%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP349-1 : 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 : 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 07:28:41 AM UTC 2026
% Result : Unsatisfiable 8.13s 6.43s
% Output : CNFRefutation 8.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 12
% Syntax : Number of formulae : 114 ( 25 unt; 0 def)
% Number of atoms : 383 ( 382 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 503 ( 234 ~; 269 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 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 : 84 ( 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_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_12,axiom,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_17,axiom,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c8 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c8 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_27,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_35,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('theBenchmark.p',prove_this_35) ).
cnf(c_38,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_35]) ).
fof(prove_this_65,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_c9) != sk_c8
| inverse(VAR_2) != sk_c8
| multiply(VAR_1,sk_c8) != sk_c9
| inverse(VAR_0) != VAR_1
| multiply(VAR_0,VAR_1) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
file('theBenchmark.p',prove_this_65) ).
cnf(c_68,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_c9) != sk_c8
| inverse(C) != sk_c8
| multiply(B,sk_c8) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(clausify,[status(thm)],[prove_this_65]) ).
cnf(c_70,plain,
( multiply(F,sk_c8) != sk_c9
| inverse(E) != F
| multiply(E,F) != sk_c9
| multiply(D,sk_c9) != sk_c10
| inverse(D) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(C) != sk_c10
| multiply(C,sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(B,sk_c8) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_68]) ).
cnf(c_3245,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
| inverse(A) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_70]) ).
cnf(c_3246,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_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(copy,[status(thm)],[c_3245]) ).
cnf(c_76,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_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(copy,[status(thm)],[c_3246]) ).
cnf(c_3247,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(B,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_76]) ).
cnf(c_3248,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(B,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(copy,[status(thm)],[c_3247]) ).
cnf(c_83,plain,
( multiply(B,sk_c9) != sk_c10
| inverse(B) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(copy,[status(thm)],[c_3248]) ).
cnf(c_87,plain,
( multiply(A,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(factor,[status(thm)],[c_83]) ).
cnf(c_3249,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3250,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3249]) ).
cnf(c_88,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3250]) ).
cnf(c_3251,plain,
( multiply(multiply(A,sk_c9),sk_c10) = multiply(A,sk_c8)
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_97,plain,
( multiply(A,multiply(sk_c9,sk_c10)) = multiply(A,sk_c8)
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_3,c_3251]) ).
cnf(c_129,plain,
( multiply(sk_c10,sk_c5) = identity
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_151,plain,
( multiply(sk_c10,sk_c4) = identity
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_298,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_88]) ).
cnf(c_299,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))) = C,
inference(paramod,[status(thm)],[c_3,c_88]) ).
cnf(c_324,plain,
( multiply(inverse(sk_c9),sk_c10) = sk_c8
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_16,c_88]) ).
cnf(c_337,plain,
( multiply(inverse(sk_c10),sk_c9) = sk_c8
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_22,c_88]) ).
cnf(c_428,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_88,c_88]) ).
cnf(c_429,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_428,c_298]) ).
cnf(c_434,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_429,c_2]) ).
cnf(c_3252,plain,
( multiply(inverse(sk_c10),identity) = sk_c4
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_151,c_88]) ).
cnf(c_446,plain,
( inverse(sk_c10) = sk_c4
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_429,c_3252]) ).
cnf(c_461,plain,
( multiply(sk_c4,sk_c10) = identity
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_446,c_2]) ).
cnf(c_582,plain,
( multiply(inverse(sk_c8),multiply(sk_c9,sk_c10)) = identity
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_2,c_97]) ).
cnf(c_3253,plain,
( identity = sk_c9
| inverse(sk_c10) = sk_c8
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_461,c_20]) ).
cnf(c_1182,plain,
( identity = sk_c9
| inverse(sk_c10) = sk_c8 ),
inference(copy,[status(thm)],[c_3253]) ).
cnf(c_1187,plain,
( multiply(sk_c8,sk_c10) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1182,c_2]) ).
cnf(c_3254,plain,
( multiply(inverse(sk_c8),identity) = sk_c10
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1187,c_88]) ).
cnf(c_1269,plain,
( inverse(sk_c8) = sk_c10
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_429,c_3254]) ).
cnf(c_1295,plain,
( multiply(sk_c10,sk_c8) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1269,c_2]) ).
cnf(c_3255,plain,
( identity = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1295,c_30]) ).
cnf(c_1367,plain,
( multiply(sk_c1,sk_c2) = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_3255]) ).
cnf(c_3256,plain,
( identity = sk_c9
| inverse(sk_c1) = sk_c2
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1295,c_38]) ).
cnf(c_1368,plain,
( inverse(sk_c1) = sk_c2
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_3256]) ).
cnf(c_1407,plain,
( multiply(sk_c2,sk_c1) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1368,c_2]) ).
cnf(c_3257,plain,
( multiply(inverse(sk_c2),identity) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1407,c_88]) ).
cnf(c_1590,plain,
( inverse(sk_c2) = sk_c1
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_429,c_3257]) ).
cnf(c_1598,plain,
( multiply(sk_c1,sk_c2) = identity
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1590,c_2]) ).
cnf(c_3258,plain,
( multiply(inverse(sk_c10),identity) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(paramod,[status(thm)],[c_129,c_88]) ).
cnf(c_1819,plain,
( inverse(sk_c10) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(paramod,[status(thm)],[c_429,c_3258]) ).
cnf(c_3259,plain,
( identity = sk_c9
| identity = sk_c9
| identity = sk_c9 ),
inference(paramod,[status(thm)],[c_1598,c_1367]) ).
cnf(c_3260,plain,
( identity = sk_c9
| identity = sk_c9 ),
inference(copy,[status(thm)],[c_3259]) ).
cnf(c_2022,plain,
identity = sk_c9,
inference(copy,[status(thm)],[c_3260]) ).
cnf(c_2175,plain,
( multiply(inverse(sk_c8),multiply(sk_c9,sk_c10)) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_2022,c_582]) ).
cnf(c_3261,plain,
inverse(sk_c9) = identity,
inference(paramod,[status(thm)],[c_2022,c_434]) ).
cnf(c_2208,plain,
inverse(sk_c9) = sk_c9,
inference(paramod,[status(thm)],[c_2022,c_3261]) ).
cnf(c_2209,plain,
multiply(A,sk_c9) = A,
inference(paramod,[status(thm)],[c_2022,c_429]) ).
cnf(c_2244,plain,
multiply(sk_c9,A) = A,
inference(paramod,[status(thm)],[c_2022,c_1]) ).
cnf(c_3262,plain,
( multiply(inverse(sk_c9),sk_c10) = sk_c8
| sk_c5 = sk_c10 ),
inference(paramod,[status(thm)],[c_2209,c_324]) ).
cnf(c_3263,plain,
( multiply(sk_c9,sk_c10) = sk_c8
| sk_c5 = sk_c10 ),
inference(paramod,[status(thm)],[c_2208,c_3262]) ).
cnf(c_3264,plain,
( sk_c10 = sk_c8
| sk_c5 = sk_c10 ),
inference(paramod,[status(thm)],[c_2244,c_3263]) ).
cnf(c_2267,plain,
( sk_c8 = sk_c10
| sk_c5 = sk_c10 ),
inference(copy,[status(thm)],[c_3264]) ).
cnf(c_3265,plain,
( inverse(sk_c10) = sk_c8
| inverse(sk_c10) = sk_c8 ),
inference(paramod,[status(thm)],[c_2209,c_337]) ).
cnf(c_2446,plain,
inverse(sk_c10) = sk_c8,
inference(copy,[status(thm)],[c_3265]) ).
cnf(c_3266,plain,
( multiply(A,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| sk_c10 != sk_c8 ),
inference(paramod,[status(thm)],[c_2244,c_87]) ).
cnf(c_3267,plain,
( multiply(A,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| inverse(sk_c10) != sk_c8
| sk_c8 != sk_c10
| sk_c10 != sk_c8 ),
inference(paramod,[status(thm)],[c_2244,c_3266]) ).
cnf(c_3268,plain,
( multiply(A,sk_c9) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c8
| sk_c8 != sk_c10
| sk_c10 != sk_c8 ),
inference(paramod,[status(thm)],[c_2446,c_3267]) ).
cnf(c_3269,plain,
( multiply(A,sk_c9) != sk_c10
| sk_c10 != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c8
| sk_c8 != sk_c10
| sk_c10 != sk_c8 ),
inference(paramod,[status(thm)],[c_2209,c_3268]) ).
cnf(c_3270,plain,
( A != sk_c10
| sk_c10 != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c8
| sk_c8 != sk_c10
| sk_c10 != sk_c8 ),
inference(paramod,[status(thm)],[c_2209,c_3269]) ).
cnf(c_3271,plain,
( A != sk_c10
| sk_c10 != sk_c8
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c8
| sk_c8 != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3270]) ).
cnf(c_3272,plain,
( A != sk_c10
| sk_c8 != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c8
| sk_c8 != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3271]) ).
cnf(c_3273,plain,
( sk_c10 != A
| sk_c8 != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c8
| sk_c8 != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3272]) ).
cnf(c_3274,plain,
( sk_c10 != A
| sk_c8 != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3273]) ).
cnf(c_3275,plain,
( sk_c10 != A
| sk_c8 != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3274]) ).
cnf(c_2507,plain,
( sk_c10 != A
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3275]) ).
cnf(c_2524,plain,
( multiply(inverse(sk_c8),sk_c10) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(paramod,[status(thm)],[c_2244,c_2175]) ).
cnf(c_3276,plain,
( inverse(sk_c10) = sk_c5
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2244,c_1819]) ).
cnf(c_3277,plain,
( sk_c8 = sk_c5
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2446,c_3276]) ).
cnf(c_2565,plain,
( sk_c5 = sk_c8
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_3277]) ).
cnf(c_3278,plain,
C = multiply(inverse(multiply(A,B)),multiply(A,multiply(B,C))),
inference(copy,[status(thm)],[c_299]) ).
cnf(c_3279,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c10)))) != sk_c10
| multiply(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c10))),sk_c10) != sk_c9
| sk_c8 != sk_c10 ),
inference(resolve,[status(thm)],[c_2507,c_3278]) ).
cnf(c_3280,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(B,sk_c10)))) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c8 != sk_c10 ),
inference(paramod,[status(thm)],[c_299,c_3279]) ).
cnf(c_3281,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| inverse(sk_c10) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c8 != sk_c10 ),
inference(paramod,[status(thm)],[c_299,c_3280]) ).
cnf(c_3282,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| sk_c8 != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c8 != sk_c10 ),
inference(paramod,[status(thm)],[c_2446,c_3281]) ).
cnf(c_2781,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3282]) ).
cnf(c_3283,plain,
( sk_c8 = sk_c10
| sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2565,c_2267]) ).
cnf(c_3284,plain,
( sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_3283]) ).
cnf(c_3088,plain,
sk_c8 = sk_c10,
inference(copy,[status(thm)],[c_3284]) ).
cnf(c_3285,plain,
( multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_3088,c_2781]) ).
cnf(c_3286,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_3088,c_3285]) ).
cnf(c_3287,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_3286]) ).
cnf(c_3196,plain,
multiply(sk_c10,sk_c10) != sk_c9,
inference(copy,[status(thm)],[c_3287]) ).
cnf(c_3288,plain,
( multiply(inverse(sk_c8),sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_3088,c_2524]) ).
cnf(c_3289,plain,
( multiply(inverse(sk_c10),sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_3088,c_3288]) ).
cnf(c_3290,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_2446,c_3289]) ).
cnf(c_3291,plain,
( multiply(sk_c10,sk_c10) = sk_c9
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_3088,c_3290]) ).
cnf(c_3292,plain,
multiply(sk_c10,sk_c10) = sk_c9,
inference(copy,[status(thm)],[c_3291]) ).
cnf(c_3244,plain,
$false,
inference(resolve,[status(thm)],[c_3196,c_3292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP349-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 14:47:35 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 3145626 was started by sandbox on n006,
% 0.09/5.38 % Fri Sep 25 14:47:35 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 8.13/6.43
% 8.13/6.43 % SZS status Unsatisfiable for theBenchmark
% 8.13/6.43
% 8.13/6.43 % Proof 1 at 0.77 (+ 0.26) seconds.
% 8.13/6.43 % Length of proof is 54.
% 8.13/6.43 % Level of proof is 20.
% 8.13/6.43 % Maximum clause weight is 78.000.
% 8.13/6.43 % Given clauses 242.
% 8.13/6.43
% 8.13/6.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------