%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP216-1 : 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 : n014.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 07:28:23 AM UTC 2026
% Result : Unsatisfiable 53.39s 8.07s
% Output : CNFRefutation 53.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 20
% Syntax : Number of formulae : 195 ( 28 unt; 0 def)
% Number of atoms : 471 ( 470 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 409 ( 133 ~; 276 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 48 ( 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,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_16,axiom,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_19,axiom,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_22,axiom,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_25,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( inverse(VAR_4) != sk_c7
| multiply(VAR_4,sk_c7) != VAR_3
| multiply(sk_c7,VAR_3) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(VAR_2) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_1,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(VAR_0,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(E) != sk_c7
| multiply(E,sk_c7) != D
| multiply(sk_c7,D) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(C) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
cnf(c_31,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_44,plain,
( multiply(A,sk_c7) != C
| multiply(sk_c7,C) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_31]) ).
cnf(c_60,plain,
( multiply(A,sk_c7) != B
| multiply(sk_c7,B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(A,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_44]) ).
cnf(c_11111,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_11112,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_11111]) ).
cnf(c_67,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_11112]) ).
cnf(c_89,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_91,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_102,plain,
( multiply(sk_c7,sk_c1) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_103,plain,
( multiply(sk_c7,sk_c4) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_2]) ).
cnf(c_125,plain,
( multiply(sk_c6,sk_c2) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_22,c_2]) ).
cnf(c_11113,plain,
( multiply(identity,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| multiply(identity,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_60]) ).
cnf(c_11114,plain,
( multiply(identity,sk_c7) != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_11113]) ).
cnf(c_11115,plain,
( sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramod,[status(thm)],[c_1,c_11114]) ).
cnf(c_11116,plain,
( sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(identity) != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_11115]) ).
cnf(c_159,plain,
( sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| inverse(identity) != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_11116]) ).
cnf(c_171,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_67]) ).
cnf(c_177,plain,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_67]) ).
cnf(c_179,plain,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_67]) ).
cnf(c_181,plain,
( multiply(inverse(sk_c1),sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_8,c_67]) ).
cnf(c_203,plain,
( multiply(inverse(sk_c2),sk_c7) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_67]) ).
cnf(c_221,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_67,c_67]) ).
cnf(c_222,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_221,c_171]) ).
cnf(c_244,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_222,c_2]) ).
cnf(c_262,plain,
( sk_c7 != A
| multiply(sk_c7,A) != sk_c6
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_244,c_159]) ).
cnf(c_11117,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_89,c_67]) ).
cnf(c_276,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_222,c_11117]) ).
cnf(c_280,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_276,c_2]) ).
cnf(c_11118,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_91,c_67]) ).
cnf(c_318,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_222,c_11118]) ).
cnf(c_320,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_318,c_2]) ).
cnf(c_11119,plain,
( sk_c7 != identity
| sk_c7 != sk_c6
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_222,c_262]) ).
cnf(c_11120,plain,
( sk_c7 != identity
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_11119]) ).
cnf(c_11121,plain,
( identity != sk_c7
| sk_c6 != sk_c7
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_11120]) ).
cnf(c_11122,plain,
( identity != sk_c7
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_11121]) ).
cnf(c_413,plain,
( inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_11122]) ).
cnf(c_11123,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_102,c_67]) ).
cnf(c_609,plain,
( inverse(sk_c7) = sk_c1
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_222,c_11123]) ).
cnf(c_614,plain,
( multiply(sk_c1,sk_c7) = identity
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_609,c_2]) ).
cnf(c_11124,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_103,c_67]) ).
cnf(c_628,plain,
( inverse(sk_c7) = sk_c4
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_222,c_11124]) ).
cnf(c_632,plain,
( multiply(sk_c4,sk_c7) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_628,c_2]) ).
cnf(c_11125,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_125,c_67]) ).
cnf(c_828,plain,
( inverse(sk_c6) = sk_c2
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_222,c_11125]) ).
cnf(c_845,plain,
( multiply(sk_c2,sk_c6) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_828,c_2]) ).
cnf(c_11126,plain,
( inverse(sk_c7) = sk_c6
| identity = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_280,c_4]) ).
cnf(c_1294,plain,
( identity = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_11126]) ).
cnf(c_1330,plain,
( inverse(sk_c6) = identity
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1294,c_244]) ).
cnf(c_11127,plain,
( inverse(sk_c6) = sk_c6
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_1294,c_1330]) ).
cnf(c_1560,plain,
( inverse(sk_c6) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_11127]) ).
cnf(c_11128,plain,
( inverse(sk_c3) = sk_c7
| identity = sk_c6
| inverse(sk_c3) = sk_c7 ),
inference(paramod,[status(thm)],[c_320,c_5]) ).
cnf(c_2753,plain,
( identity = sk_c6
| inverse(sk_c3) = sk_c7 ),
inference(copy,[status(thm)],[c_11128]) ).
cnf(c_2767,plain,
( multiply(sk_c7,sk_c3) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2753,c_2]) ).
cnf(c_11129,plain,
( multiply(inverse(sk_c7),identity) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2767,c_67]) ).
cnf(c_2789,plain,
( inverse(sk_c7) = sk_c3
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_222,c_11129]) ).
cnf(c_11130,plain,
( identity = sk_c6
| sk_c3 = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_2789,c_1294]) ).
cnf(c_2938,plain,
( sk_c3 = sk_c6
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_11130]) ).
cnf(c_2946,plain,
( multiply(sk_c6,A) = A
| sk_c3 = sk_c6 ),
inference(paramod,[status(thm)],[c_2938,c_1]) ).
cnf(c_2951,plain,
( inverse(sk_c6) = identity
| sk_c3 = sk_c6 ),
inference(paramod,[status(thm)],[c_2938,c_244]) ).
cnf(c_11131,plain,
( inverse(sk_c6) = sk_c6
| sk_c3 = sk_c6
| sk_c3 = sk_c6 ),
inference(paramod,[status(thm)],[c_2938,c_2951]) ).
cnf(c_3069,plain,
( inverse(sk_c6) = sk_c6
| sk_c3 = sk_c6 ),
inference(copy,[status(thm)],[c_11131]) ).
cnf(c_11132,plain,
( inverse(sk_c4) = sk_c7
| identity = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(paramod,[status(thm)],[c_614,c_9]) ).
cnf(c_4697,plain,
( identity = sk_c6
| inverse(sk_c4) = sk_c7 ),
inference(copy,[status(thm)],[c_11132]) ).
cnf(c_4717,plain,
( multiply(sk_c7,sk_c4) = identity
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_4697,c_2]) ).
cnf(c_11133,plain,
( multiply(inverse(sk_c7),identity) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_4717,c_67]) ).
cnf(c_4742,plain,
( inverse(sk_c7) = sk_c4
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_222,c_11133]) ).
cnf(c_11134,plain,
( sk_c4 = sk_c3
| identity = sk_c6
| identity = sk_c6 ),
inference(paramod,[status(thm)],[c_4742,c_2789]) ).
cnf(c_4846,plain,
( sk_c4 = sk_c3
| identity = sk_c6 ),
inference(copy,[status(thm)],[c_11134]) ).
cnf(c_4893,plain,
( multiply(sk_c6,A) = A
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_4846,c_1]) ).
cnf(c_4898,plain,
( inverse(sk_c6) = identity
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_4846,c_244]) ).
cnf(c_11135,plain,
( inverse(sk_c6) = sk_c6
| sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_4846,c_4898]) ).
cnf(c_5055,plain,
( inverse(sk_c6) = sk_c6
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_11135]) ).
cnf(c_11136,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_12,c_177]) ).
cnf(c_6703,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_11136]) ).
cnf(c_11137,plain,
( identity = sk_c5
| inverse(sk_c1) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_632,c_14]) ).
cnf(c_6782,plain,
( identity = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(copy,[status(thm)],[c_11137]) ).
cnf(c_6793,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_6782,c_2]) ).
cnf(c_11138,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_13,c_179]) ).
cnf(c_6808,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_11138]) ).
cnf(c_11139,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_6793,c_67]) ).
cnf(c_6844,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_222,c_11139]) ).
cnf(c_6890,plain,
( multiply(sk_c1,sk_c7) = identity
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_6844,c_2]) ).
cnf(c_11140,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_14,c_181]) ).
cnf(c_7129,plain,
( multiply(sk_c7,sk_c6) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_11140]) ).
cnf(c_7478,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| identity = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_6890,c_8]) ).
cnf(c_11141,plain,
( inverse(sk_c7) = sk_c6
| identity = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_845,c_16]) ).
cnf(c_7706,plain,
( identity = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_11141]) ).
cnf(c_11142,plain,
( sk_c7 = sk_c6
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7706,c_1294]) ).
cnf(c_11143,plain,
( sk_c6 = sk_c7
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_11142]) ).
cnf(c_7763,plain,
( sk_c6 = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_11143]) ).
cnf(c_11144,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7763,c_1560]) ).
cnf(c_11145,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_11144]) ).
cnf(c_7920,plain,
inverse(sk_c7) = sk_c6,
inference(copy,[status(thm)],[c_11145]) ).
cnf(c_11146,plain,
( sk_c6 != sk_c6
| multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_7920,c_413]) ).
cnf(c_8534,plain,
( multiply(sk_c7,sk_c6) != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_11146]) ).
cnf(c_8586,plain,
multiply(sk_c6,sk_c7) = identity,
inference(paramod,[status(thm)],[c_7920,c_2]) ).
cnf(c_11147,plain,
multiply(inverse(sk_c6),identity) = sk_c7,
inference(paramod,[status(thm)],[c_8586,c_67]) ).
cnf(c_8927,plain,
inverse(sk_c6) = sk_c7,
inference(paramod,[status(thm)],[c_222,c_11147]) ).
cnf(c_8937,plain,
( identity = sk_c7
| sk_c3 = sk_c6 ),
inference(paramod,[status(thm)],[c_8586,c_2946]) ).
cnf(c_8940,plain,
( identity = sk_c7
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_8586,c_4893]) ).
cnf(c_11148,plain,
( sk_c7 = sk_c6
| sk_c4 = sk_c3 ),
inference(paramod,[status(thm)],[c_8927,c_5055]) ).
cnf(c_9108,plain,
( sk_c6 = sk_c7
| sk_c4 = sk_c3 ),
inference(copy,[status(thm)],[c_11148]) ).
cnf(c_11149,plain,
( sk_c7 = sk_c6
| sk_c3 = sk_c6 ),
inference(paramod,[status(thm)],[c_8927,c_3069]) ).
cnf(c_9147,plain,
( sk_c6 = sk_c7
| sk_c3 = sk_c6 ),
inference(copy,[status(thm)],[c_11149]) ).
cnf(c_9188,plain,
multiply(sk_c7,sk_c6) = identity,
inference(paramod,[status(thm)],[c_8927,c_2]) ).
cnf(c_11150,plain,
( identity != sk_c7
| identity != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_9188,c_8534]) ).
cnf(c_9210,plain,
( identity != sk_c7
| sk_c6 != sk_c7 ),
inference(copy,[status(thm)],[c_11150]) ).
cnf(c_9301,plain,
( identity = sk_c7
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_9188,c_7129]) ).
cnf(c_9302,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_9188,c_6808]) ).
cnf(c_9303,plain,
( identity = sk_c7
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_9188,c_6703]) ).
cnf(c_9401,plain,
( sk_c4 = sk_c3
| sk_c6 != sk_c7 ),
inference(resolve,[status(thm)],[c_9210,c_8940]) ).
cnf(c_9403,plain,
( sk_c3 = sk_c6
| sk_c6 != sk_c7 ),
inference(resolve,[status(thm)],[c_9210,c_8937]) ).
cnf(c_11151,plain,
( sk_c4 = sk_c3
| sk_c4 = sk_c3 ),
inference(resolve,[status(thm)],[c_9401,c_9108]) ).
cnf(c_9951,plain,
sk_c4 = sk_c3,
inference(copy,[status(thm)],[c_11151]) ).
cnf(c_9999,plain,
( identity = sk_c7
| multiply(sk_c3,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_9951,c_9301]) ).
cnf(c_10034,plain,
( multiply(sk_c3,sk_c7) = sk_c5
| identity = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_9951,c_7478]) ).
cnf(c_11152,plain,
( sk_c3 = sk_c6
| sk_c3 = sk_c6 ),
inference(resolve,[status(thm)],[c_9403,c_9147]) ).
cnf(c_10246,plain,
sk_c3 = sk_c6,
inference(copy,[status(thm)],[c_11152]) ).
cnf(c_11153,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| identity = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_10246,c_10034]) ).
cnf(c_11154,plain,
( identity = sk_c5
| identity = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_8586,c_11153]) ).
cnf(c_10367,plain,
( identity = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_11154]) ).
cnf(c_11155,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_10246,c_9999]) ).
cnf(c_10390,plain,
( identity = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_8586,c_11155]) ).
cnf(c_10450,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_10246,c_9303]) ).
cnf(c_11156,plain,
( multiply(sk_c6,sk_c7) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_25,c_203]) ).
cnf(c_11157,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_8586,c_11156]) ).
cnf(c_10628,plain,
( identity = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_11157]) ).
cnf(c_11158,plain,
( sk_c6 != sk_c7
| sk_c6 != sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_10367,c_9210]) ).
cnf(c_10655,plain,
( sk_c6 != sk_c7
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_11158]) ).
cnf(c_11159,plain,
( sk_c7 = sk_c6
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_10390,c_10367]) ).
cnf(c_11160,plain,
( sk_c6 = sk_c7
| identity = sk_c5
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_11159]) ).
cnf(c_10686,plain,
( sk_c6 = sk_c7
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_11160]) ).
cnf(c_11161,plain,
( identity = sk_c5
| identity = sk_c5 ),
inference(resolve,[status(thm)],[c_10686,c_10655]) ).
cnf(c_10705,plain,
identity = sk_c5,
inference(copy,[status(thm)],[c_11161]) ).
cnf(c_10732,plain,
( sk_c5 = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_10705,c_10628]) ).
cnf(c_10771,plain,
( sk_c5 = sk_c7
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_10705,c_10450]) ).
cnf(c_10842,plain,
( sk_c5 = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_10705,c_9302]) ).
cnf(c_10844,plain,
( sk_c5 != sk_c7
| sk_c6 != sk_c7 ),
inference(paramod,[status(thm)],[c_10705,c_9210]) ).
cnf(c_10857,plain,
multiply(sk_c6,sk_c7) = sk_c5,
inference(paramod,[status(thm)],[c_10705,c_8586]) ).
cnf(c_10895,plain,
multiply(A,sk_c5) = A,
inference(paramod,[status(thm)],[c_10705,c_222]) ).
cnf(c_11162,plain,
( sk_c5 = sk_c7
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_10895,c_10842]) ).
cnf(c_10918,plain,
( sk_c5 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_11162]) ).
cnf(c_11163,plain,
( sk_c5 = sk_c6
| sk_c7 = sk_c6 ),
inference(paramod,[status(thm)],[c_10895,c_10732]) ).
cnf(c_10931,plain,
( sk_c5 = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_11163]) ).
cnf(c_11164,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_10931,c_10918]) ).
cnf(c_11165,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_11164]) ).
cnf(c_11072,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_11165]) ).
cnf(c_11105,plain,
multiply(sk_c7,sk_c7) = sk_c5,
inference(paramod,[status(thm)],[c_11072,c_10857]) ).
cnf(c_11166,plain,
( sk_c5 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_11072,c_10844]) ).
cnf(c_11108,plain,
sk_c5 != sk_c7,
inference(copy,[status(thm)],[c_11166]) ).
cnf(c_11167,plain,
( sk_c5 = sk_c7
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_11072,c_10771]) ).
cnf(c_11168,plain,
( sk_c5 = sk_c7
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(paramod,[status(thm)],[c_11072,c_11167]) ).
cnf(c_11169,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(paramod,[status(thm)],[c_11105,c_11168]) ).
cnf(c_11170,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_11169]) ).
cnf(c_11110,plain,
$false,
inference(resolve,[status(thm)],[c_11108,c_11170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP216-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:38:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 446321 was started by sandbox on n014,
% 0.09/0.37 % Fri Sep 25 14:38:33 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 53.39/8.07
% 53.39/8.07 % SZS status Unsatisfiable for theBenchmark
% 53.39/8.07
% 53.39/8.07 % Proof 1 at 5.93 (+ 1.72) seconds.
% 53.39/8.07 % Length of proof is 115.
% 53.39/8.07 % Level of proof is 24.
% 53.39/8.07 % Maximum clause weight is 49.000.
% 53.39/8.07 % Given clauses 482.
% 53.39/8.07
% 53.39/8.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------