%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP218-1 : 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 : n017.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 11.04s 6.84s
% Output : CNFRefutation 11.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 38
% Syntax : Number of formulae : 230 ( 37 unt; 0 def)
% Number of atoms : 794 ( 793 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 845 ( 281 ~; 564 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 13 !; 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_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_2,axiom,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_2) ).
cnf(c_5,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_2]) ).
fof(prove_this_3,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_6,axiom,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_6) ).
cnf(c_9,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_6]) ).
fof(prove_this_7,axiom,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_7) ).
cnf(c_10,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_7]) ).
fof(prove_this_8,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_8) ).
cnf(c_11,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_8]) ).
fof(prove_this_9,axiom,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_13,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_16,axiom,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_16) ).
cnf(c_19,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_16]) ).
fof(prove_this_18,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c6) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_23,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_25,axiom,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_28,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_29,axiom,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_30,axiom,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('theBenchmark.p',prove_this_30) ).
cnf(c_33,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_30]) ).
fof(prove_this_31,axiom,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('theBenchmark.p',prove_this_31) ).
cnf(c_34,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_31]) ).
fof(prove_this_33,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_34,axiom,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('theBenchmark.p',prove_this_34) ).
cnf(c_37,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_34]) ).
fof(prove_this_35,axiom,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('theBenchmark.p',prove_this_35) ).
cnf(c_38,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_35]) ).
fof(prove_this_36,axiom,
( inverse(sk_c6) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('theBenchmark.p',prove_this_36) ).
cnf(c_39,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c4) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_36]) ).
fof(prove_this_38,axiom,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('theBenchmark.p',prove_this_38) ).
cnf(c_41,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_38]) ).
fof(prove_this_39,axiom,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
file('theBenchmark.p',prove_this_39) ).
cnf(c_42,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_39]) ).
fof(prove_this_40,axiom,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('theBenchmark.p',prove_this_40) ).
cnf(c_43,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_40]) ).
fof(prove_this_41,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( inverse(VAR_7) != sk_c10
| multiply(VAR_7,sk_c10) != VAR_6
| multiply(sk_c10,VAR_6) != sk_c9
| multiply(VAR_5,sk_c9) != sk_c10
| inverse(VAR_5) != sk_c10
| inverse(VAR_4) != sk_c10
| multiply(VAR_4,sk_c10) != VAR_3
| multiply(sk_c10,VAR_3) != sk_c9
| multiply(VAR_2,sk_c10) != sk_c9
| inverse(VAR_1) != VAR_2
| multiply(VAR_1,VAR_2) != sk_c9
| multiply(VAR_0,sk_c9) != sk_c10
| inverse(VAR_0) != sk_c10 ),
file('theBenchmark.p',prove_this_41) ).
cnf(c_44,plain,
( inverse(V7) != sk_c10
| multiply(V7,sk_c10) != V6
| multiply(sk_c10,V6) != sk_c9
| multiply(F,sk_c9) != sk_c10
| inverse(F) != sk_c10
| inverse(E) != sk_c10
| multiply(E,sk_c10) != D
| multiply(sk_c10,D) != sk_c9
| multiply(C,sk_c10) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10 ),
inference(clausify,[status(thm)],[prove_this_41]) ).
cnf(c_3037,plain,
( inverse(V6) != sk_c10
| multiply(V6,sk_c10) != F
| multiply(sk_c10,F) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(E) != sk_c10
| multiply(E,sk_c10) != D
| multiply(sk_c10,D) != sk_c9
| multiply(C,sk_c10) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10 ),
inference(factor,[status(thm)],[c_44]) ).
cnf(c_47,plain,
( inverse(V6) != sk_c10
| multiply(V6,sk_c10) != F
| multiply(sk_c10,F) != sk_c9
| inverse(E) != sk_c10
| multiply(E,sk_c10) != D
| multiply(sk_c10,D) != sk_c9
| multiply(C,sk_c10) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10 ),
inference(copy,[status(thm)],[c_3037]) ).
cnf(c_3038,plain,
( inverse(E) != sk_c10
| multiply(sk_c10,D) != sk_c9
| inverse(E) != sk_c10
| multiply(E,sk_c10) != D
| multiply(sk_c10,D) != sk_c9
| multiply(C,sk_c10) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10 ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_3039,plain,
( inverse(E) != sk_c10
| inverse(E) != sk_c10
| multiply(E,sk_c10) != D
| multiply(sk_c10,D) != sk_c9
| multiply(C,sk_c10) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10 ),
inference(copy,[status(thm)],[c_3038]) ).
cnf(c_61,plain,
( inverse(E) != sk_c10
| multiply(E,sk_c10) != D
| multiply(sk_c10,D) != sk_c9
| multiply(C,sk_c10) != sk_c9
| inverse(B) != C
| multiply(B,C) != sk_c9
| multiply(A,sk_c9) != sk_c10
| inverse(A) != sk_c10 ),
inference(copy,[status(thm)],[c_3039]) ).
cnf(c_3040,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_3041,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_3040]) ).
cnf(c_115,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_3041]) ).
cnf(c_3042,plain,
( multiply(sk_c10,A) = multiply(sk_c6,multiply(sk_c9,A))
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_117,plain,
( multiply(sk_c6,multiply(sk_c9,A)) = multiply(sk_c10,A)
| inverse(sk_c1) = sk_c10 ),
inference(copy,[status(thm)],[c_3042]) ).
cnf(c_3043,plain,
( multiply(sk_c10,A) = multiply(sk_c1,multiply(sk_c9,A))
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_10,c_3]) ).
cnf(c_126,plain,
( multiply(sk_c1,multiply(sk_c9,A)) = multiply(sk_c10,A)
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(copy,[status(thm)],[c_3043]) ).
cnf(c_3044,plain,
( inverse(sk_c7) = sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9
| multiply(sk_c1,sk_c9) != sk_c10 ),
inference(resolve,[status(thm)],[c_61,c_8]) ).
cnf(c_3045,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9 ),
inference(resolve,[status(thm)],[c_3044,c_13]) ).
cnf(c_3046,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c3,sk_c10) != sk_c9
| inverse(sk_c2) != sk_c3 ),
inference(resolve,[status(thm)],[c_3045,c_18]) ).
cnf(c_3047,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c3,sk_c10) != sk_c9 ),
inference(resolve,[status(thm)],[c_3046,c_23]) ).
cnf(c_3048,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9 ),
inference(resolve,[status(thm)],[c_3047,c_28]) ).
cnf(c_3049,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c5 ),
inference(resolve,[status(thm)],[c_3048,c_33]) ).
cnf(c_3050,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c4) != sk_c10 ),
inference(resolve,[status(thm)],[c_3049,c_38]) ).
cnf(c_3051,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10 ),
inference(resolve,[status(thm)],[c_3050,c_43]) ).
cnf(c_3052,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10 ),
inference(copy,[status(thm)],[c_3051]) ).
cnf(c_3053,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10 ),
inference(copy,[status(thm)],[c_3052]) ).
cnf(c_3054,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10 ),
inference(copy,[status(thm)],[c_3053]) ).
cnf(c_3055,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10 ),
inference(copy,[status(thm)],[c_3054]) ).
cnf(c_3056,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10 ),
inference(copy,[status(thm)],[c_3055]) ).
cnf(c_3057,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c7) = sk_c10 ),
inference(copy,[status(thm)],[c_3056]) ).
cnf(c_245,plain,
inverse(sk_c7) = sk_c10,
inference(copy,[status(thm)],[c_3057]) ).
cnf(c_3058,plain,
( inverse(sk_c6) = sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9
| multiply(sk_c1,sk_c9) != sk_c10 ),
inference(resolve,[status(thm)],[c_61,c_4]) ).
cnf(c_3059,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9 ),
inference(resolve,[status(thm)],[c_3058,c_9]) ).
cnf(c_3060,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c3,sk_c10) != sk_c9
| inverse(sk_c2) != sk_c3 ),
inference(resolve,[status(thm)],[c_3059,c_14]) ).
cnf(c_3061,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c3,sk_c10) != sk_c9 ),
inference(resolve,[status(thm)],[c_3060,c_19]) ).
cnf(c_3062,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9 ),
inference(resolve,[status(thm)],[c_3061,c_24]) ).
cnf(c_3063,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c5 ),
inference(resolve,[status(thm)],[c_3062,c_29]) ).
cnf(c_3064,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c4) != sk_c10 ),
inference(resolve,[status(thm)],[c_3063,c_34]) ).
cnf(c_3065,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10 ),
inference(resolve,[status(thm)],[c_3064,c_39]) ).
cnf(c_3066,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10 ),
inference(copy,[status(thm)],[c_3065]) ).
cnf(c_3067,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10 ),
inference(copy,[status(thm)],[c_3066]) ).
cnf(c_3068,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10 ),
inference(copy,[status(thm)],[c_3067]) ).
cnf(c_3069,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10 ),
inference(copy,[status(thm)],[c_3068]) ).
cnf(c_3070,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10 ),
inference(copy,[status(thm)],[c_3069]) ).
cnf(c_3071,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c6) = sk_c10 ),
inference(copy,[status(thm)],[c_3070]) ).
cnf(c_250,plain,
inverse(sk_c6) = sk_c10,
inference(copy,[status(thm)],[c_3071]) ).
cnf(c_255,plain,
( inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9
| identity != sk_c10
| inverse(inverse(sk_c9)) != sk_c10 ),
inference(paramod,[status(thm)],[c_2,c_61]) ).
cnf(c_478,plain,
( inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(sk_c9),sk_c10) != sk_c9
| identity != sk_c10
| inverse(inverse(sk_c9)) != sk_c10 ),
inference(factor,[status(thm)],[c_255]) ).
cnf(c_3072,plain,
( inverse(inverse(sk_c9)) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(sk_c9),sk_c10) != sk_c9
| identity != sk_c10
| inverse(inverse(sk_c9)) != sk_c10 ),
inference(factor,[status(thm)],[c_478]) ).
cnf(c_796,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(sk_c9),sk_c10) != sk_c9
| identity != sk_c10
| inverse(inverse(sk_c9)) != sk_c10 ),
inference(copy,[status(thm)],[c_3072]) ).
cnf(c_1101,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_115]) ).
cnf(c_1131,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_115,c_115]) ).
cnf(c_1138,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_1131,c_1101]) ).
cnf(c_1157,plain,
multiply(sk_c10,sk_c7) = identity,
inference(paramod,[status(thm)],[c_245,c_2]) ).
cnf(c_1168,plain,
multiply(sk_c10,sk_c6) = identity,
inference(paramod,[status(thm)],[c_250,c_2]) ).
cnf(c_1174,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_1138,c_2]) ).
cnf(c_3073,plain,
multiply(inverse(sk_c10),identity) = sk_c7,
inference(paramod,[status(thm)],[c_1157,c_115]) ).
cnf(c_1229,plain,
inverse(sk_c10) = sk_c7,
inference(paramod,[status(thm)],[c_1138,c_3073]) ).
cnf(c_1611,plain,
multiply(sk_c7,sk_c10) = identity,
inference(paramod,[status(thm)],[c_1229,c_2]) ).
cnf(c_1775,plain,
( identity = sk_c8
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_1611,c_42]) ).
cnf(c_1776,plain,
( identity = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(paramod,[status(thm)],[c_1611,c_37]) ).
cnf(c_1777,plain,
( identity = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(paramod,[status(thm)],[c_1611,c_32]) ).
cnf(c_1778,plain,
( identity = sk_c8
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_1611,c_27]) ).
cnf(c_1779,plain,
( identity = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(paramod,[status(thm)],[c_1611,c_22]) ).
cnf(c_1780,plain,
( identity = sk_c8
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_1611,c_17]) ).
cnf(c_1781,plain,
( identity = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_1611,c_12]) ).
cnf(c_1782,plain,
( identity = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_1611,c_7]) ).
cnf(c_3074,plain,
( multiply(sk_c6,multiply(sk_c9,sk_c8)) = sk_c9
| inverse(sk_c1) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_6,c_117]) ).
cnf(c_1792,plain,
( multiply(sk_c6,multiply(sk_c9,sk_c8)) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(copy,[status(thm)],[c_3074]) ).
cnf(c_3075,plain,
multiply(inverse(sk_c10),identity) = sk_c6,
inference(paramod,[status(thm)],[c_1168,c_115]) ).
cnf(c_3076,plain,
multiply(sk_c7,identity) = sk_c6,
inference(paramod,[status(thm)],[c_1229,c_3075]) ).
cnf(c_1818,plain,
sk_c7 = sk_c6,
inference(paramod,[status(thm)],[c_1138,c_3076]) ).
cnf(c_1880,plain,
multiply(sk_c6,sk_c10) = identity,
inference(paramod,[status(thm)],[c_1818,c_1611]) ).
cnf(c_2183,plain,
inverse(sk_c10) = sk_c6,
inference(paramod,[status(thm)],[c_1818,c_1229]) ).
cnf(c_3077,plain,
( identity = sk_c8
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9
| multiply(sk_c1,sk_c9) != sk_c10 ),
inference(resolve,[status(thm)],[c_61,c_1782]) ).
cnf(c_3078,plain,
( identity = sk_c8
| identity = sk_c8
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9 ),
inference(resolve,[status(thm)],[c_3077,c_1781]) ).
cnf(c_3079,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c3,sk_c10) != sk_c9
| inverse(sk_c2) != sk_c3 ),
inference(resolve,[status(thm)],[c_3078,c_1780]) ).
cnf(c_3080,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c3,sk_c10) != sk_c9 ),
inference(resolve,[status(thm)],[c_3079,c_1779]) ).
cnf(c_3081,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9 ),
inference(resolve,[status(thm)],[c_3080,c_1778]) ).
cnf(c_3082,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c5 ),
inference(resolve,[status(thm)],[c_3081,c_1777]) ).
cnf(c_3083,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| inverse(sk_c4) != sk_c10 ),
inference(resolve,[status(thm)],[c_3082,c_1776]) ).
cnf(c_3084,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(resolve,[status(thm)],[c_3083,c_1775]) ).
cnf(c_3085,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3084]) ).
cnf(c_3086,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3085]) ).
cnf(c_3087,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3086]) ).
cnf(c_3088,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3087]) ).
cnf(c_3089,plain,
( identity = sk_c8
| identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3088]) ).
cnf(c_3090,plain,
( identity = sk_c8
| identity = sk_c8 ),
inference(copy,[status(thm)],[c_3089]) ).
cnf(c_2308,plain,
identity = sk_c8,
inference(copy,[status(thm)],[c_3090]) ).
cnf(c_2388,plain,
multiply(sk_c6,sk_c10) = sk_c8,
inference(paramod,[status(thm)],[c_2308,c_1880]) ).
cnf(c_3091,plain,
inverse(sk_c8) = identity,
inference(paramod,[status(thm)],[c_2308,c_1174]) ).
cnf(c_2424,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_2308,c_3091]) ).
cnf(c_2427,plain,
multiply(sk_c10,sk_c6) = sk_c8,
inference(paramod,[status(thm)],[c_2308,c_1168]) ).
cnf(c_2430,plain,
multiply(A,sk_c8) = A,
inference(paramod,[status(thm)],[c_2308,c_1138]) ).
cnf(c_2436,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(sk_c9),sk_c10) != sk_c9
| sk_c8 != sk_c10
| inverse(inverse(sk_c9)) != sk_c10 ),
inference(paramod,[status(thm)],[c_2308,c_796]) ).
cnf(c_2446,plain,
multiply(sk_c8,A) = A,
inference(paramod,[status(thm)],[c_2308,c_1]) ).
cnf(c_2493,plain,
( multiply(sk_c6,sk_c9) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_2430,c_1792]) ).
cnf(c_3092,plain,
( sk_c10 = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(paramod,[status(thm)],[c_2430,c_41]) ).
cnf(c_2588,plain,
( sk_c9 = sk_c10
| inverse(sk_c4) = sk_c10 ),
inference(copy,[status(thm)],[c_3092]) ).
cnf(c_3093,plain,
( sk_c10 = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(paramod,[status(thm)],[c_2430,c_36]) ).
cnf(c_2589,plain,
( sk_c9 = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(copy,[status(thm)],[c_3093]) ).
cnf(c_3094,plain,
( sk_c10 = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(paramod,[status(thm)],[c_2430,c_31]) ).
cnf(c_2590,plain,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(copy,[status(thm)],[c_3094]) ).
cnf(c_3095,plain,
( sk_c10 = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_2430,c_26]) ).
cnf(c_2591,plain,
( sk_c9 = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(copy,[status(thm)],[c_3095]) ).
cnf(c_3096,plain,
( sk_c10 = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(paramod,[status(thm)],[c_2430,c_21]) ).
cnf(c_2592,plain,
( sk_c9 = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(copy,[status(thm)],[c_3096]) ).
cnf(c_3097,plain,
( sk_c10 = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(paramod,[status(thm)],[c_2430,c_16]) ).
cnf(c_2593,plain,
( sk_c9 = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(copy,[status(thm)],[c_3097]) ).
cnf(c_3098,plain,
( sk_c10 = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_2430,c_11]) ).
cnf(c_2594,plain,
( sk_c9 = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(copy,[status(thm)],[c_3098]) ).
cnf(c_3099,plain,
( sk_c10 = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_2430,c_6]) ).
cnf(c_2595,plain,
( sk_c9 = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(copy,[status(thm)],[c_3099]) ).
cnf(c_2617,plain,
( multiply(sk_c1,multiply(sk_c9,sk_c6)) = sk_c8
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(paramod,[status(thm)],[c_2427,c_126]) ).
cnf(c_3100,plain,
( sk_c9 = sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9
| multiply(sk_c1,sk_c9) != sk_c10 ),
inference(resolve,[status(thm)],[c_61,c_2595]) ).
cnf(c_3101,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != C
| multiply(sk_c10,C) != sk_c9
| multiply(B,sk_c10) != sk_c9
| inverse(A) != B
| multiply(A,B) != sk_c9 ),
inference(resolve,[status(thm)],[c_3100,c_2594]) ).
cnf(c_3102,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c3,sk_c10) != sk_c9
| inverse(sk_c2) != sk_c3 ),
inference(resolve,[status(thm)],[c_3101,c_2593]) ).
cnf(c_3103,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9
| multiply(sk_c3,sk_c10) != sk_c9 ),
inference(resolve,[status(thm)],[c_3102,c_2592]) ).
cnf(c_3104,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| inverse(B) != sk_c10
| multiply(B,sk_c10) != A
| multiply(sk_c10,A) != sk_c9 ),
inference(resolve,[status(thm)],[c_3103,c_2591]) ).
cnf(c_3105,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c5 ),
inference(resolve,[status(thm)],[c_3104,c_2590]) ).
cnf(c_3106,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| inverse(sk_c4) != sk_c10 ),
inference(resolve,[status(thm)],[c_3105,c_2589]) ).
cnf(c_3107,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(resolve,[status(thm)],[c_3106,c_2588]) ).
cnf(c_3108,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_3107]) ).
cnf(c_3109,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_3108]) ).
cnf(c_3110,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_3109]) ).
cnf(c_3111,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_3110]) ).
cnf(c_3112,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_3111]) ).
cnf(c_3113,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_3112]) ).
cnf(c_2721,plain,
sk_c9 = sk_c10,
inference(copy,[status(thm)],[c_3113]) ).
cnf(c_3114,plain,
( multiply(sk_c1,multiply(sk_c9,sk_c6)) = sk_c8
| multiply(sk_c6,sk_c10) = sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_2617]) ).
cnf(c_3115,plain,
( multiply(sk_c1,multiply(sk_c9,sk_c6)) = sk_c8
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2388,c_3114]) ).
cnf(c_3116,plain,
( multiply(sk_c1,multiply(sk_c10,sk_c6)) = sk_c8
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_3115]) ).
cnf(c_3117,plain,
( multiply(sk_c1,sk_c8) = sk_c8
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2427,c_3116]) ).
cnf(c_2776,plain,
( sk_c1 = sk_c8
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2430,c_3117]) ).
cnf(c_3118,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_2493]) ).
cnf(c_3119,plain,
( sk_c8 = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_2388,c_3118]) ).
cnf(c_2792,plain,
( sk_c8 = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_3119]) ).
cnf(c_3120,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(sk_c9),sk_c10) != sk_c9
| sk_c8 != sk_c10
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_2436]) ).
cnf(c_3121,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(sk_c9),sk_c10) != sk_c9
| sk_c8 != sk_c10
| inverse(sk_c6) != sk_c10 ),
inference(paramod,[status(thm)],[c_2183,c_3120]) ).
cnf(c_3122,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(sk_c9),sk_c10) != sk_c9
| sk_c8 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_250,c_3121]) ).
cnf(c_3123,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(inverse(sk_c10),sk_c10) != sk_c9
| sk_c8 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_3122]) ).
cnf(c_3124,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c6,sk_c10) != sk_c9
| sk_c8 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2183,c_3123]) ).
cnf(c_3125,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c8 != sk_c9
| sk_c8 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2388,c_3124]) ).
cnf(c_3126,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c9
| sk_c8 != sk_c10
| sk_c8 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_3125]) ).
cnf(c_3127,plain,
( multiply(sk_c10,sk_c9) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c10
| sk_c8 != sk_c10
| sk_c8 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_3126]) ).
cnf(c_3128,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c10,sk_c10) != sk_c10
| sk_c8 != sk_c10
| sk_c8 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_3127]) ).
cnf(c_3129,plain,
( multiply(sk_c10,sk_c10) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c10
| sk_c8 != sk_c10
| sk_c8 != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_2721,c_3128]) ).
cnf(c_3130,plain,
( multiply(sk_c10,sk_c10) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c10
| sk_c8 != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3129]) ).
cnf(c_3131,plain,
( multiply(sk_c10,sk_c10) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3130]) ).
cnf(c_2798,plain,
( multiply(sk_c10,sk_c10) != sk_c10
| sk_c8 != sk_c10 ),
inference(copy,[status(thm)],[c_3131]) ).
cnf(c_3132,plain,
( sk_c8 = sk_c10
| inverse(sk_c8) = sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2776,c_2792]) ).
cnf(c_3133,plain,
( sk_c8 = sk_c10
| sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(paramod,[status(thm)],[c_2424,c_3132]) ).
cnf(c_3134,plain,
( sk_c8 = sk_c10
| sk_c8 = sk_c10 ),
inference(copy,[status(thm)],[c_3133]) ).
cnf(c_3012,plain,
sk_c8 = sk_c10,
inference(copy,[status(thm)],[c_3134]) ).
cnf(c_3135,plain,
( multiply(sk_c10,sk_c10) != sk_c10
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_3012,c_2798]) ).
cnf(c_3032,plain,
multiply(sk_c10,sk_c10) != sk_c10,
inference(copy,[status(thm)],[c_3135]) ).
cnf(c_3035,plain,
multiply(sk_c10,A) = A,
inference(paramod,[status(thm)],[c_3012,c_2446]) ).
cnf(c_3036,plain,
$false,
inference(resolve,[status(thm)],[c_3035,c_3032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP218-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.42 % Computer : n017.cluster.edu
% 0.16/5.42 % Model : x86_64 x86_64
% 0.16/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.42 % Memory : 8046.5625MB
% 0.16/5.42 % OS : Linux 6.8.0-71-generic
% 0.16/5.42 % CPULimit : 300
% 0.16/5.42 % WCLimit : 300
% 0.16/5.42 % DateTime : Fri Sep 25 14:34:22 UTC 2026
% 0.16/5.42 % CPUTime :
% 0.16/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.42 % Process 2499733 was started by sandbox2 on n017,
% 0.16/5.42 % Fri Sep 25 14:34:22 2026
% 0.16/5.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.43
% 0.16/5.43 % From the command line: assign(max_seconds, 300).
% 11.04/6.84
% 11.04/6.84 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 11.04/6.84
% 11.04/6.84 % SZS status Unsatisfiable for theBenchmark
% 11.04/6.84
% 11.04/6.84 % Proof 1 at 1.11 (+ 0.28) seconds.
% 11.04/6.84 % Length of proof is 93.
% 11.04/6.84 % Level of proof is 15.
% 11.04/6.84 % Maximum clause weight is 70.000.
% 11.04/6.84 % Given clauses 145.
% 11.04/6.84
% 11.04/6.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------