%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP336-1 : 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 : n006.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 07:28:39 AM UTC 2026
% Result : Unsatisfiable 19.51s 3.23s
% Output : CNFRefutation 19.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 134 ( 24 unt; 0 def)
% Number of atoms : 359 ( 358 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 372 ( 147 ~; 225 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 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 : 60 ( 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_c9,sk_c10) = sk_c8 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_3,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_12,axiom,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_19,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_25,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_33,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_34,axiom,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_34) ).
cnf(c_37,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_34]) ).
fof(prove_this_49,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6] :
( multiply(VAR_6,sk_c8) != sk_c9
| inverse(VAR_5) != VAR_6
| multiply(VAR_5,VAR_6) != sk_c9
| multiply(VAR_4,sk_c9) != sk_c10
| inverse(VAR_4) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(VAR_3) != sk_c10
| multiply(VAR_3,sk_c10) != sk_c9
| multiply(VAR_2,sk_c10) != sk_c9
| inverse(VAR_1) != VAR_2
| multiply(VAR_1,VAR_2) != sk_c9
| multiply(VAR_0,sk_c9) != sk_c10
| inverse(VAR_0) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
file('theBenchmark.p',prove_this_49) ).
cnf(c_52,plain,
( multiply(V6,sk_c8) != sk_c9
| inverse(F) != V6
| multiply(F,V6) != sk_c9
| multiply(E,sk_c9) != sk_c10
| inverse(E) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(C,sk_c10) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_49]) ).
cnf(c_53,plain,
( multiply(E,sk_c8) != sk_c9
| inverse(D) != E
| multiply(D,E) != sk_c9
| multiply(C,sk_c9) != sk_c10
| inverse(C) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_52]) ).
cnf(c_4487,plain,
( multiply(D,sk_c8) != sk_c9
| inverse(C) != D
| multiply(C,D) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_59,plain,
( multiply(D,sk_c8) != sk_c9
| inverse(C) != D
| multiply(C,D) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(copy,[status(thm)],[c_4487]) ).
cnf(c_4488,plain,
( multiply(C,sk_c8) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(A,sk_c9) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_59]) ).
cnf(c_70,plain,
( multiply(C,sk_c8) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(copy,[status(thm)],[c_4488]) ).
cnf(c_4489,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_70]) ).
cnf(c_4490,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(copy,[status(thm)],[c_4489]) ).
cnf(c_80,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(A,sk_c10) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(copy,[status(thm)],[c_4490]) ).
cnf(c_85,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_80]) ).
cnf(c_4491,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_4492,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_4491]) ).
cnf(c_87,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_4492]) ).
cnf(c_4493,plain,
( multiply(sk_c9,A) = multiply(sk_c4,multiply(sk_c10,A))
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_90,plain,
( multiply(sk_c4,multiply(sk_c10,A)) = multiply(sk_c9,A)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(copy,[status(thm)],[c_4493]) ).
cnf(c_99,plain,
( multiply(sk_c10,sk_c5) = identity
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_125,plain,
( multiply(sk_c10,sk_c1) = identity
| inverse(sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_127,plain,
( multiply(sk_c10,sk_c1) = identity
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_199,plain,
( multiply(sk_c3,sk_c2) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_37,c_2]) ).
cnf(c_262,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_87]) ).
cnf(c_272,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_8,c_87]) ).
cnf(c_300,plain,
( multiply(inverse(sk_c1),sk_c10) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_22,c_87]) ).
cnf(c_301,plain,
( multiply(inverse(sk_c10),sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_22,c_87]) ).
cnf(c_360,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_87,c_87]) ).
cnf(c_361,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_360,c_262]) ).
cnf(c_417,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_361,c_2]) ).
cnf(c_4494,plain,
( multiply(sk_c4,sk_c9) = multiply(sk_c9,sk_c8)
| multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_6,c_90]) ).
cnf(c_491,plain,
( multiply(sk_c4,sk_c9) = multiply(sk_c9,sk_c8)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(copy,[status(thm)],[c_4494]) ).
cnf(c_4495,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| inverse(sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_125,c_87]) ).
cnf(c_516,plain,
( inverse(sk_c10) = sk_c1
| inverse(sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_361,c_4495]) ).
cnf(c_4496,plain,
( multiply(inverse(sk_c3),identity) = sk_c2
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_199,c_87]) ).
cnf(c_655,plain,
( inverse(sk_c3) = sk_c2
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_361,c_4496]) ).
cnf(c_658,plain,
( multiply(sk_c2,sk_c3) = identity
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_655,c_2]) ).
cnf(c_4497,plain,
( multiply(sk_c4,identity) = multiply(sk_c9,sk_c5)
| multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_99,c_90]) ).
cnf(c_4498,plain,
( sk_c4 = multiply(sk_c9,sk_c5)
| multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_361,c_4497]) ).
cnf(c_4499,plain,
( multiply(sk_c9,sk_c5) = sk_c4
| multiply(sk_c9,sk_c10) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(copy,[status(thm)],[c_4498]) ).
cnf(c_768,plain,
( multiply(sk_c9,sk_c5) = sk_c4
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(copy,[status(thm)],[c_4499]) ).
cnf(c_4500,plain,
( inverse(sk_c4) = sk_c10
| identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_658,c_29]) ).
cnf(c_1161,plain,
( identity = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(copy,[status(thm)],[c_4500]) ).
cnf(c_1166,plain,
( multiply(sk_c10,sk_c4) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1161,c_2]) ).
cnf(c_4501,plain,
( multiply(inverse(sk_c10),identity) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1166,c_87]) ).
cnf(c_1184,plain,
( inverse(sk_c10) = sk_c4
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_361,c_4501]) ).
cnf(c_1232,plain,
( multiply(sk_c4,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1184,c_2]) ).
cnf(c_4502,plain,
( identity = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1232,c_28]) ).
cnf(c_1364,plain,
( multiply(sk_c2,sk_c3) = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_4502]) ).
cnf(c_4503,plain,
( identity = sk_c9
| inverse(sk_c2) = sk_c3
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1232,c_36]) ).
cnf(c_1365,plain,
( inverse(sk_c2) = sk_c3
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_4503]) ).
cnf(c_1390,plain,
( multiply(sk_c3,sk_c2) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1365,c_2]) ).
cnf(c_4504,plain,
( multiply(inverse(sk_c3),identity) = sk_c2
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1390,c_87]) ).
cnf(c_1778,plain,
( inverse(sk_c3) = sk_c2
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_361,c_4504]) ).
cnf(c_1789,plain,
( multiply(sk_c2,sk_c3) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1778,c_2]) ).
cnf(c_4505,plain,
( multiply(inverse(sk_c10),identity) = sk_c1
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_127,c_87]) ).
cnf(c_1812,plain,
( inverse(sk_c10) = sk_c1
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_361,c_4505]) ).
cnf(c_4506,plain,
( identity = sk_c9
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1789,c_1364]) ).
cnf(c_4507,plain,
( identity = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_4506]) ).
cnf(c_2230,plain,
identity = sk_c9,
inference(copy,[status(thm)],[c_4507]) ).
cnf(c_4508,plain,
inverse(sk_c9) = identity,
inference(paramod,[status(thm)],[c_2230,c_417]) ).
cnf(c_2562,plain,
inverse(sk_c9) = sk_c9,
inference(paramod,[status(thm)],[c_2230,c_4508]) ).
cnf(c_2563,plain,
multiply(A,sk_c9) = A,
inference(paramod,[status(thm)],[c_2230,c_361]) ).
cnf(c_2585,plain,
multiply(sk_c9,A) = A,
inference(paramod,[status(thm)],[c_2230,c_1]) ).
cnf(c_4509,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c10
| sk_c5 = sk_c10 ),
inference(paramod,[status(thm)],[c_2563,c_272]) ).
cnf(c_4510,plain,
( multiply(sk_c9,sk_c8) = sk_c10
| sk_c5 = sk_c10 ),
inference(paramod,[status(thm)],[c_2562,c_4509]) ).
cnf(c_2615,plain,
( sk_c8 = sk_c10
| sk_c5 = sk_c10 ),
inference(paramod,[status(thm)],[c_2585,c_4510]) ).
cnf(c_2692,plain,
( inverse(sk_c10) = sk_c1
| sk_c5 = sk_c10 ),
inference(paramod,[status(thm)],[c_2563,c_1812]) ).
cnf(c_4511,plain,
( multiply(sk_c4,sk_c9) = multiply(sk_c9,sk_c8)
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_2585,c_491]) ).
cnf(c_4512,plain,
( sk_c4 = multiply(sk_c9,sk_c8)
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_2563,c_4511]) ).
cnf(c_4513,plain,
( sk_c4 = sk_c8
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_2585,c_4512]) ).
cnf(c_2787,plain,
( sk_c4 = sk_c8
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4513]) ).
cnf(c_4514,plain,
( multiply(inverse(sk_c10),sk_c9) = sk_c8
| sk_c1 = sk_c10 ),
inference(paramod,[status(thm)],[c_2563,c_301]) ).
cnf(c_2814,plain,
( inverse(sk_c10) = sk_c8
| sk_c1 = sk_c10 ),
inference(paramod,[status(thm)],[c_2563,c_4514]) ).
cnf(c_4515,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(sk_c10) != sk_c10
| sk_c10 != sk_c8 ),
inference(paramod,[status(thm)],[c_2585,c_85]) ).
cnf(c_4516,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c10 != sk_c10
| inverse(sk_c10) != sk_c10
| sk_c10 != sk_c8 ),
inference(paramod,[status(thm)],[c_2563,c_4515]) ).
cnf(c_4517,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c10 != sk_c10
| inverse(sk_c10) != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_4516]) ).
cnf(c_2891,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_4517]) ).
cnf(c_2899,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| sk_c1 = sk_c10 ),
inference(paramod,[status(thm)],[c_2563,c_22]) ).
cnf(c_4518,plain,
( multiply(sk_c9,sk_c5) = sk_c4
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_2585,c_768]) ).
cnf(c_4519,plain,
( sk_c5 = sk_c4
| sk_c10 = sk_c8 ),
inference(paramod,[status(thm)],[c_2585,c_4518]) ).
cnf(c_2989,plain,
( sk_c5 = sk_c4
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4519]) ).
cnf(c_4520,plain,
( sk_c8 = sk_c10
| sk_c4 = sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2989,c_2615]) ).
cnf(c_3263,plain,
( sk_c4 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4520]) ).
cnf(c_4521,plain,
( sk_c10 = sk_c8
| sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_3263,c_2787]) ).
cnf(c_4522,plain,
( sk_c8 = sk_c10
| sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4521]) ).
cnf(c_4523,plain,
( sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_4522]) ).
cnf(c_3292,plain,
sk_c8 = sk_c10,
inference(copy,[status(thm)],[c_4523]) ).
cnf(c_3403,plain,
( multiply(sk_c10,sk_c10) = sk_c9
| sk_c1 = sk_c10 ),
inference(paramod,[status(thm)],[c_3292,c_2899]) ).
cnf(c_4524,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_3292,c_2891]) ).
cnf(c_4525,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_3292,c_4524]) ).
cnf(c_4526,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c10 ),
inference(copy,[status(thm)],[c_4525]) ).
cnf(c_3406,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c10 ),
inference(copy,[status(thm)],[c_4526]) ).
cnf(c_3427,plain,
( inverse(sk_c10) = sk_c10
| sk_c1 = sk_c10 ),
inference(paramod,[status(thm)],[c_3292,c_2814]) ).
cnf(c_3460,plain,
( multiply(inverse(sk_c1),sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_3292,c_300]) ).
cnf(c_4527,plain,
( inverse(sk_c10) = sk_c1
| inverse(sk_c10) = sk_c10
| inverse(sk_c10) = sk_c1 ),
inference(paramod,[status(thm)],[c_2692,c_516]) ).
cnf(c_3531,plain,
( inverse(sk_c10) = sk_c10
| inverse(sk_c10) = sk_c1 ),
inference(copy,[status(thm)],[c_4527]) ).
cnf(c_4378,plain,
( inverse(sk_c10) != sk_c10
| sk_c1 = sk_c10 ),
inference(resolve,[status(thm)],[c_3403,c_3406]) ).
cnf(c_4528,plain,
( sk_c1 = sk_c10
| sk_c1 = sk_c10 ),
inference(resolve,[status(thm)],[c_4378,c_3427]) ).
cnf(c_4401,plain,
sk_c1 = sk_c10,
inference(copy,[status(thm)],[c_4528]) ).
cnf(c_4529,plain,
( inverse(sk_c10) = sk_c10
| inverse(sk_c10) = sk_c10 ),
inference(paramod,[status(thm)],[c_4401,c_3531]) ).
cnf(c_4467,plain,
inverse(sk_c10) = sk_c10,
inference(copy,[status(thm)],[c_4529]) ).
cnf(c_4530,plain,
( multiply(inverse(sk_c10),sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_4401,c_3460]) ).
cnf(c_4531,plain,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_4467,c_4530]) ).
cnf(c_4471,plain,
multiply(sk_c10,sk_c10) = sk_c9,
inference(copy,[status(thm)],[c_4531]) ).
cnf(c_4532,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_4467,c_3406]) ).
cnf(c_4533,plain,
( sk_c9 != sk_c9
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_4471,c_4532]) ).
cnf(c_4534,plain,
sk_c9 != sk_c9,
inference(copy,[status(thm)],[c_4533]) ).
cnf(c_4486,plain,
$false,
inference(copy,[status(thm)],[c_4534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP336-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.63 % Computer : n006.cluster.edu
% 0.18/0.63 % Model : x86_64 x86_64
% 0.18/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.63 % Memory : 8046.5625MB
% 0.18/0.63 % OS : Linux 6.8.0-71-generic
% 0.18/0.63 % CPULimit : 300
% 0.18/0.63 % WCLimit : 300
% 0.18/0.63 % DateTime : Fri Sep 25 14:46:32 UTC 2026
% 0.18/0.64 % CPUTime :
% 0.18/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.64 % Process 3144685 was started by sandbox2 on n006,
% 0.18/0.64 % Fri Sep 25 14:46:32 2026
% 0.18/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.65
% 0.18/0.65 % From the command line: assign(max_seconds, 300).
% 19.51/3.23
% 19.51/3.23 % SZS status Unsatisfiable for theBenchmark
% 19.51/3.23
% 19.51/3.23 % Proof 1 at 1.86 (+ 0.63) seconds.
% 19.51/3.23 % Length of proof is 71.
% 19.51/3.23 % Level of proof is 24.
% 19.51/3.23 % Maximum clause weight is 69.000.
% 19.51/3.23 % Given clauses 349.
% 19.51/3.23
% 19.51/3.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------