%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP271-1 : 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 : n019.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 07:28:31 AM UTC 2026
% Result : Unsatisfiable 37.40s 5.13s
% Output : CNFRefutation 37.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 18
% Syntax : Number of formulae : 185 ( 29 unt; 0 def)
% Number of atoms : 509 ( 508 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 538 ( 214 ~; 324 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 13 !; 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_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_11,axiom,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_16,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_25,axiom,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_29,axiom,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_33,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_34,axiom,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_34) ).
cnf(c_37,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_34]) ).
fof(prove_this_43,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('theBenchmark.p',prove_this_43) ).
cnf(c_46,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_43]) ).
fof(prove_this_44,axiom,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('theBenchmark.p',prove_this_44) ).
cnf(c_47,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_44]) ).
fof(prove_this_51,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( multiply(VAR_6,VAR_5) != VAR_7
| inverse(VAR_7) != VAR_5
| inverse(VAR_6) != VAR_7
| multiply(VAR_5,sk_c10) != sk_c11
| inverse(VAR_4) != VAR_5
| multiply(VAR_4,VAR_5) != sk_c11
| inverse(VAR_3) != sk_c10
| multiply(VAR_3,sk_c10) != sk_c9
| inverse(VAR_2) != sk_c11
| multiply(VAR_2,sk_c11) != sk_c10
| inverse(VAR_1) != sk_c10
| multiply(VAR_1,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(VAR_0) != sk_c11
| multiply(VAR_0,sk_c11) != sk_c10 ),
file('theBenchmark.p',prove_this_51) ).
cnf(c_54,plain,
( multiply(V6,F) != V7
| inverse(V7) != F
| inverse(V6) != V7
| multiply(F,sk_c10) != sk_c11
| inverse(E) != F
| multiply(E,F) != sk_c11
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| inverse(C) != sk_c11
| multiply(C,sk_c11) != sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(clausify,[status(thm)],[prove_this_51]) ).
cnf(c_5641,plain,
( multiply(F,E) != V6
| inverse(V6) != E
| inverse(F) != V6
| multiply(E,sk_c10) != sk_c11
| inverse(D) != E
| multiply(D,E) != sk_c11
| inverse(C) != sk_c10
| multiply(C,sk_c10) != sk_c9
| inverse(A) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_54]) ).
cnf(c_55,plain,
( multiply(F,E) != V6
| inverse(V6) != E
| inverse(F) != V6
| multiply(E,sk_c10) != sk_c11
| inverse(D) != E
| multiply(D,E) != sk_c11
| inverse(C) != sk_c10
| multiply(C,sk_c10) != sk_c9
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_5641]) ).
cnf(c_57,plain,
( inverse(sk_c10) != sk_c11
| inverse(A) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| inverse(D) != sk_c11
| multiply(D,sk_c11) != sk_c11
| inverse(C) != sk_c10
| multiply(C,sk_c10) != sk_c9
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_55]) ).
cnf(c_5642,plain,
( inverse(sk_c10) != sk_c11
| inverse(A) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| inverse(C) != sk_c11
| multiply(C,sk_c11) != sk_c11
| inverse(B) != sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_57]) ).
cnf(c_64,plain,
( inverse(sk_c10) != sk_c11
| inverse(A) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| inverse(C) != sk_c11
| multiply(C,sk_c11) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(copy,[status(thm)],[c_5642]) ).
cnf(c_83,plain,
( inverse(sk_c10) != sk_c11
| inverse(A) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(A,sk_c11) != sk_c11
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(A) != sk_c11
| multiply(A,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_64]) ).
cnf(c_124,plain,
( inverse(sk_c10) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c11
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c10 ),
inference(factor,[status(thm)],[c_83]) ).
cnf(c_5643,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_5644,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_5643]) ).
cnf(c_155,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_5644]) ).
cnf(c_194,plain,
( multiply(sk_c11,sk_c1) = identity
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_204,plain,
( multiply(sk_c11,sk_c1) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_205,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c1) = sk_c11 ),
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_5645,plain,
( multiply(sk_c11,A) = multiply(sk_c5,multiply(sk_c8,A))
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_28,c_3]) ).
cnf(c_232,plain,
( multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c11,A)
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(copy,[status(thm)],[c_5645]) ).
cnf(c_5646,plain,
( multiply(sk_c10,A) = multiply(sk_c11,multiply(sk_c9,A))
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_29,c_3]) ).
cnf(c_235,plain,
( multiply(sk_c11,multiply(sk_c9,A)) = multiply(sk_c10,A)
| inverse(sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_5646]) ).
cnf(c_244,plain,
( multiply(sk_c8,sk_c6) = identity
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_32,c_2]) ).
cnf(c_5647,plain,
( multiply(multiply(A,sk_c7),sk_c8) = multiply(A,sk_c6)
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_33,c_3]) ).
cnf(c_250,plain,
( multiply(A,multiply(sk_c7,sk_c8)) = multiply(A,sk_c6)
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_3,c_5647]) ).
cnf(c_262,plain,
( multiply(sk_c10,sk_c4) = identity
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_37,c_2]) ).
cnf(c_291,plain,
( multiply(sk_c10,sk_c2) = identity
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_46,c_2]) ).
cnf(c_294,plain,
( multiply(sk_c10,sk_c2) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_47,c_2]) ).
cnf(c_312,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_155]) ).
cnf(c_414,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_155,c_155]) ).
cnf(c_415,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_414,c_312]) ).
cnf(c_421,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_415,c_2]) ).
cnf(c_5648,plain,
( multiply(inverse(sk_c11),identity) = sk_c1
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_194,c_155]) ).
cnf(c_429,plain,
( inverse(sk_c11) = sk_c1
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_415,c_5648]) ).
cnf(c_432,plain,
( multiply(sk_c1,sk_c11) = identity
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_429,c_2]) ).
cnf(c_5649,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c1) = sk_c11 ),
inference(paramod,[status(thm)],[c_205,c_155]) ).
cnf(c_652,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c1) = sk_c11 ),
inference(paramod,[status(thm)],[c_415,c_5649]) ).
cnf(c_656,plain,
( multiply(sk_c5,sk_c8) = identity
| inverse(sk_c1) = sk_c11 ),
inference(paramod,[status(thm)],[c_652,c_2]) ).
cnf(c_5650,plain,
( multiply(inverse(sk_c10),identity) = sk_c2
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_294,c_155]) ).
cnf(c_926,plain,
( inverse(sk_c10) = sk_c2
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_415,c_5650]) ).
cnf(c_932,plain,
( multiply(sk_c10,sk_c4) = identity
| inverse(sk_c10) = sk_c2 ),
inference(paramod,[status(thm)],[c_926,c_2]) ).
cnf(c_5651,plain,
( inverse(sk_c3) = sk_c11
| identity = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(paramod,[status(thm)],[c_432,c_5]) ).
cnf(c_1295,plain,
( identity = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(copy,[status(thm)],[c_5651]) ).
cnf(c_1304,plain,
( multiply(sk_c11,sk_c3) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1295,c_2]) ).
cnf(c_5652,plain,
( multiply(inverse(sk_c11),identity) = sk_c3
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1304,c_155]) ).
cnf(c_1322,plain,
( inverse(sk_c11) = sk_c3
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_415,c_5652]) ).
cnf(c_1369,plain,
( multiply(sk_c3,sk_c11) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1322,c_2]) ).
cnf(c_5653,plain,
( identity = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1369,c_4]) ).
cnf(c_1497,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_5653]) ).
cnf(c_5654,plain,
( identity = sk_c10
| inverse(sk_c1) = sk_c11
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1369,c_14]) ).
cnf(c_1498,plain,
( inverse(sk_c1) = sk_c11
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_5654]) ).
cnf(c_1534,plain,
( multiply(sk_c11,sk_c1) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1498,c_2]) ).
cnf(c_5655,plain,
( multiply(inverse(sk_c11),identity) = sk_c1
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_1534,c_155]) ).
cnf(c_2254,plain,
( inverse(sk_c11) = sk_c1
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_415,c_5655]) ).
cnf(c_2270,plain,
( multiply(sk_c1,sk_c11) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_2254,c_2]) ).
cnf(c_5656,plain,
( identity = sk_c10
| identity = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_2270,c_1497]) ).
cnf(c_5657,plain,
( identity = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_5656]) ).
cnf(c_3228,plain,
identity = sk_c10,
inference(copy,[status(thm)],[c_5657]) ).
cnf(c_3555,plain,
( multiply(sk_c10,sk_c4) = sk_c10
| inverse(sk_c10) = sk_c2 ),
inference(paramod,[status(thm)],[c_3228,c_932]) ).
cnf(c_3617,plain,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(paramod,[status(thm)],[c_3228,c_656]) ).
cnf(c_5658,plain,
inverse(sk_c10) = identity,
inference(paramod,[status(thm)],[c_3228,c_421]) ).
cnf(c_3797,plain,
inverse(sk_c10) = sk_c10,
inference(paramod,[status(thm)],[c_3228,c_5658]) ).
cnf(c_3798,plain,
multiply(A,sk_c10) = A,
inference(paramod,[status(thm)],[c_3228,c_415]) ).
cnf(c_5659,plain,
( multiply(sk_c10,sk_c2) = identity
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_3798,c_291]) ).
cnf(c_3806,plain,
( multiply(sk_c10,sk_c2) = sk_c10
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_3228,c_5659]) ).
cnf(c_5660,plain,
( multiply(sk_c10,sk_c4) = identity
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_3798,c_262]) ).
cnf(c_3810,plain,
( multiply(sk_c10,sk_c4) = sk_c10
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_3228,c_5660]) ).
cnf(c_3812,plain,
( multiply(sk_c8,sk_c6) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_3228,c_244]) ).
cnf(c_3820,plain,
( multiply(sk_c11,sk_c1) = sk_c10
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_3228,c_204]) ).
cnf(c_3825,plain,
multiply(sk_c10,A) = A,
inference(paramod,[status(thm)],[c_3228,c_1]) ).
cnf(c_5661,plain,
( multiply(sk_c10,sk_c4) = sk_c10
| sk_c10 = sk_c2 ),
inference(paramod,[status(thm)],[c_3797,c_3555]) ).
cnf(c_5662,plain,
( sk_c4 = sk_c10
| sk_c10 = sk_c2 ),
inference(paramod,[status(thm)],[c_3825,c_5661]) ).
cnf(c_3857,plain,
( sk_c4 = sk_c10
| sk_c2 = sk_c10 ),
inference(copy,[status(thm)],[c_5662]) ).
cnf(c_5663,plain,
( inverse(sk_c10) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c11
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c11
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_3825,c_124]) ).
cnf(c_5664,plain,
( inverse(sk_c10) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c11
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c10 != sk_c11
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_3797,c_5663]) ).
cnf(c_5665,plain,
( inverse(sk_c10) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c11
| inverse(A) != sk_c10
| A != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c10 != sk_c11
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_5664]) ).
cnf(c_5666,plain,
( inverse(sk_c10) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c11
| sk_c11 != sk_c11
| inverse(A) != sk_c10
| A != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c10 != sk_c11
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_3825,c_5665]) ).
cnf(c_5667,plain,
( inverse(sk_c10) != sk_c10
| sk_c11 != sk_c11
| sk_c11 != sk_c11
| inverse(A) != sk_c10
| A != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c10 != sk_c11
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_5666]) ).
cnf(c_5668,plain,
( sk_c10 != sk_c10
| sk_c11 != sk_c11
| sk_c11 != sk_c11
| inverse(A) != sk_c10
| A != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c10 != sk_c11
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_3797,c_5667]) ).
cnf(c_5669,plain,
( sk_c10 != sk_c10
| sk_c11 != sk_c11
| sk_c11 != sk_c11
| inverse(A) != sk_c10
| A != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(copy,[status(thm)],[c_5668]) ).
cnf(c_5670,plain,
( sk_c10 != sk_c10
| sk_c11 != sk_c11
| sk_c11 != sk_c11
| inverse(A) != sk_c10
| sk_c9 != A
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(copy,[status(thm)],[c_5669]) ).
cnf(c_5671,plain,
( sk_c10 != sk_c10
| sk_c11 != sk_c11
| inverse(A) != sk_c10
| sk_c9 != A
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(copy,[status(thm)],[c_5670]) ).
cnf(c_5672,plain,
( sk_c10 != sk_c10
| inverse(A) != sk_c10
| sk_c9 != A
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(copy,[status(thm)],[c_5671]) ).
cnf(c_5673,plain,
( inverse(A) != sk_c10
| sk_c9 != A
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(copy,[status(thm)],[c_5672]) ).
cnf(c_3887,plain,
( inverse(A) != sk_c10
| sk_c9 != A
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c11 != sk_c10 ),
inference(copy,[status(thm)],[c_5673]) ).
cnf(c_5674,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_3798,c_36]) ).
cnf(c_4383,plain,
( sk_c4 = sk_c9
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_3798,c_5674]) ).
cnf(c_4385,plain,
( sk_c8 = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_30]) ).
cnf(c_4388,plain,
( sk_c4 = sk_c10
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_3825,c_3810]) ).
cnf(c_4389,plain,
( sk_c2 = sk_c10
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_3825,c_3806]) ).
cnf(c_4527,plain,
( multiply(sk_c11,multiply(sk_c9,A)) = A
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_3825,c_235]) ).
cnf(c_5675,plain,
B = multiply(inverse(A),multiply(A,B)),
inference(copy,[status(thm)],[c_155]) ).
cnf(c_5676,plain,
( inverse(multiply(inverse(A),multiply(A,sk_c9))) != sk_c10
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c11 != sk_c10 ),
inference(resolve,[status(thm)],[c_3887,c_5675]) ).
cnf(c_4591,plain,
( inverse(sk_c9) != sk_c10
| multiply(sk_c11,sk_c9) != sk_c10
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_155,c_5676]) ).
cnf(c_5677,plain,
( sk_c10 = sk_c9
| sk_c2 = sk_c9
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_4388,c_4383]) ).
cnf(c_5678,plain,
( sk_c9 = sk_c10
| sk_c2 = sk_c9
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_5677]) ).
cnf(c_4944,plain,
( sk_c9 = sk_c10
| sk_c2 = sk_c9 ),
inference(copy,[status(thm)],[c_5678]) ).
cnf(c_5679,plain,
( multiply(sk_c5,multiply(sk_c8,sk_c6)) = multiply(sk_c11,multiply(sk_c7,sk_c8))
| multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_250,c_232]) ).
cnf(c_5680,plain,
( multiply(sk_c11,multiply(sk_c7,sk_c8)) = multiply(sk_c5,multiply(sk_c8,sk_c6))
| multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(copy,[status(thm)],[c_5679]) ).
cnf(c_4988,plain,
( multiply(sk_c11,multiply(sk_c7,sk_c8)) = multiply(sk_c5,multiply(sk_c8,sk_c6))
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(copy,[status(thm)],[c_5680]) ).
cnf(c_5681,plain,
( sk_c9 = sk_c10
| sk_c2 = sk_c10
| sk_c2 = sk_c10 ),
inference(paramod,[status(thm)],[c_4389,c_3857]) ).
cnf(c_5075,plain,
( sk_c9 = sk_c10
| sk_c2 = sk_c10 ),
inference(copy,[status(thm)],[c_5681]) ).
cnf(c_5682,plain,
( sk_c9 = sk_c10
| sk_c10 = sk_c9
| sk_c9 = sk_c10 ),
inference(paramod,[status(thm)],[c_5075,c_4944]) ).
cnf(c_5683,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_5682]) ).
cnf(c_5684,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_5683]) ).
cnf(c_5165,plain,
sk_c9 = sk_c10,
inference(copy,[status(thm)],[c_5684]) ).
cnf(c_5685,plain,
( multiply(sk_c11,multiply(sk_c7,sk_c8)) = multiply(sk_c5,multiply(sk_c8,sk_c6))
| multiply(sk_c11,sk_c10) = sk_c10 ),
inference(paramod,[status(thm)],[c_5165,c_4988]) ).
cnf(c_5211,plain,
( multiply(sk_c11,multiply(sk_c7,sk_c8)) = multiply(sk_c5,multiply(sk_c8,sk_c6))
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_5685]) ).
cnf(c_5686,plain,
( inverse(sk_c9) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c10
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_5165,c_4591]) ).
cnf(c_5687,plain,
( inverse(sk_c9) != sk_c10
| sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_5686]) ).
cnf(c_5688,plain,
( inverse(sk_c10) != sk_c10
| sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_5165,c_5687]) ).
cnf(c_5689,plain,
( sk_c10 != sk_c10
| sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(paramod,[status(thm)],[c_3797,c_5688]) ).
cnf(c_5690,plain,
( sk_c11 != sk_c10
| sk_c11 != sk_c10 ),
inference(copy,[status(thm)],[c_5689]) ).
cnf(c_5387,plain,
sk_c11 != sk_c10,
inference(copy,[status(thm)],[c_5690]) ).
cnf(c_5691,plain,
( multiply(sk_c11,multiply(sk_c10,A)) = A
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_5165,c_4527]) ).
cnf(c_5437,plain,
( multiply(sk_c11,A) = A
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_3825,c_5691]) ).
cnf(c_5692,plain,
( sk_c8 = sk_c11
| multiply(sk_c11,sk_c10) = sk_c10 ),
inference(paramod,[status(thm)],[c_5165,c_4385]) ).
cnf(c_5693,plain,
( sk_c8 = sk_c11
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_5692]) ).
cnf(c_5454,plain,
sk_c8 = sk_c11,
inference(resolve,[status(thm)],[c_5387,c_5693]) ).
cnf(c_5694,plain,
( multiply(sk_c8,sk_c6) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c10 ),
inference(paramod,[status(thm)],[c_5165,c_3812]) ).
cnf(c_5695,plain,
( multiply(sk_c8,sk_c6) = sk_c10
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_5694]) ).
cnf(c_5696,plain,
( multiply(sk_c11,sk_c6) = sk_c10
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_5454,c_5695]) ).
cnf(c_5534,plain,
multiply(sk_c11,sk_c6) = sk_c10,
inference(resolve,[status(thm)],[c_5387,c_5696]) ).
cnf(c_5697,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c11,sk_c10) = sk_c10 ),
inference(paramod,[status(thm)],[c_5165,c_33]) ).
cnf(c_5698,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_5697]) ).
cnf(c_5699,plain,
( multiply(sk_c7,sk_c11) = sk_c6
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_5454,c_5698]) ).
cnf(c_5580,plain,
multiply(sk_c7,sk_c11) = sk_c6,
inference(resolve,[status(thm)],[c_5387,c_5699]) ).
cnf(c_5700,plain,
( multiply(sk_c11,multiply(sk_c7,sk_c11)) = multiply(sk_c5,multiply(sk_c8,sk_c6))
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_5454,c_5211]) ).
cnf(c_5701,plain,
( multiply(sk_c11,sk_c6) = multiply(sk_c5,multiply(sk_c8,sk_c6))
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_5580,c_5700]) ).
cnf(c_5702,plain,
( sk_c10 = multiply(sk_c5,multiply(sk_c8,sk_c6))
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_5534,c_5701]) ).
cnf(c_5703,plain,
( sk_c10 = multiply(sk_c5,multiply(sk_c11,sk_c6))
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_5454,c_5702]) ).
cnf(c_5704,plain,
( sk_c10 = multiply(sk_c5,sk_c10)
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_5534,c_5703]) ).
cnf(c_5705,plain,
( sk_c10 = sk_c5
| sk_c11 = sk_c10 ),
inference(paramod,[status(thm)],[c_3798,c_5704]) ).
cnf(c_5706,plain,
( sk_c5 = sk_c10
| sk_c11 = sk_c10 ),
inference(copy,[status(thm)],[c_5705]) ).
cnf(c_5607,plain,
sk_c5 = sk_c10,
inference(resolve,[status(thm)],[c_5387,c_5706]) ).
cnf(c_5707,plain,
( multiply(sk_c11,A) = A
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_5607,c_5437]) ).
cnf(c_5708,plain,
( multiply(sk_c11,A) = A
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_3797,c_5707]) ).
cnf(c_5709,plain,
( multiply(sk_c11,A) = A
| sk_c10 = sk_c11 ),
inference(paramod,[status(thm)],[c_5454,c_5708]) ).
cnf(c_5710,plain,
( multiply(sk_c11,A) = A
| sk_c11 = sk_c10 ),
inference(copy,[status(thm)],[c_5709]) ).
cnf(c_5635,plain,
multiply(sk_c11,A) = A,
inference(resolve,[status(thm)],[c_5387,c_5710]) ).
cnf(c_5711,plain,
( multiply(sk_c11,sk_c1) = sk_c10
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_5607,c_3820]) ).
cnf(c_5712,plain,
( multiply(sk_c11,sk_c1) = sk_c10
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_3797,c_5711]) ).
cnf(c_5713,plain,
( multiply(sk_c11,sk_c1) = sk_c10
| sk_c10 = sk_c11 ),
inference(paramod,[status(thm)],[c_5454,c_5712]) ).
cnf(c_5714,plain,
( sk_c1 = sk_c10
| sk_c10 = sk_c11 ),
inference(paramod,[status(thm)],[c_5635,c_5713]) ).
cnf(c_5715,plain,
( sk_c1 = sk_c10
| sk_c11 = sk_c10 ),
inference(copy,[status(thm)],[c_5714]) ).
cnf(c_5639,plain,
sk_c1 = sk_c10,
inference(resolve,[status(thm)],[c_5387,c_5715]) ).
cnf(c_5716,plain,
( multiply(sk_c5,sk_c8) = sk_c10
| inverse(sk_c10) = sk_c11 ),
inference(paramod,[status(thm)],[c_5639,c_3617]) ).
cnf(c_5717,plain,
( multiply(sk_c5,sk_c8) = sk_c10
| sk_c10 = sk_c11 ),
inference(paramod,[status(thm)],[c_3797,c_5716]) ).
cnf(c_5718,plain,
( multiply(sk_c10,sk_c8) = sk_c10
| sk_c10 = sk_c11 ),
inference(paramod,[status(thm)],[c_5607,c_5717]) ).
cnf(c_5719,plain,
( multiply(sk_c10,sk_c11) = sk_c10
| sk_c10 = sk_c11 ),
inference(paramod,[status(thm)],[c_5454,c_5718]) ).
cnf(c_5720,plain,
( sk_c11 = sk_c10
| sk_c10 = sk_c11 ),
inference(paramod,[status(thm)],[c_3825,c_5719]) ).
cnf(c_5721,plain,
( sk_c11 = sk_c10
| sk_c11 = sk_c10 ),
inference(copy,[status(thm)],[c_5720]) ).
cnf(c_5722,plain,
sk_c11 = sk_c10,
inference(copy,[status(thm)],[c_5721]) ).
cnf(c_5640,plain,
$false,
inference(resolve,[status(thm)],[c_5387,c_5722]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP271-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n019.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:41:48 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3002370 was started by sandbox2 on n019,
% 0.09/0.35 % Fri Sep 25 14:41:48 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 37.40/5.13
% 37.40/5.13 % SZS status Unsatisfiable for theBenchmark
% 37.40/5.13
% 37.40/5.13 % Proof 1 at 3.62 (+ 1.11) seconds.
% 37.40/5.13 % Length of proof is 85.
% 37.40/5.13 % Level of proof is 26.
% 37.40/5.13 % Maximum clause weight is 72.000.
% 37.40/5.13 % Given clauses 367.
% 37.40/5.13
% 37.40/5.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------