%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP257-1 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:29 AM UTC 2026
% Result : Unsatisfiable 19.30s 6.42s
% Output : CNFRefutation 19.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 18
% Syntax : Number of formulae : 178 ( 25 unt; 0 def)
% Number of atoms : 490 ( 489 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 501 ( 189 ~; 312 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 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 : 89 ( 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_1,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_11,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_14,axiom,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_17,axiom,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_19,axiom,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_25,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_43,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) != VAR_5
| multiply(sk_c8,VAR_5) != sk_c9
| inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != sk_c9
| inverse(VAR_3) != sk_c10
| multiply(VAR_3,sk_c10) != sk_c9
| multiply(VAR_2,sk_c9) != sk_c8
| inverse(VAR_2) != sk_c8
| inverse(VAR_1) != sk_c9
| multiply(VAR_1,sk_c9) != sk_c8
| inverse(VAR_0) != sk_c10
| multiply(VAR_0,sk_c10) != sk_c9 ),
file('theBenchmark.p',prove_this_43) ).
cnf(c_46,plain,
( inverse(V6) != sk_c8
| multiply(V6,sk_c8) != F
| multiply(sk_c8,F) != sk_c9
| inverse(E) != sk_c8
| multiply(E,sk_c8) != sk_c9
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(C,sk_c9) != sk_c8
| inverse(C) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(clausify,[status(thm)],[prove_this_43]) ).
cnf(c_5756,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c9
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(C,sk_c9) != sk_c8
| inverse(C) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_46]) ).
cnf(c_47,plain,
( inverse(F) != sk_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c9
| inverse(D) != sk_c8
| multiply(D,sk_c8) != sk_c9
| multiply(C,sk_c9) != sk_c8
| inverse(C) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5756]) ).
cnf(c_54,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c9
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(B) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_70,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c9
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_54]) ).
cnf(c_86,plain,
( multiply(B,sk_c8) != C
| multiply(sk_c8,C) != sk_c9
| multiply(B,sk_c8) != sk_c9
| inverse(B) != sk_c8
| inverse(B) != sk_c9
| multiply(B,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_70]) ).
cnf(c_5757,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_5758,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_5757]) ).
cnf(c_94,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_5758]) ).
cnf(c_123,plain,
( multiply(sk_c10,sk_c1) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_129,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_137,plain,
( multiply(sk_c8,sk_c6) = identity
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_5759,plain,
( multiply(sk_c9,A) = multiply(sk_c5,multiply(sk_c8,A))
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_20,c_3]) ).
cnf(c_147,plain,
( multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c9,A)
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_5759]) ).
cnf(c_160,plain,
( multiply(sk_c8,sk_c6) = identity
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_172,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_180,plain,
( multiply(sk_c8,sk_c6) = identity
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_228,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_94]) ).
cnf(c_266,plain,
( multiply(inverse(sk_c2),sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_22,c_94]) ).
cnf(c_267,plain,
( multiply(inverse(sk_c8),sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_22,c_94]) ).
cnf(c_268,plain,
( multiply(inverse(sk_c2),sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_94]) ).
cnf(c_314,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_94,c_94]) ).
cnf(c_315,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_314,c_228]) ).
cnf(c_374,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_315,c_2]) ).
cnf(c_5760,plain,
( multiply(identity,sk_c8) != B
| multiply(sk_c8,B) != sk_c9
| multiply(identity,sk_c8) != sk_c9
| inverse(identity) != sk_c8
| identity != sk_c9
| multiply(identity,sk_c9) != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_374,c_86]) ).
cnf(c_5761,plain,
( multiply(identity,sk_c8) != B
| multiply(sk_c8,B) != sk_c9
| multiply(identity,sk_c8) != sk_c9
| inverse(identity) != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_5760]) ).
cnf(c_5762,plain,
( multiply(identity,sk_c8) != B
| multiply(sk_c8,B) != sk_c9
| multiply(identity,sk_c8) != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_374,c_5761]) ).
cnf(c_5763,plain,
( multiply(identity,sk_c8) != B
| multiply(sk_c8,B) != sk_c9
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_5762]) ).
cnf(c_5764,plain,
( sk_c8 != B
| multiply(sk_c8,B) != sk_c9
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_5763]) ).
cnf(c_5765,plain,
( sk_c8 != B
| multiply(sk_c8,B) != sk_c9
| sk_c9 != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5764]) ).
cnf(c_432,plain,
( sk_c8 != B
| multiply(sk_c8,B) != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5765]) ).
cnf(c_5766,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_123,c_94]) ).
cnf(c_436,plain,
( inverse(sk_c10) = sk_c1
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_315,c_5766]) ).
cnf(c_439,plain,
( multiply(sk_c1,sk_c10) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_436,c_2]) ).
cnf(c_5767,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_129,c_94]) ).
cnf(c_494,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_315,c_5767]) ).
cnf(c_5768,plain,
( sk_c8 != identity
| sk_c8 != sk_c9
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_315,c_432]) ).
cnf(c_5769,plain,
( sk_c8 != identity
| sk_c9 != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5768]) ).
cnf(c_5770,plain,
( identity != sk_c8
| sk_c9 != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5769]) ).
cnf(c_5771,plain,
( identity != sk_c8
| identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5770]) ).
cnf(c_570,plain,
( identity != sk_c8
| identity != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5771]) ).
cnf(c_5772,plain,
( multiply(inverse(sk_c8),identity) = sk_c6
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_137,c_94]) ).
cnf(c_582,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_315,c_5772]) ).
cnf(c_5773,plain,
( sk_c6 = sk_c5
| inverse(sk_c1) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_582,c_494]) ).
cnf(c_587,plain,
( sk_c6 = sk_c5
| inverse(sk_c1) = sk_c10 ),
inference(copy,[status(thm)],[c_5773]) ).
cnf(c_588,plain,
( multiply(sk_c10,sk_c1) = identity
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_587,c_2]) ).
cnf(c_5774,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_588,c_94]) ).
cnf(c_697,plain,
( inverse(sk_c10) = sk_c1
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_315,c_5774]) ).
cnf(c_701,plain,
( multiply(sk_c1,sk_c10) = identity
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_697,c_2]) ).
cnf(c_5775,plain,
( multiply(inverse(sk_c8),identity) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_172,c_94]) ).
cnf(c_821,plain,
( inverse(sk_c8) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_315,c_5775]) ).
cnf(c_857,plain,
( multiply(sk_c9,sk_c2) = identity
| inverse(sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_821,c_2]) ).
cnf(c_5776,plain,
( multiply(inverse(sk_c8),identity) = sk_c6
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_180,c_94]) ).
cnf(c_879,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_315,c_5776]) ).
cnf(c_5777,plain,
( sk_c6 = sk_c5
| inverse(sk_c2) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(paramod,[status(thm)],[c_879,c_821]) ).
cnf(c_889,plain,
( sk_c6 = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(copy,[status(thm)],[c_5777]) ).
cnf(c_905,plain,
( multiply(sk_c9,sk_c2) = identity
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_889,c_2]) ).
cnf(c_5778,plain,
( multiply(inverse(sk_c9),identity) = sk_c2
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_905,c_94]) ).
cnf(c_916,plain,
( inverse(sk_c9) = sk_c2
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_315,c_5778]) ).
cnf(c_5779,plain,
( inverse(sk_c4) = sk_c10
| identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_439,c_5]) ).
cnf(c_1192,plain,
( identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(copy,[status(thm)],[c_5779]) ).
cnf(c_1205,plain,
( multiply(sk_c10,sk_c4) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1192,c_2]) ).
cnf(c_5780,plain,
( multiply(inverse(sk_c10),identity) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1205,c_94]) ).
cnf(c_1232,plain,
( inverse(sk_c10) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_315,c_5780]) ).
cnf(c_1305,plain,
( multiply(sk_c4,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1232,c_2]) ).
cnf(c_5781,plain,
( identity = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1305,c_4]) ).
cnf(c_1421,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_5781]) ).
cnf(c_5782,plain,
( identity = sk_c9
| inverse(sk_c1) = sk_c10
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1305,c_11]) ).
cnf(c_1422,plain,
( inverse(sk_c1) = sk_c10
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_5782]) ).
cnf(c_1464,plain,
( multiply(sk_c10,sk_c1) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1422,c_2]) ).
cnf(c_5783,plain,
( sk_c9 = identity
| sk_c6 = sk_c5
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1421,c_701]) ).
cnf(c_5784,plain,
( identity = sk_c9
| sk_c6 = sk_c5
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_5783]) ).
cnf(c_1743,plain,
( sk_c6 = sk_c5
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_5784]) ).
cnf(c_1762,plain,
( inverse(sk_c9) = identity
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_1743,c_374]) ).
cnf(c_5785,plain,
( identity = sk_c2
| sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_1762,c_916]) ).
cnf(c_1805,plain,
( identity = sk_c2
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_5785]) ).
cnf(c_5786,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c9
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_1805,c_1743]) ).
cnf(c_1830,plain,
( sk_c2 = sk_c9
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_5786]) ).
cnf(c_5787,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1464,c_94]) ).
cnf(c_1959,plain,
( inverse(sk_c10) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_315,c_5787]) ).
cnf(c_1984,plain,
( multiply(sk_c1,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1959,c_2]) ).
cnf(c_5788,plain,
( multiply(sk_c5,sk_c9) = multiply(sk_c9,sk_c7)
| multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_22,c_147]) ).
cnf(c_2692,plain,
( multiply(sk_c5,sk_c9) = multiply(sk_c9,sk_c7)
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_5788]) ).
cnf(c_5789,plain,
( identity = sk_c9
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1984,c_1421]) ).
cnf(c_5790,plain,
( identity = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_5789]) ).
cnf(c_2755,plain,
identity = sk_c9,
inference(copy,[status(thm)],[c_5790]) ).
cnf(c_3217,plain,
( multiply(sk_c9,sk_c2) = sk_c9
| inverse(sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_2755,c_857]) ).
cnf(c_5791,plain,
( identity != sk_c8
| sk_c9 != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_2755,c_570]) ).
cnf(c_5792,plain,
( sk_c9 != sk_c8
| sk_c9 != sk_c9
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_2755,c_5791]) ).
cnf(c_5793,plain,
( sk_c9 != sk_c8
| sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5792]) ).
cnf(c_3378,plain,
( sk_c9 != sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_5793]) ).
cnf(c_3396,plain,
multiply(A,sk_c9) = A,
inference(paramod,[status(thm)],[c_2755,c_315]) ).
cnf(c_5794,plain,
( multiply(sk_c8,sk_c6) = identity
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3396,c_160]) ).
cnf(c_3411,plain,
( multiply(sk_c8,sk_c6) = sk_c9
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_2755,c_5794]) ).
cnf(c_3419,plain,
multiply(inverse(A),A) = sk_c9,
inference(paramod,[status(thm)],[c_2755,c_2]) ).
cnf(c_3420,plain,
multiply(sk_c9,A) = A,
inference(paramod,[status(thm)],[c_2755,c_1]) ).
cnf(c_5795,plain,
( multiply(sk_c5,sk_c9) = multiply(sk_c9,sk_c7)
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3396,c_2692]) ).
cnf(c_5796,plain,
( sk_c5 = multiply(sk_c9,sk_c7)
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3396,c_5795]) ).
cnf(c_5797,plain,
( sk_c5 = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3420,c_5796]) ).
cnf(c_3490,plain,
( sk_c7 = sk_c5
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_5797]) ).
cnf(c_5798,plain,
( multiply(inverse(sk_c8),sk_c9) = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3396,c_267]) ).
cnf(c_3667,plain,
( inverse(sk_c8) = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3396,c_5798]) ).
cnf(c_3732,plain,
( sk_c2 = sk_c9
| inverse(sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_3420,c_3217]) ).
cnf(c_5799,plain,
( inverse(sk_c8) = sk_c5
| sk_c2 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3490,c_3667]) ).
cnf(c_4187,plain,
( inverse(sk_c8) = sk_c5
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_5799]) ).
cnf(c_5800,plain,
( sk_c8 = sk_c9
| inverse(sk_c8) = sk_c5
| inverse(sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_4187,c_3732]) ).
cnf(c_5801,plain,
( sk_c9 = sk_c8
| inverse(sk_c8) = sk_c5
| inverse(sk_c8) = sk_c5 ),
inference(copy,[status(thm)],[c_5800]) ).
cnf(c_4419,plain,
( sk_c9 = sk_c8
| inverse(sk_c8) = sk_c5 ),
inference(copy,[status(thm)],[c_5801]) ).
cnf(c_5802,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_29,c_266]) ).
cnf(c_5803,plain,
( sk_c8 = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_3420,c_5802]) ).
cnf(c_5804,plain,
( sk_c9 = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_5803]) ).
cnf(c_4850,plain,
( sk_c9 = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(copy,[status(thm)],[c_5804]) ).
cnf(c_5805,plain,
( multiply(sk_c9,sk_c8) = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_268]) ).
cnf(c_5806,plain,
( sk_c8 = sk_c9
| multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_3420,c_5805]) ).
cnf(c_5807,plain,
( sk_c9 = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_5806]) ).
cnf(c_4873,plain,
( sk_c9 = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_5807]) ).
cnf(c_5808,plain,
( multiply(inverse(sk_c8),sk_c9) = sk_c6
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3411,c_94]) ).
cnf(c_5347,plain,
( inverse(sk_c8) = sk_c6
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_3396,c_5808]) ).
cnf(c_5809,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_5347,c_4187]) ).
cnf(c_5390,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_5809]) ).
cnf(c_5810,plain,
( sk_c8 = sk_c9
| sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_5390,c_1830]) ).
cnf(c_5811,plain,
( sk_c9 = sk_c8
| sk_c6 = sk_c5
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_5810]) ).
cnf(c_5465,plain,
( sk_c9 = sk_c8
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_5811]) ).
cnf(c_5812,plain,
multiply(inverse(inverse(A)),sk_c9) = A,
inference(paramod,[status(thm)],[c_3419,c_94]) ).
cnf(c_5709,plain,
inverse(inverse(A)) = A,
inference(paramod,[status(thm)],[c_3396,c_5812]) ).
cnf(c_5813,plain,
( sk_c9 != sk_c8
| inverse(inverse(sk_c10)) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_3419,c_3378]) ).
cnf(c_5814,plain,
( sk_c9 != sk_c8
| sk_c10 != sk_c10
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_5709,c_5813]) ).
cnf(c_5815,plain,
( sk_c9 != sk_c8
| sk_c10 != sk_c10 ),
inference(copy,[status(thm)],[c_5814]) ).
cnf(c_5714,plain,
sk_c9 != sk_c8,
inference(copy,[status(thm)],[c_5815]) ).
cnf(c_5816,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| sk_c9 = sk_c8 ),
inference(paramod,[status(thm)],[c_4419,c_3419]) ).
cnf(c_5733,plain,
multiply(sk_c5,sk_c8) = sk_c9,
inference(resolve,[status(thm)],[c_5714,c_5816]) ).
cnf(c_5817,plain,
( multiply(inverse(A),A) = sk_c8
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_5465,c_3419]) ).
cnf(c_5818,plain,
( sk_c9 = sk_c8
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_3419,c_5817]) ).
cnf(c_5739,plain,
sk_c6 = sk_c5,
inference(resolve,[status(thm)],[c_5714,c_5818]) ).
cnf(c_5819,plain,
( sk_c9 = sk_c8
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_5739,c_4873]) ).
cnf(c_5820,plain,
( sk_c9 = sk_c8
| sk_c9 = sk_c7 ),
inference(paramod,[status(thm)],[c_5733,c_5819]) ).
cnf(c_5821,plain,
( sk_c9 = sk_c8
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_5820]) ).
cnf(c_5754,plain,
sk_c7 = sk_c9,
inference(resolve,[status(thm)],[c_5714,c_5821]) ).
cnf(c_5822,plain,
( sk_c9 = sk_c8
| multiply(sk_c8,sk_c9) = sk_c9 ),
inference(paramod,[status(thm)],[c_5754,c_4850]) ).
cnf(c_5823,plain,
( sk_c9 = sk_c8
| sk_c8 = sk_c9 ),
inference(paramod,[status(thm)],[c_3396,c_5822]) ).
cnf(c_5824,plain,
( sk_c9 = sk_c8
| sk_c9 = sk_c8 ),
inference(copy,[status(thm)],[c_5823]) ).
cnf(c_5825,plain,
sk_c9 = sk_c8,
inference(copy,[status(thm)],[c_5824]) ).
cnf(c_5755,plain,
$false,
inference(resolve,[status(thm)],[c_5714,c_5825]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP257-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:41:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3717026 was started by sandbox on n005,
% 0.14/0.36 % Fri Sep 25 14:41:32 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 19.30/6.42
% 19.30/6.42 % SZS status Unsatisfiable for theBenchmark
% 19.30/6.42
% 19.30/6.42 % Proof 1 at 2.09 (+ 0.64) seconds.
% 19.30/6.42 % Length of proof is 90.
% 19.30/6.42 % Level of proof is 22.
% 19.30/6.42 % Maximum clause weight is 63.000.
% 19.30/6.42 % Given clauses 418.
% 19.30/6.42
% 19.30/6.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------