%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP313-1 : 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 : n005.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 07:28:37 AM UTC 2026
% Result : Unsatisfiable 43.14s 5.86s
% Output : CNFRefutation 43.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 14
% Syntax : Number of formulae : 136 ( 23 unt; 0 def)
% Number of atoms : 456 ( 455 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 588 ( 268 ~; 320 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 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 : 68 ( 0 sgn 11 !; 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_8,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_24,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_31,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
fof(prove_this_32,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_40,axiom,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('theBenchmark.p',prove_this_40) ).
cnf(c_43,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_40]) ).
fof(prove_this_47,axiom,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_47) ).
cnf(c_50,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_47]) ).
fof(prove_this_50,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( inverse(VAR_5) != sk_c7
| multiply(VAR_5,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c7
| inverse(VAR_3) != sk_c9
| multiply(VAR_3,sk_c9) != sk_c8
| inverse(VAR_2) != sk_c8
| multiply(VAR_2,sk_c8) != sk_c9
| inverse(VAR_1) != sk_c8
| multiply(VAR_1,sk_c8) != sk_c7
| inverse(VAR_0) != sk_c9
| multiply(VAR_0,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('theBenchmark.p',prove_this_50) ).
cnf(c_53,plain,
( inverse(F) != sk_c7
| multiply(F,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c7
| inverse(D) != sk_c9
| multiply(D,sk_c9) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_50]) ).
cnf(c_15534,plain,
( inverse(E) != sk_c7
| multiply(E,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c7
| inverse(A) != sk_c9
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_54,plain,
( inverse(E) != sk_c7
| multiply(E,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15534]) ).
cnf(c_15535,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(B) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(factor,[status(thm)],[c_54]) ).
cnf(c_57,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15535]) ).
cnf(c_15536,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_15537,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_15536]) ).
cnf(c_61,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_15537]) ).
cnf(c_75,plain,
( multiply(sk_c9,sk_c4) = identity
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_84,plain,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_85,plain,
( multiply(sk_c9,sk_c4) = identity
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_96,plain,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_104,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_34,c_2]) ).
cnf(c_105,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_35,c_2]) ).
cnf(c_124,plain,
( multiply(sk_c8,sk_c3) = identity
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_50,c_2]) ).
cnf(c_15538,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c9
| inverse(identity) != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_57]) ).
cnf(c_176,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c9
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15538]) ).
cnf(c_15539,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| multiply(identity,sk_c8) != sk_c9
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(factor,[status(thm)],[c_176]) ).
cnf(c_15540,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != sk_c9
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_15539]) ).
cnf(c_321,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c9 != sk_c8
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15540]) ).
cnf(c_530,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_61]) ).
cnf(c_581,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_61,c_61]) ).
cnf(c_582,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_581,c_530]) ).
cnf(c_15541,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c9 != sk_c8
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| inverse(identity) != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_321]) ).
cnf(c_680,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| inverse(identity) != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15541]) ).
cnf(c_725,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_582,c_2]) ).
cnf(c_15542,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_725,c_680]) ).
cnf(c_770,plain,
( inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| identity != sk_c8
| sk_c7 != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_725,c_15542]) ).
cnf(c_874,plain,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c9,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_85,c_2]) ).
cnf(c_15543,plain,
( inverse(identity) != sk_c7
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| identity != sk_c8
| sk_c7 != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_770]) ).
cnf(c_953,plain,
( identity != sk_c7
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| identity != sk_c8
| sk_c7 != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_725,c_15543]) ).
cnf(c_991,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c8,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_105,c_2]) ).
cnf(c_15544,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| multiply(sk_c9,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_874,c_61]) ).
cnf(c_2482,plain,
( inverse(sk_c9) = sk_c4
| multiply(sk_c9,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_582,c_15544]) ).
cnf(c_2486,plain,
( multiply(sk_c4,sk_c9) = identity
| multiply(sk_c9,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2482,c_2]) ).
cnf(c_15545,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| multiply(sk_c8,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_991,c_61]) ).
cnf(c_3082,plain,
( inverse(sk_c8) = sk_c5
| multiply(sk_c8,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_582,c_15545]) ).
cnf(c_15546,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c8
| multiply(sk_c9,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2486,c_84]) ).
cnf(c_4369,plain,
( identity = sk_c8
| multiply(sk_c9,sk_c1) = identity ),
inference(copy,[status(thm)],[c_15546]) ).
cnf(c_15547,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_4369,c_61]) ).
cnf(c_4704,plain,
( inverse(sk_c9) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_582,c_15547]) ).
cnf(c_4713,plain,
( multiply(sk_c1,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_4704,c_2]) ).
cnf(c_15548,plain,
( multiply(sk_c9,sk_c4) = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_4713,c_75]) ).
cnf(c_4754,plain,
( multiply(sk_c9,sk_c4) = identity
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15548]) ).
cnf(c_15549,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_4754,c_61]) ).
cnf(c_4827,plain,
( inverse(sk_c9) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_582,c_15549]) ).
cnf(c_5386,plain,
( multiply(sk_c4,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_4827,c_2]) ).
cnf(c_15550,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_5386,c_11]) ).
cnf(c_6319,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15550]) ).
cnf(c_15551,plain,
( sk_c8 = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_6319,c_4713]) ).
cnf(c_15552,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15551]) ).
cnf(c_15553,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15552]) ).
cnf(c_8265,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_15553]) ).
cnf(c_10811,plain,
( inverse(sk_c8) = sk_c5
| multiply(sk_c8,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_8265,c_3082]) ).
cnf(c_15554,plain,
( identity != sk_c7
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| identity != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_8265,c_953]) ).
cnf(c_15555,plain,
( identity != sk_c7
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_8265,c_15554]) ).
cnf(c_15556,plain,
( sk_c8 != sk_c7
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| sk_c8 != sk_c9
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(paramod,[status(thm)],[c_8265,c_15555]) ).
cnf(c_15557,plain,
( sk_c8 != sk_c7
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15556]) ).
cnf(c_15558,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15557]) ).
cnf(c_15559,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15558]) ).
cnf(c_15560,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15559]) ).
cnf(c_11902,plain,
( sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(copy,[status(thm)],[c_15560]) ).
cnf(c_15561,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_8265,c_725]) ).
cnf(c_11963,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_8265,c_15561]) ).
cnf(c_11965,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_8265,c_582]) ).
cnf(c_11978,plain,
( multiply(sk_c8,sk_c3) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_8265,c_124]) ).
cnf(c_15562,plain,
( multiply(sk_c8,sk_c2) = identity
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_11965,c_104]) ).
cnf(c_11989,plain,
( multiply(sk_c8,sk_c2) = sk_c8
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_8265,c_15562]) ).
cnf(c_15563,plain,
( multiply(sk_c8,sk_c5) = identity
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_11965,c_96]) ).
cnf(c_11992,plain,
( multiply(sk_c8,sk_c5) = sk_c8
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_8265,c_15563]) ).
cnf(c_12006,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_8265,c_1]) ).
cnf(c_15564,plain,
( inverse(sk_c8) = sk_c5
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_12006,c_10811]) ).
cnf(c_15565,plain,
( sk_c8 = sk_c5
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_11963,c_15564]) ).
cnf(c_12816,plain,
( sk_c5 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_15565]) ).
cnf(c_14337,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c3 = sk_c9 ),
inference(paramod,[status(thm)],[c_11965,c_43]) ).
cnf(c_15566,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_11965,c_27]) ).
cnf(c_14345,plain,
( sk_c5 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_11965,c_15566]) ).
cnf(c_14352,plain,
( sk_c5 = sk_c8
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12006,c_11992]) ).
cnf(c_14353,plain,
( sk_c2 = sk_c8
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_12006,c_11989]) ).
cnf(c_14360,plain,
( sk_c3 = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_12006,c_11978]) ).
cnf(c_15567,plain,
( sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| sk_c9 != sk_c7 ),
inference(paramod,[status(thm)],[c_12006,c_11902]) ).
cnf(c_15568,plain,
( sk_c7 != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| sk_c7 != sk_c9 ),
inference(copy,[status(thm)],[c_15567]) ).
cnf(c_14372,plain,
( multiply(sk_c7,sk_c9) != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| sk_c7 != sk_c9 ),
inference(copy,[status(thm)],[c_15568]) ).
cnf(c_15569,plain,
( sk_c8 = sk_c7
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_14352,c_14345]) ).
cnf(c_15570,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_15569]) ).
cnf(c_15169,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_15570]) ).
cnf(c_15571,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_14353,c_12816]) ).
cnf(c_15174,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_15571]) ).
cnf(c_15572,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_15174,c_15169]) ).
cnf(c_15573,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15572]) ).
cnf(c_15574,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15573]) ).
cnf(c_15286,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_15574]) ).
cnf(c_15575,plain,
( multiply(sk_c7,sk_c9) != sk_c8
| sk_c7 != sk_c8
| sk_c9 != sk_c8
| sk_c8 != sk_c9 ),
inference(paramod,[status(thm)],[c_15286,c_14372]) ).
cnf(c_15576,plain,
( multiply(sk_c7,sk_c9) != sk_c8
| sk_c8 != sk_c8
| sk_c9 != sk_c8
| sk_c8 != sk_c9 ),
inference(paramod,[status(thm)],[c_15286,c_15575]) ).
cnf(c_15577,plain,
( multiply(sk_c8,sk_c9) != sk_c8
| sk_c8 != sk_c8
| sk_c9 != sk_c8
| sk_c8 != sk_c9 ),
inference(paramod,[status(thm)],[c_15286,c_15576]) ).
cnf(c_15578,plain,
( sk_c9 != sk_c8
| sk_c8 != sk_c8
| sk_c9 != sk_c8
| sk_c8 != sk_c9 ),
inference(paramod,[status(thm)],[c_12006,c_15577]) ).
cnf(c_15579,plain,
( sk_c9 != sk_c8
| sk_c8 != sk_c8
| sk_c9 != sk_c8
| sk_c9 != sk_c8 ),
inference(copy,[status(thm)],[c_15578]) ).
cnf(c_15580,plain,
( sk_c9 != sk_c8
| sk_c9 != sk_c8
| sk_c9 != sk_c8 ),
inference(copy,[status(thm)],[c_15579]) ).
cnf(c_15581,plain,
( sk_c9 != sk_c8
| sk_c9 != sk_c8 ),
inference(copy,[status(thm)],[c_15580]) ).
cnf(c_15525,plain,
sk_c9 != sk_c8,
inference(copy,[status(thm)],[c_15581]) ).
cnf(c_15582,plain,
( sk_c3 = sk_c8
| multiply(sk_c8,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_15286,c_14360]) ).
cnf(c_15583,plain,
( sk_c3 = sk_c8
| sk_c9 = sk_c8 ),
inference(paramod,[status(thm)],[c_12006,c_15582]) ).
cnf(c_15527,plain,
sk_c3 = sk_c8,
inference(resolve,[status(thm)],[c_15525,c_15583]) ).
cnf(c_15584,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_15527,c_14337]) ).
cnf(c_15585,plain,
( multiply(sk_c8,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_15286,c_15584]) ).
cnf(c_15586,plain,
( sk_c9 = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_12006,c_15585]) ).
cnf(c_15587,plain,
( sk_c9 = sk_c8
| sk_c9 = sk_c8 ),
inference(copy,[status(thm)],[c_15586]) ).
cnf(c_15588,plain,
sk_c9 = sk_c8,
inference(copy,[status(thm)],[c_15587]) ).
cnf(c_15533,plain,
$false,
inference(resolve,[status(thm)],[c_15525,c_15588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP313-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:44:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3728054 was started by sandbox2 on n005,
% 0.10/0.37 % Fri Sep 25 14:44:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 43.14/5.86
% 43.14/5.86 % SZS status Unsatisfiable for theBenchmark
% 43.14/5.86
% 43.14/5.86 % Proof 1 at 4.76 (+ 0.69) seconds.
% 43.14/5.86 % Length of proof is 67.
% 43.14/5.86 % Level of proof is 21.
% 43.14/5.86 % Maximum clause weight is 74.000.
% 43.14/5.86 % Given clauses 301.
% 43.14/5.86
% 43.14/5.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------