%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP298-1 : 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 : n015.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 07:28:35 AM UTC 2026
% Result : Unsatisfiable 2.57s 0.74s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 17
% Syntax : Number of formulae : 172 ( 26 unt; 0 def)
% Number of atoms : 536 ( 535 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 660 ( 296 ~; 364 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 67 ( 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_c2,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_3,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_9,axiom,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_9) ).
cnf(c_12,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_9]) ).
fof(prove_this_10,axiom,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_10) ).
cnf(c_13,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_10]) ).
fof(prove_this_11,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_17,axiom,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_17) ).
cnf(c_20,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_17]) ).
fof(prove_this_18,axiom,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_20,axiom,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_27,axiom,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_27) ).
cnf(c_30,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_27]) ).
fof(prove_this_28,axiom,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_28) ).
cnf(c_31,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_28]) ).
fof(prove_this_29,axiom,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('theBenchmark.p',prove_this_29) ).
cnf(c_32,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_29]) ).
fof(prove_this_33,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( multiply(VAR_4,sk_c6) != sk_c7
| inverse(VAR_3) != VAR_4
| multiply(VAR_3,VAR_4) != sk_c7
| multiply(VAR_2,sk_c7) != sk_c8
| inverse(VAR_2) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(VAR_1) != sk_c8
| multiply(VAR_1,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(VAR_0) != sk_c8
| multiply(VAR_0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( multiply(E,sk_c6) != sk_c7
| inverse(D) != E
| multiply(D,E) != sk_c7
| multiply(C,sk_c7) != sk_c8
| inverse(C) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(B) != sk_c8
| multiply(B,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
cnf(c_37,plain,
( multiply(D,sk_c6) != sk_c7
| inverse(C) != D
| multiply(C,D) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_1541,plain,
( multiply(D,sk_c6) != sk_c7
| inverse(C) != D
| multiply(C,D) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_36]) ).
cnf(c_38,plain,
( multiply(D,sk_c6) != sk_c7
| inverse(C) != D
| multiply(C,D) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1541]) ).
cnf(c_1542,plain,
( multiply(C,sk_c6) != sk_c7
| inverse(B) != C
| multiply(B,C) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_37]) ).
cnf(c_40,plain,
( multiply(C,sk_c6) != sk_c7
| inverse(B) != C
| multiply(B,C) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1542]) ).
cnf(c_1543,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| inverse(A) != sk_c8
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_38]) ).
cnf(c_1544,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1543]) ).
cnf(c_42,plain,
( multiply(B,sk_c7) != sk_c8
| inverse(B) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1544]) ).
cnf(c_1545,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_1546,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1545]) ).
cnf(c_44,plain,
( multiply(A,sk_c7) != sk_c8
| inverse(A) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(copy,[status(thm)],[c_1546]) ).
cnf(c_46,plain,
( multiply(A,sk_c7) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_47,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(factor,[status(thm)],[c_44]) ).
cnf(c_1547,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_1548,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_1547]) ).
cnf(c_48,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_1548]) ).
cnf(c_1549,plain,
( multiply(sk_c7,A) = multiply(sk_c2,multiply(sk_c8,A))
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_4,c_3]) ).
cnf(c_51,plain,
( multiply(sk_c2,multiply(sk_c8,A)) = multiply(sk_c7,A)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_1549]) ).
cnf(c_56,plain,
( multiply(sk_c6,A) = multiply(sk_c8,multiply(sk_c7,A))
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_60,plain,
( multiply(sk_c8,sk_c3) = identity
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_110,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_21,c_2]) ).
cnf(c_115,plain,
( multiply(sk_c8,sk_c1) = identity
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_116,plain,
( multiply(sk_c8,sk_c3) = identity
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_23,c_2]) ).
cnf(c_176,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_48]) ).
cnf(c_199,plain,
( multiply(inverse(sk_c8),sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_14,c_48]) ).
cnf(c_232,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_31,c_48]) ).
cnf(c_234,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(paramod,[status(thm)],[c_32,c_48]) ).
cnf(c_242,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_48,c_48]) ).
cnf(c_243,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_242,c_176]) ).
cnf(c_1550,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_110,c_48]) ).
cnf(c_286,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_243,c_1550]) ).
cnf(c_288,plain,
( multiply(sk_c1,sk_c8) = identity
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_286,c_2]) ).
cnf(c_1551,plain,
( multiply(sk_c2,sk_c7) = multiply(sk_c7,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_6,c_51]) ).
cnf(c_301,plain,
( multiply(sk_c2,sk_c7) = multiply(sk_c7,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_1551]) ).
cnf(c_1552,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_115,c_48]) ).
cnf(c_312,plain,
( inverse(sk_c8) = sk_c1
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_243,c_1552]) ).
cnf(c_1553,plain,
( multiply(inverse(sk_c8),identity) = sk_c3
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_116,c_48]) ).
cnf(c_319,plain,
( inverse(sk_c8) = sk_c3
| inverse(sk_c1) = sk_c8 ),
inference(paramod,[status(thm)],[c_243,c_1553]) ).
cnf(c_1554,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,multiply(sk_c7,sk_c8)) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_56,c_30]) ).
cnf(c_401,plain,
( multiply(sk_c8,multiply(sk_c7,sk_c8)) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_1554]) ).
cnf(c_1555,plain,
( inverse(sk_c2) = sk_c8
| identity = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(paramod,[status(thm)],[c_288,c_13]) ).
cnf(c_413,plain,
( identity = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(copy,[status(thm)],[c_1555]) ).
cnf(c_416,plain,
( multiply(sk_c8,sk_c2) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_413,c_2]) ).
cnf(c_1556,plain,
( multiply(inverse(sk_c8),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_416,c_48]) ).
cnf(c_424,plain,
( inverse(sk_c8) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_243,c_1556]) ).
cnf(c_432,plain,
( multiply(sk_c2,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_424,c_2]) ).
cnf(c_1557,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_432,c_12]) ).
cnf(c_477,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1557]) ).
cnf(c_1558,plain,
( identity = sk_c7
| inverse(sk_c1) = sk_c8
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_432,c_20]) ).
cnf(c_478,plain,
( inverse(sk_c1) = sk_c8
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1558]) ).
cnf(c_491,plain,
( multiply(sk_c8,sk_c1) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_478,c_2]) ).
cnf(c_1559,plain,
( multiply(sk_c2,identity) = multiply(sk_c7,sk_c3)
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_60,c_51]) ).
cnf(c_1560,plain,
( sk_c2 = multiply(sk_c7,sk_c3)
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(paramod,[status(thm)],[c_243,c_1559]) ).
cnf(c_1561,plain,
( multiply(sk_c7,sk_c3) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_1560]) ).
cnf(c_515,plain,
( multiply(sk_c7,sk_c3) = sk_c2
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(copy,[status(thm)],[c_1561]) ).
cnf(c_1562,plain,
( multiply(inverse(sk_c8),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_491,c_48]) ).
cnf(c_585,plain,
( inverse(sk_c8) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_243,c_1562]) ).
cnf(c_591,plain,
( multiply(sk_c1,sk_c8) = identity
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_585,c_2]) ).
cnf(c_1563,plain,
( identity = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_591,c_477]) ).
cnf(c_1564,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_1563]) ).
cnf(c_847,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_1564]) ).
cnf(c_938,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_847,c_243]) ).
cnf(c_955,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_847,c_1]) ).
cnf(c_1565,plain,
( multiply(sk_c7,sk_c3) = sk_c2
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_515]) ).
cnf(c_1566,plain,
( sk_c3 = sk_c2
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_955,c_1565]) ).
cnf(c_1056,plain,
( sk_c3 = sk_c2
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1566]) ).
cnf(c_1567,plain,
( multiply(sk_c2,sk_c7) = multiply(sk_c7,sk_c6)
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_301]) ).
cnf(c_1568,plain,
( sk_c2 = multiply(sk_c7,sk_c6)
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_1567]) ).
cnf(c_1569,plain,
( sk_c2 = sk_c6
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_955,c_1568]) ).
cnf(c_1084,plain,
( sk_c2 = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1569]) ).
cnf(c_1570,plain,
( multiply(inverse(sk_c6),sk_c7) = sk_c8
| sk_c3 = sk_c8 ),
inference(paramod,[status(thm)],[c_938,c_234]) ).
cnf(c_1096,plain,
( inverse(sk_c6) = sk_c8
| sk_c3 = sk_c8 ),
inference(paramod,[status(thm)],[c_938,c_1570]) ).
cnf(c_1097,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_938,c_232]) ).
cnf(c_1107,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_938,c_199]) ).
cnf(c_1571,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_47]) ).
cnf(c_1572,plain,
( sk_c6 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_1571]) ).
cnf(c_1573,plain,
( sk_c6 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1572]) ).
cnf(c_1173,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1573]) ).
cnf(c_1574,plain,
( multiply(A,sk_c7) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_46]) ).
cnf(c_1575,plain,
( A != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_1574]) ).
cnf(c_1576,plain,
( A != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1575]) ).
cnf(c_1174,plain,
( sk_c8 != A
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(A) != sk_c8
| multiply(A,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1576]) ).
cnf(c_1577,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_8]) ).
cnf(c_1578,plain,
( sk_c3 = sk_c8
| sk_c8 = sk_c6 ),
inference(paramod,[status(thm)],[c_938,c_1577]) ).
cnf(c_1179,plain,
( sk_c3 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1578]) ).
cnf(c_1195,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_955,c_401]) ).
cnf(c_1579,plain,
( inverse(sk_c8) = sk_c3
| sk_c8 != sk_c1
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c1,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(resolve,[status(thm)],[c_1174,c_319]) ).
cnf(c_1307,plain,
( inverse(sk_c8) = sk_c3
| sk_c1 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c1,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1579]) ).
cnf(c_1580,plain,
( inverse(sk_c8) = sk_c1
| sk_c8 != sk_c3
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c3,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(resolve,[status(thm)],[c_1174,c_312]) ).
cnf(c_1308,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c3,sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(copy,[status(thm)],[c_1580]) ).
cnf(c_1581,plain,
( sk_c3 = sk_c6
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1084,c_1056]) ).
cnf(c_1393,plain,
( sk_c3 = sk_c6
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1581]) ).
cnf(c_1582,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(paramod,[status(thm)],[c_1393,c_1179]) ).
cnf(c_1583,plain,
( sk_c6 = sk_c8
| sk_c6 = sk_c8 ),
inference(copy,[status(thm)],[c_1582]) ).
cnf(c_1425,plain,
sk_c6 = sk_c8,
inference(copy,[status(thm)],[c_1583]) ).
cnf(c_1584,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c3,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1308]) ).
cnf(c_1585,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c3,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1584]) ).
cnf(c_1586,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c3,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1585]) ).
cnf(c_1587,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c3,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1586]) ).
cnf(c_1471,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c3,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1587]) ).
cnf(c_1588,plain,
( inverse(sk_c8) = sk_c3
| sk_c1 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c1,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1307]) ).
cnf(c_1589,plain,
( inverse(sk_c8) = sk_c3
| sk_c1 != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c1,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1588]) ).
cnf(c_1590,plain,
( inverse(sk_c8) = sk_c3
| sk_c1 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c1,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1589]) ).
cnf(c_1591,plain,
( inverse(sk_c8) = sk_c3
| sk_c1 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c1,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1590]) ).
cnf(c_1472,plain,
( inverse(sk_c8) = sk_c3
| sk_c1 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c1,sk_c8) != sk_c7 ),
inference(copy,[status(thm)],[c_1591]) ).
cnf(c_1592,plain,
( multiply(sk_c8,sk_c8) = sk_c7
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1425,c_1195]) ).
cnf(c_1520,plain,
multiply(sk_c8,sk_c8) = sk_c7,
inference(copy,[status(thm)],[c_1592]) ).
cnf(c_1593,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c6,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1173]) ).
cnf(c_1594,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1593]) ).
cnf(c_1595,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c8
| sk_c7 != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1520,c_1594]) ).
cnf(c_1596,plain,
( multiply(sk_c8,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c8
| sk_c7 != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1595]) ).
cnf(c_1597,plain,
( multiply(sk_c8,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c8
| sk_c7 != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1596]) ).
cnf(c_1598,plain,
( sk_c7 != sk_c7
| inverse(sk_c8) != sk_c8
| sk_c7 != sk_c7
| sk_c8 != sk_c8 ),
inference(paramod,[status(thm)],[c_1520,c_1597]) ).
cnf(c_1599,plain,
( sk_c7 != sk_c7
| inverse(sk_c8) != sk_c8
| sk_c7 != sk_c7 ),
inference(copy,[status(thm)],[c_1598]) ).
cnf(c_1600,plain,
( sk_c7 != sk_c7
| inverse(sk_c8) != sk_c8 ),
inference(copy,[status(thm)],[c_1599]) ).
cnf(c_1522,plain,
inverse(sk_c8) != sk_c8,
inference(copy,[status(thm)],[c_1600]) ).
cnf(c_1601,plain,
( inverse(sk_c8) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(paramod,[status(thm)],[c_1425,c_1107]) ).
cnf(c_1527,plain,
multiply(sk_c1,sk_c8) = sk_c7,
inference(resolve,[status(thm)],[c_1522,c_1601]) ).
cnf(c_1602,plain,
( inverse(sk_c8) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1097]) ).
cnf(c_1531,plain,
inverse(sk_c3) = sk_c8,
inference(resolve,[status(thm)],[c_1522,c_1602]) ).
cnf(c_1603,plain,
( inverse(sk_c8) = sk_c8
| sk_c3 = sk_c8 ),
inference(paramod,[status(thm)],[c_1425,c_1096]) ).
cnf(c_1532,plain,
sk_c3 = sk_c8,
inference(resolve,[status(thm)],[c_1522,c_1603]) ).
cnf(c_1604,plain,
( inverse(sk_c8) = sk_c3
| sk_c1 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_1527,c_1472]) ).
cnf(c_1605,plain,
( inverse(sk_c8) = sk_c3
| sk_c1 != sk_c8
| sk_c7 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_1520,c_1604]) ).
cnf(c_1606,plain,
( inverse(sk_c8) = sk_c8
| sk_c1 != sk_c8
| sk_c7 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_1532,c_1605]) ).
cnf(c_1607,plain,
( inverse(sk_c8) = sk_c8
| sk_c1 != sk_c8
| sk_c7 != sk_c7 ),
inference(copy,[status(thm)],[c_1606]) ).
cnf(c_1608,plain,
( inverse(sk_c8) = sk_c8
| sk_c1 != sk_c8 ),
inference(copy,[status(thm)],[c_1607]) ).
cnf(c_1538,plain,
sk_c1 != sk_c8,
inference(resolve,[status(thm)],[c_1522,c_1608]) ).
cnf(c_1609,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramod,[status(thm)],[c_1532,c_1471]) ).
cnf(c_1610,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_1520,c_1609]) ).
cnf(c_1611,plain,
( inverse(sk_c8) = sk_c1
| sk_c3 != sk_c8
| sk_c7 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_1520,c_1610]) ).
cnf(c_1612,plain,
( inverse(sk_c8) = sk_c1
| sk_c8 != sk_c8
| sk_c7 != sk_c7
| sk_c7 != sk_c7 ),
inference(paramod,[status(thm)],[c_1532,c_1611]) ).
cnf(c_1613,plain,
( inverse(sk_c8) = sk_c1
| sk_c8 != sk_c8
| sk_c7 != sk_c7 ),
inference(copy,[status(thm)],[c_1612]) ).
cnf(c_1614,plain,
( inverse(sk_c8) = sk_c1
| sk_c8 != sk_c8 ),
inference(copy,[status(thm)],[c_1613]) ).
cnf(c_1539,plain,
inverse(sk_c8) = sk_c1,
inference(copy,[status(thm)],[c_1614]) ).
cnf(c_1615,plain,
inverse(sk_c8) = sk_c8,
inference(paramod,[status(thm)],[c_1532,c_1531]) ).
cnf(c_1616,plain,
sk_c1 = sk_c8,
inference(paramod,[status(thm)],[c_1539,c_1615]) ).
cnf(c_1540,plain,
$false,
inference(resolve,[status(thm)],[c_1538,c_1616]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP298-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:47:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1634931 was started by sandbox2 on n015,
% 0.09/0.37 % Fri Sep 25 14:47:12 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 2.57/0.74
% 2.57/0.74 % SZS status Unsatisfiable for theBenchmark
% 2.57/0.74
% 2.57/0.74 % Proof 1 at 0.26 (+ 0.09) seconds.
% 2.57/0.74 % Length of proof is 79.
% 2.57/0.74 % Level of proof is 23.
% 2.57/0.74 % Maximum clause weight is 60.000.
% 2.57/0.74 % Given clauses 128.
% 2.57/0.74
% 2.57/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------