%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP367-1 : 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 : n010.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 07:28:43 AM UTC 2026
% Result : Unsatisfiable 99.87s 18.31s
% Output : CNFRefutation 99.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 23
% Syntax : Number of formulae : 175 ( 26 unt; 0 def)
% Number of atoms : 475 ( 474 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 480 ( 180 ~; 300 |; 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 : 58 ( 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,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_7,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_11,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_14,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_19,axiom,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_22,axiom,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_22) ).
cnf(c_25,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_22]) ).
fof(prove_this_23,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_27,axiom,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_29,axiom,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( multiply(VAR_4,sk_c6) != sk_c7
| inverse(VAR_4) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c8
| inverse(VAR_3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(VAR_2) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c8
| inverse(VAR_1) != sk_c8
| multiply(VAR_1,sk_c8) != VAR_0
| multiply(sk_c8,VAR_0) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( multiply(E,sk_c6) != sk_c7
| inverse(E) != sk_c7
| multiply(D,sk_c7) != sk_c8
| inverse(D) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c8
| inverse(B) != sk_c8
| multiply(B,sk_c8) != A
| multiply(sk_c8,A) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
cnf(c_36,plain,
( inverse(sk_c8) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(B) != sk_c6
| multiply(B,sk_c6) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(factor,[status(thm)],[c_34]) ).
cnf(c_15216,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_15217,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_15216]) ).
cnf(c_44,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_15217]) ).
cnf(c_15218,plain,
( multiply(multiply(A,sk_c6),sk_c8) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_46,plain,
( multiply(A,multiply(sk_c6,sk_c8)) = multiply(A,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_3,c_15218]) ).
cnf(c_55,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_66,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_76,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_25,c_2]) ).
cnf(c_79,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(paramod,[status(thm)],[c_27,c_2]) ).
cnf(c_472,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_44]) ).
cnf(c_504,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_44,c_44]) ).
cnf(c_505,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_504,c_472]) ).
cnf(c_592,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_505,c_2]) ).
cnf(c_794,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_504,c_2]) ).
cnf(c_15219,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_504,c_505]) ).
cnf(c_15220,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_505,c_15219]) ).
cnf(c_816,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_15220]) ).
cnf(c_15221,plain,
( inverse(sk_c8) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(inverse(sk_c6),sk_c6) != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(resolve,[status(thm)],[c_816,c_36]) ).
cnf(c_890,plain,
( inverse(sk_c8) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| identity != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_15221]) ).
cnf(c_945,plain,
( multiply(inverse(sk_c7),multiply(sk_c6,sk_c8)) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_2,c_46]) ).
cnf(c_978,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_19,c_794]) ).
cnf(c_981,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_794]) ).
cnf(c_982,plain,
( multiply(sk_c1,sk_c8) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_23,c_794]) ).
cnf(c_985,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_29,c_794]) ).
cnf(c_986,plain,
( multiply(sk_c3,sk_c6) = identity
| inverse(sk_c4) = sk_c8 ),
inference(paramod,[status(thm)],[c_30,c_794]) ).
cnf(c_987,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_31,c_794]) ).
cnf(c_988,plain,
( multiply(sk_c3,sk_c6) = identity
| inverse(sk_c5) = sk_c7 ),
inference(paramod,[status(thm)],[c_32,c_794]) ).
cnf(c_989,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_33,c_794]) ).
cnf(c_2560,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c1,sk_c8) = identity ),
inference(paramod,[status(thm)],[c_981,c_2]) ).
cnf(c_2606,plain,
( multiply(sk_c8,sk_c4) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_986,c_2]) ).
cnf(c_2654,plain,
( multiply(sk_c7,sk_c5) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_988,c_2]) ).
cnf(c_15222,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c2
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_978,c_14]) ).
cnf(c_5624,plain,
( identity = sk_c2
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_15222]) ).
cnf(c_5630,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c2 ),
inference(paramod,[status(thm)],[c_5624,c_44]) ).
cnf(c_15223,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| identity = sk_c2
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_982,c_18]) ).
cnf(c_5964,plain,
( identity = sk_c2
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_15223]) ).
cnf(c_15224,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_985,c_24]) ).
cnf(c_6514,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(copy,[status(thm)],[c_15224]) ).
cnf(c_6520,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_6514,c_44]) ).
cnf(c_15225,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| identity = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_987,c_26]) ).
cnf(c_6562,plain,
( identity = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(copy,[status(thm)],[c_15225]) ).
cnf(c_6850,plain,
( multiply(inverse(sk_c4),sk_c8) = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_6562,c_44]) ).
cnf(c_15226,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| identity = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_989,c_28]) ).
cnf(c_6870,plain,
( identity = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_15226]) ).
cnf(c_15227,plain,
( multiply(sk_c7,sk_c5) = identity
| identity = sk_c2
| multiply(sk_c7,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_2560,c_66]) ).
cnf(c_8001,plain,
( identity = sk_c2
| multiply(sk_c7,sk_c5) = identity ),
inference(copy,[status(thm)],[c_15227]) ).
cnf(c_15228,plain,
( multiply(inverse(sk_c7),identity) = sk_c5
| identity = sk_c2 ),
inference(paramod,[status(thm)],[c_8001,c_44]) ).
cnf(c_8004,plain,
( inverse(sk_c7) = sk_c5
| identity = sk_c2 ),
inference(paramod,[status(thm)],[c_505,c_15228]) ).
cnf(c_15229,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c2
| identity = sk_c2 ),
inference(paramod,[status(thm)],[c_8004,c_5630]) ).
cnf(c_8070,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c2 ),
inference(copy,[status(thm)],[c_15229]) ).
cnf(c_15230,plain,
( identity = sk_c2
| sk_c8 = sk_c7
| identity = sk_c2 ),
inference(paramod,[status(thm)],[c_8070,c_5964]) ).
cnf(c_15231,plain,
( identity = sk_c2
| sk_c7 = sk_c8
| identity = sk_c2 ),
inference(copy,[status(thm)],[c_15230]) ).
cnf(c_8327,plain,
( sk_c7 = sk_c8
| identity = sk_c2 ),
inference(copy,[status(thm)],[c_15231]) ).
cnf(c_8329,plain,
( multiply(A,sk_c2) = A
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_8327,c_505]) ).
cnf(c_15232,plain,
( multiply(sk_c8,sk_c4) = identity
| sk_c8 = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_8329,c_55]) ).
cnf(c_15233,plain,
( multiply(sk_c8,sk_c4) = identity
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15232]) ).
cnf(c_9080,plain,
( multiply(sk_c8,sk_c4) = identity
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15233]) ).
cnf(c_15234,plain,
( multiply(sk_c8,sk_c4) = sk_c2
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_8327,c_9080]) ).
cnf(c_9111,plain,
( multiply(sk_c8,sk_c4) = sk_c2
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15234]) ).
cnf(c_9264,plain,
( inverse(sk_c8) != sk_c7
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| identity != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(resolve,[status(thm)],[c_890,c_816]) ).
cnf(c_9450,plain,
( multiply(inverse(sk_c8),sk_c2) = sk_c4
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_9111,c_44]) ).
cnf(c_15235,plain,
( multiply(sk_c8,sk_c4) = identity
| identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_2606,c_76]) ).
cnf(c_9831,plain,
( identity = sk_c8
| multiply(sk_c8,sk_c4) = identity ),
inference(copy,[status(thm)],[c_15235]) ).
cnf(c_15236,plain,
( multiply(inverse(sk_c8),identity) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_9831,c_44]) ).
cnf(c_9834,plain,
( inverse(sk_c8) = sk_c4
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_505,c_15236]) ).
cnf(c_9952,plain,
( inverse(sk_c4) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_9834,c_816]) ).
cnf(c_15237,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_9952,c_6850]) ).
cnf(c_10023,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15237]) ).
cnf(c_10027,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10023,c_44]) ).
cnf(c_15238,plain,
( multiply(sk_c7,sk_c5) = identity
| identity = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_2654,c_79]) ).
cnf(c_10147,plain,
( identity = sk_c8
| multiply(sk_c7,sk_c5) = identity ),
inference(copy,[status(thm)],[c_15238]) ).
cnf(c_15239,plain,
( multiply(inverse(sk_c7),identity) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10147,c_44]) ).
cnf(c_10151,plain,
( inverse(sk_c7) = sk_c5
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_505,c_15239]) ).
cnf(c_15240,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10151,c_6520]) ).
cnf(c_10265,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15240]) ).
cnf(c_15241,plain,
( identity = sk_c8
| sk_c8 = sk_c7
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_10265,c_6870]) ).
cnf(c_15242,plain,
( identity = sk_c8
| sk_c7 = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15241]) ).
cnf(c_10289,plain,
( sk_c7 = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_15242]) ).
cnf(c_15243,plain,
( sk_c7 = sk_c8
| sk_c8 = sk_c2
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10289,c_8327]) ).
cnf(c_15244,plain,
( sk_c7 = sk_c8
| sk_c2 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15243]) ).
cnf(c_10385,plain,
( sk_c2 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15244]) ).
cnf(c_15245,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c4
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10385,c_9450]) ).
cnf(c_15246,plain,
( identity = sk_c4
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_15245]) ).
cnf(c_10401,plain,
( identity = sk_c4
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15246]) ).
cnf(c_10403,plain,
( multiply(sk_c4,A) = A
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10401,c_1]) ).
cnf(c_15247,plain,
( sk_c7 = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_10403,c_11]) ).
cnf(c_11107,plain,
( multiply(sk_c8,sk_c2) = sk_c7
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15247]) ).
cnf(c_15248,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(paramod,[status(thm)],[c_11107,c_8329]) ).
cnf(c_15249,plain,
( sk_c7 = sk_c8
| sk_c7 = sk_c8 ),
inference(copy,[status(thm)],[c_15248]) ).
cnf(c_11928,plain,
sk_c7 = sk_c8,
inference(copy,[status(thm)],[c_15249]) ).
cnf(c_15250,plain,
( multiply(inverse(sk_c8),sk_c8) = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_11928,c_10027]) ).
cnf(c_15251,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_15250]) ).
cnf(c_12700,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_15251]) ).
cnf(c_15252,plain,
( inverse(sk_c8) != sk_c7
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| identity != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_11928,c_9264]) ).
cnf(c_15253,plain,
( inverse(sk_c8) != sk_c7
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| identity != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_11928,c_15252]) ).
cnf(c_15254,plain,
( inverse(sk_c8) != sk_c7
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_12700,c_15253]) ).
cnf(c_15255,plain,
( inverse(sk_c8) != sk_c7
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_11928,c_15254]) ).
cnf(c_15256,plain,
( inverse(sk_c8) != sk_c7
| multiply(inverse(sk_c8),sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_11928,c_15255]) ).
cnf(c_15257,plain,
( inverse(sk_c8) != sk_c7
| identity != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_2,c_15256]) ).
cnf(c_15258,plain,
( inverse(sk_c8) != sk_c7
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_12700,c_15257]) ).
cnf(c_15259,plain,
( inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c8 != sk_c8
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(paramod,[status(thm)],[c_11928,c_15258]) ).
cnf(c_15260,plain,
( inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_15259]) ).
cnf(c_13048,plain,
( inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_15260]) ).
cnf(c_15261,plain,
( multiply(inverse(sk_c7),multiply(sk_c6,sk_c8)) = identity
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_11928,c_945]) ).
cnf(c_15262,plain,
( multiply(inverse(sk_c8),multiply(sk_c6,sk_c8)) = identity
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_11928,c_15261]) ).
cnf(c_14954,plain,
( multiply(inverse(sk_c8),multiply(sk_c6,sk_c8)) = sk_c8
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(paramod,[status(thm)],[c_12700,c_15262]) ).
cnf(c_15263,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_12700,c_592]) ).
cnf(c_15168,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_12700,c_15263]) ).
cnf(c_15169,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_12700,c_505]) ).
cnf(c_15172,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_12700,c_1]) ).
cnf(c_15264,plain,
( inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(factor,[status(thm)],[c_13048]) ).
cnf(c_15265,plain,
( inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c8
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_15169,c_15264]) ).
cnf(c_15266,plain,
( inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c6
| sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_15172,c_15265]) ).
cnf(c_15267,plain,
( inverse(sk_c8) != sk_c8
| inverse(sk_c8) != sk_c8
| sk_c8 != sk_c6
| sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_15169,c_15266]) ).
cnf(c_15268,plain,
( inverse(sk_c8) != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c6
| sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_15168,c_15267]) ).
cnf(c_15269,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c8 != sk_c6
| sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(paramod,[status(thm)],[c_15168,c_15268]) ).
cnf(c_15270,plain,
( sk_c8 != sk_c8
| sk_c8 != sk_c8
| sk_c6 != sk_c8
| sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_15269]) ).
cnf(c_15271,plain,
( sk_c8 != sk_c8
| sk_c6 != sk_c8
| sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_15270]) ).
cnf(c_15272,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_15271]) ).
cnf(c_15273,plain,
( sk_c6 != sk_c8
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_15272]) ).
cnf(c_15200,plain,
sk_c6 != sk_c8,
inference(copy,[status(thm)],[c_15273]) ).
cnf(c_15274,plain,
( multiply(inverse(sk_c8),multiply(sk_c6,sk_c8)) = sk_c8
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_15169,c_14954]) ).
cnf(c_15275,plain,
( multiply(sk_c8,multiply(sk_c6,sk_c8)) = sk_c8
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_15168,c_15274]) ).
cnf(c_15276,plain,
( multiply(sk_c8,sk_c6) = sk_c8
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_15169,c_15275]) ).
cnf(c_15277,plain,
( sk_c6 = sk_c8
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_15172,c_15276]) ).
cnf(c_15278,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_15277]) ).
cnf(c_15279,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_15278]) ).
cnf(c_15215,plain,
$false,
inference(resolve,[status(thm)],[c_15200,c_15279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP367-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.58 % Computer : n010.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Fri Sep 25 14:49:14 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.59 % Process 1012409 was started by sandbox on n010,
% 0.10/5.59 % Fri Sep 25 14:49:14 2026
% 0.10/5.59 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.60
% 0.10/5.60 % From the command line: assign(max_seconds, 300).
% 99.87/18.31
% 99.87/18.31 % SZS status Unsatisfiable for theBenchmark
% 99.87/18.31
% 99.87/18.31 % Proof 1 at 11.13 (+ 1.49) seconds.
% 99.87/18.31 % Length of proof is 88.
% 99.87/18.31 % Level of proof is 21.
% 99.87/18.31 % Maximum clause weight is 51.000.
% 99.87/18.31 % Given clauses 473.
% 99.87/18.31
% 99.87/18.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------