%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP247-1 : 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 07:28:28 AM UTC 2026
% Result : Unsatisfiable 19.02s 5.73s
% Output : CNFRefutation 19.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 18
% Syntax : Number of formulae : 201 ( 30 unt; 0 def)
% Number of atoms : 519 ( 518 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 541 ( 223 ~; 318 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 79 ( 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_1,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_7,axiom,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_11,axiom,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_15,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_21,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_26,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_29,axiom,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_35,axiom,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_35) ).
cnf(c_38,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_35]) ).
fof(prove_this_36,axiom,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_36) ).
cnf(c_39,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_36]) ).
fof(prove_this_37,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( multiply(VAR_5,sk_c8) != sk_c9
| inverse(VAR_5) != sk_c9
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c7
| inverse(VAR_3) != sk_c9
| multiply(VAR_3,sk_c9) != sk_c8
| multiply(VAR_2,sk_c7) != sk_c9
| inverse(VAR_2) != 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 ),
file('theBenchmark.p',prove_this_37) ).
cnf(c_40,plain,
( multiply(F,sk_c8) != sk_c9
| inverse(F) != sk_c9
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c7
| inverse(D) != sk_c9
| multiply(D,sk_c9) != sk_c8
| multiply(C,sk_c7) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_37]) ).
cnf(c_8906,plain,
( multiply(E,sk_c8) != sk_c9
| inverse(E) != sk_c9
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(C,sk_c7) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_41,plain,
( multiply(E,sk_c8) != sk_c9
| inverse(E) != sk_c9
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c7
| multiply(C,sk_c7) != sk_c9
| inverse(C) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8906]) ).
cnf(c_43,plain,
( multiply(D,sk_c8) != sk_c9
| inverse(D) != sk_c9
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_41]) ).
cnf(c_47,plain,
( multiply(A,sk_c8) != sk_c9
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_43]) ).
cnf(c_8907,plain,
( multiply(A,sk_c8) != sk_c9
| inverse(B) != sk_c8
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_51,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c7) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8907]) ).
cnf(c_8908,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_8909,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_8908]) ).
cnf(c_52,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_8909]) ).
cnf(c_74,plain,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_77,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_84,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_100,plain,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_115,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_118,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_129,plain,
( multiply(sk_c9,sk_c4) = identity
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_135,plain,
( multiply(sk_c9,sk_c3) = identity
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_32,c_2]) ).
cnf(c_136,plain,
( multiply(sk_c9,sk_c6) = identity
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_32,c_2]) ).
cnf(c_8910,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c7) != sk_c9
| inverse(identity) != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_51]) ).
cnf(c_163,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c7) != sk_c9
| inverse(identity) != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8910]) ).
cnf(c_165,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_52]) ).
cnf(c_239,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_52,c_52]) ).
cnf(c_240,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_239,c_165]) ).
cnf(c_392,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_240,c_2]) ).
cnf(c_540,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c7) != sk_c9
| identity != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_392,c_163]) ).
cnf(c_8911,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_77,c_52]) ).
cnf(c_546,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_240,c_8911]) ).
cnf(c_549,plain,
( multiply(sk_c1,sk_c9) = identity
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_546,c_2]) ).
cnf(c_8912,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_84,c_52]) ).
cnf(c_803,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_240,c_8912]) ).
cnf(c_8913,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_118,c_52]) ).
cnf(c_993,plain,
( inverse(sk_c8) = sk_c2
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_240,c_8913]) ).
cnf(c_1001,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c8) = sk_c2 ),
inference(paramod,[status(thm)],[c_993,c_2]) ).
cnf(c_8914,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_129,c_52]) ).
cnf(c_1295,plain,
( inverse(sk_c9) = sk_c4
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_240,c_8914]) ).
cnf(c_8915,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_135,c_52]) ).
cnf(c_1524,plain,
( inverse(sk_c9) = sk_c3
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_240,c_8915]) ).
cnf(c_8916,plain,
( sk_c3 = sk_c1
| inverse(sk_c6) = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_1524,c_803]) ).
cnf(c_1543,plain,
( sk_c3 = sk_c1
| inverse(sk_c6) = sk_c9 ),
inference(copy,[status(thm)],[c_8916]) ).
cnf(c_8917,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c7) = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_1543,c_38]) ).
cnf(c_1550,plain,
( multiply(sk_c1,sk_c7) = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(copy,[status(thm)],[c_8917]) ).
cnf(c_8918,plain,
( multiply(inverse(sk_c9),identity) = sk_c6
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_136,c_52]) ).
cnf(c_1613,plain,
( inverse(sk_c9) = sk_c6
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_240,c_8918]) ).
cnf(c_8919,plain,
( sk_c6 = sk_c4
| inverse(sk_c3) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_1613,c_1295]) ).
cnf(c_1649,plain,
( sk_c6 = sk_c4
| inverse(sk_c3) = sk_c9 ),
inference(copy,[status(thm)],[c_8919]) ).
cnf(c_8920,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_1649,c_33]) ).
cnf(c_1656,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(copy,[status(thm)],[c_8920]) ).
cnf(c_8921,plain,
( inverse(sk_c4) = sk_c9
| identity = sk_c8
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_549,c_5]) ).
cnf(c_1737,plain,
( identity = sk_c8
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_8921]) ).
cnf(c_1751,plain,
( multiply(sk_c9,sk_c4) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1737,c_2]) ).
cnf(c_8922,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1751,c_52]) ).
cnf(c_1780,plain,
( inverse(sk_c9) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_240,c_8922]) ).
cnf(c_1839,plain,
( multiply(sk_c4,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1780,c_2]) ).
cnf(c_8923,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1839,c_4]) ).
cnf(c_2035,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_8923]) ).
cnf(c_8924,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1839,c_74]) ).
cnf(c_2070,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_8924]) ).
cnf(c_8925,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2070,c_52]) ).
cnf(c_2805,plain,
( inverse(sk_c9) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_240,c_8925]) ).
cnf(c_2833,plain,
( multiply(sk_c1,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2805,c_2]) ).
cnf(c_8926,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_100,c_52]) ).
cnf(c_2950,plain,
( inverse(sk_c8) = sk_c5
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_240,c_8926]) ).
cnf(c_8927,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_115,c_52]) ).
cnf(c_3972,plain,
( inverse(sk_c8) = sk_c2
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_240,c_8927]) ).
cnf(c_8928,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2833,c_2035]) ).
cnf(c_8929,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_8928]) ).
cnf(c_4749,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_8929]) ).
cnf(c_5684,plain,
( multiply(sk_c8,sk_c5) = sk_c8
| inverse(sk_c8) = sk_c2 ),
inference(paramod,[status(thm)],[c_4749,c_1001]) ).
cnf(c_8930,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c7) != sk_c9
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_4749,c_540]) ).
cnf(c_6003,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c7) != sk_c9
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8930]) ).
cnf(c_8931,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_4749,c_392]) ).
cnf(c_6144,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_4749,c_8931]) ).
cnf(c_6145,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_4749,c_240]) ).
cnf(c_6164,plain,
multiply(inverse(A),A) = sk_c8,
inference(paramod,[status(thm)],[c_4749,c_2]) ).
cnf(c_6165,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_4749,c_1]) ).
cnf(c_8932,plain,
( multiply(sk_c8,sk_c5) = sk_c8
| sk_c8 = sk_c2 ),
inference(paramod,[status(thm)],[c_6144,c_5684]) ).
cnf(c_8933,plain,
( sk_c5 = sk_c8
| sk_c8 = sk_c2 ),
inference(paramod,[status(thm)],[c_6165,c_8932]) ).
cnf(c_6188,plain,
( sk_c5 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_8933]) ).
cnf(c_8934,plain,
( inverse(sk_c8) = sk_c2
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_6145,c_3972]) ).
cnf(c_8935,plain,
( sk_c8 = sk_c2
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_6144,c_8934]) ).
cnf(c_6220,plain,
( sk_c2 = sk_c8
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_8935]) ).
cnf(c_8936,plain,
( inverse(sk_c8) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_6145,c_2950]) ).
cnf(c_8937,plain,
( sk_c8 = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_6144,c_8936]) ).
cnf(c_6225,plain,
( sk_c5 = sk_c8
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_8937]) ).
cnf(c_8938,plain,
( A != sk_c9
| multiply(A,sk_c7) != sk_c9
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_6145,c_6003]) ).
cnf(c_6348,plain,
( sk_c9 != A
| multiply(A,sk_c7) != sk_c9
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8938]) ).
cnf(c_7070,plain,
( sk_c4 = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_6145,c_1656]) ).
cnf(c_7187,plain,
( sk_c6 = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_6145,c_39]) ).
cnf(c_7189,plain,
( sk_c6 = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_6145,c_33]) ).
cnf(c_8939,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_6145,c_18]) ).
cnf(c_7196,plain,
( sk_c5 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_6145,c_8939]) ).
cnf(c_8940,plain,
( sk_c5 = sk_c8
| sk_c7 = sk_c8
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_6225,c_6188]) ).
cnf(c_7404,plain,
( sk_c7 = sk_c8
| sk_c5 = sk_c8 ),
inference(copy,[status(thm)],[c_8940]) ).
cnf(c_8941,plain,
( sk_c7 = sk_c8
| sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_7196,c_6220]) ).
cnf(c_7597,plain,
( sk_c7 = sk_c8
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_8941]) ).
cnf(c_8942,plain,
B = multiply(inverse(A),multiply(A,B)),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_8943,plain,
( multiply(multiply(inverse(A),multiply(A,sk_c9)),sk_c7) != sk_c9
| sk_c7 != sk_c8
| inverse(multiply(inverse(A),multiply(A,sk_c9))) != sk_c9
| multiply(multiply(inverse(A),multiply(A,sk_c9)),sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_6348,c_8942]) ).
cnf(c_8944,plain,
( multiply(multiply(inverse(A),multiply(A,sk_c9)),sk_c7) != sk_c9
| sk_c7 != sk_c8
| inverse(multiply(inverse(A),multiply(A,sk_c9))) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_52,c_8943]) ).
cnf(c_8945,plain,
( multiply(multiply(inverse(A),multiply(A,sk_c9)),sk_c7) != sk_c9
| sk_c7 != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_52,c_8944]) ).
cnf(c_7693,plain,
( multiply(sk_c9,sk_c7) != sk_c9
| sk_c7 != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_52,c_8945]) ).
cnf(c_8946,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_7597,c_7404]) ).
cnf(c_8947,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_8946]) ).
cnf(c_7820,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_8947]) ).
cnf(c_8948,plain,
( multiply(sk_c9,sk_c7) != sk_c9
| sk_c8 != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_7820,c_7693]) ).
cnf(c_8949,plain,
( multiply(sk_c9,sk_c8) != sk_c9
| sk_c8 != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_7820,c_8948]) ).
cnf(c_8950,plain,
( sk_c9 != sk_c9
| sk_c8 != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_6145,c_8949]) ).
cnf(c_8951,plain,
( sk_c9 != sk_c9
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8950]) ).
cnf(c_7862,plain,
( inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8951]) ).
cnf(c_8952,plain,
( sk_c6 = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_7820,c_7187]) ).
cnf(c_7947,plain,
( sk_c6 = sk_c9
| sk_c3 = sk_c9 ),
inference(paramod,[status(thm)],[c_6145,c_8952]) ).
cnf(c_8953,plain,
( sk_c9 != A
| multiply(A,sk_c7) != sk_c9
| sk_c8 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_7820,c_6348]) ).
cnf(c_8954,plain,
( sk_c9 != A
| multiply(A,sk_c8) != sk_c9
| sk_c8 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_7820,c_8953]) ).
cnf(c_8955,plain,
( sk_c9 != A
| A != sk_c9
| sk_c8 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_6145,c_8954]) ).
cnf(c_8956,plain,
( sk_c9 != A
| sk_c9 != A
| sk_c8 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8955]) ).
cnf(c_8957,plain,
( sk_c9 != A
| sk_c9 != A
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8956]) ).
cnf(c_8186,plain,
( sk_c9 != A
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8957]) ).
cnf(c_8958,plain,
( multiply(sk_c1,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_7820,c_1550]) ).
cnf(c_8196,plain,
( sk_c1 = sk_c9
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_6145,c_8958]) ).
cnf(c_8959,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_7820,c_38]) ).
cnf(c_8220,plain,
( inverse(sk_c6) = sk_c9
| sk_c3 = sk_c9 ),
inference(paramod,[status(thm)],[c_6145,c_8959]) ).
cnf(c_8960,plain,
( inverse(sk_c4) = sk_c9
| sk_c9 = inverse(sk_c1) ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_8289,plain,
( inverse(sk_c4) = sk_c9
| inverse(inverse(sk_c1)) != sk_c9
| multiply(inverse(sk_c1),sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_8186,c_8960]) ).
cnf(c_8961,plain,
( sk_c9 = inverse(sk_c4)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_8292,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(inverse(sk_c4)) != sk_c9
| multiply(inverse(sk_c4),sk_c9) != sk_c8 ),
inference(resolve,[status(thm)],[c_8186,c_8961]) ).
cnf(c_8962,plain,
( sk_c6 = sk_c9
| inverse(sk_c9) = sk_c9
| sk_c6 = sk_c9 ),
inference(paramod,[status(thm)],[c_7947,c_7189]) ).
cnf(c_8490,plain,
( inverse(sk_c9) = sk_c9
| sk_c6 = sk_c9 ),
inference(copy,[status(thm)],[c_8962]) ).
cnf(c_8963,plain,
( inverse(sk_c9) = sk_c9
| sk_c3 = sk_c9
| sk_c3 = sk_c9 ),
inference(paramod,[status(thm)],[c_7947,c_8220]) ).
cnf(c_8585,plain,
( inverse(sk_c9) = sk_c9
| sk_c3 = sk_c9 ),
inference(copy,[status(thm)],[c_8963]) ).
cnf(c_8964,plain,
( sk_c1 = sk_c9
| inverse(sk_c9) = sk_c9
| inverse(sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_8490,c_8196]) ).
cnf(c_8712,plain,
( sk_c1 = sk_c9
| inverse(sk_c9) = sk_c9 ),
inference(copy,[status(thm)],[c_8964]) ).
cnf(c_8965,plain,
( sk_c4 = sk_c9
| inverse(sk_c9) = sk_c9
| inverse(sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_8585,c_7070]) ).
cnf(c_8756,plain,
( sk_c4 = sk_c9
| inverse(sk_c9) = sk_c9 ),
inference(copy,[status(thm)],[c_8965]) ).
cnf(c_8966,plain,
( A != sk_c9
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8186]) ).
cnf(c_8967,plain,
( inverse(inverse(sk_c9)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8
| sk_c1 = sk_c9 ),
inference(resolve,[status(thm)],[c_8712,c_8966]) ).
cnf(c_8968,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8
| sk_c1 = sk_c9 ),
inference(paramod,[status(thm)],[c_6164,c_8967]) ).
cnf(c_8801,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c1 = sk_c9 ),
inference(copy,[status(thm)],[c_8968]) ).
cnf(c_8969,plain,
( A != sk_c9
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_8186]) ).
cnf(c_8970,plain,
( inverse(inverse(sk_c9)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8
| sk_c4 = sk_c9 ),
inference(resolve,[status(thm)],[c_8756,c_8969]) ).
cnf(c_8971,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_6164,c_8970]) ).
cnf(c_8811,plain,
( inverse(inverse(sk_c9)) != sk_c9
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_8971]) ).
cnf(c_8972,plain,
multiply(A,sk_c8) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_239,c_6145]) ).
cnf(c_8973,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_6145,c_8972]) ).
cnf(c_8861,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_8973]) ).
cnf(c_8974,plain,
( sk_c9 != sk_c9
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_8861,c_8811]) ).
cnf(c_8894,plain,
sk_c4 = sk_c9,
inference(copy,[status(thm)],[c_8974]) ).
cnf(c_8975,plain,
( sk_c9 != sk_c9
| sk_c1 = sk_c9 ),
inference(paramod,[status(thm)],[c_8861,c_8801]) ).
cnf(c_8896,plain,
sk_c1 = sk_c9,
inference(copy,[status(thm)],[c_8975]) ).
cnf(c_8976,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(inverse(sk_c4)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_8894,c_8292]) ).
cnf(c_8977,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(inverse(sk_c4)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6164,c_8976]) ).
cnf(c_8978,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8894,c_8977]) ).
cnf(c_8979,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8861,c_8978]) ).
cnf(c_8980,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8896,c_8979]) ).
cnf(c_8981,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c9 != sk_c9 ),
inference(copy,[status(thm)],[c_8980]) ).
cnf(c_8903,plain,
multiply(sk_c9,sk_c9) = sk_c8,
inference(copy,[status(thm)],[c_8981]) ).
cnf(c_8982,plain,
( inverse(sk_c4) = sk_c9
| inverse(inverse(sk_c1)) != sk_c9
| multiply(inverse(sk_c9),sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_8896,c_8289]) ).
cnf(c_8983,plain,
( inverse(sk_c4) = sk_c9
| inverse(inverse(sk_c1)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_6164,c_8982]) ).
cnf(c_8984,plain,
( inverse(sk_c4) = sk_c9
| inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8896,c_8983]) ).
cnf(c_8985,plain,
( inverse(sk_c4) = sk_c9
| sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8861,c_8984]) ).
cnf(c_8986,plain,
( inverse(sk_c9) = sk_c9
| sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8894,c_8985]) ).
cnf(c_8987,plain,
( inverse(sk_c9) = sk_c9
| sk_c9 != sk_c9 ),
inference(copy,[status(thm)],[c_8986]) ).
cnf(c_8904,plain,
inverse(sk_c9) = sk_c9,
inference(copy,[status(thm)],[c_8987]) ).
cnf(c_8988,plain,
( inverse(sk_c9) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8903,c_7862]) ).
cnf(c_8989,plain,
( sk_c9 != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_8904,c_8988]) ).
cnf(c_8990,plain,
sk_c9 != sk_c9,
inference(copy,[status(thm)],[c_8989]) ).
cnf(c_8905,plain,
$false,
inference(copy,[status(thm)],[c_8990]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP247-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:42:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 417044 was started by sandbox on n003,
% 0.08/0.36 % Fri Sep 25 14:42:22 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 19.02/5.73
% 19.02/5.73 % SZS status Unsatisfiable for theBenchmark
% 19.02/5.73
% 19.02/5.73 % Proof 1 at 2.16 (+ 0.55) seconds.
% 19.02/5.73 % Length of proof is 98.
% 19.02/5.73 % Level of proof is 24.
% 19.02/5.73 % Maximum clause weight is 58.000.
% 19.02/5.73 % Given clauses 402.
% 19.02/5.73
% 19.02/5.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------