%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP346-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 07:28:40 AM UTC 2026
% Result : Unsatisfiable 83.41s 17.44s
% Output : CNFRefutation 83.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 20
% Syntax : Number of formulae : 158 ( 26 unt; 0 def)
% Number of atoms : 472 ( 471 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 539 ( 225 ~; 314 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 9 !; 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_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_1) ).
cnf(c_4,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_1]) ).
fof(prove_this_3,axiom,
( inverse(sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_3) ).
cnf(c_6,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_3]) ).
fof(prove_this_4,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_4) ).
cnf(c_7,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_4]) ).
fof(prove_this_5,axiom,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('theBenchmark.p',prove_this_5) ).
cnf(c_8,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(clausify,[status(thm)],[prove_this_5]) ).
fof(prove_this_11,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_11) ).
cnf(c_14,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_11]) ).
fof(prove_this_12,axiom,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_12) ).
cnf(c_15,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_12]) ).
fof(prove_this_13,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_13) ).
cnf(c_16,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_13]) ).
fof(prove_this_14,axiom,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('theBenchmark.p',prove_this_14) ).
cnf(c_17,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_14]) ).
fof(prove_this_18,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_18) ).
cnf(c_21,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_18]) ).
fof(prove_this_19,axiom,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_19) ).
cnf(c_22,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_19]) ).
fof(prove_this_20,axiom,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_20) ).
cnf(c_23,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_20]) ).
fof(prove_this_21,axiom,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('theBenchmark.p',prove_this_21) ).
cnf(c_24,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(clausify,[status(thm)],[prove_this_21]) ).
fof(prove_this_25,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_25) ).
cnf(c_28,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_25]) ).
fof(prove_this_26,axiom,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('theBenchmark.p',prove_this_26) ).
cnf(c_29,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_26]) ).
fof(prove_this_32,axiom,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_32) ).
cnf(c_35,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_32]) ).
fof(prove_this_33,axiom,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('theBenchmark.p',prove_this_33) ).
cnf(c_36,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(clausify,[status(thm)],[prove_this_33]) ).
fof(prove_this_36,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( inverse(VAR_3) != sk_c7
| multiply(VAR_3,sk_c7) != sk_c5
| inverse(VAR_2) != sk_c6
| multiply(VAR_2,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(VAR_1,sk_c5) != sk_c6
| inverse(VAR_1) != sk_c6
| multiply(VAR_0,sk_c6) != sk_c7
| inverse(VAR_0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('theBenchmark.p',prove_this_36) ).
cnf(c_39,plain,
( inverse(D) != sk_c7
| multiply(D,sk_c7) != sk_c5
| inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(clausify,[status(thm)],[prove_this_36]) ).
cnf(c_40,plain,
( inverse(sk_c6) != sk_c7
| inverse(C) != sk_c6
| multiply(C,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(factor,[status(thm)],[c_39]) ).
cnf(c_15435,plain,
multiply(identity,A) = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_15436,plain,
A = multiply(inverse(B),multiply(B,A)),
inference(paramod,[status(thm)],[c_1,c_15435]) ).
cnf(c_70,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(copy,[status(thm)],[c_15436]) ).
cnf(c_85,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_14,c_2]) ).
cnf(c_87,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_103,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_28,c_2]) ).
cnf(c_965,plain,
multiply(inverse(inverse(A)),identity) = A,
inference(paramod,[status(thm)],[c_2,c_70]) ).
cnf(c_1002,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(paramod,[status(thm)],[c_70,c_70]) ).
cnf(c_1003,plain,
multiply(A,identity) = A,
inference(paramod,[status(thm)],[c_1002,c_965]) ).
cnf(c_1004,plain,
inverse(identity) = identity,
inference(paramod,[status(thm)],[c_1003,c_2]) ).
cnf(c_1460,plain,
multiply(A,inverse(A)) = identity,
inference(paramod,[status(thm)],[c_1002,c_2]) ).
cnf(c_15437,plain,
multiply(A,identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1002,c_1003]) ).
cnf(c_15438,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_1003,c_15437]) ).
cnf(c_1485,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_15438]) ).
cnf(c_15439,plain,
( inverse(sk_c6) != sk_c7
| multiply(inverse(sk_c6),sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(resolve,[status(thm)],[c_1485,c_40]) ).
cnf(c_1534,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(B,sk_c5) != sk_c6
| inverse(B) != sk_c6
| multiply(A,sk_c6) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_15439]) ).
cnf(c_1630,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_8,c_1460]) ).
cnf(c_1636,plain,
( multiply(sk_c3,sk_c6) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_15,c_1460]) ).
cnf(c_1638,plain,
( multiply(sk_c4,sk_c7) = identity
| inverse(sk_c1) = sk_c7 ),
inference(paramod,[status(thm)],[c_17,c_1460]) ).
cnf(c_1640,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_22,c_1460]) ).
cnf(c_1641,plain,
( multiply(sk_c4,sk_c7) = identity
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_24,c_1460]) ).
cnf(c_1646,plain,
( multiply(sk_c3,sk_c6) = identity
| inverse(sk_c2) = sk_c6 ),
inference(paramod,[status(thm)],[c_29,c_1460]) ).
cnf(c_1650,plain,
( multiply(sk_c3,sk_c6) = identity
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_36,c_1460]) ).
cnf(c_4327,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_1636,c_2]) ).
cnf(c_4405,plain,
( multiply(sk_c7,sk_c1) = identity
| multiply(sk_c4,sk_c7) = identity ),
inference(paramod,[status(thm)],[c_1638,c_2]) ).
cnf(c_4601,plain,
( multiply(sk_c6,sk_c2) = identity
| multiply(sk_c3,sk_c6) = identity ),
inference(paramod,[status(thm)],[c_1646,c_2]) ).
cnf(c_15440,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_1630,c_7]) ).
cnf(c_10084,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(copy,[status(thm)],[c_15440]) ).
cnf(c_10088,plain,
( multiply(inverse(sk_c6),sk_c5) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10084,c_70]) ).
cnf(c_15441,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1640,c_21]) ).
cnf(c_10409,plain,
( identity = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_15441]) ).
cnf(c_10413,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_10409,c_70]) ).
cnf(c_15442,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(paramod,[status(thm)],[c_1641,c_23]) ).
cnf(c_10432,plain,
( identity = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(copy,[status(thm)],[c_15442]) ).
cnf(c_10518,plain,
( multiply(inverse(sk_c1),sk_c7) = sk_c6
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_10432,c_70]) ).
cnf(c_15443,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(paramod,[status(thm)],[c_1650,c_35]) ).
cnf(c_10626,plain,
( identity = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(copy,[status(thm)],[c_15443]) ).
cnf(c_11324,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(resolve,[status(thm)],[c_1534,c_1485]) ).
cnf(c_15444,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_4327,c_85]) ).
cnf(c_11625,plain,
( identity = sk_c7
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_15444]) ).
cnf(c_15445,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11625,c_70]) ).
cnf(c_11628,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1003,c_15445]) ).
cnf(c_11655,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11628,c_1485]) ).
cnf(c_15446,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11655,c_10413]) ).
cnf(c_11719,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15446]) ).
cnf(c_11726,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_11719,c_70]) ).
cnf(c_15447,plain,
( multiply(sk_c7,sk_c1) = identity
| identity = sk_c5
| multiply(sk_c7,sk_c1) = identity ),
inference(paramod,[status(thm)],[c_4405,c_87]) ).
cnf(c_11807,plain,
( identity = sk_c5
| multiply(sk_c7,sk_c1) = identity ),
inference(copy,[status(thm)],[c_15447]) ).
cnf(c_15448,plain,
( multiply(inverse(sk_c7),identity) = sk_c1
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_11807,c_70]) ).
cnf(c_11810,plain,
( inverse(sk_c7) = sk_c1
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_1003,c_15448]) ).
cnf(c_11842,plain,
( inverse(sk_c1) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_11810,c_1485]) ).
cnf(c_15449,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c5
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_11842,c_10518]) ).
cnf(c_11927,plain,
( multiply(sk_c7,sk_c7) = sk_c6
| identity = sk_c5 ),
inference(copy,[status(thm)],[c_15449]) ).
cnf(c_11932,plain,
( multiply(inverse(sk_c7),sk_c6) = sk_c7
| identity = sk_c5 ),
inference(paramod,[status(thm)],[c_11927,c_70]) ).
cnf(c_15450,plain,
( multiply(sk_c6,sk_c2) = identity
| identity = sk_c7
| multiply(sk_c6,sk_c2) = identity ),
inference(paramod,[status(thm)],[c_4601,c_103]) ).
cnf(c_12173,plain,
( identity = sk_c7
| multiply(sk_c6,sk_c2) = identity ),
inference(copy,[status(thm)],[c_15450]) ).
cnf(c_15451,plain,
( multiply(inverse(sk_c6),identity) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12173,c_70]) ).
cnf(c_12176,plain,
( inverse(sk_c6) = sk_c2
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_1003,c_15451]) ).
cnf(c_15452,plain,
( multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12176,c_10088]) ).
cnf(c_12272,plain,
( multiply(sk_c2,sk_c5) = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15452]) ).
cnf(c_15453,plain,
( identity = sk_c7
| sk_c7 = sk_c6
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_12272,c_10626]) ).
cnf(c_15454,plain,
( identity = sk_c7
| sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15453]) ).
cnf(c_12320,plain,
( sk_c6 = sk_c7
| identity = sk_c7 ),
inference(copy,[status(thm)],[c_15454]) ).
cnf(c_12333,plain,
( multiply(A,sk_c7) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_12320,c_1003]) ).
cnf(c_12334,plain,
( inverse(sk_c7) = identity
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_12320,c_1004]) ).
cnf(c_15455,plain,
( multiply(identity,sk_c6) = sk_c7
| identity = sk_c5
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_12334,c_11932]) ).
cnf(c_15456,plain,
( sk_c6 = sk_c7
| identity = sk_c5
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_1,c_15455]) ).
cnf(c_12452,plain,
( identity = sk_c5
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_15456]) ).
cnf(c_12460,plain,
( multiply(A,sk_c5) = A
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_12452,c_1003]) ).
cnf(c_15457,plain,
( sk_c6 = sk_c7
| sk_c5 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_12452,c_12320]) ).
cnf(c_12490,plain,
( sk_c5 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_15457]) ).
cnf(c_15458,plain,
( sk_c6 = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_12460,c_4]) ).
cnf(c_12921,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_15458]) ).
cnf(c_15459,plain,
( sk_c5 = sk_c6
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_12921,c_12333]) ).
cnf(c_13026,plain,
( sk_c5 = sk_c6
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_15459]) ).
cnf(c_15460,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(paramod,[status(thm)],[c_13026,c_12490]) ).
cnf(c_15461,plain,
( sk_c6 = sk_c7
| sk_c6 = sk_c7 ),
inference(copy,[status(thm)],[c_15460]) ).
cnf(c_13070,plain,
sk_c6 = sk_c7,
inference(copy,[status(thm)],[c_15461]) ).
cnf(c_15462,plain,
( multiply(inverse(sk_c7),sk_c7) = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_13070,c_11726]) ).
cnf(c_15463,plain,
( identity = sk_c7
| identity = sk_c7 ),
inference(paramod,[status(thm)],[c_2,c_15462]) ).
cnf(c_13482,plain,
identity = sk_c7,
inference(copy,[status(thm)],[c_15463]) ).
cnf(c_15464,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c6) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13070,c_11324]) ).
cnf(c_15465,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| multiply(inverse(sk_c7),sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13070,c_15464]) ).
cnf(c_15466,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| identity != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_2,c_15465]) ).
cnf(c_15467,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c6
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13482,c_15466]) ).
cnf(c_15468,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c6
| inverse(A) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13070,c_15467]) ).
cnf(c_15469,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c7
| inverse(A) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13070,c_15468]) ).
cnf(c_15470,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c6
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c7
| inverse(A) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13070,c_15469]) ).
cnf(c_15471,plain,
( inverse(sk_c6) != sk_c7
| identity != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c7
| inverse(A) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13070,c_15470]) ).
cnf(c_15472,plain,
( inverse(sk_c6) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c7
| inverse(A) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13482,c_15471]) ).
cnf(c_15473,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c7
| inverse(A) != sk_c7
| sk_c7 != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(paramod,[status(thm)],[c_13070,c_15472]) ).
cnf(c_15474,plain,
( inverse(sk_c7) != sk_c7
| sk_c7 != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(copy,[status(thm)],[c_15473]) ).
cnf(c_15475,plain,
( inverse(sk_c7) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(copy,[status(thm)],[c_15474]) ).
cnf(c_13647,plain,
( inverse(sk_c7) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(A,sk_c5) != sk_c7
| inverse(A) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(copy,[status(thm)],[c_15475]) ).
cnf(c_15353,plain,
( inverse(sk_c7) = sk_c5
| multiply(sk_c7,sk_c7) = sk_c5 ),
inference(paramod,[status(thm)],[c_13070,c_6]) ).
cnf(c_15476,plain,
inverse(sk_c7) = identity,
inference(paramod,[status(thm)],[c_13482,c_1004]) ).
cnf(c_15421,plain,
inverse(sk_c7) = sk_c7,
inference(paramod,[status(thm)],[c_13482,c_15476]) ).
cnf(c_15422,plain,
multiply(A,sk_c7) = A,
inference(paramod,[status(thm)],[c_13482,c_1003]) ).
cnf(c_15424,plain,
multiply(sk_c7,A) = A,
inference(paramod,[status(thm)],[c_13482,c_1]) ).
cnf(c_15477,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(factor,[status(thm)],[c_13647]) ).
cnf(c_15478,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c7
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_15422,c_15477]) ).
cnf(c_15479,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_15421,c_15478]) ).
cnf(c_15480,plain,
( inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c5) != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_15424,c_15479]) ).
cnf(c_15481,plain,
( inverse(sk_c7) != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_15424,c_15480]) ).
cnf(c_15482,plain,
( sk_c7 != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7
| sk_c7 != sk_c5 ),
inference(paramod,[status(thm)],[c_15421,c_15481]) ).
cnf(c_15483,plain,
( sk_c7 != sk_c5
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_15482]) ).
cnf(c_15484,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c7 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_15483]) ).
cnf(c_15485,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_15484]) ).
cnf(c_15486,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_15485]) ).
cnf(c_15487,plain,
( sk_c5 != sk_c7
| sk_c5 != sk_c7 ),
inference(copy,[status(thm)],[c_15486]) ).
cnf(c_15429,plain,
sk_c5 != sk_c7,
inference(copy,[status(thm)],[c_15487]) ).
cnf(c_15488,plain,
( inverse(sk_c7) = sk_c5
| sk_c7 = sk_c5 ),
inference(paramod,[status(thm)],[c_15422,c_15353]) ).
cnf(c_15489,plain,
( sk_c7 = sk_c5
| sk_c7 = sk_c5 ),
inference(paramod,[status(thm)],[c_15421,c_15488]) ).
cnf(c_15490,plain,
( sk_c7 = sk_c5
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_15489]) ).
cnf(c_15491,plain,
( sk_c5 = sk_c7
| sk_c5 = sk_c7 ),
inference(copy,[status(thm)],[c_15490]) ).
cnf(c_15492,plain,
sk_c5 = sk_c7,
inference(copy,[status(thm)],[c_15491]) ).
cnf(c_15434,plain,
$false,
inference(resolve,[status(thm)],[c_15429,c_15492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP346-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 14:46:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3735159 was started by sandbox on n005,
% 0.08/0.36 % Fri Sep 25 14:46:48 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 83.41/17.44
% 83.41/17.44 % given #500 (F,wt=40): 11936 multiply(sk_c6,sk_c7) != sk_c5 | inverse(A) != sk_c7 | multiply(A,sk_c6) != sk_c7 | multiply(inverse(sk_c6),sk_c5) != sk_c6 | multiply(sk_c6,sk_c5) != sk_c7 | multiply(sk_c7,sk_c5) != sk_c6 | inverse(sk_c7) != sk_c5 | identity != sk_c7 | identity != sk_c5. [resolve(1525,d,1485,a),rewrite([2(36)])].
% 83.41/17.44
% 83.41/17.44 % SZS status Unsatisfiable for theBenchmark
% 83.41/17.44
% 83.41/17.44 % Proof 1 at 10.15 (+ 1.25) seconds.
% 83.41/17.44 % Length of proof is 80.
% 83.41/17.44 % Level of proof is 19.
% 83.41/17.44 % Maximum clause weight is 55.000.
% 83.41/17.44 % Given clauses 575.
% 83.41/17.44
% 83.41/17.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------