%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP275-1 : 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 : n007.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 07:28:31 AM UTC 2026
% Result : Unsatisfiable 8.07s 1.58s
% Output : CNFRefutation 8.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 20
% Syntax : Number of formulae : 168 ( 26 unt; 0 def)
% Number of atoms : 397 ( 396 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 331 ( 102 ~; 229 |; 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 : 47 ( 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,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_8,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_13,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_15,axiom,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_19,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_25,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( multiply(VAR_4,sk_c8) != sk_c7
| inverse(VAR_3) != VAR_4
| multiply(VAR_3,VAR_4) != sk_c7
| multiply(VAR_2,sk_c7) != sk_c8
| inverse(VAR_2) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(VAR_1,sk_c7) != sk_c8
| inverse(VAR_1) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(E,sk_c8) != sk_c7
| inverse(D) != E
| multiply(D,E) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_2938,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_35,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2938]) ).
cnf(c_40,plain,
( multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_35]) ).
cnf(c_2939,plain,
( multiply(A,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_47,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2939]) ).
cnf(c_52,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(sk_c8,sk_c7) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_2940,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_2941,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_2940]) ).
cnf(c_54,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_2941]) ).
cnf(c_59,plain,
( multiply(sk_c8,sk_c3) = identity
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_2942,plain,
( multiply(sk_c7,A) = multiply(sk_c4,multiply(sk_c5,A))
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_68,plain,
( multiply(sk_c4,multiply(sk_c5,A)) = multiply(sk_c7,A)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_2942]) ).
cnf(c_2943,plain,
( multiply(sk_c7,A) = multiply(sk_c5,multiply(sk_c8,A))
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_75,plain,
( multiply(sk_c5,multiply(sk_c8,A)) = multiply(sk_c7,A)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_2943]) ).
cnf(c_80,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_82,plain,
( multiply(sk_c8,sk_c1) = identity
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_12,c_2]) ).
cnf(c_88,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_118,plain,
( multiply(sk_c8,sk_c2) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_167,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_54]) ).
cnf(c_173,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_6,c_54]) ).
cnf(c_193,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_16,c_54]) ).
cnf(c_197,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_18,c_54]) ).
cnf(c_206,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_22,c_54]) ).
cnf(c_218,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_28,c_54]) ).
cnf(c_229,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_54,c_54]) ).
cnf(c_230,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_229,c_167]) ).
cnf(c_275,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_230,c_2]) ).
cnf(c_2944,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_80,c_54]) ).
cnf(c_321,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_230,c_2944]) ).
cnf(c_2945,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_88,c_54]) ).
cnf(c_359,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_230,c_2945]) ).
cnf(c_362,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_359,c_2]) ).
cnf(c_2946,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_118,c_54]) ).
cnf(c_420,plain,
( inverse(sk_c8) = sk_c2
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_230,c_2946]) ).
cnf(c_2947,plain,
( sk_c2 = sk_c1
| inverse(sk_c3) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_420,c_321]) ).
cnf(c_427,plain,
( sk_c2 = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_2947]) ).
cnf(c_2948,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_427,c_29]) ).
cnf(c_432,plain,
( multiply(sk_c1,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(copy,[status(thm)],[c_2948]) ).
cnf(c_2949,plain,
( multiply(sk_c4,sk_c7) = multiply(sk_c7,sk_c8)
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_9,c_68]) ).
cnf(c_676,plain,
( multiply(sk_c4,sk_c7) = multiply(sk_c7,sk_c8)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_2949]) ).
cnf(c_2950,plain,
( inverse(sk_c4) = sk_c5
| identity = sk_c7
| inverse(sk_c4) = sk_c5 ),
inference(paramod,[status(thm)],[c_362,c_8]) ).
cnf(c_753,plain,
( identity = sk_c7
| inverse(sk_c4) = sk_c5 ),
inference(copy,[status(thm)],[c_2950]) ).
cnf(c_760,plain,
( multiply(sk_c5,sk_c4) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_753,c_2]) ).
cnf(c_2951,plain,
( multiply(inverse(sk_c5),identity) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_760,c_54]) ).
cnf(c_776,plain,
( inverse(sk_c5) = sk_c4
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_230,c_2951]) ).
cnf(c_786,plain,
( multiply(sk_c4,sk_c5) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_776,c_2]) ).
cnf(c_2952,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_786,c_7]) ).
cnf(c_817,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2952]) ).
cnf(c_2953,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_786,c_13]) ).
cnf(c_818,plain,
( inverse(sk_c1) = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2953]) ).
cnf(c_835,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_818,c_2]) ).
cnf(c_2954,plain,
( multiply(sk_c5,identity) = multiply(sk_c7,sk_c3)
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_59,c_75]) ).
cnf(c_2955,plain,
( sk_c5 = multiply(sk_c7,sk_c3)
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_230,c_2954]) ).
cnf(c_2956,plain,
( multiply(sk_c7,sk_c3) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_2955]) ).
cnf(c_887,plain,
( multiply(sk_c7,sk_c3) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(copy,[status(thm)],[c_2956]) ).
cnf(c_2957,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_835,c_54]) ).
cnf(c_953,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_230,c_2957]) ).
cnf(c_1002,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_953,c_2]) ).
cnf(c_2958,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_82,c_54]) ).
cnf(c_1167,plain,
( inverse(sk_c8) = sk_c1
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_230,c_2958]) ).
cnf(c_2959,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1002,c_817]) ).
cnf(c_2960,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_2959]) ).
cnf(c_1267,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_2960]) ).
cnf(c_2961,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_1267,c_275]) ).
cnf(c_1489,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_1267,c_2961]) ).
cnf(c_1490,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_1267,c_230]) ).
cnf(c_1502,plain,
multiply(inverse(A),A) = sk_c7,
inference(paramod,[status(thm)],[c_1267,c_2]) ).
cnf(c_1503,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_1267,c_1]) ).
cnf(c_2962,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_1490,c_218]) ).
cnf(c_2963,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_1489,c_2962]) ).
cnf(c_1524,plain,
( sk_c6 = sk_c8
| sk_c2 = sk_c8 ),
inference(paramod,[status(thm)],[c_1503,c_2963]) ).
cnf(c_2964,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_1489,c_206]) ).
cnf(c_1525,plain,
( sk_c6 = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_1503,c_2964]) ).
cnf(c_1564,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 = sk_c8 ),
inference(paramod,[status(thm)],[c_1490,c_1167]) ).
cnf(c_2965,plain,
( sk_c4 = multiply(sk_c7,sk_c8)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1490,c_676]) ).
cnf(c_1594,plain,
( sk_c4 = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1503,c_2965]) ).
cnf(c_1628,plain,
( sk_c1 = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_1490,c_432]) ).
cnf(c_2966,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| sk_c3 = sk_c8 ),
inference(paramod,[status(thm)],[c_1490,c_197]) ).
cnf(c_1647,plain,
( inverse(sk_c8) = sk_c6
| sk_c3 = sk_c8 ),
inference(paramod,[status(thm)],[c_1490,c_2966]) ).
cnf(c_2967,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_1503,c_193]) ).
cnf(c_2968,plain,
( inverse(sk_c8) = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_1490,c_2967]) ).
cnf(c_1649,plain,
( inverse(sk_c8) = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_2968]) ).
cnf(c_2969,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| sk_c3 = sk_c8 ),
inference(paramod,[status(thm)],[c_1490,c_173]) ).
cnf(c_1653,plain,
( inverse(sk_c1) = sk_c8
| sk_c3 = sk_c8 ),
inference(paramod,[status(thm)],[c_1490,c_2969]) ).
cnf(c_2970,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1490,c_52]) ).
cnf(c_2971,plain,
( sk_c8 != sk_c6
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1503,c_2970]) ).
cnf(c_2972,plain,
( sk_c6 != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2971]) ).
cnf(c_1699,plain,
( sk_c6 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2972]) ).
cnf(c_1733,plain,
( sk_c3 = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1503,c_887]) ).
cnf(c_2973,plain,
( sk_c6 = sk_c8
| inverse(sk_c8) = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1524,c_1525]) ).
cnf(c_1918,plain,
( inverse(sk_c8) = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_2973]) ).
cnf(c_2974,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c1 ),
inference(paramod,[status(thm)],[c_1564,c_321]) ).
cnf(c_1958,plain,
( inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c1 ),
inference(copy,[status(thm)],[c_2974]) ).
cnf(c_2064,plain,
( sk_c1 = sk_c8
| inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_1647,c_1628]) ).
cnf(c_2975,plain,
( sk_c8 = sk_c6
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1918,c_1649]) ).
cnf(c_2976,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_2975]) ).
cnf(c_2977,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_2976]) ).
cnf(c_2133,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_2977]) ).
cnf(c_2978,plain,
( sk_c1 = sk_c8
| inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_2133,c_2064]) ).
cnf(c_2146,plain,
( sk_c1 = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(copy,[status(thm)],[c_2978]) ).
cnf(c_2979,plain,
( sk_c6 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_2133,c_1699]) ).
cnf(c_2980,plain,
( sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_2133,c_2979]) ).
cnf(c_2981,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2980]) ).
cnf(c_2242,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_2981]) ).
cnf(c_2264,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_2133,c_19]) ).
cnf(c_2982,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| sk_c4 = sk_c8 ),
inference(paramod,[status(thm)],[c_1594,c_54]) ).
cnf(c_2765,plain,
( inverse(sk_c1) = sk_c8
| sk_c4 = sk_c8 ),
inference(paramod,[status(thm)],[c_1490,c_2982]) ).
cnf(c_2983,plain,
( inverse(sk_c8) = sk_c8
| sk_c4 = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_2146,c_2765]) ).
cnf(c_2775,plain,
( sk_c4 = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(copy,[status(thm)],[c_2983]) ).
cnf(c_2780,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| sk_c4 = sk_c8 ),
inference(paramod,[status(thm)],[c_2775,c_1502]) ).
cnf(c_2984,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c8
| sk_c3 = sk_c5 ),
inference(paramod,[status(thm)],[c_1733,c_54]) ).
cnf(c_2841,plain,
( inverse(sk_c1) = sk_c8
| sk_c3 = sk_c5 ),
inference(paramod,[status(thm)],[c_1490,c_2984]) ).
cnf(c_2985,plain,
( inverse(sk_c1) = sk_c8
| sk_c5 = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_2841,c_1653]) ).
cnf(c_2862,plain,
( sk_c5 = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(copy,[status(thm)],[c_2985]) ).
cnf(c_2986,plain,
( sk_c5 = sk_c8
| inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_2146,c_2862]) ).
cnf(c_2877,plain,
( sk_c5 = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(copy,[status(thm)],[c_2986]) ).
cnf(c_2886,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| sk_c5 = sk_c8 ),
inference(paramod,[status(thm)],[c_2877,c_1502]) ).
cnf(c_2987,plain,
( inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(paramod,[status(thm)],[c_2146,c_1958]) ).
cnf(c_2988,plain,
( inverse(sk_c8) = sk_c8
| inverse(sk_c8) = sk_c8 ),
inference(copy,[status(thm)],[c_2987]) ).
cnf(c_2899,plain,
inverse(sk_c8) = sk_c8,
inference(copy,[status(thm)],[c_2988]) ).
cnf(c_2989,plain,
( sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_2899,c_2242]) ).
cnf(c_2926,plain,
multiply(sk_c8,sk_c8) != sk_c7,
inference(copy,[status(thm)],[c_2989]) ).
cnf(c_2932,plain,
sk_c5 = sk_c8,
inference(resolve,[status(thm)],[c_2926,c_2886]) ).
cnf(c_2934,plain,
sk_c4 = sk_c8,
inference(resolve,[status(thm)],[c_2926,c_2780]) ).
cnf(c_2990,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_2934,c_2264]) ).
cnf(c_2991,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_2932,c_2990]) ).
cnf(c_2992,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(copy,[status(thm)],[c_2991]) ).
cnf(c_2937,plain,
$false,
inference(resolve,[status(thm)],[c_2926,c_2992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP275-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 14:40:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1245137 was started by sandbox2 on n007,
% 0.11/0.37 % Fri Sep 25 14:40:25 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 8.07/1.58
% 8.07/1.58 % SZS status Unsatisfiable for theBenchmark
% 8.07/1.58
% 8.07/1.58 % Proof 1 at 0.71 (+ 0.27) seconds.
% 8.07/1.58 % Length of proof is 93.
% 8.07/1.58 % Level of proof is 23.
% 8.07/1.58 % Maximum clause weight is 55.000.
% 8.07/1.58 % Given clauses 275.
% 8.07/1.58
% 8.07/1.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------