%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP389-1 : 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 : n005.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 07:28:45 AM UTC 2026
% Result : Unsatisfiable 94.59s 12.94s
% Output : CNFRefutation 94.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 16
% Syntax : Number of formulae : 181 ( 25 unt; 0 def)
% Number of atoms : 628 ( 627 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 820 ( 373 ~; 447 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 118 ( 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_3,axiom,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_11,axiom,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_14,axiom,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_15,axiom,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('theBenchmark.p',prove_this_15) ).
cnf(c_18,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_15]) ).
fof(prove_this_23,axiom,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('theBenchmark.p',prove_this_23) ).
cnf(c_26,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_23]) ).
fof(prove_this_24,axiom,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('theBenchmark.p',prove_this_24) ).
cnf(c_27,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(clausify,[status(thm)],[prove_this_24]) ).
fof(prove_this_28,axiom,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_29,axiom,
( inverse(sk_c4) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_32,axiom,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_43,axiom,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_43) ).
cnf(c_46,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_43]) ).
fof(prove_this_44,axiom,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('theBenchmark.p',prove_this_44) ).
cnf(c_47,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(clausify,[status(thm)],[prove_this_44]) ).
fof(prove_this_55,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( multiply(VAR_7,sk_c9) != sk_c10
| inverse(VAR_6) != VAR_7
| multiply(VAR_6,VAR_7) != sk_c10
| multiply(VAR_5,sk_c10) != sk_c11
| inverse(VAR_5) != sk_c11
| inverse(VAR_4) != sk_c10
| multiply(VAR_4,sk_c10) != sk_c9
| inverse(VAR_3) != sk_c11
| multiply(VAR_3,sk_c11) != sk_c10
| multiply(VAR_2,sk_c9) != sk_c10
| inverse(VAR_1) != VAR_2
| multiply(VAR_1,VAR_2) != sk_c10
| multiply(VAR_0,sk_c10) != sk_c11
| inverse(VAR_0) != sk_c11
| inverse(sk_c10) != sk_c9 ),
file('theBenchmark.p',prove_this_55) ).
cnf(c_58,plain,
( multiply(V7,sk_c9) != sk_c10
| inverse(V6) != V7
| multiply(V6,V7) != sk_c10
| multiply(F,sk_c10) != sk_c11
| inverse(F) != sk_c11
| inverse(E) != sk_c10
| multiply(E,sk_c10) != sk_c9
| inverse(D) != sk_c11
| multiply(D,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(clausify,[status(thm)],[prove_this_55]) ).
cnf(c_61,plain,
( multiply(V6,sk_c9) != sk_c10
| inverse(F) != V6
| multiply(F,V6) != sk_c10
| multiply(E,sk_c10) != sk_c11
| inverse(E) != sk_c11
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(A,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_58]) ).
cnf(c_14816,plain,
( multiply(V6,sk_c9) != sk_c10
| inverse(F) != V6
| multiply(F,V6) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(E) != sk_c10
| multiply(E,sk_c10) != sk_c9
| inverse(D) != sk_c11
| multiply(D,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_58]) ).
cnf(c_62,plain,
( multiply(V6,sk_c9) != sk_c10
| inverse(F) != V6
| multiply(F,V6) != sk_c10
| inverse(E) != sk_c10
| multiply(E,sk_c10) != sk_c9
| inverse(D) != sk_c11
| multiply(D,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14816]) ).
cnf(c_14817,plain,
( multiply(F,sk_c9) != sk_c10
| inverse(E) != F
| multiply(E,F) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(A,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_61]) ).
cnf(c_69,plain,
( multiply(F,sk_c9) != sk_c10
| inverse(E) != F
| multiply(E,F) != sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(A,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14817]) ).
cnf(c_14818,plain,
( multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| inverse(E) != sk_c10
| multiply(E,sk_c10) != sk_c9
| inverse(D) != sk_c11
| multiply(D,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_62]) ).
cnf(c_14819,plain,
( multiply(C,sk_c9) != sk_c10
| inverse(E) != sk_c10
| multiply(E,sk_c10) != sk_c9
| inverse(D) != sk_c11
| multiply(D,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14818]) ).
cnf(c_73,plain,
( inverse(E) != sk_c10
| multiply(E,sk_c10) != sk_c9
| inverse(D) != sk_c11
| multiply(D,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14819]) ).
cnf(c_14820,plain,
( multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(A,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_69]) ).
cnf(c_14821,plain,
( multiply(C,sk_c9) != sk_c10
| inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(A,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14820]) ).
cnf(c_80,plain,
( inverse(D) != sk_c10
| multiply(D,sk_c10) != sk_c9
| multiply(A,sk_c11) != sk_c10
| multiply(C,sk_c9) != sk_c10
| inverse(B) != C
| multiply(B,C) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14821]) ).
cnf(c_14822,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_14823,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_14822]) ).
cnf(c_88,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_14823]) ).
cnf(c_91,plain,
( multiply(sk_c9,sk_c10) = identity
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_92,plain,
( multiply(sk_c10,sk_c5) = identity
| inverse(sk_c10) = sk_c9 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_99,plain,
( multiply(sk_c11,sk_c4) = identity
| inverse(sk_c1) = sk_c11 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_102,plain,
( multiply(sk_c11,sk_c6) = identity
| inverse(sk_c1) = sk_c11 ),
inference(paramod,[status(thm)],[c_17,c_2]) ).
cnf(c_123,plain,
( multiply(sk_c11,sk_c4) = identity
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(paramod,[status(thm)],[c_32,c_2]) ).
cnf(c_127,plain,
( multiply(sk_c11,sk_c6) = identity
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(paramod,[status(thm)],[c_35,c_2]) ).
cnf(c_141,plain,
( multiply(sk_c3,sk_c2) = identity
| multiply(sk_c7,sk_c8) = sk_c10 ),
inference(paramod,[status(thm)],[c_46,c_2]) ).
cnf(c_142,plain,
( multiply(sk_c8,sk_c7) = identity
| inverse(sk_c2) = sk_c3 ),
inference(paramod,[status(thm)],[c_47,c_2]) ).
cnf(c_187,plain,
( inverse(C) != sk_c10
| multiply(C,sk_c10) != sk_c9
| inverse(B) != sk_c11
| multiply(B,sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(identity) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(resolve,[status(thm)],[c_73,c_1]) ).
cnf(c_14824,plain,
( multiply(identity,sk_c10) != sk_c9
| inverse(B) != sk_c11
| multiply(B,sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(identity) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_187]) ).
cnf(c_14825,plain,
( sk_c10 != sk_c9
| inverse(B) != sk_c11
| multiply(B,sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(identity) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_14824]) ).
cnf(c_475,plain,
( sk_c9 != sk_c10
| inverse(B) != sk_c11
| multiply(B,sk_c11) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(identity) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14825]) ).
cnf(c_1691,plain,
( multiply(sk_c9,sk_c10) = identity
| multiply(sk_c10,sk_c5) = identity ),
inference(paramod,[status(thm)],[c_92,c_2]) ).
cnf(c_1824,plain,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c11,sk_c4) = identity ),
inference(paramod,[status(thm)],[c_99,c_2]) ).
cnf(c_2079,plain,
( multiply(sk_c11,sk_c1) = identity
| multiply(sk_c11,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_102,c_2]) ).
cnf(c_2236,plain,
( multiply(sk_c3,sk_c2) = identity
| multiply(sk_c8,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_142,c_2]) ).
cnf(c_2409,plain,
( sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(identity) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_2,c_475]) ).
cnf(c_4662,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_88]) ).
cnf(c_4755,plain,
( multiply(inverse(sk_c11),identity) = sk_c4
| multiply(sk_c11,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_1824,c_88]) ).
cnf(c_4757,plain,
( multiply(inverse(sk_c11),identity) = sk_c6
| multiply(sk_c11,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_2079,c_88]) ).
cnf(c_4762,plain,
( multiply(inverse(sk_c8),identity) = sk_c7
| multiply(sk_c3,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_2236,c_88]) ).
cnf(c_4763,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_88,c_88]) ).
cnf(c_4841,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_4763,c_4662]) ).
cnf(c_4842,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_4841,c_4762]) ).
cnf(c_4847,plain,
( inverse(sk_c11) = sk_c6
| multiply(sk_c11,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_4841,c_4757]) ).
cnf(c_4849,plain,
( inverse(sk_c11) = sk_c4
| multiply(sk_c11,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_4841,c_4755]) ).
cnf(c_14826,plain,
( inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(A,sk_c11) != sk_c10
| multiply(identity,sk_c9) != sk_c10
| inverse(sk_c10) != identity
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(resolve,[status(thm)],[c_4841,c_80]) ).
cnf(c_5004,plain,
( inverse(B) != sk_c10
| multiply(B,sk_c10) != sk_c9
| multiply(A,sk_c11) != sk_c10
| sk_c9 != sk_c10
| inverse(sk_c10) != identity
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_1,c_14826]) ).
cnf(c_5006,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_4841,c_2]) ).
cnf(c_14827,plain,
( sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| identity != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_5006,c_2409]) ).
cnf(c_6263,plain,
( sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c10
| identity != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14827]) ).
cnf(c_6833,plain,
( multiply(sk_c7,sk_c8) = identity
| multiply(sk_c3,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_4842,c_2]) ).
cnf(c_14828,plain,
( sk_c4 = sk_c6
| multiply(sk_c11,sk_c1) = identity
| multiply(sk_c11,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_4849,c_4847]) ).
cnf(c_14829,plain,
( sk_c6 = sk_c4
| multiply(sk_c11,sk_c1) = identity
| multiply(sk_c11,sk_c1) = identity ),
inference(copy,[status(thm)],[c_14828]) ).
cnf(c_7159,plain,
( sk_c6 = sk_c4
| multiply(sk_c11,sk_c1) = identity ),
inference(copy,[status(thm)],[c_14829]) ).
cnf(c_14830,plain,
( multiply(inverse(sk_c11),identity) = sk_c1
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_7159,c_88]) ).
cnf(c_7169,plain,
( inverse(sk_c11) = sk_c1
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_4841,c_14830]) ).
cnf(c_7172,plain,
( multiply(sk_c1,sk_c11) = identity
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_7169,c_2]) ).
cnf(c_14831,plain,
( multiply(inverse(sk_c1),identity) = sk_c11
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_7172,c_88]) ).
cnf(c_7219,plain,
( inverse(sk_c1) = sk_c11
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_4841,c_14831]) ).
cnf(c_14832,plain,
( multiply(sk_c3,sk_c2) = identity
| identity = sk_c10
| multiply(sk_c3,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_6833,c_141]) ).
cnf(c_7673,plain,
( identity = sk_c10
| multiply(sk_c3,sk_c2) = identity ),
inference(copy,[status(thm)],[c_14832]) ).
cnf(c_14833,plain,
( multiply(inverse(sk_c3),identity) = sk_c2
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_7673,c_88]) ).
cnf(c_7678,plain,
( inverse(sk_c3) = sk_c2
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_4841,c_14833]) ).
cnf(c_7681,plain,
( multiply(sk_c2,sk_c3) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_7678,c_2]) ).
cnf(c_14834,plain,
( multiply(sk_c11,sk_c4) = identity
| identity = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_7681,c_123]) ).
cnf(c_7720,plain,
( multiply(sk_c11,sk_c4) = identity
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_14834]) ).
cnf(c_14835,plain,
( multiply(sk_c11,sk_c6) = identity
| identity = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_7681,c_127]) ).
cnf(c_7722,plain,
( multiply(sk_c11,sk_c6) = identity
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_14835]) ).
cnf(c_14836,plain,
( multiply(inverse(sk_c11),identity) = sk_c4
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_7720,c_88]) ).
cnf(c_7854,plain,
( inverse(sk_c11) = sk_c4
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_4841,c_14836]) ).
cnf(c_7857,plain,
( multiply(sk_c4,sk_c11) = identity
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_7854,c_2]) ).
cnf(c_14837,plain,
( multiply(inverse(sk_c11),identity) = sk_c6
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_7722,c_88]) ).
cnf(c_8014,plain,
( inverse(sk_c11) = sk_c6
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_4841,c_14837]) ).
cnf(c_14838,plain,
( sk_c6 = sk_c4
| identity = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_8014,c_7854]) ).
cnf(c_8293,plain,
( sk_c6 = sk_c4
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_14838]) ).
cnf(c_14839,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c6 = sk_c4
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_8293,c_7172]) ).
cnf(c_8329,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c6 = sk_c4 ),
inference(copy,[status(thm)],[c_14839]) ).
cnf(c_14840,plain,
( identity = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_7857,c_31]) ).
cnf(c_8491,plain,
( multiply(sk_c2,sk_c3) = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_14840]) ).
cnf(c_9262,plain,
( inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c9 != sk_c10
| inverse(sk_c10) != identity
| multiply(sk_c1,sk_c10) != sk_c11
| inverse(sk_c1) != sk_c11
| inverse(sk_c10) != sk_c9
| sk_c6 = sk_c4 ),
inference(resolve,[status(thm)],[c_8329,c_5004]) ).
cnf(c_14841,plain,
( sk_c10 = identity
| identity = sk_c10
| identity = sk_c10 ),
inference(paramod,[status(thm)],[c_8491,c_7681]) ).
cnf(c_14842,plain,
( identity = sk_c10
| identity = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_14841]) ).
cnf(c_14843,plain,
( identity = sk_c10
| identity = sk_c10 ),
inference(copy,[status(thm)],[c_14842]) ).
cnf(c_9355,plain,
identity = sk_c10,
inference(copy,[status(thm)],[c_14843]) ).
cnf(c_9366,plain,
( inverse(A) != sk_c10
| multiply(A,sk_c10) != sk_c9
| sk_c9 != sk_c10
| inverse(sk_c10) != sk_c10
| multiply(sk_c1,sk_c10) != sk_c11
| inverse(sk_c1) != sk_c11
| inverse(sk_c10) != sk_c9
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_9355,c_9262]) ).
cnf(c_14844,plain,
( sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c10
| sk_c10 != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(paramod,[status(thm)],[c_9355,c_6263]) ).
cnf(c_11055,plain,
( sk_c9 != sk_c10
| inverse(inverse(sk_c11)) != sk_c11
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(A,sk_c10) != sk_c11
| inverse(A) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(copy,[status(thm)],[c_14844]) ).
cnf(c_14845,plain,
inverse(sk_c10) = identity,
inference(paramod,[status(thm)],[c_9355,c_5006]) ).
cnf(c_11947,plain,
inverse(sk_c10) = sk_c10,
inference(paramod,[status(thm)],[c_9355,c_14845]) ).
cnf(c_11974,plain,
multiply(A,sk_c10) = A,
inference(paramod,[status(thm)],[c_9355,c_4841]) ).
cnf(c_14846,plain,
( multiply(sk_c9,sk_c10) = identity
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_9355,c_1691]) ).
cnf(c_14847,plain,
( sk_c9 = identity
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_11974,c_14846]) ).
cnf(c_12573,plain,
( sk_c9 = sk_c10
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(paramod,[status(thm)],[c_9355,c_14847]) ).
cnf(c_14848,plain,
( multiply(sk_c9,sk_c10) = identity
| sk_c5 = sk_c9 ),
inference(paramod,[status(thm)],[c_11974,c_91]) ).
cnf(c_14849,plain,
( sk_c9 = identity
| sk_c5 = sk_c9 ),
inference(paramod,[status(thm)],[c_11974,c_14848]) ).
cnf(c_12666,plain,
( sk_c9 = sk_c10
| sk_c5 = sk_c9 ),
inference(paramod,[status(thm)],[c_9355,c_14849]) ).
cnf(c_12669,plain,
multiply(sk_c10,A) = A,
inference(paramod,[status(thm)],[c_9355,c_1]) ).
cnf(c_14850,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| sk_c9 != sk_c10
| inverse(sk_c10) != sk_c10
| multiply(sk_c1,sk_c10) != sk_c11
| inverse(sk_c1) != sk_c11
| inverse(sk_c10) != sk_c9
| sk_c6 = sk_c4 ),
inference(factor,[status(thm)],[c_9366]) ).
cnf(c_14851,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| sk_c9 != sk_c10
| inverse(sk_c10) != sk_c10
| multiply(sk_c1,sk_c10) != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c10 != sk_c9
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_11947,c_14850]) ).
cnf(c_14852,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| sk_c9 != sk_c10
| inverse(sk_c10) != sk_c10
| sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c10 != sk_c9
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_11974,c_14851]) ).
cnf(c_14853,plain,
( multiply(sk_c10,sk_c10) != sk_c9
| sk_c9 != sk_c10
| sk_c10 != sk_c10
| sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c10 != sk_c9
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_11947,c_14852]) ).
cnf(c_14854,plain,
( sk_c10 != sk_c9
| sk_c9 != sk_c10
| sk_c10 != sk_c10
| sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c10 != sk_c9
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_11974,c_14853]) ).
cnf(c_14855,plain,
( sk_c10 != sk_c9
| sk_c9 != sk_c10
| sk_c10 != sk_c10
| sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c9 != sk_c10
| sk_c6 = sk_c4 ),
inference(copy,[status(thm)],[c_14854]) ).
cnf(c_14856,plain,
( sk_c9 != sk_c10
| sk_c9 != sk_c10
| sk_c10 != sk_c10
| sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c9 != sk_c10
| sk_c6 = sk_c4 ),
inference(copy,[status(thm)],[c_14855]) ).
cnf(c_14857,plain,
( sk_c9 != sk_c10
| sk_c9 != sk_c10
| sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c9 != sk_c10
| sk_c6 = sk_c4 ),
inference(copy,[status(thm)],[c_14856]) ).
cnf(c_14858,plain,
( sk_c9 != sk_c10
| sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c9 != sk_c10
| sk_c6 = sk_c4 ),
inference(copy,[status(thm)],[c_14857]) ).
cnf(c_12670,plain,
( sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c9 != sk_c10
| sk_c6 = sk_c4 ),
inference(copy,[status(thm)],[c_14858]) ).
cnf(c_14859,plain,
( sk_c9 != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(inverse(sk_c11),sk_c10) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(factor,[status(thm)],[c_11055]) ).
cnf(c_14860,plain,
( sk_c9 != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(inverse(sk_c11),sk_c10) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11
| sk_c10 != sk_c9 ),
inference(paramod,[status(thm)],[c_11947,c_14859]) ).
cnf(c_14861,plain,
( sk_c9 != sk_c10
| multiply(sk_c10,sk_c9) != sk_c10
| inverse(sk_c11) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11
| sk_c10 != sk_c9 ),
inference(paramod,[status(thm)],[c_11974,c_14860]) ).
cnf(c_14862,plain,
( sk_c9 != sk_c10
| sk_c9 != sk_c10
| inverse(sk_c11) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11
| sk_c10 != sk_c9 ),
inference(paramod,[status(thm)],[c_12669,c_14861]) ).
cnf(c_14863,plain,
( sk_c9 != sk_c10
| sk_c9 != sk_c10
| inverse(sk_c11) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11
| sk_c9 != sk_c10 ),
inference(copy,[status(thm)],[c_14862]) ).
cnf(c_14864,plain,
( sk_c9 != sk_c10
| inverse(sk_c11) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11
| sk_c9 != sk_c10 ),
inference(copy,[status(thm)],[c_14863]) ).
cnf(c_12817,plain,
( inverse(sk_c11) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11
| sk_c9 != sk_c10 ),
inference(copy,[status(thm)],[c_14864]) ).
cnf(c_14865,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| sk_c1 = sk_c11 ),
inference(paramod,[status(thm)],[c_11974,c_27]) ).
cnf(c_13191,plain,
( sk_c6 = sk_c11
| sk_c1 = sk_c11 ),
inference(paramod,[status(thm)],[c_11974,c_14865]) ).
cnf(c_13192,plain,
( inverse(sk_c6) = sk_c11
| sk_c1 = sk_c11 ),
inference(paramod,[status(thm)],[c_11974,c_26]) ).
cnf(c_13196,plain,
( sk_c6 = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(paramod,[status(thm)],[c_11974,c_18]) ).
cnf(c_13208,plain,
( sk_c9 = sk_c10
| sk_c5 = sk_c10 ),
inference(paramod,[status(thm)],[c_12669,c_12573]) ).
cnf(c_14866,plain,
( sk_c9 = sk_c10
| sk_c10 = sk_c9
| sk_c9 = sk_c10 ),
inference(paramod,[status(thm)],[c_13208,c_12666]) ).
cnf(c_14867,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_14866]) ).
cnf(c_14868,plain,
( sk_c9 = sk_c10
| sk_c9 = sk_c10 ),
inference(copy,[status(thm)],[c_14867]) ).
cnf(c_13294,plain,
sk_c9 = sk_c10,
inference(copy,[status(thm)],[c_14868]) ).
cnf(c_14869,plain,
( inverse(sk_c11) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramod,[status(thm)],[c_13294,c_12817]) ).
cnf(c_13511,plain,
( inverse(sk_c11) != sk_c11
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(copy,[status(thm)],[c_14869]) ).
cnf(c_14870,plain,
( sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c10 != sk_c10
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_13294,c_12670]) ).
cnf(c_13572,plain,
( sk_c1 != sk_c11
| inverse(sk_c1) != sk_c11
| sk_c6 = sk_c4 ),
inference(copy,[status(thm)],[c_14870]) ).
cnf(c_14871,plain,
( inverse(sk_c11) = sk_c11
| sk_c1 = sk_c11
| sk_c1 = sk_c11 ),
inference(paramod,[status(thm)],[c_13191,c_13192]) ).
cnf(c_13754,plain,
( inverse(sk_c11) = sk_c11
| sk_c1 = sk_c11 ),
inference(copy,[status(thm)],[c_14871]) ).
cnf(c_14872,plain,
( inverse(sk_c11) != sk_c11
| inverse(sk_c11) != sk_c11
| sk_c1 = sk_c11 ),
inference(paramod,[status(thm)],[c_13754,c_13511]) ).
cnf(c_14066,plain,
( inverse(sk_c11) != sk_c11
| sk_c1 = sk_c11 ),
inference(copy,[status(thm)],[c_14872]) ).
cnf(c_14873,plain,
( sk_c1 = sk_c11
| sk_c1 = sk_c11 ),
inference(resolve,[status(thm)],[c_14066,c_13754]) ).
cnf(c_14153,plain,
sk_c1 = sk_c11,
inference(copy,[status(thm)],[c_14873]) ).
cnf(c_14874,plain,
( sk_c1 != sk_c11
| inverse(sk_c11) != sk_c11
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_14153,c_13572]) ).
cnf(c_14875,plain,
( sk_c11 != sk_c11
| inverse(sk_c11) != sk_c11
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_14153,c_14874]) ).
cnf(c_14312,plain,
( inverse(sk_c11) != sk_c11
| sk_c6 = sk_c4 ),
inference(copy,[status(thm)],[c_14875]) ).
cnf(c_14363,plain,
( sk_c6 = sk_c11
| inverse(sk_c11) = sk_c11 ),
inference(paramod,[status(thm)],[c_14153,c_13196]) ).
cnf(c_14397,plain,
( inverse(sk_c11) = sk_c11
| sk_c6 = sk_c4 ),
inference(paramod,[status(thm)],[c_14153,c_7219]) ).
cnf(c_14409,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c11) = sk_c11 ),
inference(paramod,[status(thm)],[c_14153,c_14]) ).
cnf(c_14876,plain,
( inverse(sk_c11) != sk_c11
| inverse(sk_c11) != sk_c11
| sk_c6 = sk_c11 ),
inference(paramod,[status(thm)],[c_14363,c_13511]) ).
cnf(c_14658,plain,
( inverse(sk_c11) != sk_c11
| sk_c6 = sk_c11 ),
inference(copy,[status(thm)],[c_14876]) ).
cnf(c_14877,plain,
( sk_c6 = sk_c4
| sk_c6 = sk_c4 ),
inference(resolve,[status(thm)],[c_14397,c_14312]) ).
cnf(c_14659,plain,
sk_c6 = sk_c4,
inference(copy,[status(thm)],[c_14877]) ).
cnf(c_14660,plain,
( inverse(sk_c11) != sk_c11
| sk_c4 = sk_c11 ),
inference(paramod,[status(thm)],[c_14659,c_14658]) ).
cnf(c_14680,plain,
( sk_c4 = sk_c11
| inverse(sk_c11) = sk_c11 ),
inference(paramod,[status(thm)],[c_14659,c_14363]) ).
cnf(c_14878,plain,
( sk_c4 = sk_c11
| sk_c4 = sk_c11 ),
inference(resolve,[status(thm)],[c_14680,c_14660]) ).
cnf(c_14742,plain,
sk_c4 = sk_c11,
inference(copy,[status(thm)],[c_14878]) ).
cnf(c_14879,plain,
( inverse(sk_c11) = sk_c11
| inverse(sk_c11) = sk_c11 ),
inference(paramod,[status(thm)],[c_14742,c_14409]) ).
cnf(c_14803,plain,
inverse(sk_c11) = sk_c11,
inference(copy,[status(thm)],[c_14879]) ).
cnf(c_14880,plain,
( inverse(sk_c11) != sk_c11
| inverse(sk_c11) != sk_c11 ),
inference(paramod,[status(thm)],[c_14803,c_13511]) ).
cnf(c_14881,plain,
( inverse(sk_c11) != sk_c11
| sk_c11 != sk_c11 ),
inference(paramod,[status(thm)],[c_14803,c_14880]) ).
cnf(c_14882,plain,
( sk_c11 != sk_c11
| sk_c11 != sk_c11 ),
inference(paramod,[status(thm)],[c_14803,c_14881]) ).
cnf(c_14883,plain,
sk_c11 != sk_c11,
inference(copy,[status(thm)],[c_14882]) ).
cnf(c_14815,plain,
$false,
inference(copy,[status(thm)],[c_14883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP389-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:50:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3749381 was started by sandbox2 on n005,
% 0.09/0.36 % Fri Sep 25 14:50:18 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 94.59/12.94
% 94.59/12.94 % SZS status Unsatisfiable for theBenchmark
% 94.59/12.94
% 94.59/12.94 % Proof 1 at 3.93 (+ 0.60) seconds.
% 94.59/12.94 % Length of proof is 97.
% 94.59/12.94 % Level of proof is 26.
% 94.59/12.94 % Maximum clause weight is 78.000.
% 94.59/12.94 % Given clauses 342.
% 94.59/12.94
% 94.59/12.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
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