%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO014-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 06:55:06 AM UTC 2026
% Result : Unsatisfiable 2.13s 0.67s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 9
% Syntax : Number of formulae : 152 ( 152 unt; 0 def)
% Number of atoms : 152 ( 151 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 282 ( 29 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_of_add,axiom,
! [VAR_0,VAR_1] : add(VAR_0,VAR_1) = add(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_add) ).
cnf(c_1,plain,
add(A,B) = add(B,A),
inference(clausify,[status(thm)],[commutativity_of_add]) ).
fof(commutativity_of_multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = multiply(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_multiply) ).
cnf(c_2,plain,
multiply(A,B) = multiply(B,A),
inference(clausify,[status(thm)],[commutativity_of_multiply]) ).
fof(distributivity1,axiom,
! [VAR_0,VAR_1,VAR_2] : add(VAR_0,multiply(VAR_1,VAR_2)) = multiply(add(VAR_0,VAR_1),add(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity1) ).
cnf(c_3,plain,
add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)),
inference(clausify,[status(thm)],[distributivity1]) ).
cnf(c_4,plain,
multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)),
inference(copy,[status(thm)],[c_3]) ).
fof(distributivity2,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(VAR_0,add(VAR_1,VAR_2)) = add(multiply(VAR_0,VAR_1),multiply(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity2) ).
cnf(c_5,plain,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
inference(clausify,[status(thm)],[distributivity2]) ).
fof(additive_id1,axiom,
! [VAR_0] : add(VAR_0,additive_identity) = VAR_0,
file('theBenchmark.p',additive_id1) ).
cnf(c_6,plain,
add(A,additive_identity) = A,
inference(clausify,[status(thm)],[additive_id1]) ).
fof(multiplicative_id1,axiom,
! [VAR_0] : multiply(VAR_0,multiplicative_identity) = VAR_0,
file('theBenchmark.p',multiplicative_id1) ).
cnf(c_7,plain,
multiply(A,multiplicative_identity) = A,
inference(clausify,[status(thm)],[multiplicative_id1]) ).
fof(additive_inverse1,axiom,
! [VAR_0] : add(VAR_0,inverse(VAR_0)) = multiplicative_identity,
file('theBenchmark.p',additive_inverse1) ).
cnf(c_8,plain,
add(A,inverse(A)) = multiplicative_identity,
inference(clausify,[status(thm)],[additive_inverse1]) ).
fof(multiplicative_inverse1,axiom,
! [VAR_0] : multiply(VAR_0,inverse(VAR_0)) = additive_identity,
file('theBenchmark.p',multiplicative_inverse1) ).
cnf(c_9,plain,
multiply(A,inverse(A)) = additive_identity,
inference(clausify,[status(thm)],[multiplicative_inverse1]) ).
fof(prove_c_inverse_is_d,axiom,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
file('theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c_10,plain,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
inference(clausify,[status(thm)],[prove_c_inverse_is_d]) ).
cnf(c_654,plain,
add(multiply(add(A,B),A),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_655,plain,
add(multiply(A,add(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_2,c_654]) ).
cnf(c_11,plain,
add(add(multiply(A,A),multiply(A,B)),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(paramod,[status(thm)],[c_5,c_655]) ).
cnf(c_656,plain,
add(multiply(A,B),multiply(A,C)) = multiply(add(B,C),A),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_12,plain,
multiply(add(A,B),C) = add(multiply(C,A),multiply(C,B)),
inference(copy,[status(thm)],[c_656]) ).
cnf(c_657,plain,
A = add(additive_identity,A),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_13,plain,
add(additive_identity,A) = A,
inference(copy,[status(thm)],[c_657]) ).
cnf(c_658,plain,
multiply(A,B) = add(multiply(A,B),multiply(A,additive_identity)),
inference(paramod,[status(thm)],[c_6,c_5]) ).
cnf(c_14,plain,
add(multiply(A,B),multiply(A,additive_identity)) = multiply(A,B),
inference(copy,[status(thm)],[c_658]) ).
cnf(c_659,plain,
A = multiply(multiplicative_identity,A),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_15,plain,
multiply(multiplicative_identity,A) = A,
inference(copy,[status(thm)],[c_659]) ).
cnf(c_660,plain,
multiply(A,multiplicative_identity) = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_661,plain,
A = add(multiply(A,B),multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_7,c_660]) ).
cnf(c_16,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(copy,[status(thm)],[c_661]) ).
cnf(c_662,plain,
add(add(multiply(A,A),multiply(A,inverse(A))),multiply(multiplicative_identity,B)) = add(A,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_8,c_11]) ).
cnf(c_663,plain,
add(add(multiply(A,A),additive_identity),multiply(multiplicative_identity,B)) = add(A,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_9,c_662]) ).
cnf(c_664,plain,
add(add(additive_identity,multiply(A,A)),multiply(multiplicative_identity,B)) = add(A,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_1,c_663]) ).
cnf(c_665,plain,
add(multiply(A,A),multiply(multiplicative_identity,B)) = add(A,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_13,c_664]) ).
cnf(c_666,plain,
add(multiply(A,A),B) = add(A,multiply(inverse(A),B)),
inference(paramod,[status(thm)],[c_15,c_665]) ).
cnf(c_24,plain,
add(A,multiply(inverse(A),B)) = add(multiply(A,A),B),
inference(copy,[status(thm)],[c_666]) ).
cnf(c_667,plain,
add(add(multiply(A,A),multiply(A,B)),additive_identity) = add(A,multiply(B,inverse(add(A,B)))),
inference(paramod,[status(thm)],[c_9,c_11]) ).
cnf(c_668,plain,
add(additive_identity,add(multiply(A,A),multiply(A,B))) = add(A,multiply(B,inverse(add(A,B)))),
inference(paramod,[status(thm)],[c_1,c_667]) ).
cnf(c_669,plain,
add(multiply(A,A),multiply(A,B)) = add(A,multiply(B,inverse(add(A,B)))),
inference(paramod,[status(thm)],[c_13,c_668]) ).
cnf(c_25,plain,
add(A,multiply(B,inverse(add(A,B)))) = add(multiply(A,A),multiply(A,B)),
inference(copy,[status(thm)],[c_669]) ).
cnf(c_26,plain,
multiply(add(A,B),C) = add(multiply(C,B),multiply(C,A)),
inference(paramod,[status(thm)],[c_12,c_1]) ).
cnf(c_27,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(C,B)),
inference(paramod,[status(thm)],[c_2,c_12]) ).
cnf(c_670,plain,
add(multiply(inverse(add(A,B)),A),multiply(inverse(add(A,B)),B)) = additive_identity,
inference(paramod,[status(thm)],[c_12,c_9]) ).
cnf(c_671,plain,
add(multiply(A,inverse(add(A,B))),multiply(inverse(add(A,B)),B)) = additive_identity,
inference(paramod,[status(thm)],[c_2,c_670]) ).
cnf(c_31,plain,
add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))) = additive_identity,
inference(paramod,[status(thm)],[c_2,c_671]) ).
cnf(c_33,plain,
inverse(additive_identity) = multiplicative_identity,
inference(paramod,[status(thm)],[c_13,c_8]) ).
cnf(c_672,plain,
add(additive_identity,multiply(A,additive_identity)) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_9,c_14]) ).
cnf(c_673,plain,
multiply(A,additive_identity) = multiply(A,inverse(A)),
inference(paramod,[status(thm)],[c_13,c_672]) ).
cnf(c_40,plain,
multiply(A,additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_9,c_673]) ).
cnf(c_674,plain,
additive_identity = multiply(additive_identity,A),
inference(paramod,[status(thm)],[c_40,c_2]) ).
cnf(c_42,plain,
multiply(additive_identity,A) = additive_identity,
inference(copy,[status(thm)],[c_674]) ).
cnf(c_675,plain,
add(add(multiply(A,A),additive_identity),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_40,c_11]) ).
cnf(c_676,plain,
add(add(additive_identity,multiply(A,A)),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_1,c_675]) ).
cnf(c_677,plain,
add(multiply(A,A),multiply(add(A,additive_identity),B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_13,c_676]) ).
cnf(c_678,plain,
add(multiply(A,A),multiply(A,B)) = add(A,multiply(additive_identity,B)),
inference(paramod,[status(thm)],[c_6,c_677]) ).
cnf(c_679,plain,
add(multiply(A,A),multiply(A,B)) = add(A,additive_identity),
inference(paramod,[status(thm)],[c_42,c_678]) ).
cnf(c_43,plain,
add(multiply(A,A),multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_6,c_679]) ).
cnf(c_44,plain,
add(A,multiply(B,inverse(add(A,B)))) = A,
inference(paramod,[status(thm)],[c_43,c_25]) ).
cnf(c_48,plain,
add(multiply(A,B),multiply(B,inverse(A))) = B,
inference(paramod,[status(thm)],[c_2,c_16]) ).
cnf(c_680,plain,
add(additive_identity,multiply(A,inverse(inverse(A)))) = A,
inference(paramod,[status(thm)],[c_9,c_16]) ).
cnf(c_52,plain,
multiply(A,inverse(inverse(A))) = A,
inference(paramod,[status(thm)],[c_13,c_680]) ).
cnf(c_681,plain,
add(multiply(A,A),additive_identity) = A,
inference(paramod,[status(thm)],[c_9,c_16]) ).
cnf(c_682,plain,
add(additive_identity,multiply(A,A)) = A,
inference(paramod,[status(thm)],[c_1,c_681]) ).
cnf(c_53,plain,
multiply(A,A) = A,
inference(paramod,[status(thm)],[c_13,c_682]) ).
cnf(c_55,plain,
add(A,multiply(A,B)) = A,
inference(paramod,[status(thm)],[c_53,c_43]) ).
cnf(c_56,plain,
add(A,multiply(inverse(A),B)) = add(A,B),
inference(paramod,[status(thm)],[c_53,c_24]) ).
cnf(c_683,plain,
add(multiply(inverse(add(A,B)),B),multiply(inverse(add(A,B)),A)) = additive_identity,
inference(paramod,[status(thm)],[c_26,c_9]) ).
cnf(c_684,plain,
add(multiply(B,inverse(add(A,B))),multiply(inverse(add(A,B)),A)) = additive_identity,
inference(paramod,[status(thm)],[c_2,c_683]) ).
cnf(c_65,plain,
add(multiply(A,inverse(add(B,A))),multiply(B,inverse(add(B,A)))) = additive_identity,
inference(paramod,[status(thm)],[c_2,c_684]) ).
cnf(c_67,plain,
add(A,multiply(B,A)) = A,
inference(paramod,[status(thm)],[c_2,c_55]) ).
cnf(c_75,plain,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
inference(paramod,[status(thm)],[c_2,c_27]) ).
cnf(c_77,plain,
add(add(A,B),add(multiply(A,C),multiply(C,B))) = add(A,B),
inference(paramod,[status(thm)],[c_27,c_55]) ).
cnf(c_685,plain,
add(multiply(A,inverse(A)),multiply(multiply(A,B),inverse(add(A,multiply(A,B))))) = additive_identity,
inference(paramod,[status(thm)],[c_55,c_31]) ).
cnf(c_686,plain,
add(additive_identity,multiply(multiply(A,B),inverse(add(A,multiply(A,B))))) = additive_identity,
inference(paramod,[status(thm)],[c_9,c_685]) ).
cnf(c_687,plain,
add(additive_identity,multiply(multiply(A,B),inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_55,c_686]) ).
cnf(c_85,plain,
multiply(multiply(A,B),inverse(A)) = additive_identity,
inference(paramod,[status(thm)],[c_13,c_687]) ).
cnf(c_688,plain,
add(multiply(A,inverse(A)),multiply(multiply(B,A),inverse(add(A,multiply(B,A))))) = additive_identity,
inference(paramod,[status(thm)],[c_67,c_31]) ).
cnf(c_689,plain,
add(additive_identity,multiply(multiply(B,A),inverse(add(A,multiply(B,A))))) = additive_identity,
inference(paramod,[status(thm)],[c_9,c_688]) ).
cnf(c_690,plain,
add(additive_identity,multiply(multiply(B,A),inverse(A))) = additive_identity,
inference(paramod,[status(thm)],[c_67,c_689]) ).
cnf(c_87,plain,
multiply(multiply(A,B),inverse(B)) = additive_identity,
inference(paramod,[status(thm)],[c_13,c_690]) ).
cnf(c_691,plain,
add(multiply(multiply(A,B),A),additive_identity) = multiply(A,B),
inference(paramod,[status(thm)],[c_85,c_16]) ).
cnf(c_692,plain,
add(multiply(A,multiply(A,B)),additive_identity) = multiply(A,B),
inference(paramod,[status(thm)],[c_2,c_691]) ).
cnf(c_693,plain,
add(additive_identity,multiply(A,multiply(A,B))) = multiply(A,B),
inference(paramod,[status(thm)],[c_1,c_692]) ).
cnf(c_90,plain,
multiply(A,multiply(A,B)) = multiply(A,B),
inference(paramod,[status(thm)],[c_13,c_693]) ).
cnf(c_694,plain,
additive_identity = multiply(inverse(A),multiply(B,A)),
inference(paramod,[status(thm)],[c_87,c_2]) ).
cnf(c_91,plain,
multiply(inverse(A),multiply(B,A)) = additive_identity,
inference(copy,[status(thm)],[c_694]) ).
cnf(c_695,plain,
add(multiply(A,inverse(add(A,B))),multiply(multiply(B,inverse(add(A,B))),inverse(additive_identity))) = multiply(A,inverse(add(A,B))),
inference(paramod,[status(thm)],[c_31,c_44]) ).
cnf(c_696,plain,
add(multiply(A,inverse(add(A,B))),multiply(multiply(B,inverse(add(A,B))),multiplicative_identity)) = multiply(A,inverse(add(A,B))),
inference(paramod,[status(thm)],[c_33,c_695]) ).
cnf(c_697,plain,
add(multiply(A,inverse(add(A,B))),multiply(multiplicative_identity,multiply(B,inverse(add(A,B))))) = multiply(A,inverse(add(A,B))),
inference(paramod,[status(thm)],[c_2,c_696]) ).
cnf(c_698,plain,
add(multiply(A,inverse(add(A,B))),multiply(B,inverse(add(A,B)))) = multiply(A,inverse(add(A,B))),
inference(paramod,[status(thm)],[c_15,c_697]) ).
cnf(c_699,plain,
additive_identity = multiply(A,inverse(add(A,B))),
inference(paramod,[status(thm)],[c_31,c_698]) ).
cnf(c_98,plain,
multiply(A,inverse(add(A,B))) = additive_identity,
inference(copy,[status(thm)],[c_699]) ).
cnf(c_700,plain,
add(multiply(A,inverse(add(B,A))),additive_identity) = additive_identity,
inference(paramod,[status(thm)],[c_98,c_65]) ).
cnf(c_701,plain,
add(additive_identity,multiply(A,inverse(add(B,A)))) = additive_identity,
inference(paramod,[status(thm)],[c_1,c_700]) ).
cnf(c_99,plain,
multiply(A,inverse(add(B,A))) = additive_identity,
inference(paramod,[status(thm)],[c_13,c_701]) ).
cnf(c_702,plain,
add(additive_identity,multiply(inverse(A),inverse(multiply(B,A)))) = inverse(A),
inference(paramod,[status(thm)],[c_91,c_16]) ).
cnf(c_101,plain,
multiply(inverse(A),inverse(multiply(B,A))) = inverse(A),
inference(paramod,[status(thm)],[c_13,c_702]) ).
cnf(c_703,plain,
A = add(multiply(A,inverse(B)),multiply(B,A)),
inference(paramod,[status(thm)],[c_48,c_1]) ).
cnf(c_107,plain,
add(multiply(A,inverse(B)),multiply(B,A)) = A,
inference(copy,[status(thm)],[c_703]) ).
cnf(c_704,plain,
add(A,multiply(inverse(inverse(A)),inverse(A))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_52,c_48]) ).
cnf(c_705,plain,
add(A,multiply(inverse(A),inverse(inverse(A)))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_2,c_704]) ).
cnf(c_706,plain,
add(A,additive_identity) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_9,c_705]) ).
cnf(c_707,plain,
A = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_6,c_706]) ).
cnf(c_112,plain,
inverse(inverse(A)) = A,
inference(copy,[status(thm)],[c_707]) ).
cnf(c_123,plain,
add(A,multiply(B,inverse(A))) = add(A,B),
inference(paramod,[status(thm)],[c_2,c_56]) ).
cnf(c_128,plain,
add(inverse(A),multiply(A,B)) = add(inverse(A),B),
inference(paramod,[status(thm)],[c_112,c_56]) ).
cnf(c_145,plain,
add(inverse(A),B) = add(multiply(A,B),inverse(A)),
inference(paramod,[status(thm)],[c_128,c_1]) ).
cnf(c_708,plain,
add(inverse(A),additive_identity) = add(inverse(A),inverse(add(A,B))),
inference(paramod,[status(thm)],[c_98,c_128]) ).
cnf(c_709,plain,
add(additive_identity,inverse(A)) = add(inverse(A),inverse(add(A,B))),
inference(paramod,[status(thm)],[c_1,c_708]) ).
cnf(c_710,plain,
inverse(A) = add(inverse(A),inverse(add(A,B))),
inference(paramod,[status(thm)],[c_13,c_709]) ).
cnf(c_151,plain,
add(inverse(A),inverse(add(A,B))) = inverse(A),
inference(copy,[status(thm)],[c_710]) ).
cnf(c_155,plain,
add(multiply(A,B),inverse(A)) = add(B,inverse(A)),
inference(paramod,[status(thm)],[c_145,c_1]) ).
cnf(c_184,plain,
add(multiply(A,B),inverse(B)) = add(A,inverse(B)),
inference(paramod,[status(thm)],[c_2,c_155]) ).
cnf(c_711,plain,
multiply(A,inverse(multiply(B,inverse(A)))) = inverse(inverse(A)),
inference(paramod,[status(thm)],[c_112,c_101]) ).
cnf(c_197,plain,
multiply(A,inverse(multiply(B,inverse(A)))) = A,
inference(paramod,[status(thm)],[c_112,c_711]) ).
cnf(c_712,plain,
add(multiply(add(A,B),inverse(A)),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_151,c_155]) ).
cnf(c_713,plain,
add(add(multiply(A,inverse(A)),multiply(B,inverse(A))),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_75,c_712]) ).
cnf(c_714,plain,
add(add(additive_identity,multiply(B,inverse(A))),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_9,c_713]) ).
cnf(c_284,plain,
add(multiply(A,inverse(B)),inverse(add(B,A))) = inverse(B),
inference(paramod,[status(thm)],[c_13,c_714]) ).
cnf(c_715,plain,
add(multiply(inverse(A),add(A,B)),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_151,c_184]) ).
cnf(c_716,plain,
add(add(multiply(inverse(A),A),multiply(inverse(A),B)),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_5,c_715]) ).
cnf(c_717,plain,
add(add(multiply(A,inverse(A)),multiply(inverse(A),B)),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_2,c_716]) ).
cnf(c_718,plain,
add(add(additive_identity,multiply(inverse(A),B)),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_9,c_717]) ).
cnf(c_286,plain,
add(multiply(inverse(A),B),inverse(add(A,B))) = inverse(A),
inference(paramod,[status(thm)],[c_13,c_718]) ).
cnf(c_719,plain,
add(add(A,B),add(multiply(A,C),multiply(multiply(A,C),B))) = add(A,B),
inference(paramod,[status(thm)],[c_90,c_77]) ).
cnf(c_314,plain,
add(add(A,B),multiply(A,C)) = add(A,B),
inference(paramod,[status(thm)],[c_55,c_719]) ).
cnf(c_333,plain,
multiply(multiply(A,B),inverse(add(A,C))) = additive_identity,
inference(paramod,[status(thm)],[c_314,c_99]) ).
cnf(c_720,plain,
add(A,inverse(add(multiply(B,inverse(A)),A))) = inverse(multiply(B,inverse(A))),
inference(paramod,[status(thm)],[c_197,c_284]) ).
cnf(c_721,plain,
add(A,inverse(add(A,multiply(B,inverse(A))))) = inverse(multiply(B,inverse(A))),
inference(paramod,[status(thm)],[c_1,c_720]) ).
cnf(c_722,plain,
add(A,inverse(add(A,B))) = inverse(multiply(B,inverse(A))),
inference(paramod,[status(thm)],[c_123,c_721]) ).
cnf(c_565,plain,
inverse(multiply(A,inverse(B))) = add(B,inverse(add(B,A))),
inference(copy,[status(thm)],[c_722]) ).
cnf(c_723,plain,
add(multiply(inverse(multiply(A,inverse(B))),multiply(B,A)),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_107,c_286]) ).
cnf(c_724,plain,
add(multiply(add(B,inverse(add(B,A))),multiply(B,A)),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_565,c_723]) ).
cnf(c_725,plain,
add(multiply(multiply(B,A),add(B,inverse(add(B,A)))),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_2,c_724]) ).
cnf(c_726,plain,
add(add(multiply(multiply(B,A),B),multiply(multiply(B,A),inverse(add(B,A)))),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_5,c_725]) ).
cnf(c_727,plain,
add(add(multiply(B,multiply(B,A)),multiply(multiply(B,A),inverse(add(B,A)))),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_2,c_726]) ).
cnf(c_728,plain,
add(add(multiply(B,A),multiply(multiply(B,A),inverse(add(B,A)))),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_90,c_727]) ).
cnf(c_729,plain,
add(add(multiply(B,A),additive_identity),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_333,c_728]) ).
cnf(c_730,plain,
add(add(additive_identity,multiply(B,A)),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_1,c_729]) ).
cnf(c_731,plain,
add(multiply(B,A),inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_13,c_730]) ).
cnf(c_732,plain,
add(B,inverse(A)) = inverse(multiply(A,inverse(B))),
inference(paramod,[status(thm)],[c_184,c_731]) ).
cnf(c_733,plain,
add(B,inverse(A)) = add(B,inverse(add(B,A))),
inference(paramod,[status(thm)],[c_565,c_732]) ).
cnf(c_568,plain,
add(A,inverse(add(A,B))) = add(A,inverse(B)),
inference(copy,[status(thm)],[c_733]) ).
cnf(c_573,plain,
inverse(multiply(A,inverse(B))) = add(B,inverse(A)),
inference(paramod,[status(thm)],[c_568,c_565]) ).
cnf(c_596,plain,
inverse(add(A,inverse(B))) = multiply(B,inverse(A)),
inference(paramod,[status(thm)],[c_573,c_112]) ).
cnf(c_645,plain,
inverse(add(A,B)) = multiply(inverse(B),inverse(A)),
inference(paramod,[status(thm)],[c_112,c_596]) ).
cnf(c_734,plain,
multiply(inverse(b),inverse(a)) != multiply(inverse(a),inverse(b)),
inference(paramod,[status(thm)],[c_645,c_10]) ).
cnf(c_735,plain,
multiply(inverse(a),inverse(b)) != multiply(inverse(a),inverse(b)),
inference(paramod,[status(thm)],[c_2,c_734]) ).
cnf(c_653,plain,
$false,
inference(copy,[status(thm)],[c_735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO014-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 : Sat Sep 26 22:38:08 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 1586900 was started by sandbox on n018,
% 0.09/0.36 % Sat Sep 26 22:38:08 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 2.13/0.67
% 2.13/0.67 % SZS status Unsatisfiable for theBenchmark
% 2.13/0.67
% 2.13/0.67 % Proof 1 at 0.19 (+ 0.10) seconds.
% 2.13/0.67 % Length of proof is 61.
% 2.13/0.67 % Level of proof is 16.
% 2.13/0.67 % Maximum clause weight is 29.000.
% 2.13/0.67 % Given clauses 112.
% 2.13/0.67
% 2.13/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------