%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP354-1 : 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 : n007.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 07:28:42 AM UTC 2026
% Result : Unsatisfiable 16.57s 2.59s
% Output : CNFRefutation 16.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 17
% Syntax : Number of formulae : 152 ( 27 unt; 0 def)
% Number of atoms : 409 ( 408 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 418 ( 161 ~; 257 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 5 ( 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 : 76 ( 0 sgn 11 !; 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_4,axiom,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_9,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_13,axiom,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_17,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_20,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_27,axiom,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c7 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c9) = sk_c7 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c9) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_35,axiom,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_35) ).
cnf(c_38,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_35]) ).
fof(prove_this_44,axiom,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_44) ).
cnf(c_47,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_44]) ).
fof(prove_this_49,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( multiply(VAR_5,sk_c7) != sk_c8
| inverse(VAR_4) != VAR_5
| multiply(VAR_4,VAR_5) != sk_c8
| multiply(VAR_3,sk_c8) != sk_c9
| inverse(VAR_3) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(VAR_2) != sk_c9
| multiply(VAR_2,sk_c9) != sk_c8
| inverse(VAR_1) != sk_c7
| multiply(VAR_1,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(VAR_0) != sk_c9
| multiply(VAR_0,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
file('theBenchmark.p',prove_this_49) ).
cnf(c_52,plain,
( multiply(F,sk_c7) != sk_c8
| inverse(E) != F
| multiply(E,F) != sk_c8
| multiply(D,sk_c8) != sk_c9
| inverse(D) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(clausify,[status(thm)],[prove_this_49]) ).
cnf(c_5081,plain,
( multiply(E,sk_c7) != sk_c8
| inverse(D) != E
| multiply(D,E) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(A) != sk_c9
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(factor,[status(thm)],[c_52]) ).
cnf(c_53,plain,
( multiply(E,sk_c7) != sk_c8
| inverse(D) != E
| multiply(D,E) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(copy,[status(thm)],[c_5081]) ).
cnf(c_5082,plain,
( multiply(sk_c9,sk_c7) != sk_c8
| inverse(A) != sk_c9
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_5083,plain,
( multiply(sk_c9,sk_c7) != sk_c8
| multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(copy,[status(thm)],[c_5082]) ).
cnf(c_56,plain,
( multiply(C,sk_c8) != sk_c9
| inverse(C) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(copy,[status(thm)],[c_5083]) ).
cnf(c_60,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(factor,[status(thm)],[c_56]) ).
cnf(c_5084,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(factor,[status(thm)],[c_60]) ).
cnf(c_63,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(copy,[status(thm)],[c_5084]) ).
cnf(c_5085,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_5086,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_5085]) ).
cnf(c_64,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_5086]) ).
cnf(c_76,plain,
( multiply(sk_c9,sk_c4) = identity
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_5087,plain,
( multiply(sk_c8,A) = multiply(sk_c1,multiply(sk_c9,A))
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_101,plain,
( multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c8,A)
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_5087]) ).
cnf(c_5088,plain,
( multiply(sk_c9,A) = multiply(sk_c4,multiply(sk_c8,A))
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_110,plain,
( multiply(sk_c4,multiply(sk_c8,A)) = multiply(sk_c9,A)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_5088]) ).
cnf(c_126,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_131,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_202,plain,
( multiply(sk_c7,sk_c2) = identity
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_47,c_2]) ).
cnf(c_217,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_64]) ).
cnf(c_218,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_64]) ).
cnf(c_227,plain,
( multiply(inverse(sk_c8),sk_c9) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_8,c_64]) ).
cnf(c_272,plain,
( multiply(inverse(sk_c9),sk_c8) = sk_c7
| inverse(sk_c9) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_64]) ).
cnf(c_315,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_64,c_64]) ).
cnf(c_316,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_315,c_217]) ).
cnf(c_339,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_316,c_2]) ).
cnf(c_5089,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_126,c_64]) ).
cnf(c_362,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_316,c_5089]) ).
cnf(c_365,plain,
( multiply(sk_c1,sk_c9) = identity
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_362,c_2]) ).
cnf(c_5090,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_131,c_64]) ).
cnf(c_496,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_316,c_5090]) ).
cnf(c_5091,plain,
( inverse(sk_c4) = sk_c9
| sk_c1 = sk_c7
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_496,c_31]) ).
cnf(c_504,plain,
( sk_c1 = sk_c7
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_5091]) ).
cnf(c_508,plain,
( multiply(sk_c9,sk_c4) = identity
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_504,c_2]) ).
cnf(c_5092,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_504,c_23]) ).
cnf(c_514,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_5092]) ).
cnf(c_5093,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_76,c_64]) ).
cnf(c_730,plain,
( inverse(sk_c9) = sk_c4
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(paramod,[status(thm)],[c_316,c_5093]) ).
cnf(c_5094,plain,
( multiply(inverse(sk_c7),identity) = sk_c2
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_202,c_64]) ).
cnf(c_1160,plain,
( inverse(sk_c7) = sk_c2
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_316,c_5094]) ).
cnf(c_5095,plain,
( sk_c2 = sk_c9
| inverse(sk_c4) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(paramod,[status(thm)],[c_1160,c_514]) ).
cnf(c_1168,plain,
( sk_c2 = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(copy,[status(thm)],[c_5095]) ).
cnf(c_1169,plain,
( multiply(sk_c9,sk_c4) = identity
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_1168,c_2]) ).
cnf(c_5096,plain,
( multiply(inverse(sk_c9),identity) = sk_c4
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_1169,c_64]) ).
cnf(c_1176,plain,
( inverse(sk_c9) = sk_c4
| sk_c2 = sk_c9 ),
inference(paramod,[status(thm)],[c_316,c_5096]) ).
cnf(c_5097,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c4 ),
inference(paramod,[status(thm)],[c_1176,c_38]) ).
cnf(c_1190,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c4 ),
inference(copy,[status(thm)],[c_5097]) ).
cnf(c_5098,plain,
( multiply(sk_c1,identity) = multiply(sk_c8,sk_c4)
| multiply(sk_c9,sk_c7) = sk_c8
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_508,c_101]) ).
cnf(c_5099,plain,
( sk_c1 = multiply(sk_c8,sk_c4)
| multiply(sk_c9,sk_c7) = sk_c8
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_316,c_5098]) ).
cnf(c_1732,plain,
( multiply(sk_c8,sk_c4) = sk_c1
| multiply(sk_c9,sk_c7) = sk_c8
| sk_c1 = sk_c7 ),
inference(copy,[status(thm)],[c_5099]) ).
cnf(c_5100,plain,
( inverse(sk_c3) = sk_c9
| identity = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_365,c_13]) ).
cnf(c_1796,plain,
( identity = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(copy,[status(thm)],[c_5100]) ).
cnf(c_1803,plain,
( multiply(sk_c9,sk_c3) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1796,c_2]) ).
cnf(c_5101,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1803,c_64]) ).
cnf(c_1811,plain,
( inverse(sk_c9) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_316,c_5101]) ).
cnf(c_1829,plain,
( multiply(sk_c3,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1811,c_2]) ).
cnf(c_5102,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1829,c_12]) ).
cnf(c_1882,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_5102]) ).
cnf(c_5103,plain,
( identity = sk_c8
| inverse(sk_c1) = sk_c9
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1829,c_20]) ).
cnf(c_1883,plain,
( inverse(sk_c1) = sk_c9
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_5103]) ).
cnf(c_1911,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1883,c_2]) ).
cnf(c_5104,plain,
( multiply(sk_c4,multiply(sk_c8,sk_c7)) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_14,c_110]) ).
cnf(c_2312,plain,
( multiply(sk_c4,multiply(sk_c8,sk_c7)) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(copy,[status(thm)],[c_5104]) ).
cnf(c_5105,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_1911,c_64]) ).
cnf(c_2406,plain,
( inverse(sk_c9) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_316,c_5105]) ).
cnf(c_2428,plain,
( multiply(sk_c1,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2406,c_2]) ).
cnf(c_5106,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2428,c_1882]) ).
cnf(c_5107,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_5106]) ).
cnf(c_3428,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_5107]) ).
cnf(c_5108,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_3428,c_339]) ).
cnf(c_3770,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_3428,c_5108]) ).
cnf(c_3771,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_3428,c_316]) ).
cnf(c_3792,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_3428,c_1]) ).
cnf(c_5109,plain,
( multiply(inverse(sk_c8),sk_c9) = sk_c7
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_3771,c_227]) ).
cnf(c_5110,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_3770,c_5109]) ).
cnf(c_5111,plain,
( sk_c9 = sk_c7
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_3792,c_5110]) ).
cnf(c_3820,plain,
( sk_c7 = sk_c9
| sk_c4 = sk_c9 ),
inference(copy,[status(thm)],[c_5111]) ).
cnf(c_5112,plain,
( inverse(sk_c9) = sk_c7
| inverse(sk_c9) = sk_c7 ),
inference(paramod,[status(thm)],[c_3771,c_272]) ).
cnf(c_4143,plain,
inverse(sk_c9) = sk_c7,
inference(copy,[status(thm)],[c_5112]) ).
cnf(c_5113,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_3792,c_63]) ).
cnf(c_5114,plain,
( multiply(A,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| sk_c7 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_4143,c_5113]) ).
cnf(c_5115,plain,
( A != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| sk_c7 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_3771,c_5114]) ).
cnf(c_5116,plain,
( sk_c9 != A
| multiply(sk_c9,sk_c7) != sk_c8
| sk_c7 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(copy,[status(thm)],[c_5115]) ).
cnf(c_4181,plain,
( sk_c9 != A
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(copy,[status(thm)],[c_5116]) ).
cnf(c_4269,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_3792,c_2312]) ).
cnf(c_4280,plain,
( sk_c4 = sk_c1
| multiply(sk_c9,sk_c7) = sk_c8
| sk_c1 = sk_c7 ),
inference(paramod,[status(thm)],[c_3792,c_1732]) ).
cnf(c_5117,plain,
( inverse(sk_c9) = sk_c4
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_3792,c_730]) ).
cnf(c_5118,plain,
( sk_c7 = sk_c4
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4143,c_5117]) ).
cnf(c_4337,plain,
( sk_c4 = sk_c7
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_5118]) ).
cnf(c_5119,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c7 = sk_c4 ),
inference(paramod,[status(thm)],[c_4143,c_1190]) ).
cnf(c_4418,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c4 = sk_c7 ),
inference(copy,[status(thm)],[c_5119]) ).
cnf(c_5120,plain,
C = multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))),
inference(copy,[status(thm)],[c_218]) ).
cnf(c_5121,plain,
( multiply(sk_c9,sk_c7) != sk_c8
| inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c9)))) != sk_c9
| multiply(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c9))),sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(resolve,[status(thm)],[c_4181,c_5120]) ).
cnf(c_5122,plain,
( multiply(sk_c9,sk_c7) != sk_c8
| inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c9)))) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_218,c_5121]) ).
cnf(c_5123,plain,
( multiply(sk_c9,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_218,c_5122]) ).
cnf(c_5124,plain,
( multiply(sk_c9,sk_c7) != sk_c8
| sk_c7 != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramod,[status(thm)],[c_4143,c_5123]) ).
cnf(c_4532,plain,
( multiply(sk_c9,sk_c7) != sk_c8
| multiply(sk_c9,sk_c9) != sk_c8
| sk_c7 != sk_c9 ),
inference(copy,[status(thm)],[c_5124]) ).
cnf(c_5125,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(paramod,[status(thm)],[c_4337,c_3820]) ).
cnf(c_5126,plain,
( sk_c7 = sk_c9
| sk_c7 = sk_c9 ),
inference(copy,[status(thm)],[c_5125]) ).
cnf(c_4905,plain,
sk_c7 = sk_c9,
inference(copy,[status(thm)],[c_5126]) ).
cnf(c_5127,plain,
( multiply(sk_c9,sk_c7) != sk_c8
| multiply(sk_c9,sk_c9) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_4905,c_4532]) ).
cnf(c_5128,plain,
( multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c9,sk_c9) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_4905,c_5127]) ).
cnf(c_5129,plain,
( multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_5128]) ).
cnf(c_5043,plain,
multiply(sk_c9,sk_c9) != sk_c8,
inference(copy,[status(thm)],[c_5129]) ).
cnf(c_5130,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4905,c_4418]) ).
cnf(c_5131,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c4 = sk_c9 ),
inference(paramod,[status(thm)],[c_4905,c_5130]) ).
cnf(c_5071,plain,
sk_c4 = sk_c9,
inference(resolve,[status(thm)],[c_5043,c_5131]) ).
cnf(c_5132,plain,
( sk_c4 = sk_c1
| multiply(sk_c9,sk_c7) = sk_c8
| sk_c1 = sk_c9 ),
inference(paramod,[status(thm)],[c_4905,c_4280]) ).
cnf(c_5133,plain,
( sk_c4 = sk_c1
| multiply(sk_c9,sk_c9) = sk_c8
| sk_c1 = sk_c9 ),
inference(paramod,[status(thm)],[c_4905,c_5132]) ).
cnf(c_5134,plain,
( sk_c9 = sk_c1
| multiply(sk_c9,sk_c9) = sk_c8
| sk_c1 = sk_c9 ),
inference(paramod,[status(thm)],[c_5071,c_5133]) ).
cnf(c_5135,plain,
( sk_c1 = sk_c9
| multiply(sk_c9,sk_c9) = sk_c8
| sk_c1 = sk_c9 ),
inference(copy,[status(thm)],[c_5134]) ).
cnf(c_5136,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| sk_c1 = sk_c9 ),
inference(copy,[status(thm)],[c_5135]) ).
cnf(c_5079,plain,
sk_c1 = sk_c9,
inference(resolve,[status(thm)],[c_5043,c_5136]) ).
cnf(c_5137,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_5079,c_4269]) ).
cnf(c_5138,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_5071,c_5137]) ).
cnf(c_5139,plain,
( multiply(sk_c9,sk_c9) = sk_c8
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_4905,c_5138]) ).
cnf(c_5140,plain,
multiply(sk_c9,sk_c9) = sk_c8,
inference(copy,[status(thm)],[c_5139]) ).
cnf(c_5080,plain,
$false,
inference(resolve,[status(thm)],[c_5043,c_5140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP354-1 : 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 : n007.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 14:45:53 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 1257694 was started by sandbox on n007,
% 0.13/0.37 % Fri Sep 25 14:45:53 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 16.57/2.59
% 16.57/2.59 % SZS status Unsatisfiable for theBenchmark
% 16.57/2.59
% 16.57/2.59 % Proof 1 at 1.70 (+ 0.48) seconds.
% 16.57/2.59 % Length of proof is 75.
% 16.57/2.59 % Level of proof is 22.
% 16.57/2.59 % Maximum clause weight is 68.000.
% 16.57/2.59 % Given clauses 281.
% 16.57/2.59
% 16.57/2.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------