%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP341-1 : 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 : n014.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 07:28:40 AM UTC 2026
% Result : Unsatisfiable 41.16s 11.52s
% Output : CNFRefutation 41.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 20
% Syntax : Number of formulae : 170 ( 50 unt; 0 def)
% Number of atoms : 401 ( 400 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 361 ( 130 ~; 231 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 54 ( 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_3,axiom,
( inverse(sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_15,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_22,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_25,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_29,axiom,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_32,axiom,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_33,axiom,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_36,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(VAR_3) != sk_c6
| multiply(VAR_3,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| inverse(VAR_2) != sk_c7
| multiply(VAR_2,sk_c7) != sk_c6
| multiply(VAR_1,sk_c5) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('theBenchmark.p',prove_this_36) ).
cnf(c_39,plain,
( multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(D) != sk_c6
| multiply(D,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c6
| 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 ),
inference(clausify,[status(thm)],[prove_this_36]) ).
cnf(c_40,plain,
( multiply(sk_c5,sk_c6) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| multiply(A,sk_c7) != sk_c6
| 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 ),
inference(factor,[status(thm)],[c_39]) ).
cnf(c_22531,plain,
( multiply(sk_c5,sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_45,plain,
( inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(copy,[status(thm)],[c_22531]) ).
cnf(c_51,plain,
( multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(factor,[status(thm)],[c_45]) ).
cnf(c_55,plain,
multiply(multiply(A,identity),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_56,plain,
multiply(multiply(identity,A),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_22532,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_57,plain,
multiply(inverse(A),multiply(A,B)) = multiply(identity,B),
inference(copy,[status(thm)],[c_22532]) ).
cnf(c_66,plain,
( multiply(sk_c6,sk_c5) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_68,plain,
( multiply(multiply(A,sk_c4),sk_c6) = multiply(A,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_69,plain,
( multiply(sk_c6,sk_c4) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_71,plain,
( multiply(multiply(A,sk_c5),sk_c7) = multiply(A,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_648,plain,
multiply(multiply(identity,identity),A) = A,
inference(paramod,[status(thm)],[c_1,c_55]) ).
cnf(c_22533,plain,
multiply(identity,A) = multiply(inverse(identity),A),
inference(paramod,[status(thm)],[c_2,c_55]) ).
cnf(c_649,plain,
multiply(inverse(identity),A) = multiply(identity,A),
inference(copy,[status(thm)],[c_22533]) ).
cnf(c_650,plain,
multiply(multiply(inverse(A),identity),A) = identity,
inference(paramod,[status(thm)],[c_2,c_55]) ).
cnf(c_861,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(paramod,[status(thm)],[c_1,c_57]) ).
cnf(c_862,plain,
multiply(inverse(inverse(A)),identity) = multiply(identity,A),
inference(paramod,[status(thm)],[c_2,c_57]) ).
cnf(c_22534,plain,
A = multiply(identity,multiply(identity,A)),
inference(paramod,[status(thm)],[c_648,c_3]) ).
cnf(c_1566,plain,
multiply(identity,multiply(identity,A)) = A,
inference(copy,[status(thm)],[c_22534]) ).
cnf(c_22535,plain,
( multiply(identity,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_69,c_68]) ).
cnf(c_1622,plain,
( multiply(identity,sk_c6) = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22535]) ).
cnf(c_22536,plain,
( multiply(identity,sk_c7) = multiply(sk_c6,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_66,c_71]) ).
cnf(c_1767,plain,
( multiply(identity,sk_c7) = multiply(sk_c6,sk_c6)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22536]) ).
cnf(c_22537,plain,
( multiply(identity,sk_c6) = identity
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_66,c_1622]) ).
cnf(c_1828,plain,
( multiply(identity,sk_c6) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22537]) ).
cnf(c_1876,plain,
( multiply(identity,A) = multiply(sk_c6,A)
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1828,c_56]) ).
cnf(c_1889,plain,
( multiply(identity,identity) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1828,c_1566]) ).
cnf(c_1982,plain,
( multiply(sk_c6,A) = A
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1889,c_648]) ).
cnf(c_22538,plain,
( multiply(identity,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1982,c_1767]) ).
cnf(c_2485,plain,
( multiply(identity,sk_c7) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22538]) ).
cnf(c_2519,plain,
( multiply(identity,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_2485,c_1566]) ).
cnf(c_22539,plain,
( sk_c7 = multiply(sk_c6,sk_c5)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_2519,c_1622]) ).
cnf(c_22540,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22539]) ).
cnf(c_2643,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22540]) ).
cnf(c_22541,plain,
( multiply(identity,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_2643,c_1876]) ).
cnf(c_3144,plain,
( multiply(identity,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22541]) ).
cnf(c_3205,plain,
( multiply(identity,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3144,c_1566]) ).
cnf(c_22542,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_3205,c_1876]) ).
cnf(c_22543,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22542]) ).
cnf(c_22544,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_22543]) ).
cnf(c_3383,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(copy,[status(thm)],[c_22544]) ).
cnf(c_4007,plain,
( multiply(A,sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7 ),
inference(resolve,[status(thm)],[c_3383,c_51]) ).
cnf(c_4020,plain,
multiply(multiply(A,sk_c6),sk_c7) = multiply(A,sk_c5),
inference(paramod,[status(thm)],[c_3383,c_3]) ).
cnf(c_4022,plain,
multiply(multiply(identity,sk_c6),sk_c7) = sk_c5,
inference(paramod,[status(thm)],[c_3383,c_56]) ).
cnf(c_4042,plain,
multiply(inverse(identity),A) = A,
inference(paramod,[status(thm)],[c_1,c_649]) ).
cnf(c_22545,plain,
sk_c5 = multiply(identity,multiply(sk_c6,sk_c7)),
inference(paramod,[status(thm)],[c_4022,c_3]) ).
cnf(c_4580,plain,
multiply(identity,multiply(sk_c6,sk_c7)) = sk_c5,
inference(copy,[status(thm)],[c_22545]) ).
cnf(c_5035,plain,
multiply(identity,sk_c5) = multiply(sk_c6,sk_c7),
inference(paramod,[status(thm)],[c_4580,c_1566]) ).
cnf(c_5569,plain,
multiply(inverse(sk_c6),sk_c5) = sk_c7,
inference(paramod,[status(thm)],[c_3383,c_861]) ).
cnf(c_11075,plain,
multiply(multiply(identity,A),inverse(A)) = identity,
inference(paramod,[status(thm)],[c_862,c_650]) ).
cnf(c_11571,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_1,c_11075]) ).
cnf(c_22546,plain,
identity = inverse(identity),
inference(paramod,[status(thm)],[c_11075,c_648]) ).
cnf(c_11616,plain,
inverse(identity) = identity,
inference(copy,[status(thm)],[c_22546]) ).
cnf(c_11722,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_11,c_11571]) ).
cnf(c_11723,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_11571]) ).
cnf(c_11729,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_19,c_11571]) ).
cnf(c_11732,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_25,c_11571]) ).
cnf(c_11733,plain,
( multiply(sk_c3,sk_c7) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_26,c_11571]) ).
cnf(c_11735,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(paramod,[status(thm)],[c_28,c_11571]) ).
cnf(c_11736,plain,
( multiply(sk_c4,sk_c6) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_29,c_11571]) ).
cnf(c_11739,plain,
( multiply(sk_c3,sk_c7) = identity
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_33,c_11571]) ).
cnf(c_11741,plain,
( multiply(sk_c4,sk_c6) = identity
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_36,c_11571]) ).
cnf(c_22547,plain,
identity = inverse(inverse(identity)),
inference(paramod,[status(thm)],[c_11571,c_4042]) ).
cnf(c_11779,plain,
inverse(inverse(identity)) = identity,
inference(copy,[status(thm)],[c_22547]) ).
cnf(c_12374,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_11723,c_11571]) ).
cnf(c_12414,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c3,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_11733,c_11571]) ).
cnf(c_12814,plain,
( multiply(sk_c2,sk_c6) = identity
| multiply(sk_c4,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_11736,c_11571]) ).
cnf(c_22548,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_11729,c_18]) ).
cnf(c_12962,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_22548]) ).
cnf(c_22549,plain,
( identity = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_11739,c_32]) ).
cnf(c_13637,plain,
( identity = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_22549]) ).
cnf(c_22550,plain,
( identity = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_11741,c_35]) ).
cnf(c_13737,plain,
( identity = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_22550]) ).
cnf(c_14246,plain,
( multiply(inverse(identity),sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(inverse(identity),sk_c5) != sk_c6
| identity != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_11779,c_4007]) ).
cnf(c_22551,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_12374,c_11722]) ).
cnf(c_14609,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c7) = identity ),
inference(copy,[status(thm)],[c_22551]) ).
cnf(c_14973,plain,
( multiply(inverse(identity),sk_c6) != sk_c5
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_4042,c_14246]) ).
cnf(c_22552,plain,
( sk_c6 != sk_c5
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7 ),
inference(paramod,[status(thm)],[c_4042,c_14973]) ).
cnf(c_22553,plain,
( sk_c5 != sk_c6
| inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_22552]) ).
cnf(c_14976,plain,
( inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c7 ),
inference(copy,[status(thm)],[c_22553]) ).
cnf(c_22554,plain,
( multiply(sk_c2,sk_c6) = identity
| identity = sk_c6
| multiply(sk_c2,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_12414,c_11732]) ).
cnf(c_15072,plain,
( identity = sk_c6
| multiply(sk_c2,sk_c6) = identity ),
inference(copy,[status(thm)],[c_22554]) ).
cnf(c_15101,plain,
( multiply(identity,sk_c7) = multiply(sk_c2,sk_c5)
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15072,c_4020]) ).
cnf(c_22555,plain,
( multiply(sk_c2,sk_c6) = identity
| identity = sk_c5
| multiply(sk_c2,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_12814,c_11735]) ).
cnf(c_15386,plain,
( identity = sk_c5
| multiply(sk_c2,sk_c6) = identity ),
inference(copy,[status(thm)],[c_22555]) ).
cnf(c_15409,plain,
( multiply(identity,sk_c7) = multiply(sk_c2,sk_c5)
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15386,c_4020]) ).
cnf(c_16070,plain,
( multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_15101,c_1]) ).
cnf(c_22556,plain,
( identity = sk_c6
| sk_c7 = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_16070,c_13637]) ).
cnf(c_16170,plain,
( sk_c7 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_22556]) ).
cnf(c_16171,plain,
( multiply(sk_c6,A) = A
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_16170,c_1]) ).
cnf(c_22557,plain,
( sk_c7 = sk_c5
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_16171,c_3383]) ).
cnf(c_16543,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_22557]) ).
cnf(c_18683,plain,
( multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_15409,c_1]) ).
cnf(c_22558,plain,
( identity = sk_c5
| sk_c7 = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_18683,c_13737]) ).
cnf(c_18847,plain,
( sk_c7 = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_22558]) ).
cnf(c_22559,plain,
( sk_c7 = sk_c6
| sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_18847,c_16170]) ).
cnf(c_19018,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_22559]) ).
cnf(c_22560,plain,
( sk_c6 = sk_c7
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_19018,c_16543]) ).
cnf(c_22561,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_22560]) ).
cnf(c_22562,plain,
( sk_c7 = sk_c6
| sk_c7 = sk_c6 ),
inference(copy,[status(thm)],[c_22561]) ).
cnf(c_19115,plain,
sk_c7 = sk_c6,
inference(copy,[status(thm)],[c_22562]) ).
cnf(c_19151,plain,
multiply(sk_c6,sk_c6) = sk_c5,
inference(paramod,[status(thm)],[c_19115,c_3383]) ).
cnf(c_19171,plain,
multiply(identity,sk_c5) = multiply(sk_c6,sk_c6),
inference(paramod,[status(thm)],[c_19115,c_5035]) ).
cnf(c_19254,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(paramod,[status(thm)],[c_19115,c_12962]) ).
cnf(c_19272,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_19115,c_14609]) ).
cnf(c_22563,plain,
( inverse(sk_c5) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c6 ),
inference(paramod,[status(thm)],[c_19115,c_14976]) ).
cnf(c_19283,plain,
( multiply(sk_c5,sk_c7) != sk_c6
| sk_c5 != sk_c6
| identity != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c6 ),
inference(copy,[status(thm)],[c_22563]) ).
cnf(c_19333,plain,
multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c5),
inference(paramod,[status(thm)],[c_19151,c_4020]) ).
cnf(c_22564,plain,
multiply(sk_c6,sk_c6) = multiply(sk_c6,sk_c7),
inference(paramod,[status(thm)],[c_19171,c_5035]) ).
cnf(c_19355,plain,
multiply(sk_c6,sk_c7) = multiply(sk_c6,sk_c6),
inference(copy,[status(thm)],[c_22564]) ).
cnf(c_19642,plain,
multiply(sk_c5,sk_c6) = multiply(sk_c6,sk_c5),
inference(paramod,[status(thm)],[c_19115,c_19333]) ).
cnf(c_22565,plain,
( identity = sk_c6
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_19272,c_19254]) ).
cnf(c_22566,plain,
( identity = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_22565]) ).
cnf(c_20094,plain,
identity = sk_c6,
inference(copy,[status(thm)],[c_22566]) ).
cnf(c_20118,plain,
( multiply(sk_c5,sk_c7) != sk_c6
| sk_c5 != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c6 ),
inference(resolve,[status(thm)],[c_20094,c_19283]) ).
cnf(c_20137,plain,
multiply(sk_c6,A) = A,
inference(paramod,[status(thm)],[c_20094,c_1]) ).
cnf(c_20278,plain,
inverse(sk_c6) = identity,
inference(paramod,[status(thm)],[c_20094,c_11616]) ).
cnf(c_20395,plain,
inverse(sk_c6) = sk_c6,
inference(paramod,[status(thm)],[c_20094,c_20278]) ).
cnf(c_20405,plain,
multiply(sk_c6,sk_c5) = sk_c7,
inference(paramod,[status(thm)],[c_20395,c_5569]) ).
cnf(c_22567,plain,
sk_c6 = sk_c5,
inference(paramod,[status(thm)],[c_20137,c_19151]) ).
cnf(c_20510,plain,
sk_c5 = sk_c6,
inference(copy,[status(thm)],[c_22567]) ).
cnf(c_20516,plain,
multiply(sk_c6,sk_c7) = sk_c6,
inference(paramod,[status(thm)],[c_20137,c_19355]) ).
cnf(c_20523,plain,
( multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c5) != sk_c6 ),
inference(resolve,[status(thm)],[c_20510,c_20118]) ).
cnf(c_22568,plain,
( multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c6 ),
inference(paramod,[status(thm)],[c_20510,c_20523]) ).
cnf(c_20725,plain,
( multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(resolve,[status(thm)],[c_20395,c_22568]) ).
cnf(c_22569,plain,
( multiply(sk_c6,sk_c7) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(paramod,[status(thm)],[c_20510,c_20725]) ).
cnf(c_21537,plain,
multiply(sk_c5,sk_c6) != sk_c7,
inference(resolve,[status(thm)],[c_20516,c_22569]) ).
cnf(c_22570,plain,
multiply(sk_c6,sk_c5) != sk_c7,
inference(paramod,[status(thm)],[c_19642,c_21537]) ).
cnf(c_22530,plain,
$false,
inference(resolve,[status(thm)],[c_20405,c_22570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP341-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.59 % Computer : n014.cluster.edu
% 0.13/5.59 % Model : x86_64 x86_64
% 0.13/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.59 % Memory : 8046.5625MB
% 0.13/5.59 % OS : Linux 6.8.0-71-generic
% 0.13/5.59 % CPULimit : 300
% 0.13/5.59 % WCLimit : 300
% 0.13/5.59 % DateTime : Fri Sep 25 14:47:10 UTC 2026
% 0.13/5.59 % CPUTime :
% 0.13/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.59 % Process 478086 was started by sandbox2 on n014,
% 0.13/5.59 % Fri Sep 25 14:47:10 2026
% 0.13/5.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/5.59
% 0.13/5.59 % From the command line: assign(max_seconds, 300).
% 41.16/11.52
% 41.16/11.52 % given #500 (F,wt=52): 15846 inverse(sk_c5) != sk_c7 | multiply(sk_c5,sk_c6) != sk_c7 | identity != sk_c6 | multiply(multiply(identity,identity),sk_c5) != sk_c6 | multiply(sk_c5,sk_c7) != sk_c6 | inverse(sk_c5) != sk_c6 | multiply(A,sk_c6) != sk_c5 | inverse(A) != sk_c6. [para(11760(a,1),14248(d,1,1))].
% 41.16/11.52
% 41.16/11.52 % SZS status Unsatisfiable for theBenchmark
% 41.16/11.52
% 41.16/11.52 % Proof 1 at 4.78 (+ 0.89) seconds.
% 41.16/11.52 % Length of proof is 110.
% 41.16/11.52 % Level of proof is 26.
% 41.16/11.52 % Maximum clause weight is 65.000.
% 41.16/11.52 % Given clauses 629.
% 41.16/11.52
% 41.16/11.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------