%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP279-1 : 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 : n014.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 07:28:32 AM UTC 2026
% Result : Unsatisfiable 59.34s 9.04s
% Output : CNFRefutation 59.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 21
% Syntax : Number of formulae : 152 ( 28 unt; 0 def)
% Number of atoms : 433 ( 432 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 482 ( 201 ~; 281 |; 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 : 75 ( 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_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_6,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_9,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_14,axiom,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( multiply(VAR_4,sk_c6) != sk_c7
| inverse(VAR_4) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(VAR_2,sk_c7) != sk_c8
| inverse(VAR_1) != VAR_2
| multiply(VAR_1,VAR_2) != sk_c8
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(E,sk_c6) != sk_c7
| inverse(E) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(D) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(C,sk_c7) != sk_c8
| inverse(B) != C
| multiply(B,C) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_36,plain,
( multiply(D,sk_c6) != sk_c7
| inverse(D) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(C,sk_c7) != sk_c8
| inverse(B) != C
| multiply(B,C) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_47,plain,
( multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(A,sk_c7) != sk_c8
| inverse(B) != A
| multiply(B,A) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_15843,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_15844,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_15843]) ).
cnf(c_60,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_15844]) ).
cnf(c_74,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_84,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_87,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_22,c_2]) ).
cnf(c_1079,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_60]) ).
cnf(c_1115,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_60,c_60]) ).
cnf(c_1116,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_1115,c_1079]) ).
cnf(c_1157,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_1116,c_2]) ).
cnf(c_1509,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_1115,c_2]) ).
cnf(c_15845,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1115,c_1116]) ).
cnf(c_15846,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1116,c_15845]) ).
cnf(c_1535,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_15846]) ).
cnf(c_15847,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| inverse(A) != inverse(sk_c8)
| multiply(A,inverse(sk_c8)) != sk_c8
| multiply(inverse(sk_c8),sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_1535,c_47]) ).
cnf(c_15848,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| inverse(A) != inverse(sk_c8)
| multiply(A,inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_15847]) ).
cnf(c_1584,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| inverse(sk_c8) != inverse(A)
| multiply(A,inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_15848]) ).
cnf(c_1748,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_14,c_1509]) ).
cnf(c_1751,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_1509]) ).
cnf(c_1752,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_1509]) ).
cnf(c_1755,plain,
( multiply(sk_c2,sk_c3) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_24,c_1509]) ).
cnf(c_1756,plain,
( multiply(sk_c2,sk_c3) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_25,c_1509]) ).
cnf(c_1757,plain,
( multiply(sk_c2,sk_c3) = identity
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_26,c_1509]) ).
cnf(c_1758,plain,
( multiply(sk_c2,sk_c3) = identity
| inverse(sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_27,c_1509]) ).
cnf(c_1759,plain,
( multiply(sk_c2,sk_c3) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_28,c_1509]) ).
cnf(c_4156,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c1,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_1751,c_2]) ).
cnf(c_4237,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c2,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_1756,c_2]) ).
cnf(c_4322,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c2,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_1758,c_2]) ).
cnf(c_15849,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1748,c_9]) ).
cnf(c_7968,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_15849]) ).
cnf(c_8131,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_7968,c_60]) ).
cnf(c_15850,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| identity = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1752,c_13]) ).
cnf(c_8304,plain,
( identity = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_15850]) ).
cnf(c_15851,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1755,c_19]) ).
cnf(c_8441,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_15851]) ).
cnf(c_8445,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_8441,c_60]) ).
cnf(c_15852,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| identity = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_1757,c_21]) ).
cnf(c_8816,plain,
( identity = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_15852]) ).
cnf(c_8825,plain,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_8816,c_60]) ).
cnf(c_15853,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| identity = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1759,c_23]) ).
cnf(c_9124,plain,
( identity = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_15853]) ).
cnf(c_10089,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1535,c_1584]) ).
cnf(c_15854,plain,
( multiply(sk_c7,sk_c5) = identity
| identity = sk_c7
| multiply(sk_c7,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_4156,c_74]) ).
cnf(c_10314,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c5) = identity ),
inference(copy,[status(thm)],[c_15854]) ).
cnf(c_15855,plain,
( multiply(inverse(sk_c7),identity) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10314,c_60]) ).
cnf(c_10404,plain,
( inverse(sk_c7) = sk_c5
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1116,c_15855]) ).
cnf(c_15856,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10404,c_8131]) ).
cnf(c_10445,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15856]) ).
cnf(c_15857,plain,
( identity = sk_c7
| sk_c8 = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10445,c_8304]) ).
cnf(c_15858,plain,
( identity = sk_c7
| sk_c7 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15857]) ).
cnf(c_10581,plain,
( sk_c7 = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15858]) ).
cnf(c_15859,plain,
( multiply(sk_c8,sk_c4) = identity
| identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_4237,c_84]) ).
cnf(c_11258,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(copy,[status(thm)],[c_15859]) ).
cnf(c_15860,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11258,c_60]) ).
cnf(c_11263,plain,
( inverse(sk_c8) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1116,c_15860]) ).
cnf(c_11279,plain,
( inverse(sk_c4) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11263,c_1535]) ).
cnf(c_15861,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11279,c_8825]) ).
cnf(c_11414,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15861]) ).
cnf(c_11486,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11414,c_60]) ).
cnf(c_15862,plain,
( multiply(sk_c7,sk_c5) = identity
| identity = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_4322,c_87]) ).
cnf(c_11700,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(copy,[status(thm)],[c_15862]) ).
cnf(c_15863,plain,
( multiply(inverse(sk_c7),identity) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11700,c_60]) ).
cnf(c_11705,plain,
( inverse(sk_c7) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1116,c_15863]) ).
cnf(c_15864,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11705,c_8445]) ).
cnf(c_11780,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15864]) ).
cnf(c_15865,plain,
( identity = sk_c8
| sk_c8 = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11780,c_9124]) ).
cnf(c_15866,plain,
( identity = sk_c8
| sk_c7 = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15865]) ).
cnf(c_12058,plain,
( sk_c7 = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15866]) ).
cnf(c_15867,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_12058,c_10581]) ).
cnf(c_15868,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15867]) ).
cnf(c_15869,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15868]) ).
cnf(c_12085,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_15869]) ).
cnf(c_15870,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_12085,c_11486]) ).
cnf(c_15871,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_15870]) ).
cnf(c_12456,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_15871]) ).
cnf(c_15872,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| identity != sk_c7
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_12085,c_10089]) ).
cnf(c_15873,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_12456,c_15872]) ).
cnf(c_15874,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_12085,c_15873]) ).
cnf(c_15875,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c8),sk_c8) != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_12085,c_15874]) ).
cnf(c_15876,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| identity != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_15875]) ).
cnf(c_15877,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_12456,c_15876]) ).
cnf(c_15878,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_12085,c_15877]) ).
cnf(c_15879,plain,
( multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_12085,c_15878]) ).
cnf(c_15880,plain,
( multiply(B,sk_c6) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_12085,c_15879]) ).
cnf(c_15881,plain,
( multiply(B,sk_c6) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_15880]) ).
cnf(c_15882,plain,
( multiply(B,sk_c6) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_15881]) ).
cnf(c_12809,plain,
( multiply(B,sk_c6) != sk_c8
| inverse(B) != sk_c8
| inverse(sk_c8) != A
| multiply(inverse(A),inverse(sk_c8)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(copy,[status(thm)],[c_15882]) ).
cnf(c_15883,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_12085,c_4]) ).
cnf(c_15884,plain,
( multiply(sk_c8,sk_c8) = sk_c6
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_12085,c_15883]) ).
cnf(c_15603,plain,
multiply(sk_c8,sk_c8) = sk_c6,
inference(copy,[status(thm)],[c_15884]) ).
cnf(c_15885,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_12456,c_1157]) ).
cnf(c_15745,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_12456,c_15885]) ).
cnf(c_15746,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_12456,c_1116]) ).
cnf(c_15748,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_12456,c_1]) ).
cnf(c_15886,plain,
( multiply(sk_c8,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(inverse(sk_c8),inverse(sk_c8)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_12809]) ).
cnf(c_15887,plain,
( multiply(sk_c8,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(inverse(sk_c8),inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_15746,c_15886]) ).
cnf(c_15888,plain,
( multiply(sk_c8,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,inverse(sk_c8)) != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_15745,c_15887]) ).
cnf(c_15889,plain,
( multiply(sk_c8,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_15745,c_15888]) ).
cnf(c_15890,plain,
( multiply(sk_c8,sk_c6) != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_15746,c_15889]) ).
cnf(c_15891,plain,
( multiply(sk_c8,sk_c6) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_15745,c_15890]) ).
cnf(c_15892,plain,
( sk_c6 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_15748,c_15891]) ).
cnf(c_15893,plain,
( sk_c6 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_15892]) ).
cnf(c_15894,plain,
( sk_c6 != sk_c8
| sk_c8 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_15893]) ).
cnf(c_15895,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_15894]) ).
cnf(c_15761,plain,
sk_c6 != sk_c8,
inference(copy,[status(thm)],[c_15895]) ).
cnf(c_15896,plain,
sk_c8 = sk_c6,
inference(paramod,[status(thm)],[c_15746,c_15603]) ).
cnf(c_15897,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_15896]) ).
cnf(c_15842,plain,
$false,
inference(resolve,[status(thm)],[c_15761,c_15897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP279-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.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 14:43:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 465152 was started by sandbox on n014,
% 0.09/0.37 % Fri Sep 25 14:43:03 2026
% 0.09/0.37 % 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).
% 59.34/9.04
% 59.34/9.04 % SZS status Unsatisfiable for theBenchmark
% 59.34/9.04
% 59.34/9.04 % Proof 1 at 7.50 (+ 0.85) seconds.
% 59.34/9.04 % Length of proof is 76.
% 59.34/9.04 % Level of proof is 14.
% 59.34/9.04 % Maximum clause weight is 51.000.
% 59.34/9.04 % Given clauses 409.
% 59.34/9.04
% 59.34/9.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------