%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP332-1 : 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 : n016.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 43.47s 22.51s
% Output : CNFRefutation 43.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 24
% Syntax : Number of formulae : 199 ( 36 unt; 0 def)
% Number of atoms : 494 ( 493 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 440 ( 145 ~; 295 |; 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 10 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_14,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_17,axiom,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_20,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_26,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != sk_c8
| multiply(VAR_4,sk_c8) != VAR_3
| multiply(sk_c8,VAR_3) != sk_c7
| inverse(VAR_2) != sk_c8
| multiply(VAR_2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| inverse(VAR_1) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_56,plain,
multiply(multiply(A,identity),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_57,plain,
multiply(multiply(identity,A),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_36093,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_58,plain,
multiply(inverse(A),multiply(A,B)) = multiply(identity,B),
inference(copy,[status(thm)],[c_36093]) ).
cnf(c_59,plain,
multiply(multiply(A,inverse(B)),B) = multiply(A,identity),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_64,plain,
( multiply(sk_c6,A) = multiply(sk_c8,multiply(sk_c7,A))
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_36094,plain,
( multiply(sk_c7,A) = multiply(sk_c3,multiply(sk_c8,A))
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_66,plain,
( multiply(sk_c3,multiply(sk_c8,A)) = multiply(sk_c7,A)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36094]) ).
cnf(c_67,plain,
( multiply(multiply(A,sk_c3),sk_c8) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_68,plain,
( multiply(sk_c8,sk_c3) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_70,plain,
( multiply(multiply(A,sk_c8),sk_c5) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_72,plain,
( multiply(multiply(A,sk_c4),sk_c8) = multiply(A,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_73,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_155,plain,
( inverse(identity) != sk_c8
| sk_c8 != D
| multiply(sk_c8,D) != sk_c7
| inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(B) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_34]) ).
cnf(c_355,plain,
( inverse(identity) != sk_c8
| sk_c8 != C
| multiply(sk_c8,C) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_155]) ).
cnf(c_605,plain,
( sk_c8 != B
| multiply(sk_c8,B) != sk_c7
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(factor,[status(thm)],[c_355]) ).
cnf(c_966,plain,
multiply(multiply(identity,identity),A) = A,
inference(paramod,[status(thm)],[c_1,c_56]) ).
cnf(c_968,plain,
multiply(multiply(inverse(A),identity),A) = identity,
inference(paramod,[status(thm)],[c_2,c_56]) ).
cnf(c_1312,plain,
multiply(inverse(inverse(A)),identity) = multiply(identity,A),
inference(paramod,[status(thm)],[c_2,c_58]) ).
cnf(c_36095,plain,
( multiply(sk_c3,sk_c8) = multiply(identity,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_67]) ).
cnf(c_2774,plain,
( multiply(identity,sk_c7) = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36095]) ).
cnf(c_36096,plain,
( multiply(identity,sk_c8) = multiply(sk_c8,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_68,c_67]) ).
cnf(c_2783,plain,
( multiply(identity,sk_c8) = multiply(sk_c8,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36096]) ).
cnf(c_36097,plain,
( multiply(identity,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_2783]) ).
cnf(c_2945,plain,
( multiply(identity,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36097]) ).
cnf(c_36098,plain,
( multiply(sk_c8,sk_c5) = multiply(identity,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_70]) ).
cnf(c_3001,plain,
( multiply(identity,sk_c7) = multiply(sk_c8,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36098]) ).
cnf(c_3152,plain,
( multiply(sk_c6,A) = multiply(sk_c8,A)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_2945,c_57]) ).
cnf(c_36099,plain,
( multiply(identity,sk_c8) = multiply(sk_c8,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_73,c_72]) ).
cnf(c_3276,plain,
( multiply(identity,sk_c8) = multiply(sk_c8,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36099]) ).
cnf(c_4012,plain,
( multiply(sk_c8,sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_3276,c_1]) ).
cnf(c_36100,plain,
( multiply(identity,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_3276]) ).
cnf(c_4015,plain,
( multiply(identity,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36100]) ).
cnf(c_36101,plain,
( multiply(sk_c8,sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_3276,c_2945]) ).
cnf(c_4034,plain,
( multiply(sk_c8,sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36101]) ).
cnf(c_36102,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4012,c_66]) ).
cnf(c_4196,plain,
( multiply(sk_c3,sk_c8) = multiply(sk_c7,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36102]) ).
cnf(c_36103,plain,
( multiply(identity,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4012,c_3001]) ).
cnf(c_4199,plain,
( multiply(identity,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36103]) ).
cnf(c_36104,plain,
( multiply(sk_c7,A) = multiply(sk_c8,A)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4015,c_57]) ).
cnf(c_4229,plain,
( multiply(sk_c8,A) = multiply(sk_c7,A)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36104]) ).
cnf(c_36105,plain,
( multiply(sk_c6,sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4034,c_3152]) ).
cnf(c_4289,plain,
( multiply(sk_c6,sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36105]) ).
cnf(c_36106,plain,
( sk_c8 = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4199,c_2774]) ).
cnf(c_36107,plain,
( multiply(sk_c3,sk_c8) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36106]) ).
cnf(c_4304,plain,
( multiply(sk_c3,sk_c8) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36107]) ).
cnf(c_36108,plain,
( multiply(sk_c7,sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4196,c_4304]) ).
cnf(c_5710,plain,
( multiply(sk_c7,sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36108]) ).
cnf(c_36109,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c8,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_5710,c_64]) ).
cnf(c_5743,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c8,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36109]) ).
cnf(c_36110,plain,
( multiply(sk_c8,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_5743,c_4289]) ).
cnf(c_8620,plain,
( multiply(sk_c8,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36110]) ).
cnf(c_36111,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_8620,c_4229]) ).
cnf(c_36112,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36111]) ).
cnf(c_36113,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_36112]) ).
cnf(c_8685,plain,
multiply(sk_c7,sk_c8) = sk_c6,
inference(copy,[status(thm)],[c_36113]) ).
cnf(c_13033,plain,
( sk_c8 != B
| multiply(sk_c8,B) != sk_c7
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8 ),
inference(resolve,[status(thm)],[c_8685,c_605]) ).
cnf(c_13557,plain,
multiply(sk_c6,A) = multiply(sk_c7,multiply(sk_c8,A)),
inference(paramod,[status(thm)],[c_8685,c_3]) ).
cnf(c_13559,plain,
multiply(multiply(sk_c7,identity),sk_c8) = sk_c6,
inference(paramod,[status(thm)],[c_8685,c_56]) ).
cnf(c_13560,plain,
multiply(multiply(identity,sk_c7),sk_c8) = sk_c6,
inference(paramod,[status(thm)],[c_8685,c_57]) ).
cnf(c_36114,plain,
sk_c6 = multiply(identity,multiply(sk_c7,sk_c8)),
inference(paramod,[status(thm)],[c_13560,c_3]) ).
cnf(c_13874,plain,
multiply(identity,multiply(sk_c7,sk_c8)) = sk_c6,
inference(copy,[status(thm)],[c_36114]) ).
cnf(c_20860,plain,
multiply(multiply(identity,A),inverse(A)) = identity,
inference(paramod,[status(thm)],[c_1312,c_968]) ).
cnf(c_20999,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_1,c_20860]) ).
cnf(c_36115,plain,
identity = inverse(identity),
inference(paramod,[status(thm)],[c_20860,c_966]) ).
cnf(c_21037,plain,
inverse(identity) = identity,
inference(copy,[status(thm)],[c_36115]) ).
cnf(c_21202,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_20999]) ).
cnf(c_21203,plain,
( multiply(sk_c4,sk_c8) = identity
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_15,c_20999]) ).
cnf(c_21205,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_20999]) ).
cnf(c_21206,plain,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_18,c_20999]) ).
cnf(c_21207,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_19,c_20999]) ).
cnf(c_21208,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(paramod,[status(thm)],[c_20,c_20999]) ).
cnf(c_21209,plain,
( multiply(sk_c4,sk_c8) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_21,c_20999]) ).
cnf(c_21211,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_20999]) ).
cnf(c_21212,plain,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_20999]) ).
cnf(c_21216,plain,
( multiply(sk_c3,sk_c8) = identity
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_30,c_20999]) ).
cnf(c_21224,plain,
multiply(identity,A) = multiply(A,identity),
inference(paramod,[status(thm)],[c_20999,c_59]) ).
cnf(c_21418,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_21224,c_1]) ).
cnf(c_36116,plain,
( sk_c8 != identity
| multiply(identity,sk_c8) != sk_c7
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_21224,c_13033]) ).
cnf(c_36117,plain,
( identity != sk_c8
| multiply(identity,sk_c8) != sk_c7
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_36116]) ).
cnf(c_21502,plain,
( identity != sk_c8
| inverse(identity) != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_36117]) ).
cnf(c_22108,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c3,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_21206,c_20999]) ).
cnf(c_22123,plain,
( multiply(sk_c1,sk_c7) = identity
| multiply(sk_c4,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_21209,c_20999]) ).
cnf(c_22138,plain,
( multiply(sk_c2,sk_c7) = identity
| multiply(sk_c3,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_21212,c_20999]) ).
cnf(c_36118,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_21202,c_11]) ).
cnf(c_22158,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_36118]) ).
cnf(c_36119,plain,
( identity != sk_c8
| identity != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_21037,c_21502]) ).
cnf(c_22531,plain,
( identity != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c8 ),
inference(copy,[status(thm)],[c_36119]) ).
cnf(c_22551,plain,
( identity != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_21037,c_22531]) ).
cnf(c_36120,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_21203,c_14]) ).
cnf(c_22593,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_36120]) ).
cnf(c_22798,plain,
( identity != sk_c8
| multiply(identity,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_22551]) ).
cnf(c_22802,plain,
( identity != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7
| multiply(identity,sk_c7) != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_22798]) ).
cnf(c_36121,plain,
( identity != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7
| sk_c7 != sk_c8 ),
inference(paramod,[status(thm)],[c_1,c_22802]) ).
cnf(c_36122,plain,
( identity != sk_c8
| sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_36121]) ).
cnf(c_22804,plain,
( identity != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c6 != sk_c7
| identity != sk_c7
| sk_c8 != sk_c7 ),
inference(copy,[status(thm)],[c_36122]) ).
cnf(c_36123,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| identity = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_21207,c_13]) ).
cnf(c_22829,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(copy,[status(thm)],[c_36123]) ).
cnf(c_22896,plain,
( multiply(sk_c6,sk_c5) = multiply(sk_c7,sk_c7)
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_22829,c_13557]) ).
cnf(c_36124,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_21216,c_29]) ).
cnf(c_23174,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_36124]) ).
cnf(c_36125,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c7
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_22108,c_21205]) ).
cnf(c_24228,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c7) = identity ),
inference(copy,[status(thm)],[c_36125]) ).
cnf(c_36126,plain,
( identity = sk_c7
| identity = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_24228,c_22158]) ).
cnf(c_24266,plain,
( identity = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_36126]) ).
cnf(c_24420,plain,
( multiply(A,sk_c8) = A
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_24266,c_21418]) ).
cnf(c_36127,plain,
( sk_c7 = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_24420,c_8685]) ).
cnf(c_24693,plain,
( sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_36127]) ).
cnf(c_24772,plain,
( multiply(sk_c7,A) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_24693,c_1]) ).
cnf(c_25516,plain,
( multiply(identity,sk_c8) = sk_c6
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_24772,c_13559]) ).
cnf(c_36128,plain,
( sk_c6 = multiply(sk_c8,identity)
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_25516,c_21224]) ).
cnf(c_26379,plain,
( multiply(sk_c8,identity) = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_36128]) ).
cnf(c_36129,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_24693,c_26379]) ).
cnf(c_26468,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_36129]) ).
cnf(c_36130,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c5
| multiply(sk_c1,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_22123,c_21208]) ).
cnf(c_27600,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c7) = identity ),
inference(copy,[status(thm)],[c_36130]) ).
cnf(c_36131,plain,
( identity = sk_c5
| identity = sk_c8
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_27600,c_22593]) ).
cnf(c_27624,plain,
( identity = sk_c8
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_36131]) ).
cnf(c_27767,plain,
( multiply(A,sk_c5) = A
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_27624,c_21418]) ).
cnf(c_36132,plain,
( identity = sk_c8
| sk_c8 = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_27767,c_22829]) ).
cnf(c_28203,plain,
( sk_c8 = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_36132]) ).
cnf(c_36133,plain,
( multiply(sk_c2,sk_c7) = identity
| identity = sk_c7
| multiply(sk_c2,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_22138,c_21211]) ).
cnf(c_30003,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c7) = identity ),
inference(copy,[status(thm)],[c_36133]) ).
cnf(c_36134,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_22896,c_27767]) ).
cnf(c_31102,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_36134]) ).
cnf(c_36135,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_31102,c_24772]) ).
cnf(c_31127,plain,
( sk_c6 = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_36135]) ).
cnf(c_31234,plain,
( multiply(sk_c8,A) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_31127,c_1]) ).
cnf(c_36136,plain,
( sk_c7 = sk_c6
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_31234,c_26468]) ).
cnf(c_36137,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_36136]) ).
cnf(c_36138,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_36137]) ).
cnf(c_32158,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_36138]) ).
cnf(c_32211,plain,
( identity != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| identity != sk_c7
| sk_c8 != sk_c7 ),
inference(resolve,[status(thm)],[c_32158,c_22804]) ).
cnf(c_32226,plain,
multiply(sk_c7,sk_c8) = sk_c7,
inference(paramod,[status(thm)],[c_32158,c_8685]) ).
cnf(c_32291,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_32158,c_23174]) ).
cnf(c_32389,plain,
multiply(identity,sk_c7) = sk_c6,
inference(paramod,[status(thm)],[c_32226,c_13874]) ).
cnf(c_36139,plain,
( identity = sk_c7
| sk_c7 = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_32291,c_30003]) ).
cnf(c_36140,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_36139]) ).
cnf(c_36141,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_36140]) ).
cnf(c_34062,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_36141]) ).
cnf(c_34162,plain,
( identity != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| sk_c8 != sk_c7 ),
inference(resolve,[status(thm)],[c_34062,c_32211]) ).
cnf(c_36142,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_34062,c_28203]) ).
cnf(c_36143,plain,
( sk_c8 = sk_c7
| sk_c8 = sk_c7 ),
inference(copy,[status(thm)],[c_36142]) ).
cnf(c_34532,plain,
sk_c8 = sk_c7,
inference(copy,[status(thm)],[c_36143]) ).
cnf(c_34579,plain,
multiply(sk_c7,sk_c7) = sk_c6,
inference(paramod,[status(thm)],[c_34062,c_32389]) ).
cnf(c_34708,plain,
( identity != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(resolve,[status(thm)],[c_34532,c_34162]) ).
cnf(c_36144,plain,
( identity != sk_c8
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramod,[status(thm)],[c_34532,c_34708]) ).
cnf(c_35278,plain,
identity != sk_c8,
inference(resolve,[status(thm)],[c_34579,c_36144]) ).
cnf(c_36145,plain,
sk_c7 != sk_c8,
inference(paramod,[status(thm)],[c_34062,c_35278]) ).
cnf(c_36146,plain,
sk_c8 != sk_c7,
inference(copy,[status(thm)],[c_36145]) ).
cnf(c_36092,plain,
$false,
inference(resolve,[status(thm)],[c_34532,c_36146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP332-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.02/16.26 % CPULimit : 300
% 0.02/16.26 % WCLimit : 300
% 0.02/16.26 % DateTime : Fri Sep 25 14:46:28 UTC 2026
% 0.02/16.26 % CPUTime :
% 0.02/16.26 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/16.26 % Process 2348953 was started by sandbox on n012,
% 0.02/16.26 % Fri Sep 25 14:46:28 2026
% 0.02/16.26 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/16.27
% 0.02/16.27 % From the command line: assign(max_seconds, 300).
% 43.47/22.51
% 43.47/22.51 % given #500 (A,wt=31): 1036 multiply(multiply(multiply(identity,A),identity),B) = multiply(A,B). [para(57(a,1),56(a,2))].
% 43.47/22.51
% 43.47/22.51 % SZS status Unsatisfiable for theBenchmark
% 43.47/22.51
% 43.47/22.51 % Proof 1 at 5.38 (+ 0.83) seconds.
% 43.47/22.51 % Length of proof is 121.
% 43.47/22.51 % Level of proof is 21.
% 43.47/22.51 % Maximum clause weight is 61.000.
% 43.47/22.51 % Given clauses 935.
% 43.47/22.51
% 43.47/22.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------