%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP265-1 : 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 : n004.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 07:28:30 AM UTC 2026
% Result : Unsatisfiable 55.66s 7.45s
% Output : CNFRefutation 55.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 16
% Syntax : Number of formulae : 176 ( 33 unt; 0 def)
% Number of atoms : 438 ( 437 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 417 ( 155 ~; 262 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 92 ( 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_1,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_17,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_26,axiom,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_29,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( inverse(VAR_5) != sk_c7
| multiply(VAR_5,sk_c7) != VAR_4
| multiply(sk_c7,VAR_4) != sk_c8
| inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_2) != sk_c9
| multiply(VAR_2,sk_c9) != sk_c8
| inverse(VAR_1) != sk_c8
| multiply(VAR_1,sk_c8) != sk_c7
| inverse(VAR_0) != sk_c9
| multiply(VAR_0,sk_c9) != sk_c8 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(F) != sk_c7
| multiply(F,sk_c7) != E
| multiply(sk_c7,E) != sk_c8
| inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(C) != sk_c9
| multiply(C,sk_c9) != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
cnf(c_18392,plain,
( inverse(E) != sk_c7
| multiply(E,sk_c7) != D
| multiply(sk_c7,D) != sk_c8
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(A) != sk_c9
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_32]) ).
cnf(c_33,plain,
( inverse(E) != sk_c7
| multiply(E,sk_c7) != D
| multiply(sk_c7,D) != sk_c8
| inverse(C) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_18392]) ).
cnf(c_18393,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_18394,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_18393]) ).
cnf(c_42,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_18394]) ).
cnf(c_45,plain,
( multiply(sk_c9,sk_c3) = identity
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_54,plain,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_55,plain,
( multiply(sk_c9,sk_c3) = identity
| inverse(sk_c1) = sk_c9 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_66,plain,
( multiply(sk_c7,sk_c4) = identity
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_71,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_77,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_78,plain,
( multiply(sk_c7,sk_c5) = identity
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_121,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c8
| inverse(identity) != sk_c7
| sk_c7 != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_33]) ).
cnf(c_18395,plain,
( multiply(identity,sk_c7) != C
| multiply(sk_c7,C) != sk_c8
| inverse(identity) != sk_c7
| sk_c7 != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_121]) ).
cnf(c_285,plain,
( sk_c7 != C
| multiply(sk_c7,C) != sk_c8
| inverse(identity) != sk_c7
| sk_c7 != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_18395]) ).
cnf(c_618,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_42]) ).
cnf(c_619,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_42]) ).
cnf(c_636,plain,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_20,c_42]) ).
cnf(c_638,plain,
( multiply(inverse(sk_c2),sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_22,c_42]) ).
cnf(c_648,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_42,c_42]) ).
cnf(c_649,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_648,c_618]) ).
cnf(c_761,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_649,c_2]) ).
cnf(c_869,plain,
( sk_c7 != C
| multiply(sk_c7,C) != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_761,c_285]) ).
cnf(c_890,plain,
( multiply(sk_c9,sk_c1) = identity
| multiply(sk_c9,sk_c3) = identity ),
inference(paramod,[status(thm)],[c_55,c_2]) ).
cnf(c_1058,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c7,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_78,c_2]) ).
cnf(c_18396,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| multiply(sk_c9,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_890,c_42]) ).
cnf(c_1495,plain,
( inverse(sk_c9) = sk_c3
| multiply(sk_c9,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_649,c_18396]) ).
cnf(c_1498,plain,
( multiply(sk_c3,sk_c9) = identity
| multiply(sk_c9,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_1495,c_2]) ).
cnf(c_18397,plain,
( multiply(inverse(sk_c7),identity) = sk_c5
| multiply(sk_c8,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_1058,c_42]) ).
cnf(c_2188,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c8,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_649,c_18397]) ).
cnf(c_2193,plain,
( multiply(sk_c5,sk_c7) = identity
| multiply(sk_c8,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_2188,c_2]) ).
cnf(c_18398,plain,
( sk_c7 != identity
| sk_c7 != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_649,c_869]) ).
cnf(c_18399,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c7
| sk_c7 != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_18398]) ).
cnf(c_18400,plain,
( identity != sk_c7
| identity != sk_c7
| sk_c7 != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_18399]) ).
cnf(c_2957,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_18400]) ).
cnf(c_18401,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| inverse(identity) != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_2957]) ).
cnf(c_18402,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_761,c_18401]) ).
cnf(c_18403,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| identity != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_18402]) ).
cnf(c_3016,plain,
( identity != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_18403]) ).
cnf(c_18404,plain,
( identity != sk_c7
| identity != sk_c8
| sk_c7 != sk_c8
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_3016]) ).
cnf(c_3095,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c8 ),
inference(copy,[status(thm)],[c_18404]) ).
cnf(c_18405,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c8
| multiply(sk_c9,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_1498,c_54]) ).
cnf(c_3210,plain,
( identity = sk_c8
| multiply(sk_c9,sk_c1) = identity ),
inference(copy,[status(thm)],[c_18405]) ).
cnf(c_18406,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_3210,c_42]) ).
cnf(c_3867,plain,
( inverse(sk_c9) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_649,c_18406]) ).
cnf(c_3870,plain,
( multiply(sk_c1,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_3867,c_2]) ).
cnf(c_18407,plain,
( multiply(sk_c9,sk_c3) = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_3870,c_45]) ).
cnf(c_3928,plain,
( multiply(sk_c9,sk_c3) = identity
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_18407]) ).
cnf(c_18408,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_3928,c_42]) ).
cnf(c_3970,plain,
( inverse(sk_c9) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_649,c_18408]) ).
cnf(c_3973,plain,
( multiply(sk_c3,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_3970,c_2]) ).
cnf(c_18409,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_3973,c_4]) ).
cnf(c_7222,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_18409]) ).
cnf(c_18410,plain,
( sk_c8 = identity
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_7222,c_3870]) ).
cnf(c_18411,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_18410]) ).
cnf(c_18412,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_18411]) ).
cnf(c_10234,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_18412]) ).
cnf(c_18413,plain,
( identity != sk_c7
| sk_c7 != sk_c8
| inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_10234,c_3095]) ).
cnf(c_18414,plain,
( sk_c8 != sk_c7
| sk_c7 != sk_c8
| inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_10234,c_18413]) ).
cnf(c_18415,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8
| inverse(inverse(sk_c9)) != sk_c9
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_18414]) ).
cnf(c_18416,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8
| inverse(inverse(sk_c9)) != sk_c9 ),
inference(copy,[status(thm)],[c_18415]) ).
cnf(c_12145,plain,
( sk_c7 != sk_c8
| inverse(inverse(sk_c9)) != sk_c9 ),
inference(copy,[status(thm)],[c_18416]) ).
cnf(c_18417,plain,
( multiply(sk_c5,sk_c7) = identity
| multiply(sk_c8,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_10234,c_2193]) ).
cnf(c_12300,plain,
( multiply(sk_c5,sk_c7) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_10234,c_18417]) ).
cnf(c_12796,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_10234,c_649]) ).
cnf(c_12806,plain,
( multiply(sk_c8,sk_c2) = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_10234,c_77]) ).
cnf(c_18418,plain,
( multiply(sk_c7,sk_c5) = identity
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_71]) ).
cnf(c_12810,plain,
( multiply(sk_c7,sk_c5) = sk_c8
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_10234,c_18418]) ).
cnf(c_18419,plain,
( multiply(sk_c7,sk_c4) = identity
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_66]) ).
cnf(c_12811,plain,
( multiply(sk_c7,sk_c4) = sk_c8
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_10234,c_18419]) ).
cnf(c_12820,plain,
multiply(inverse(A),A) = sk_c8,
inference(paramod,[status(thm)],[c_10234,c_2]) ).
cnf(c_12821,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_10234,c_1]) ).
cnf(c_18420,plain,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_636]) ).
cnf(c_15211,plain,
( inverse(sk_c4) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_18420]) ).
cnf(c_15432,plain,
( inverse(sk_c5) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_24]) ).
cnf(c_15433,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_23]) ).
cnf(c_15434,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_22]) ).
cnf(c_15436,plain,
( sk_c2 = sk_c8
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_12821,c_12806]) ).
cnf(c_15468,plain,
( multiply(sk_c5,sk_c7) = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_12821,c_12300]) ).
cnf(c_18421,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12810,c_42]) ).
cnf(c_15973,plain,
( inverse(sk_c7) = sk_c5
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_18421]) ).
cnf(c_18422,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c4
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12811,c_42]) ).
cnf(c_15992,plain,
( inverse(sk_c7) = sk_c4
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_18422]) ).
cnf(c_16232,plain,
( multiply(inverse(multiply(A,sk_c5)),multiply(A,sk_c6)) = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_15433,c_619]) ).
cnf(c_18423,plain,
( multiply(sk_c8,sk_c7) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_29,c_638]) ).
cnf(c_18424,plain,
( sk_c7 = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_12821,c_18423]) ).
cnf(c_16246,plain,
( sk_c7 = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(copy,[status(thm)],[c_18424]) ).
cnf(c_18425,plain,
( multiply(inverse(sk_c7),sk_c8) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_15434,c_42]) ).
cnf(c_16495,plain,
( inverse(sk_c7) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_12796,c_18425]) ).
cnf(c_18426,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_16495,c_15973]) ).
cnf(c_16512,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_18426]) ).
cnf(c_18427,plain,
( sk_c6 = sk_c4
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_16495,c_15992]) ).
cnf(c_16513,plain,
( sk_c6 = sk_c4
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_18427]) ).
cnf(c_18428,plain,
( multiply(sk_c5,sk_c7) = sk_c5
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_16512,c_15433]) ).
cnf(c_16532,plain,
( multiply(sk_c5,sk_c7) = sk_c5
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_18428]) ).
cnf(c_18429,plain,
( multiply(sk_c5,sk_c7) = sk_c4
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_16513,c_15433]) ).
cnf(c_16538,plain,
( multiply(sk_c5,sk_c7) = sk_c4
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_18429]) ).
cnf(c_18430,plain,
multiply(A,sk_c8) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_648,c_12796]) ).
cnf(c_18431,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_12796,c_18430]) ).
cnf(c_16596,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_18431]) ).
cnf(c_16600,plain,
( multiply(inverse(sk_c7),A) = multiply(sk_c4,A)
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_15211,c_648]) ).
cnf(c_16602,plain,
( multiply(inverse(sk_c7),A) = multiply(sk_c5,A)
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_15432,c_648]) ).
cnf(c_18432,plain,
( sk_c7 != sk_c8
| sk_c9 != sk_c9 ),
inference(paramod,[status(thm)],[c_16596,c_12145]) ).
cnf(c_16773,plain,
sk_c7 != sk_c8,
inference(copy,[status(thm)],[c_18432]) ).
cnf(c_16783,plain,
multiply(sk_c7,sk_c6) = sk_c8,
inference(resolve,[status(thm)],[c_16773,c_16246]) ).
cnf(c_18433,plain,
multiply(inverse(sk_c7),sk_c8) = sk_c6,
inference(paramod,[status(thm)],[c_16783,c_42]) ).
cnf(c_17118,plain,
inverse(sk_c7) = sk_c6,
inference(paramod,[status(thm)],[c_12796,c_18433]) ).
cnf(c_17250,plain,
( multiply(sk_c6,A) = multiply(sk_c5,A)
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_17118,c_16602]) ).
cnf(c_17251,plain,
( multiply(sk_c6,A) = multiply(sk_c4,A)
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_17118,c_16600]) ).
cnf(c_18434,plain,
( sk_c2 = sk_c8
| sk_c8 = sk_c6
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_15468,c_15436]) ).
cnf(c_18435,plain,
( sk_c2 = sk_c8
| sk_c6 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_18434]) ).
cnf(c_18182,plain,
( sk_c6 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_18435]) ).
cnf(c_18436,plain,
( multiply(sk_c7,sk_c8) = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_18182,c_16783]) ).
cnf(c_18437,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_12796,c_18436]) ).
cnf(c_18187,plain,
sk_c2 = sk_c8,
inference(resolve,[status(thm)],[c_16773,c_18437]) ).
cnf(c_18438,plain,
( multiply(sk_c6,A) = multiply(sk_c4,A)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18187,c_17251]) ).
cnf(c_18439,plain,
( multiply(sk_c6,A) = multiply(sk_c4,A)
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18438]) ).
cnf(c_18311,plain,
multiply(sk_c6,A) = multiply(sk_c4,A),
inference(resolve,[status(thm)],[c_16773,c_18439]) ).
cnf(c_18440,plain,
( multiply(sk_c6,A) = multiply(sk_c5,A)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18187,c_17250]) ).
cnf(c_18441,plain,
( multiply(sk_c4,A) = multiply(sk_c5,A)
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18311,c_18440]) ).
cnf(c_18442,plain,
( multiply(sk_c4,A) = multiply(sk_c5,A)
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18441]) ).
cnf(c_18443,plain,
( multiply(sk_c5,A) = multiply(sk_c4,A)
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18442]) ).
cnf(c_18312,plain,
multiply(sk_c5,A) = multiply(sk_c4,A),
inference(resolve,[status(thm)],[c_16773,c_18443]) ).
cnf(c_18444,plain,
( multiply(sk_c5,sk_c7) = sk_c4
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18187,c_16538]) ).
cnf(c_18445,plain,
( multiply(sk_c4,sk_c7) = sk_c4
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18312,c_18444]) ).
cnf(c_18446,plain,
( multiply(sk_c4,sk_c7) = sk_c4
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18445]) ).
cnf(c_18384,plain,
multiply(sk_c4,sk_c7) = sk_c4,
inference(resolve,[status(thm)],[c_16773,c_18446]) ).
cnf(c_18447,plain,
( multiply(sk_c5,sk_c7) = sk_c5
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18187,c_16532]) ).
cnf(c_18448,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18312,c_18447]) ).
cnf(c_18449,plain,
( sk_c4 = sk_c5
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18384,c_18448]) ).
cnf(c_18450,plain,
( sk_c4 = sk_c5
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18449]) ).
cnf(c_18451,plain,
( sk_c5 = sk_c4
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18450]) ).
cnf(c_18385,plain,
sk_c5 = sk_c4,
inference(resolve,[status(thm)],[c_16773,c_18451]) ).
cnf(c_18452,plain,
( sk_c6 = sk_c4
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18187,c_16513]) ).
cnf(c_18453,plain,
( sk_c6 = sk_c4
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18452]) ).
cnf(c_18386,plain,
sk_c6 = sk_c4,
inference(resolve,[status(thm)],[c_16773,c_18453]) ).
cnf(c_18454,plain,
( multiply(inverse(multiply(A,sk_c5)),multiply(A,sk_c6)) = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18187,c_16232]) ).
cnf(c_18455,plain,
( multiply(inverse(multiply(A,sk_c4)),multiply(A,sk_c6)) = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18385,c_18454]) ).
cnf(c_18456,plain,
( multiply(inverse(multiply(A,sk_c4)),multiply(A,sk_c4)) = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_18386,c_18455]) ).
cnf(c_18457,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(paramod,[status(thm)],[c_12820,c_18456]) ).
cnf(c_18458,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18457]) ).
cnf(c_18459,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_18458]) ).
cnf(c_18460,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_18459]) ).
cnf(c_18391,plain,
$false,
inference(resolve,[status(thm)],[c_16773,c_18460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP265-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:42:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3420169 was started by sandbox on n004,
% 0.09/0.36 % Fri Sep 25 14:42:06 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 55.66/7.45
% 55.66/7.45 % SZS status Unsatisfiable for theBenchmark
% 55.66/7.45
% 55.66/7.45 % Proof 1 at 6.23 (+ 0.81) seconds.
% 55.66/7.45 % Length of proof is 91.
% 55.66/7.45 % Level of proof is 24.
% 55.66/7.45 % Maximum clause weight is 60.000.
% 55.66/7.45 % Given clauses 323.
% 55.66/7.45
% 55.66/7.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------