%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP374-1 : 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 : n009.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 07:28:44 AM UTC 2026
% Result : Unsatisfiable 55.83s 8.42s
% Output : CNFRefutation 55.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 14
% Syntax : Number of formulae : 134 ( 25 unt; 0 def)
% Number of atoms : 373 ( 372 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 406 ( 167 ~; 239 |; 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 43 ( 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_2,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_8,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_14,axiom,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_19,axiom,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_37,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
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_37) ).
cnf(c_40,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
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_37]) ).
cnf(c_11860,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c7
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_41,plain,
( inverse(D) != sk_c8
| multiply(D,sk_c8) != C
| multiply(sk_c8,C) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_11860]) ).
cnf(c_44,plain,
( inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_41]) ).
cnf(c_50,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(A) != sk_c6
| multiply(A,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_44]) ).
cnf(c_56,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_50]) ).
cnf(c_11861,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_11862,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_11861]) ).
cnf(c_57,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_11862]) ).
cnf(c_65,plain,
( multiply(sk_c8,sk_c3) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_66,plain,
( multiply(sk_c7,sk_c8) = identity
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_73,plain,
( multiply(sk_c8,sk_c4) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_9,c_2]) ).
cnf(c_99,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_102,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_173,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_57]) ).
cnf(c_211,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_22,c_57]) ).
cnf(c_247,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_57,c_57]) ).
cnf(c_248,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_247,c_173]) ).
cnf(c_254,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_248,c_2]) ).
cnf(c_11863,plain,
( multiply(inverse(sk_c8),identity) = sk_c3
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_65,c_57]) ).
cnf(c_265,plain,
( inverse(sk_c8) = sk_c3
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_248,c_11863]) ).
cnf(c_274,plain,
( multiply(sk_c3,sk_c8) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_265,c_2]) ).
cnf(c_11864,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_73,c_57]) ).
cnf(c_287,plain,
( inverse(sk_c8) = sk_c4
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_248,c_11864]) ).
cnf(c_289,plain,
( multiply(sk_c4,sk_c8) = identity
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_287,c_2]) ).
cnf(c_11865,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_102,c_57]) ).
cnf(c_337,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_248,c_11865]) ).
cnf(c_11866,plain,
( multiply(inverse(sk_c7),identity) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_66,c_57]) ).
cnf(c_350,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_248,c_11866]) ).
cnf(c_352,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_337,c_2]) ).
cnf(c_11867,plain,
( identity = sk_c7
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_274,c_5]) ).
cnf(c_850,plain,
( identity = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_11867]) ).
cnf(c_871,plain,
( multiply(sk_c7,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_850,c_2]) ).
cnf(c_11868,plain,
( multiply(inverse(sk_c7),identity) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_871,c_57]) ).
cnf(c_925,plain,
( inverse(sk_c7) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_248,c_11868]) ).
cnf(c_11869,plain,
( identity = sk_c5
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_289,c_8]) ).
cnf(c_1112,plain,
( identity = sk_c5
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_11869]) ).
cnf(c_1117,plain,
( multiply(sk_c7,sk_c8) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1112,c_2]) ).
cnf(c_11870,plain,
( sk_c5 = sk_c7
| inverse(sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1112,c_850]) ).
cnf(c_1130,plain,
( sk_c5 = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_11870]) ).
cnf(c_1252,plain,
( multiply(sk_c7,sk_c8) = identity
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_1130,c_2]) ).
cnf(c_11871,plain,
( multiply(inverse(sk_c7),identity) = sk_c8
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1117,c_57]) ).
cnf(c_1438,plain,
( inverse(sk_c7) = sk_c8
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_248,c_11871]) ).
cnf(c_11872,plain,
( inverse(sk_c7) = sk_c8
| sk_c5 = sk_c7
| inverse(sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_1438,c_925]) ).
cnf(c_1469,plain,
( sk_c5 = sk_c7
| inverse(sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_11872]) ).
cnf(c_11873,plain,
( multiply(sk_c7,sk_c8) = identity
| multiply(sk_c8,sk_c7) = sk_c7
| multiply(sk_c7,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_1252,c_66]) ).
cnf(c_1548,plain,
( multiply(sk_c8,sk_c7) = sk_c7
| multiply(sk_c7,sk_c8) = identity ),
inference(copy,[status(thm)],[c_11873]) ).
cnf(c_11874,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c7
| inverse(sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_1469,c_350]) ).
cnf(c_1741,plain,
( multiply(sk_c8,sk_c7) = sk_c7
| inverse(sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_11874]) ).
cnf(c_11875,plain,
( inverse(sk_c3) = sk_c8
| identity = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_352,c_12]) ).
cnf(c_1810,plain,
( identity = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_11875]) ).
cnf(c_1816,plain,
( multiply(sk_c8,sk_c3) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1810,c_2]) ).
cnf(c_11876,plain,
( multiply(inverse(sk_c8),identity) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1816,c_57]) ).
cnf(c_1825,plain,
( inverse(sk_c8) = sk_c3
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_248,c_11876]) ).
cnf(c_1844,plain,
( multiply(sk_c3,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1825,c_2]) ).
cnf(c_11877,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1844,c_11]) ).
cnf(c_2929,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_11877]) ).
cnf(c_11878,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1844,c_99]) ).
cnf(c_2956,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_11878]) ).
cnf(c_11879,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2956,c_57]) ).
cnf(c_5199,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_248,c_11879]) ).
cnf(c_5214,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_5199,c_2]) ).
cnf(c_11880,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_5214,c_2929]) ).
cnf(c_11881,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_11880]) ).
cnf(c_9866,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_11881]) ).
cnf(c_10442,plain,
( multiply(sk_c8,sk_c7) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_9866,c_1548]) ).
cnf(c_11882,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_9866,c_254]) ).
cnf(c_10584,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_9866,c_11882]) ).
cnf(c_10588,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_9866,c_248]) ).
cnf(c_10601,plain,
multiply(inverse(A),A) = sk_c7,
inference(paramod,[status(thm)],[c_9866,c_2]) ).
cnf(c_11883,plain,
( multiply(sk_c8,sk_c7) = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10584,c_1741]) ).
cnf(c_11884,plain,
( sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10588,c_11883]) ).
cnf(c_11885,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_11884]) ).
cnf(c_10632,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_11885]) ).
cnf(c_11886,plain,
( multiply(sk_c8,sk_c7) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_10632,c_10442]) ).
cnf(c_11887,plain,
( multiply(sk_c8,sk_c7) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_10632,c_11886]) ).
cnf(c_11888,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_10632,c_11887]) ).
cnf(c_11889,plain,
( multiply(sk_c8,sk_c8) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_10632,c_11888]) ).
cnf(c_10732,plain,
multiply(sk_c8,sk_c8) = sk_c8,
inference(copy,[status(thm)],[c_11889]) ).
cnf(c_11890,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_10632,c_211]) ).
cnf(c_11891,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_10732,c_11890]) ).
cnf(c_11892,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_10632,c_11891]) ).
cnf(c_11893,plain,
( sk_c7 = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_10601,c_11892]) ).
cnf(c_11894,plain,
( sk_c8 = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_10632,c_11893]) ).
cnf(c_11895,plain,
( sk_c8 = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_11894]) ).
cnf(c_11896,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_11895]) ).
cnf(c_11544,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_11896]) ).
cnf(c_11897,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_10632,c_56]) ).
cnf(c_11898,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c7
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_10732,c_11897]) ).
cnf(c_11899,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_10632,c_11898]) ).
cnf(c_11900,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_11544,c_11899]) ).
cnf(c_11901,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| sk_c8 != sk_c7
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_10732,c_11900]) ).
cnf(c_11902,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_10632,c_11901]) ).
cnf(c_11903,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_11544,c_11902]) ).
cnf(c_11904,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_10632,c_11903]) ).
cnf(c_11905,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| sk_c8 != sk_c6
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_10732,c_11904]) ).
cnf(c_11906,plain,
( multiply(sk_c8,sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_11544,c_11905]) ).
cnf(c_11907,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_10732,c_11906]) ).
cnf(c_11908,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_11907]) ).
cnf(c_11909,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_11908]) ).
cnf(c_11910,plain,
( sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_11909]) ).
cnf(c_11911,plain,
( inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_11910]) ).
cnf(c_11912,plain,
( inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_11911]) ).
cnf(c_11571,plain,
inverse(sk_c8) != sk_c8,
inference(copy,[status(thm)],[c_11912]) ).
cnf(c_11913,plain,
inverse(sk_c8) = sk_c7,
inference(paramod,[status(thm)],[c_10632,c_10584]) ).
cnf(c_11914,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_10632,c_11913]) ).
cnf(c_11859,plain,
$false,
inference(resolve,[status(thm)],[c_11571,c_11914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP374-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n009.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 14:49:29 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1872767 was started by sandbox on n009,
% 0.17/0.43 % Fri Sep 25 14:49:29 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 55.83/8.42
% 55.83/8.42 % SZS status Unsatisfiable for theBenchmark
% 55.83/8.42
% 55.83/8.42 % Proof 1 at 6.47 (+ 1.48) seconds.
% 55.83/8.42 % Length of proof is 65.
% 55.83/8.42 % Level of proof is 19.
% 55.83/8.42 % Maximum clause weight is 59.000.
% 55.83/8.42 % Given clauses 379.
% 55.83/8.42
% 55.83/8.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------