%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP381-1 : 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 : n018.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 07:28:45 AM UTC 2026
% Result : Unsatisfiable 77.23s 11.20s
% Output : CNFRefutation 77.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 20
% Syntax : Number of formulae : 178 ( 26 unt; 0 def)
% Number of atoms : 505 ( 504 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 535 ( 208 ~; 327 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 9 !; 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_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_11,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( multiply(VAR_3,sk_c5) != sk_c6
| inverse(VAR_3) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(VAR_2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(D,sk_c5) != sk_c6
| inverse(D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_14689,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_14690,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_14689]) ).
cnf(c_54,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_14690]) ).
cnf(c_55,plain,
( multiply(sk_c6,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_56,plain,
( multiply(sk_c7,sk_c3) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_14691,plain,
( multiply(sk_c7,A) = multiply(sk_c6,multiply(sk_c5,A))
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_60,plain,
( multiply(sk_c6,multiply(sk_c5,A)) = multiply(sk_c7,A)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_14691]) ).
cnf(c_70,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_73,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_711,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_54]) ).
cnf(c_743,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_54,c_54]) ).
cnf(c_744,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_743,c_711]) ).
cnf(c_745,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_744,c_2]) ).
cnf(c_14692,plain,
( multiply(inverse(sk_c6),identity) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_55,c_54]) ).
cnf(c_852,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_744,c_14692]) ).
cnf(c_1144,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_743,c_2]) ).
cnf(c_14693,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_743,c_744]) ).
cnf(c_14694,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_744,c_14693]) ).
cnf(c_1167,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_14694]) ).
cnf(c_14695,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(inverse(sk_c7),sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_1167,c_34]) ).
cnf(c_1215,plain,
( multiply(C,sk_c5) != sk_c6
| inverse(C) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_14695]) ).
cnf(c_1217,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_1167]) ).
cnf(c_1218,plain,
( inverse(sk_c6) = sk_c4
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_1167]) ).
cnf(c_1219,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_8,c_1167]) ).
cnf(c_1276,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_56,c_1167]) ).
cnf(c_1295,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_19,c_1144]) ).
cnf(c_1296,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_20,c_1144]) ).
cnf(c_1297,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_21,c_1144]) ).
cnf(c_1298,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c4) = sk_c6 ),
inference(paramod,[status(thm)],[c_22,c_1144]) ).
cnf(c_1299,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_23,c_1144]) ).
cnf(c_1545,plain,
( multiply(sk_c6,multiply(sk_c5,inverse(sk_c7))) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1144,c_60]) ).
cnf(c_4498,plain,
( multiply(sk_c7,sk_c3) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_1296,c_2]) ).
cnf(c_4551,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_1298,c_2]) ).
cnf(c_14696,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1295,c_14]) ).
cnf(c_11297,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_14696]) ).
cnf(c_11322,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_11297,c_54]) ).
cnf(c_14697,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| identity = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1297,c_16]) ).
cnf(c_11369,plain,
( identity = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_14697]) ).
cnf(c_11374,plain,
( multiply(inverse(sk_c3),sk_c7) = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_11369,c_54]) ).
cnf(c_14698,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| identity = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_1299,c_18]) ).
cnf(c_11443,plain,
( identity = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_14698]) ).
cnf(c_14699,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_745,c_1215]) ).
cnf(c_14700,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c6 != sk_c7
| identity != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_14699]) ).
cnf(c_14701,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| identity != sk_c6
| sk_c7 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_14700]) ).
cnf(c_12015,plain,
( multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_14701]) ).
cnf(c_12055,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_12015,c_1167]) ).
cnf(c_14702,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c6
| multiply(sk_c7,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_4498,c_70]) ).
cnf(c_12231,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c3) = identity ),
inference(copy,[status(thm)],[c_14702]) ).
cnf(c_14703,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12231,c_54]) ).
cnf(c_12234,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_744,c_14703]) ).
cnf(c_12377,plain,
( inverse(sk_c3) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12234,c_1167]) ).
cnf(c_14704,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12377,c_11374]) ).
cnf(c_12452,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_14704]) ).
cnf(c_12456,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12452,c_54]) ).
cnf(c_14705,plain,
( multiply(sk_c6,sk_c4) = identity
| identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_4551,c_73]) ).
cnf(c_12539,plain,
( identity = sk_c6
| multiply(sk_c6,sk_c4) = identity ),
inference(copy,[status(thm)],[c_14705]) ).
cnf(c_14706,plain,
( multiply(inverse(sk_c6),identity) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12539,c_54]) ).
cnf(c_12542,plain,
( inverse(sk_c6) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_744,c_14706]) ).
cnf(c_14707,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12542,c_11322]) ).
cnf(c_12578,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_14707]) ).
cnf(c_14708,plain,
( identity = sk_c6
| sk_c7 = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_12578,c_11443]) ).
cnf(c_12601,plain,
( sk_c7 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_14708]) ).
cnf(c_12602,plain,
( multiply(sk_c6,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12601,c_1]) ).
cnf(c_12603,plain,
( multiply(A,sk_c6) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12601,c_744]) ).
cnf(c_12604,plain,
( inverse(sk_c6) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12601,c_745]) ).
cnf(c_14709,plain,
( inverse(sk_c6) = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12601,c_12604]) ).
cnf(c_12726,plain,
( inverse(sk_c6) = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14709]) ).
cnf(c_14710,plain,
( sk_c6 = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12726,c_852]) ).
cnf(c_14711,plain,
( sk_c7 = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14710]) ).
cnf(c_12744,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14711]) ).
cnf(c_14712,plain,
( sk_c6 = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12726,c_1217]) ).
cnf(c_14713,plain,
( sk_c7 = sk_c6
| multiply(sk_c3,sk_c6) = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14712]) ).
cnf(c_12745,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14713]) ).
cnf(c_14714,plain,
( sk_c6 = sk_c7
| multiply(sk_c4,sk_c5) = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12726,c_1219]) ).
cnf(c_14715,plain,
( sk_c7 = sk_c6
| multiply(sk_c4,sk_c5) = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14714]) ).
cnf(c_12746,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14715]) ).
cnf(c_14716,plain,
( sk_c6 = sk_c7
| multiply(sk_c7,sk_c3) = identity
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12726,c_1276]) ).
cnf(c_14717,plain,
( sk_c7 = sk_c6
| multiply(sk_c7,sk_c3) = identity
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14716]) ).
cnf(c_12750,plain,
( multiply(sk_c7,sk_c3) = identity
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14717]) ).
cnf(c_14718,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12744,c_12602]) ).
cnf(c_12851,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14718]) ).
cnf(c_14719,plain,
( sk_c7 = sk_c3
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12745,c_12603]) ).
cnf(c_14720,plain,
( sk_c3 = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14719]) ).
cnf(c_12878,plain,
( sk_c3 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14720]) ).
cnf(c_14721,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12851,c_12746]) ).
cnf(c_12900,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14721]) ).
cnf(c_14722,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12750,c_54]) ).
cnf(c_12909,plain,
( inverse(sk_c7) = sk_c3
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_744,c_14722]) ).
cnf(c_14723,plain,
( inverse(sk_c7) = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_12878,c_12909]) ).
cnf(c_13014,plain,
( inverse(sk_c7) = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14723]) ).
cnf(c_14724,plain,
( inverse(sk_c6) = sk_c4
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_13014,c_1218]) ).
cnf(c_13096,plain,
( inverse(sk_c6) = sk_c4
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14724]) ).
cnf(c_14725,plain,
( sk_c4 = identity
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_13096,c_12604]) ).
cnf(c_14726,plain,
( identity = sk_c4
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14725]) ).
cnf(c_13152,plain,
( identity = sk_c4
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14726]) ).
cnf(c_13157,plain,
( multiply(sk_c4,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_13152,c_1]) ).
cnf(c_14727,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_13157,c_12900]) ).
cnf(c_14728,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_14727]) ).
cnf(c_13289,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_14728]) ).
cnf(c_14729,plain,
( multiply(inverse(sk_c6),sk_c6) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_13289,c_12456]) ).
cnf(c_14730,plain,
( identity = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_14729]) ).
cnf(c_14731,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_13289,c_14730]) ).
cnf(c_13349,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_14731]) ).
cnf(c_14732,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_13289,c_12055]) ).
cnf(c_14733,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c6
| identity != sk_c6
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_13289,c_14732]) ).
cnf(c_14734,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c7 != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_13349,c_14733]) ).
cnf(c_14735,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_13289,c_14734]) ).
cnf(c_14736,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c6) != sk_c5
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_13289,c_14735]) ).
cnf(c_14737,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_13289,c_14736]) ).
cnf(c_14738,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| sk_c6 != sk_c6
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_13289,c_14737]) ).
cnf(c_14739,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(copy,[status(thm)],[c_14738]) ).
cnf(c_13566,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(A,sk_c6) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(copy,[status(thm)],[c_14739]) ).
cnf(c_14740,plain,
( multiply(sk_c6,multiply(sk_c5,inverse(sk_c7))) = identity
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_13289,c_1545]) ).
cnf(c_14741,plain,
( multiply(sk_c6,multiply(sk_c5,inverse(sk_c6))) = identity
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_13289,c_14740]) ).
cnf(c_14476,plain,
( multiply(sk_c6,multiply(sk_c5,inverse(sk_c6))) = sk_c6
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_13349,c_14741]) ).
cnf(c_14742,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_13349,c_745]) ).
cnf(c_14645,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_13349,c_14742]) ).
cnf(c_14646,plain,
multiply(A,sk_c6) = A,
inference(paramod,[status(thm)],[c_13349,c_744]) ).
cnf(c_14650,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_13349,c_1]) ).
cnf(c_14743,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c6 ),
inference(factor,[status(thm)],[c_13566]) ).
cnf(c_14744,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_14645,c_14743]) ).
cnf(c_14745,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c5
| sk_c5 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_14650,c_14744]) ).
cnf(c_14746,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| multiply(sk_c6,sk_c6) != sk_c6
| sk_c6 != sk_c5
| sk_c5 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_14646,c_14745]) ).
cnf(c_14747,plain,
( multiply(inverse(sk_c6),sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c5
| sk_c5 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_14646,c_14746]) ).
cnf(c_14748,plain,
( multiply(sk_c6,sk_c5) != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c5
| sk_c5 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_14645,c_14747]) ).
cnf(c_14749,plain,
( sk_c5 != sk_c6
| sk_c6 != sk_c6
| sk_c6 != sk_c5
| sk_c5 != sk_c6
| sk_c6 != sk_c6 ),
inference(paramod,[status(thm)],[c_14650,c_14748]) ).
cnf(c_14750,plain,
( sk_c5 != sk_c6
| sk_c6 != sk_c6
| sk_c5 != sk_c6
| sk_c5 != sk_c6
| sk_c6 != sk_c6 ),
inference(copy,[status(thm)],[c_14749]) ).
cnf(c_14751,plain,
( sk_c5 != sk_c6
| sk_c6 != sk_c6
| sk_c5 != sk_c6
| sk_c5 != sk_c6 ),
inference(copy,[status(thm)],[c_14750]) ).
cnf(c_14752,plain,
( sk_c5 != sk_c6
| sk_c5 != sk_c6
| sk_c5 != sk_c6 ),
inference(copy,[status(thm)],[c_14751]) ).
cnf(c_14753,plain,
( sk_c5 != sk_c6
| sk_c5 != sk_c6 ),
inference(copy,[status(thm)],[c_14752]) ).
cnf(c_14676,plain,
sk_c5 != sk_c6,
inference(copy,[status(thm)],[c_14753]) ).
cnf(c_14754,plain,
( multiply(sk_c6,multiply(sk_c5,inverse(sk_c6))) = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_14646,c_14476]) ).
cnf(c_14755,plain,
( multiply(sk_c6,multiply(sk_c5,sk_c6)) = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_14645,c_14754]) ).
cnf(c_14756,plain,
( multiply(sk_c6,sk_c5) = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_14646,c_14755]) ).
cnf(c_14757,plain,
( sk_c5 = sk_c6
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_14650,c_14756]) ).
cnf(c_14758,plain,
( sk_c5 = sk_c6
| sk_c5 = sk_c6 ),
inference(copy,[status(thm)],[c_14757]) ).
cnf(c_14759,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_14758]) ).
cnf(c_14688,plain,
$false,
inference(resolve,[status(thm)],[c_14676,c_14759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP381-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n018.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 14:51:50 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2228379 was started by sandbox2 on n018,
% 0.17/0.44 % Fri Sep 25 14:51:50 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 77.23/11.20
% 77.23/11.20 % given #500 (A,wt=50): 112 inverse(sk_c7) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | multiply(A,sk_c7) != sk_c6 | inverse(A) != sk_c7 | multiply(B,sk_c6) != sk_c7 | inverse(B) != sk_c6 | multiply(sk_c6,sk_c7) != sk_c5 | multiply(sk_c1,sk_c6) != sk_c7 | inverse(C) != sk_c6 | multiply(C,sk_c5) != sk_c6 | inverse(sk_c3) = sk_c7. [resolve(34,h,20,a)].
% 77.23/11.20
% 77.23/11.20 % SZS status Unsatisfiable for theBenchmark
% 77.23/11.20
% 77.23/11.20 % Proof 1 at 9.39 (+ 1.33) seconds.
% 77.23/11.20 % Length of proof is 87.
% 77.23/11.20 % Level of proof is 22.
% 77.23/11.20 % Maximum clause weight is 50.000.
% 77.23/11.20 % Given clauses 640.
% 77.23/11.20
% 77.23/11.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------