%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP285-1 : 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 : n013.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 3.20s 0.91s
% Output : CNFRefutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 133 ( 32 unt; 0 def)
% Number of atoms : 317 ( 316 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 297 ( 113 ~; 184 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 86 ( 11 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_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_5,axiom,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,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_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_14,axiom,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_21,axiom,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_29,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( inverse(VAR_5) != sk_c9
| multiply(VAR_5,sk_c9) != VAR_4
| multiply(sk_c9,VAR_4) != sk_c7
| inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_2) != sk_c9
| multiply(VAR_2,sk_c9) != sk_c8
| multiply(VAR_1,sk_c9) != sk_c7
| inverse(VAR_0) != sk_c9
| multiply(VAR_0,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(F) != sk_c9
| multiply(F,sk_c9) != E
| multiply(sk_c9,E) != sk_c7
| inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| multiply(B,sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
cnf(c_1560,plain,
( inverse(E) != sk_c9
| multiply(E,sk_c9) != D
| multiply(sk_c9,D) != sk_c7
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(A) != sk_c9
| multiply(B,sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_32]) ).
cnf(c_34,plain,
( inverse(E) != sk_c9
| multiply(E,sk_c9) != D
| multiply(sk_c9,D) != sk_c7
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| multiply(B,sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1560]) ).
cnf(c_1561,plain,
( inverse(A) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| multiply(B,sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_1562,plain,
( inverse(A) != sk_c9
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| multiply(B,sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1561]) ).
cnf(c_36,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| multiply(B,sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1562]) ).
cnf(c_1563,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1564,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1563]) ).
cnf(c_37,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1564]) ).
cnf(c_1565,plain,
( multiply(sk_c8,A) = multiply(sk_c3,multiply(sk_c9,A))
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_38,plain,
( multiply(sk_c3,multiply(sk_c9,A)) = multiply(sk_c8,A)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_1565]) ).
cnf(c_1566,plain,
( multiply(multiply(A,sk_c9),sk_c6) = multiply(A,sk_c7)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_45,plain,
( multiply(A,multiply(sk_c9,sk_c6)) = multiply(A,sk_c7)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_1566]) ).
cnf(c_51,plain,
( multiply(sk_c9,sk_c3) = identity
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_61,plain,
( multiply(sk_c9,sk_c3) = identity
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_97,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c8
| multiply(B,multiply(C,sk_c9)) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_3,c_36]) ).
cnf(c_114,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_37]) ).
cnf(c_144,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_37,c_37]) ).
cnf(c_145,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_144,c_114]) ).
cnf(c_1567,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| multiply(B,identity) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_97]) ).
cnf(c_1568,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| B != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_145,c_1567]) ).
cnf(c_1569,plain,
( inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| sk_c7 != B
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1568]) ).
cnf(c_198,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1569]) ).
cnf(c_212,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_145,c_2]) ).
cnf(c_263,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_144,c_2]) ).
cnf(c_280,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(paramod,[status(thm)],[c_144,c_37]) ).
cnf(c_1570,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_144,c_145]) ).
cnf(c_1571,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_145,c_1570]) ).
cnf(c_281,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_1571]) ).
cnf(c_1572,plain,
( multiply(inverse(sk_c7),sk_c7) != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(resolve,[status(thm)],[c_281,c_198]) ).
cnf(c_287,plain,
( identity != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_1572]) ).
cnf(c_289,plain,
( inverse(sk_c9) = sk_c3
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_281]) ).
cnf(c_291,plain,
( inverse(sk_c9) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_10,c_281]) ).
cnf(c_292,plain,
( inverse(sk_c9) = sk_c3
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_281]) ).
cnf(c_294,plain,
( inverse(sk_c9) = sk_c5
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_17,c_281]) ).
cnf(c_296,plain,
( inverse(sk_c9) = sk_c3
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_19,c_281]) ).
cnf(c_301,plain,
( inverse(sk_c9) = sk_c5
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_24,c_281]) ).
cnf(c_313,plain,
( multiply(sk_c3,sk_c9) = identity
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_263]) ).
cnf(c_316,plain,
( multiply(sk_c3,sk_c9) = identity
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_263]) ).
cnf(c_319,plain,
( multiply(sk_c1,sk_c9) = identity
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_18,c_263]) ).
cnf(c_329,plain,
( multiply(sk_c1,sk_c9) = identity
| multiply(sk_c9,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_61,c_263]) ).
cnf(c_1573,plain,
( identity != sk_c8
| multiply(inverse(sk_c9),sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(resolve,[status(thm)],[c_287,c_281]) ).
cnf(c_1574,plain,
( identity != sk_c8
| identity != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_1573]) ).
cnf(c_339,plain,
( identity != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1574]) ).
cnf(c_360,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(inverse(sk_c8),A))) = A
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_280,c_38]) ).
cnf(c_368,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c9) = sk_c3 ),
inference(paramod,[status(thm)],[c_296,c_281]) ).
cnf(c_386,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c9) = sk_c5 ),
inference(paramod,[status(thm)],[c_301,c_281]) ).
cnf(c_1575,plain,
( inverse(sk_c9) = sk_c1
| sk_c5 = sk_c3
| inverse(sk_c9) = sk_c1 ),
inference(paramod,[status(thm)],[c_386,c_368]) ).
cnf(c_551,plain,
( sk_c5 = sk_c3
| inverse(sk_c9) = sk_c1 ),
inference(copy,[status(thm)],[c_1575]) ).
cnf(c_552,plain,
( multiply(sk_c1,sk_c9) = identity
| sk_c5 = sk_c3 ),
inference(paramod,[status(thm)],[c_551,c_2]) ).
cnf(c_1576,plain,
( sk_c5 = sk_c3
| multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_291,c_289]) ).
cnf(c_637,plain,
( sk_c5 = sk_c3
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_1576]) ).
cnf(c_638,plain,
( identity != sk_c8
| sk_c5 = sk_c3 ),
inference(resolve,[status(thm)],[c_637,c_339]) ).
cnf(c_1577,plain,
( sk_c5 = sk_c3
| multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_294,c_292]) ).
cnf(c_657,plain,
( sk_c5 = sk_c3
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_1577]) ).
cnf(c_1578,plain,
( sk_c8 = identity
| sk_c5 = sk_c3
| sk_c5 = sk_c3 ),
inference(paramod,[status(thm)],[c_657,c_552]) ).
cnf(c_1579,plain,
( identity = sk_c8
| sk_c5 = sk_c3
| sk_c5 = sk_c3 ),
inference(copy,[status(thm)],[c_1578]) ).
cnf(c_661,plain,
( identity = sk_c8
| sk_c5 = sk_c3 ),
inference(copy,[status(thm)],[c_1579]) ).
cnf(c_1580,plain,
( sk_c5 = sk_c3
| sk_c5 = sk_c3 ),
inference(resolve,[status(thm)],[c_661,c_638]) ).
cnf(c_662,plain,
sk_c5 = sk_c3,
inference(copy,[status(thm)],[c_1580]) ).
cnf(c_693,plain,
( multiply(sk_c3,sk_c9) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_662,c_9]) ).
cnf(c_1581,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(sk_c9,sk_c6))) = multiply(sk_c8,sk_c7)
| multiply(sk_c9,sk_c8) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_45,c_38]) ).
cnf(c_699,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(sk_c9,sk_c6))) = multiply(sk_c8,sk_c7)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_1581]) ).
cnf(c_1582,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_316,c_11]) ).
cnf(c_972,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_1582]) ).
cnf(c_1583,plain,
( multiply(sk_c9,sk_c3) = identity
| identity = sk_c8
| multiply(sk_c9,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_329,c_51]) ).
cnf(c_1133,plain,
( identity = sk_c8
| multiply(sk_c9,sk_c3) = identity ),
inference(copy,[status(thm)],[c_1583]) ).
cnf(c_1584,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1133,c_37]) ).
cnf(c_1136,plain,
( inverse(sk_c9) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_145,c_1584]) ).
cnf(c_1139,plain,
( multiply(sk_c3,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1136,c_2]) ).
cnf(c_1585,plain,
( multiply(sk_c1,sk_c9) = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1139,c_319]) ).
cnf(c_1167,plain,
( multiply(sk_c1,sk_c9) = identity
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_1585]) ).
cnf(c_1586,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1167,c_972]) ).
cnf(c_1587,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_1586]) ).
cnf(c_1233,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_1587]) ).
cnf(c_1588,plain,
( sk_c8 != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1233,c_339]) ).
cnf(c_1419,plain,
multiply(sk_c9,sk_c8) != sk_c7,
inference(copy,[status(thm)],[c_1588]) ).
cnf(c_1589,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1233,c_313]) ).
cnf(c_1425,plain,
multiply(sk_c3,sk_c9) = sk_c8,
inference(resolve,[status(thm)],[c_1419,c_1589]) ).
cnf(c_1590,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_1233,c_212]) ).
cnf(c_1435,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_1233,c_1590]) ).
cnf(c_1436,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_1233,c_145]) ).
cnf(c_1445,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_1233,c_1]) ).
cnf(c_1591,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(sk_c9,sk_c6))) = multiply(sk_c8,sk_c7)
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_1436,c_699]) ).
cnf(c_1592,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(sk_c9,sk_c6))) = sk_c7
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_1445,c_1591]) ).
cnf(c_1473,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(sk_c9,sk_c6))) = sk_c7
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_1592]) ).
cnf(c_1593,plain,
( multiply(sk_c3,sk_c9) = sk_c6
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_1436,c_693]) ).
cnf(c_1594,plain,
( sk_c8 = sk_c6
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_1425,c_1593]) ).
cnf(c_1595,plain,
( sk_c8 = sk_c6
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_1594]) ).
cnf(c_1477,plain,
( sk_c6 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_1595]) ).
cnf(c_1596,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(inverse(sk_c8),A))) = A
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_1436,c_360]) ).
cnf(c_1597,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(sk_c8,A))) = A
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_1435,c_1596]) ).
cnf(c_1598,plain,
( multiply(sk_c3,multiply(sk_c9,A)) = A
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_1445,c_1597]) ).
cnf(c_1493,plain,
( multiply(sk_c3,multiply(sk_c9,A)) = A
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_1598]) ).
cnf(c_1599,plain,
sk_c9 != sk_c7,
inference(paramod,[status(thm)],[c_1436,c_1419]) ).
cnf(c_1518,plain,
sk_c7 != sk_c9,
inference(copy,[status(thm)],[c_1599]) ).
cnf(c_1544,plain,
multiply(sk_c3,multiply(sk_c9,A)) = A,
inference(resolve,[status(thm)],[c_1518,c_1493]) ).
cnf(c_1556,plain,
sk_c6 = sk_c8,
inference(resolve,[status(thm)],[c_1518,c_1477]) ).
cnf(c_1600,plain,
( multiply(sk_c3,multiply(sk_c9,multiply(sk_c9,sk_c8))) = sk_c7
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_1556,c_1473]) ).
cnf(c_1601,plain,
( multiply(sk_c3,multiply(sk_c9,sk_c9)) = sk_c7
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_1436,c_1600]) ).
cnf(c_1602,plain,
( sk_c9 = sk_c7
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_1544,c_1601]) ).
cnf(c_1603,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_1602]) ).
cnf(c_1604,plain,
sk_c7 = sk_c9,
inference(copy,[status(thm)],[c_1603]) ).
cnf(c_1559,plain,
$false,
inference(resolve,[status(thm)],[c_1518,c_1604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP285-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n013.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Fri Sep 25 14:42:06 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 652524 was started by sandbox2 on n013,
% 0.19/0.44 % Fri Sep 25 14:42:06 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.44
% 0.19/0.44 % From the command line: assign(max_seconds, 300).
% 3.20/0.91
% 3.20/0.91 % SZS status Unsatisfiable for theBenchmark
% 3.20/0.91
% 3.20/0.91 % Proof 1 at 0.34 (+ 0.11) seconds.
% 3.20/0.91 % Length of proof is 73.
% 3.20/0.91 % Level of proof is 14.
% 3.20/0.91 % Maximum clause weight is 51.000.
% 3.20/0.91 % Given clauses 176.
% 3.20/0.91
% 3.20/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------