_6,sk_c8) != VAR_5
| multiply(sk_c8,VAR_5) != sk_c9
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c9
| inverse(VAR_3) != sk_c10
| multiply(VAR_3,sk_c10) != sk_c9
| multiply(VAR_2,sk_c8) != sk_c9
| inverse(VAR_2) != sk_c9
| inverse(VAR_1) != sk_c9
| multiply(VAR_1,sk_c9) != sk_c8
| inverse(VAR_0) != sk_c10
| multiply(VAR_0,sk_c10) != sk_c9 ),
file('theBenchmark.p',prove_this_43) ).
cnf(c_46,plain,
( inverse(V6) != sk_c8
| multiply(V6,sk_c8) != F
| multiply(sk_c8,F) != sk_c9
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c9
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(clausify,[status(thm)],[prove_this_43]) ).
cnf(c_6958,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c9
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_47,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c9
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6958]) ).
cnf(c_52,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c9
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_63,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_52]) ).
cnf(c_78,plain,
( multiply(B,sk_c8) != C
| multiply(sk_c8,C) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_63]) ).
cnf(c_6959,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_6960,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_6959]) ).
cnf(c_84,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_6960]) ).
cnf(c_110,plain,
( multiply(sk_c10,sk_c1) = identity
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_113,plain,
( multiply(sk_c10,sk_c1) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_6961,plain,
( multiply(sk_c9,A) = multiply(sk_c5,multiply(sk_c8,A))
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_3]) ).
cnf(c_137,plain,
( multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c9,A)
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_6961]) ).
cnf(c_139,plain,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_150,plain,
( multiply(sk_c8,sk_c6) = identity
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_162,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_170,plain,
( multiply(sk_c8,sk_c6) = identity
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_218,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_84]) ).
cnf(c_256,plain,
( multiply(inverse(sk_c2),sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_22,c_84]) ).
cnf(c_258,plain,
( multiply(inverse(sk_c2),sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_84]) ).
cnf(c_304,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_84,c_84]) ).
cnf(c_305,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_304,c_218]) ).
cnf(c_364,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_305,c_2]) ).
cnf(c_6962,plain,
( multiply(identity,sk_c8) != B
| multiply(sk_c8,B) != sk_c9
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| identity != sk_c9
| multiply(identity,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_364,c_78]) ).
cnf(c_6963,plain,
( multiply(identity,sk_c8) != B
| multiply(sk_c8,B) != sk_c9
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_6962]) ).
cnf(c_6964,plain,
( multiply(identity,sk_c8) != B
| multiply(sk_c8,B) != sk_c9
| inverse(identity) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_6963]) ).
cnf(c_6965,plain,
( multiply(identity,sk_c8) != B
| multiply(sk_c8,B) != sk_c9
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_364,c_6964]) ).
cnf(c_6966,plain,
( sk_c8 != B
| multiply(sk_c8,B) != sk_c9
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_6965]) ).
cnf(c_6967,plain,
( sk_c8 != B
| multiply(sk_c8,B) != sk_c9
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6966]) ).
cnf(c_422,plain,
( sk_c8 != B
| multiply(sk_c8,B) != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6967]) ).
cnf(c_6968,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_113,c_84]) ).
cnf(c_426,plain,
( inverse(sk_c10) = sk_c1
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_305,c_6968]) ).
cnf(c_429,plain,
( multiply(sk_c1,sk_c10) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_426,c_2]) ).
cnf(c_6969,plain,
( sk_c8 != identity
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_305,c_422]) ).
cnf(c_6970,plain,
( identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6969]) ).
cnf(c_6971,plain,
( identity != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6970]) ).
cnf(c_559,plain,
( identity != sk_c8
| identity != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6971]) ).
cnf(c_6972,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_162,c_84]) ).
cnf(c_822,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_305,c_6972]) ).
cnf(c_844,plain,
( multiply(sk_c9,sk_c2) = identity
| inverse(sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_822,c_2]) ).
cnf(c_6973,plain,
( multiply(inverse(sk_c8),identity) = sk_c6
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_170,c_84]) ).
cnf(c_866,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_305,c_6973]) ).
cnf(c_6974,plain,
( sk_c6 = sk_c5
| inverse(sk_c2) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_866,c_822]) ).
cnf(c_876,plain,
( sk_c6 = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(copy,[status(thm)],[c_6974]) ).
cnf(c_6975,plain,
( inverse(sk_c4) = sk_c10
| identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_429,c_5]) ).
cnf(c_1415,plain,
( identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(copy,[status(thm)],[c_6975]) ).
cnf(c_1427,plain,
( multiply(sk_c10,sk_c4) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1415,c_2]) ).
cnf(c_6976,plain,
( multiply(inverse(sk_c10),identity) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1427,c_84]) ).
cnf(c_1452,plain,
( inverse(sk_c10) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_305,c_6976]) ).
cnf(c_1489,plain,
( multiply(sk_c4,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1452,c_2]) ).
cnf(c_6977,plain,
( identity = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1489,c_4]) ).
cnf(c_1636,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_6977]) ).
cnf(c_6978,plain,
( multiply(sk_c10,sk_c1) = identity
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1489,c_110]) ).
cnf(c_1670,plain,
( multiply(sk_c10,sk_c1) = identity
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_6978]) ).
cnf(c_6979,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1670,c_84]) ).
cnf(c_2539,plain,
( inverse(sk_c10) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_305,c_6979]) ).
cnf(c_2567,plain,
( multiply(sk_c1,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_2539,c_2]) ).
cnf(c_6980,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_139,c_84]) ).
cnf(c_2775,plain,
( inverse(sk_c8) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_305,c_6980]) ).
cnf(c_6981,plain,
( multiply(sk_c5,identity) = multiply(sk_c9,sk_c6)
| multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_150,c_137]) ).
cnf(c_6982,plain,
( sk_c5 = multiply(sk_c9,sk_c6)
| multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_305,c_6981]) ).
cnf(c_6983,plain,
( multiply(sk_c9,sk_c6) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_6982]) ).
cnf(c_3666,plain,
( multiply(sk_c9,sk_c6) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_6983]) ).
cnf(c_6984,plain,
( identity = sk_c9
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_2567,c_1636]) ).
cnf(c_6985,plain,
( identity = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_6984]) ).
cnf(c_4093,plain,
identity = sk_c9,
inference(copy,[status(thm)],[c_6985]) ).
cnf(c_4761,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| inverse(sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_4093,c_844]) ).
cnf(c_6986,plain,
( identity != sk_c8
| sk_c9 != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_4093,c_559]) ).
cnf(c_6987,plain,
( sk_c9 != sk_c8
| sk_c9 != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_4093,c_6986]) ).
cnf(c_6988,plain,
( sk_c8 != sk_c9
| sk_c9 != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6987]) ).
cnf(c_6989,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6988]) ).
cnf(c_4919,plain,
( sk_c8 != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_6989]) ).
cnf(c_4937,plain,
multiply(A,sk_c9) = A,
inference(paramod,[status(thm)],[c_4093,c_305]) ).
cnf(c_4959,plain,
multiply(inverse(A),A) = sk_c9,
inference(paramod,[status(thm)],[c_4093,c_2]) ).
cnf(c_4960,plain,
multiply(sk_c9,A) = A,
inference(paramod,[status(thm)],[c_4093,c_1]) ).
cnf(c_6990,plain,
( multiply(sk_c9,sk_c6) = sk_c5
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_4937,c_3666]) ).
cnf(c_5156,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_4960,c_6990]) ).
cnf(c_5275,plain,
( inverse(sk_c8) = sk_c5
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_4937,c_2775]) ).
cnf(c_5481,plain,
( sk_c2 = sk_c9
| inverse(sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_4960,c_4761]) ).
cnf(c_6991,plain,
( sk_c6 = sk_c5
| inverse(sk_c8) = sk_c9
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_5156,c_876]) ).
cnf(c_5736,plain,
( inverse(sk_c8) = sk_c9
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_6991]) ).
cnf(c_6992,plain,
( inverse(sk_c8) = sk_c5
| sk_c9 = sk_c8
| inverse(sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_5481,c_5275]) ).
cnf(c_6993,plain,
( inverse(sk_c8) = sk_c5
| sk_c8 = sk_c9
| inverse(sk_c8) = sk_c5 ),
inference(copy,[status(thm)],[c_6992]) ).
cnf(c_6210,plain,
( sk_c8 = sk_c9
| inverse(sk_c8) = sk_c5 ),
inference(copy,[status(thm)],[c_6993]) ).
cnf(c_6994,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_29,c_256]) ).
cnf(c_6995,plain,
( sk_c8 = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_4960,c_6994]) ).
cnf(c_6724,plain,
( sk_c8 = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_6995]) ).
cnf(c_6996,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_258]) ).
cnf(c_6997,plain,
( sk_c8 = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_4960,c_6996]) ).
cnf(c_6735,plain,
( sk_c8 = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_6997]) ).
cnf(c_6998,plain,
multiply(inverse(inverse(A)),sk_c9) = A,
inference(paramod,[status(thm)],[c_4959,c_84]) ).
cnf(c_6916,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_4937,c_6998]) ).
cnf(c_6999,plain,
( sk_c8 != sk_c9
| inverse(inverse(sk_c10)) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_4959,c_4919]) ).
cnf(c_7000,plain,
( sk_c8 != sk_c9
| sk_c10 != sk_c10
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_6916,c_6999]) ).
cnf(c_7001,plain,
( sk_c8 != sk_c9
| sk_c10 != sk_c10 ),
inference(copy,[status(thm)],[c_7000]) ).
cnf(c_6921,plain,
sk_c8 != sk_c9,
inference(copy,[status(thm)],[c_7001]) ).
cnf(c_7002,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_5736,c_4959]) ).
cnf(c_7003,plain,
( sk_c8 = sk_c9
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_4960,c_7002]) ).
cnf(c_6936,plain,
sk_c6 = sk_c5,
inference(resolve,[status(thm)],[c_6921,c_7003]) ).
cnf(c_7004,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_6210,c_4959]) ).
cnf(c_6941,plain,
multiply(sk_c5,sk_c8) = sk_c9,
inference(resolve,[status(thm)],[c_6921,c_7004]) ).
cnf(c_7005,plain,
( sk_c8 = sk_c9
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_6936,c_6735]) ).
cnf(c_7006,plain,
( sk_c8 = sk_c9
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_6941,c_7005]) ).
cnf(c_7007,plain,
( sk_c8 = sk_c9
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_7006]) ).
cnf(c_6956,plain,
sk_c7 = sk_c9,
inference(resolve,[status(thm)],[c_6921,c_7007]) ).
cnf(c_7008,plain,
( sk_c8 = sk_c9
| multiply(sk_c8,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_6956,c_6724]) ).
cnf(c_7009,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_4937,c_7008]) ).
cnf(c_7010,plain,
sk_c8 = sk_c9,
inference(copy,[status(thm)],[c_7009]) ).
cnf(c_6957,plain,
$false,
inference(resolve,[status(thm)],[c_6921,c_7010]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP252-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n026.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Fri Sep 25 14:43:55 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 2769030 was started by sandbox2 on n026,
% 0.15/0.44 % Fri Sep 25 14:43:55 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).
% 46.42/6.36
% 46.42/6.36 % SZS status Unsatisfiable for theBenchmark
% 46.42/6.36
% 46.42/6.36 % Proof 1 at 4.44 (+ 1.39) seconds.
% 46.42/6.36 % Length of proof is 72.
% 46.42/6.36 % Level of proof is 19.
% 46.42/6.36 % Maximum clause weight is 63.000.
% 46.42/6.36 % Given clauses 443.
% 46.42/6.36
% 46.42/6.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------