%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP264-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 7.81s 6.47s
% Output : CNFRefutation 7.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 14
% Syntax : Number of formulae : 126 ( 26 unt; 0 def)
% Number of atoms : 321 ( 320 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 319 ( 124 ~; 195 |; 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 72 ( 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_19,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c5,sk_c8) = 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_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_26,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c5) = sk_c8
| 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_c8
| multiply(VAR_5,sk_c8) != VAR_4
| multiply(sk_c8,VAR_4) != sk_c7
| 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_c8
| multiply(F,sk_c8) != E
| multiply(sk_c8,E) != sk_c7
| 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_2221,plain,
( inverse(E) != sk_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| 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_c8
| multiply(E,sk_c8) != D
| multiply(sk_c8,D) != sk_c7
| 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_2221]) ).
cnf(c_36,plain,
( inverse(C) != sk_c8
| multiply(C,sk_c8) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_33]) ).
cnf(c_39,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_2222,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_2223,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_2222]) ).
cnf(c_40,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_2223]) ).
cnf(c_69,plain,
( multiply(sk_c9,sk_c1) = identity
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_106,plain,
( multiply(sk_c8,sk_c5) = identity
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_2]) ).
cnf(c_119,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_29,c_2]) ).
cnf(c_122,plain,
( multiply(sk_c8,sk_c2) = identity
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_30,c_2]) ).
cnf(c_125,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_31,c_2]) ).
cnf(c_128,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_40]) ).
cnf(c_167,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_40]) ).
cnf(c_186,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_40,c_40]) ).
cnf(c_187,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_186,c_128]) ).
cnf(c_192,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_187,c_2]) ).
cnf(c_2224,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_69,c_40]) ).
cnf(c_196,plain,
( inverse(sk_c9) = sk_c1
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_187,c_2224]) ).
cnf(c_199,plain,
( multiply(sk_c1,sk_c9) = identity
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_196,c_2]) ).
cnf(c_2225,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_125,c_40]) ).
cnf(c_326,plain,
( inverse(sk_c8) = sk_c2
| inverse(sk_c5) = sk_c8 ),
inference(paramod,[status(thm)],[c_187,c_2225]) ).
cnf(c_329,plain,
( multiply(sk_c8,sk_c5) = identity
| inverse(sk_c8) = sk_c2 ),
inference(paramod,[status(thm)],[c_326,c_2]) ).
cnf(c_2226,plain,
( inverse(sk_c3) = sk_c9
| identity = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_199,c_5]) ).
cnf(c_370,plain,
( identity = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(copy,[status(thm)],[c_2226]) ).
cnf(c_375,plain,
( multiply(sk_c9,sk_c3) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_370,c_2]) ).
cnf(c_2227,plain,
( multiply(inverse(sk_c9),identity) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_375,c_40]) ).
cnf(c_392,plain,
( inverse(sk_c9) = sk_c3
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_187,c_2227]) ).
cnf(c_403,plain,
( multiply(sk_c3,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_392,c_2]) ).
cnf(c_2228,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_403,c_4]) ).
cnf(c_445,plain,
( multiply(sk_c1,sk_c9) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_2228]) ).
cnf(c_2229,plain,
( identity = sk_c8
| inverse(sk_c1) = sk_c9
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_403,c_11]) ).
cnf(c_446,plain,
( inverse(sk_c1) = sk_c9
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_2229]) ).
cnf(c_460,plain,
( multiply(sk_c9,sk_c1) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_446,c_2]) ).
cnf(c_2230,plain,
( multiply(inverse(sk_c9),identity) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_460,c_40]) ).
cnf(c_592,plain,
( inverse(sk_c9) = sk_c1
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_187,c_2230]) ).
cnf(c_603,plain,
( multiply(sk_c1,sk_c9) = identity
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_592,c_2]) ).
cnf(c_2231,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_603,c_445]) ).
cnf(c_2232,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_2231]) ).
cnf(c_838,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_2232]) ).
cnf(c_923,plain,
( multiply(sk_c8,sk_c5) = sk_c8
| inverse(sk_c8) = sk_c2 ),
inference(paramod,[status(thm)],[c_838,c_329]) ).
cnf(c_2233,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_838,c_192]) ).
cnf(c_961,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_838,c_2233]) ).
cnf(c_962,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_838,c_187]) ).
cnf(c_2234,plain,
( multiply(sk_c8,sk_c2) = identity
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_962,c_122]) ).
cnf(c_2235,plain,
( multiply(sk_c8,sk_c2) = sk_c8
| sk_c5 = sk_c6 ),
inference(paramod,[status(thm)],[c_838,c_2234]) ).
cnf(c_964,plain,
( multiply(sk_c8,sk_c2) = sk_c8
| sk_c6 = sk_c5 ),
inference(copy,[status(thm)],[c_2235]) ).
cnf(c_965,plain,
( multiply(sk_c8,sk_c2) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_838,c_119]) ).
cnf(c_2236,plain,
( multiply(sk_c8,sk_c5) = identity
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_962,c_106]) ).
cnf(c_968,plain,
( multiply(sk_c8,sk_c5) = sk_c8
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_838,c_2236]) ).
cnf(c_976,plain,
multiply(inverse(A),A) = sk_c8,
inference(paramod,[status(thm)],[c_838,c_2]) ).
cnf(c_977,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_838,c_1]) ).
cnf(c_2237,plain,
( multiply(sk_c8,sk_c5) = sk_c8
| sk_c8 = sk_c2 ),
inference(paramod,[status(thm)],[c_961,c_923]) ).
cnf(c_2238,plain,
( sk_c5 = sk_c8
| sk_c8 = sk_c2 ),
inference(paramod,[status(thm)],[c_977,c_2237]) ).
cnf(c_979,plain,
( sk_c5 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_2238]) ).
cnf(c_2239,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_962,c_167]) ).
cnf(c_2240,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_961,c_2239]) ).
cnf(c_2241,plain,
( sk_c7 = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_977,c_2240]) ).
cnf(c_992,plain,
( sk_c6 = sk_c7
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_2241]) ).
cnf(c_2242,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_962,c_39]) ).
cnf(c_2243,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_961,c_2242]) ).
cnf(c_2244,plain,
( sk_c8 != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c7
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_962,c_2243]) ).
cnf(c_2245,plain,
( sk_c8 != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| sk_c8 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_2244]) ).
cnf(c_2246,plain,
( sk_c8 != sk_c8
| inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_2245]) ).
cnf(c_994,plain,
( inverse(B) != sk_c7
| multiply(B,sk_c7) != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_2246]) ).
cnf(c_2247,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_962,c_23]) ).
cnf(c_2248,plain,
( sk_c5 = sk_c6
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_962,c_2247]) ).
cnf(c_1118,plain,
( sk_c6 = sk_c5
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_2248]) ).
cnf(c_1122,plain,
( sk_c5 = sk_c8
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_977,c_968]) ).
cnf(c_2249,plain,
( multiply(sk_c8,sk_c2) = sk_c8
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_977,c_965]) ).
cnf(c_1124,plain,
( sk_c2 = sk_c8
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_977,c_2249]) ).
cnf(c_1125,plain,
( sk_c2 = sk_c8
| sk_c6 = sk_c5 ),
inference(paramod,[status(thm)],[c_977,c_964]) ).
cnf(c_2250,plain,
( sk_c8 != sk_c7
| multiply(sk_c8,sk_c7) != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_961,c_994]) ).
cnf(c_2251,plain,
( sk_c8 != sk_c7
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_977,c_2250]) ).
cnf(c_2252,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_2251]) ).
cnf(c_2253,plain,
( sk_c7 != sk_c8
| sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_2252]) ).
cnf(c_1306,plain,
( sk_c7 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_2253]) ).
cnf(c_2254,plain,
( sk_c5 = sk_c7
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_1118,c_992]) ).
cnf(c_1391,plain,
( sk_c5 = sk_c7
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_2254]) ).
cnf(c_2255,plain,
( sk_c2 = sk_c8
| sk_c6 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_979,c_1125]) ).
cnf(c_1406,plain,
( sk_c6 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_2255]) ).
cnf(c_2256,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c7
| sk_c2 = sk_c7 ),
inference(paramod,[status(thm)],[c_1391,c_1122]) ).
cnf(c_1692,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c7 ),
inference(copy,[status(thm)],[c_2256]) ).
cnf(c_2257,plain,
( sk_c2 = sk_c8
| sk_c8 = sk_c7
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_1406,c_1124]) ).
cnf(c_2258,plain,
( sk_c2 = sk_c8
| sk_c7 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_2257]) ).
cnf(c_1717,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c8 ),
inference(copy,[status(thm)],[c_2258]) ).
cnf(c_2259,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_1717,c_1692]) ).
cnf(c_2260,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_2259]) ).
cnf(c_2261,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_2260]) ).
cnf(c_1800,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_2261]) ).
cnf(c_2262,plain,
( sk_c8 != sk_c8
| inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(paramod,[status(thm)],[c_1800,c_1306]) ).
cnf(c_1973,plain,
( inverse(A) != sk_c9
| multiply(A,sk_c9) != sk_c8 ),
inference(copy,[status(thm)],[c_2262]) ).
cnf(c_2263,plain,
multiply(A,sk_c8) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_186,c_962]) ).
cnf(c_2264,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_962,c_2263]) ).
cnf(c_2132,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_2264]) ).
cnf(c_2265,plain,
inverse(inverse(sk_c9)) != sk_c9,
inference(resolve,[status(thm)],[c_976,c_1973]) ).
cnf(c_2266,plain,
sk_c9 != sk_c9,
inference(paramod,[status(thm)],[c_2132,c_2265]) ).
cnf(c_2220,plain,
$false,
inference(copy,[status(thm)],[c_2266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP264-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/5.41 % Computer : n004.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Fri Sep 25 14:42:11 UTC 2026
% 0.13/5.42 % CPUTime :
% 0.13/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.42 % Process 3420192 was started by sandbox2 on n004,
% 0.13/5.42 % Fri Sep 25 14:42:11 2026
% 0.13/5.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/5.43
% 0.13/5.43 % From the command line: assign(max_seconds, 300).
% 7.81/6.47
% 7.81/6.47 % SZS status Unsatisfiable for theBenchmark
% 7.81/6.47
% 7.81/6.47 % Proof 1 at 0.74 (+ 0.27) seconds.
% 7.81/6.47 % Length of proof is 66.
% 7.81/6.47 % Level of proof is 22.
% 7.81/6.47 % Maximum clause weight is 54.000.
% 7.81/6.47 % Given clauses 211.
% 7.81/6.47
% 7.81/6.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------