%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP219-1 : 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 07:28:23 AM UTC 2026
% Result : Unsatisfiable 251.56s 38.57s
% Output : CNFRefutation 251.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 130 ( 22 unt; 0 def)
% Number of atoms : 362 ( 361 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 395 ( 163 ~; 232 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 12 !; 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_9,axiom,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_23,axiom,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c7) = sk_c8
| multiply(sk_c9,sk_c5) = sk_c8 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_27,axiom,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c7) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c5 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_31,axiom,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
fof(prove_this_32,axiom,
( inverse(sk_c7) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c4) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_33,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( inverse(VAR_6) != sk_c8
| multiply(VAR_6,sk_c8) != sk_c9
| multiply(VAR_5,sk_c8) != sk_c9
| inverse(VAR_5) != sk_c9
| inverse(VAR_4) != sk_c9
| multiply(VAR_4,sk_c9) != VAR_3
| multiply(sk_c9,VAR_3) != sk_c8
| multiply(VAR_2,sk_c9) != sk_c8
| inverse(VAR_1) != VAR_2
| multiply(VAR_1,VAR_2) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c9
| inverse(VAR_0) != sk_c9 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( inverse(V6) != sk_c8
| multiply(V6,sk_c8) != sk_c9
| multiply(F,sk_c8) != sk_c9
| inverse(F) != sk_c9
| inverse(E) != sk_c9
| multiply(E,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| multiply(C,sk_c9) != sk_c8
| inverse(B) != C
| multiply(B,C) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
cnf(c_38,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != sk_c9
| multiply(E,sk_c8) != sk_c9
| inverse(E) != sk_c9
| multiply(A,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| multiply(C,sk_c9) != sk_c8
| inverse(B) != C
| multiply(B,C) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_34651,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c9
| multiply(A,sk_c8) != sk_c9
| multiply(A,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| multiply(C,sk_c9) != sk_c8
| inverse(B) != C
| multiply(B,C) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(factor,[status(thm)],[c_38]) ).
cnf(c_43,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c9
| multiply(A,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| multiply(C,sk_c9) != sk_c8
| inverse(B) != C
| multiply(B,C) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(copy,[status(thm)],[c_34651]) ).
cnf(c_59,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c9) != D
| multiply(sk_c9,D) != sk_c8
| multiply(C,sk_c9) != sk_c8
| inverse(B) != C
| multiply(B,C) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(factor,[status(thm)],[c_43]) ).
cnf(c_34652,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_34653,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_34652]) ).
cnf(c_116,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_34653]) ).
cnf(c_127,plain,
( multiply(sk_c9,sk_c6) = identity
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_132,plain,
( multiply(sk_c8,sk_c7) = identity
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_154,plain,
( multiply(sk_c8,sk_c7) = identity
| multiply(sk_c4,sk_c9) = sk_c5 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_4590,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_116]) ).
cnf(c_4632,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_116,c_116]) ).
cnf(c_4641,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_4632,c_4590]) ).
cnf(c_4707,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_4641,c_2]) ).
cnf(c_34654,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(identity,sk_c9) != sk_c8
| multiply(identity,identity) != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(resolve,[status(thm)],[c_4707,c_59]) ).
cnf(c_34655,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| multiply(identity,sk_c9) != sk_c8
| identity != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(paramod,[status(thm)],[c_4641,c_34654]) ).
cnf(c_34656,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| sk_c9 != sk_c8
| identity != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_34655]) ).
cnf(c_4811,plain,
( inverse(A) != sk_c8
| multiply(A,sk_c9) != B
| multiply(sk_c9,B) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| multiply(A,sk_c8) != sk_c9
| inverse(A) != sk_c9 ),
inference(copy,[status(thm)],[c_34656]) ).
cnf(c_5982,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_4632,c_2]) ).
cnf(c_34657,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_4632,c_4641]) ).
cnf(c_34658,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_4641,c_34657]) ).
cnf(c_6046,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_34658]) ).
cnf(c_6450,plain,
( multiply(sk_c2,sk_c3) = identity
| inverse(sk_c6) = sk_c9 ),
inference(paramod,[status(thm)],[c_16,c_5982]) ).
cnf(c_6451,plain,
( multiply(sk_c2,sk_c3) = identity
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_17,c_5982]) ).
cnf(c_6452,plain,
( multiply(sk_c2,sk_c3) = identity
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_18,c_5982]) ).
cnf(c_6453,plain,
( multiply(sk_c2,sk_c3) = identity
| inverse(sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_19,c_5982]) ).
cnf(c_6457,plain,
( multiply(sk_c7,sk_c8) = identity
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_27,c_5982]) ).
cnf(c_6462,plain,
( multiply(sk_c4,sk_c9) = identity
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_34,c_5982]) ).
cnf(c_6463,plain,
( multiply(sk_c4,sk_c9) = identity
| inverse(sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_35,c_5982]) ).
cnf(c_11499,plain,
( multiply(sk_c9,sk_c6) = identity
| multiply(sk_c2,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_6450,c_2]) ).
cnf(c_11599,plain,
( multiply(sk_c8,sk_c7) = identity
| multiply(sk_c2,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_6453,c_2]) ).
cnf(c_12029,plain,
( multiply(sk_c8,sk_c7) = identity
| multiply(sk_c4,sk_c9) = identity ),
inference(paramod,[status(thm)],[c_6463,c_2]) ).
cnf(c_34659,plain,
( inverse(identity) != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| multiply(identity,sk_c8) != sk_c9
| inverse(identity) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_4811]) ).
cnf(c_34660,plain,
( inverse(identity) != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| multiply(identity,sk_c8) != sk_c9
| identity != sk_c9 ),
inference(paramod,[status(thm)],[c_4707,c_34659]) ).
cnf(c_34661,plain,
( inverse(identity) != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_34660]) ).
cnf(c_34662,plain,
( identity != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| sk_c8 != sk_c9
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(paramod,[status(thm)],[c_4707,c_34661]) ).
cnf(c_34663,plain,
( identity != sk_c8
| sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_34662]) ).
cnf(c_19152,plain,
( sk_c9 != A
| multiply(sk_c9,A) != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_34663]) ).
cnf(c_34664,plain,
( sk_c9 != identity
| sk_c9 != sk_c8
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(paramod,[status(thm)],[c_4641,c_19152]) ).
cnf(c_34665,plain,
( sk_c9 != identity
| sk_c8 != sk_c9
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_34664]) ).
cnf(c_34666,plain,
( identity != sk_c9
| sk_c8 != sk_c9
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_34665]) ).
cnf(c_34667,plain,
( identity != sk_c9
| identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_34666]) ).
cnf(c_19158,plain,
( identity != sk_c8
| sk_c8 != sk_c9
| identity != sk_c9 ),
inference(copy,[status(thm)],[c_34667]) ).
cnf(c_34668,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| identity = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_6451,c_13]) ).
cnf(c_22184,plain,
( identity = sk_c8
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(copy,[status(thm)],[c_34668]) ).
cnf(c_22189,plain,
( multiply(inverse(sk_c6),sk_c9) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_22184,c_116]) ).
cnf(c_34669,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_6452,c_14]) ).
cnf(c_22231,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(copy,[status(thm)],[c_34669]) ).
cnf(c_34670,plain,
( identity = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_6457,c_26]) ).
cnf(c_22359,plain,
( identity = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(copy,[status(thm)],[c_34670]) ).
cnf(c_22370,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c5
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_22359,c_116]) ).
cnf(c_34671,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| identity = sk_c5
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_6462,c_30]) ).
cnf(c_22607,plain,
( identity = sk_c5
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(copy,[status(thm)],[c_34671]) ).
cnf(c_34672,plain,
( multiply(sk_c9,sk_c6) = identity
| identity = sk_c8
| multiply(sk_c9,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_11499,c_127]) ).
cnf(c_23917,plain,
( identity = sk_c8
| multiply(sk_c9,sk_c6) = identity ),
inference(copy,[status(thm)],[c_34672]) ).
cnf(c_34673,plain,
( multiply(inverse(sk_c9),identity) = sk_c6
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_23917,c_116]) ).
cnf(c_23921,plain,
( inverse(sk_c9) = sk_c6
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_4641,c_34673]) ).
cnf(c_23936,plain,
( inverse(sk_c6) = sk_c9
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_23921,c_6046]) ).
cnf(c_34674,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_23936,c_22189]) ).
cnf(c_24016,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_34674]) ).
cnf(c_34675,plain,
( multiply(sk_c8,sk_c7) = identity
| identity = sk_c8
| multiply(sk_c8,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_11599,c_132]) ).
cnf(c_24250,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c7) = identity ),
inference(copy,[status(thm)],[c_34675]) ).
cnf(c_34676,plain,
( multiply(inverse(sk_c8),identity) = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_24250,c_116]) ).
cnf(c_24254,plain,
( inverse(sk_c8) = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_4641,c_34676]) ).
cnf(c_24262,plain,
( multiply(sk_c7,sk_c8) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_24254,c_2]) ).
cnf(c_34677,plain,
( identity = sk_c8
| identity = sk_c9
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_24262,c_22231]) ).
cnf(c_24288,plain,
( identity = sk_c9
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_34677]) ).
cnf(c_24290,plain,
( multiply(A,sk_c8) = A
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_24288,c_4641]) ).
cnf(c_34678,plain,
( inverse(sk_c9) = sk_c5
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_24290,c_22370]) ).
cnf(c_24480,plain,
( inverse(sk_c9) = sk_c5
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_34678]) ).
cnf(c_24606,plain,
( inverse(sk_c5) = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_24480,c_6046]) ).
cnf(c_34679,plain,
( multiply(sk_c8,sk_c7) = identity
| identity = sk_c5
| multiply(sk_c8,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_12029,c_154]) ).
cnf(c_31106,plain,
( identity = sk_c5
| multiply(sk_c8,sk_c7) = identity ),
inference(copy,[status(thm)],[c_34679]) ).
cnf(c_34680,plain,
( multiply(inverse(sk_c8),identity) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_31106,c_116]) ).
cnf(c_31126,plain,
( inverse(sk_c8) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_4641,c_34680]) ).
cnf(c_31147,plain,
( multiply(sk_c7,sk_c8) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_31126,c_2]) ).
cnf(c_34681,plain,
( identity = sk_c5
| identity = sk_c9
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_31147,c_22607]) ).
cnf(c_31189,plain,
( identity = sk_c9
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_34681]) ).
cnf(c_31194,plain,
( inverse(sk_c5) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_31189,c_4707]) ).
cnf(c_34682,plain,
( identity = sk_c9
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_31194,c_24606]) ).
cnf(c_34683,plain,
( identity = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_34682]) ).
cnf(c_31312,plain,
identity = sk_c9,
inference(copy,[status(thm)],[c_34683]) ).
cnf(c_34684,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c9 = sk_c8 ),
inference(paramod,[status(thm)],[c_31312,c_24016]) ).
cnf(c_33188,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_34684]) ).
cnf(c_34685,plain,
( identity != sk_c8
| sk_c8 != sk_c9
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_31312,c_19158]) ).
cnf(c_34686,plain,
( sk_c9 != sk_c8
| sk_c8 != sk_c9
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_31312,c_34685]) ).
cnf(c_34687,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9
| sk_c9 != sk_c9 ),
inference(copy,[status(thm)],[c_34686]) ).
cnf(c_34688,plain,
( sk_c8 != sk_c9
| sk_c8 != sk_c9 ),
inference(copy,[status(thm)],[c_34687]) ).
cnf(c_33884,plain,
sk_c8 != sk_c9,
inference(copy,[status(thm)],[c_34688]) ).
cnf(c_34610,plain,
multiply(A,sk_c9) = A,
inference(paramod,[status(thm)],[c_31312,c_4641]) ).
cnf(c_34689,plain,
( sk_c9 = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_34610,c_33188]) ).
cnf(c_34690,plain,
( sk_c8 = sk_c9
| sk_c8 = sk_c9 ),
inference(copy,[status(thm)],[c_34689]) ).
cnf(c_34691,plain,
sk_c8 = sk_c9,
inference(copy,[status(thm)],[c_34690]) ).
cnf(c_34650,plain,
$false,
inference(resolve,[status(thm)],[c_33884,c_34691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP219-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.65 % Computer : n013.cluster.edu
% 0.17/5.65 % Model : x86_64 x86_64
% 0.17/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.65 % Memory : 8046.5625MB
% 0.17/5.65 % OS : Linux 6.8.0-71-generic
% 0.17/5.65 % CPULimit : 300
% 0.17/5.65 % WCLimit : 300
% 0.17/5.65 % DateTime : Fri Sep 25 14:38:27 UTC 2026
% 0.17/5.66 % CPUTime :
% 0.17/5.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.66 % Process 644135 was started by sandbox2 on n013,
% 0.17/5.66 % Fri Sep 25 14:38:27 2026
% 0.17/5.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.66
% 0.17/5.66 % From the command line: assign(max_seconds, 300).
% 251.56/38.57
% 251.56/38.57 % given #500 (F,wt=28): 18197 multiply(inverse(sk_c9),sk_c8) != sk_c9 | inverse(A) != sk_c8 | inverse(multiply(A,B)) != inverse(B) | multiply(inverse(multiply(A,B)),sk_c9) != sk_c8 | sk_c8 != sk_c9. [para(116(a,1),17815(c,1,1)),flip(b),flip(c)].
% 251.56/38.57
% 251.56/38.57 % given #1000 (T,wt=6): 26174 sk_c5 = sk_c4 | identity = sk_c6. [para(25122(b,1),24550(b,1)),merge(b)].
% 251.56/38.57
% 251.56/38.57 % SZS status Unsatisfiable for theBenchmark
% 251.56/38.57
% 251.56/38.57 % Proof 1 at 25.45 (+ 6.54) seconds.
% 251.56/38.57 % Length of proof is 71.
% 251.56/38.57 % Level of proof is 15.
% 251.56/38.57 % Maximum clause weight is 55.000.
% 251.56/38.57 % Given clauses 1447.
% 251.56/38.57
% 251.56/38.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------