%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE078+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 07:44:16 AM UTC 2026
% Result : Theorem 8.29s 1.56s
% Output : CNFRefutation 8.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 93 ( 89 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 5 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 141 ( 7 sgn 26 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('theBenchmark.p',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('theBenchmark.p',additive_associativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('theBenchmark.p',additive_identity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('theBenchmark.p',additive_idempotence) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('theBenchmark.p',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('theBenchmark.p',right_distributivity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('theBenchmark.p',left_distributivity) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('theBenchmark.p',left_annihilation) ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('theBenchmark.p',domain1) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',domain2) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one,
file('theBenchmark.p',domain3) ).
fof(goals,conjecture,
! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> domain(antidomain(X0)) = antidomain(X0) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one )
=> domain(antidomain(X0)) = antidomain(X0) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0] :
( antidomain(X0) != domain(antidomain(X0))
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( antidomain(sK0) != domain(antidomain(sK0))
& ! [X1] :
( multiplication(domain(X1),antidomain(X1)) = zero
& addition(domain(X1),antidomain(X1)) = one ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
antidomain(sK0) != domain(antidomain(sK0)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_21,negated_conjecture,
domain(antidomain(sK0)) != antidomain(sK0),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
multiplication(domain(A),antidomain(A)) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_23,negated_conjecture,
addition(domain(A),antidomain(A)) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
fof(domain4,axiom,
domain(zero) = zero,
file('theBenchmark.p',domain4) ).
cnf(c_25,plain,
domain(zero) = zero,
inference(clausify,[status(thm)],[domain4]) ).
cnf(c_26,plain,
addition(domain(A),one) = one,
inference(clausify,[status(thm)],[domain3]) ).
cnf(c_27,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_28,plain,
multiplication(domain(A),A) = addition(A,multiplication(domain(A),A)),
inference(clausify,[status(thm)],[domain1]) ).
cnf(c_29,plain,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_30,plain,
multiplication(zero,A) = zero,
inference(clausify,[status(thm)],[left_annihilation]) ).
cnf(c_32,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(clausify,[status(thm)],[left_distributivity]) ).
cnf(c_33,plain,
addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_34,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(clausify,[status(thm)],[right_distributivity]) ).
cnf(c_35,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_36,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_37,plain,
multiplication(A,one) = A,
inference(clausify,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_39,plain,
addition(A,A) = A,
inference(clausify,[status(thm)],[additive_idempotence]) ).
cnf(c_40,plain,
addition(A,zero) = A,
inference(clausify,[status(thm)],[additive_identity]) ).
cnf(c_41,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(clausify,[status(thm)],[additive_associativity]) ).
cnf(c_42,plain,
addition(A,B) = addition(B,A),
inference(clausify,[status(thm)],[additive_commutativity]) ).
cnf(c_43,plain,
addition(one,domain(A)) = one,
inference(paramod,[status(thm)],[c_42,c_26]) ).
cnf(c_4001,plain,
addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,domain(B))),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_27,c_29]) ).
cnf(c_55,plain,
addition(multiplication(A,domain(B)),multiplication(domain(multiplication(A,B)),multiplication(A,domain(B)))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_27,c_4001]) ).
cnf(c_4002,plain,
addition(zero,multiplication(A,antidomain(B))) = multiplication(addition(domain(B),A),antidomain(B)),
inference(paramod,[status(thm)],[c_22,c_33]) ).
cnf(c_56,plain,
multiplication(addition(domain(A),B),antidomain(A)) = addition(zero,multiplication(B,antidomain(A))),
inference(copy,[status(thm)],[c_4002]) ).
cnf(c_60,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(zero,A),B),
inference(paramod,[status(thm)],[c_30,c_33]) ).
cnf(c_4003,plain,
addition(multiplication(A,B),zero) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_30,c_33]) ).
cnf(c_4004,plain,
addition(zero,multiplication(A,B)) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_42,c_4003]) ).
cnf(c_4005,plain,
multiplication(addition(zero,A),B) = multiplication(addition(A,zero),B),
inference(paramod,[status(thm)],[c_60,c_4004]) ).
cnf(c_61,plain,
multiplication(addition(zero,A),B) = multiplication(A,B),
inference(paramod,[status(thm)],[c_40,c_4005]) ).
cnf(c_4006,plain,
multiplication(addition(domain(A),B),antidomain(A)) = multiplication(addition(zero,B),antidomain(A)),
inference(paramod,[status(thm)],[c_60,c_56]) ).
cnf(c_63,plain,
multiplication(addition(domain(A),B),antidomain(A)) = multiplication(B,antidomain(A)),
inference(paramod,[status(thm)],[c_61,c_4006]) ).
cnf(c_4007,plain,
addition(A,multiplication(B,A)) = multiplication(addition(one,B),A),
inference(paramod,[status(thm)],[c_36,c_33]) ).
cnf(c_70,plain,
multiplication(addition(one,A),B) = addition(B,multiplication(A,B)),
inference(copy,[status(thm)],[c_4007]) ).
cnf(c_4008,plain,
multiplication(addition(one,domain(multiplication(A,B))),multiplication(A,domain(B))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_70,c_55]) ).
cnf(c_4009,plain,
multiplication(one,multiplication(A,domain(B))) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_43,c_4008]) ).
cnf(c_4010,plain,
multiplication(A,domain(B)) = multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))),
inference(paramod,[status(thm)],[c_36,c_4009]) ).
cnf(c_74,plain,
multiplication(domain(multiplication(A,B)),multiplication(A,domain(B))) = multiplication(A,domain(B)),
inference(copy,[status(thm)],[c_4010]) ).
cnf(c_4011,plain,
addition(A,multiplication(A,B)) = multiplication(A,addition(one,B)),
inference(paramod,[status(thm)],[c_37,c_35]) ).
cnf(c_76,plain,
multiplication(A,addition(one,B)) = addition(A,multiplication(A,B)),
inference(copy,[status(thm)],[c_4011]) ).
cnf(c_4012,plain,
addition(addition(A,B),B) = addition(A,B),
inference(paramod,[status(thm)],[c_39,c_41]) ).
cnf(c_88,plain,
addition(A,addition(B,A)) = addition(B,A),
inference(paramod,[status(thm)],[c_42,c_4012]) ).
cnf(c_91,plain,
addition(zero,A) = A,
inference(paramod,[status(thm)],[c_42,c_40]) ).
cnf(c_4013,plain,
addition(multiplication(one,A),multiplication(domain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_43,c_33]) ).
cnf(c_4014,plain,
addition(A,multiplication(domain(B),A)) = multiplication(one,A),
inference(paramod,[status(thm)],[c_36,c_4013]) ).
cnf(c_95,plain,
addition(A,multiplication(domain(B),A)) = A,
inference(paramod,[status(thm)],[c_36,c_4014]) ).
cnf(c_4015,plain,
A = multiplication(domain(A),A),
inference(paramod,[status(thm)],[c_95,c_29]) ).
cnf(c_98,plain,
multiplication(domain(A),A) = A,
inference(copy,[status(thm)],[c_4015]) ).
cnf(c_4016,plain,
multiplication(domain(A),addition(one,A)) = addition(domain(A),A),
inference(paramod,[status(thm)],[c_98,c_76]) ).
cnf(c_4017,plain,
multiplication(domain(A),addition(one,A)) = addition(A,domain(A)),
inference(paramod,[status(thm)],[c_42,c_4016]) ).
cnf(c_210,plain,
addition(A,domain(A)) = multiplication(domain(A),addition(one,A)),
inference(copy,[status(thm)],[c_4017]) ).
cnf(c_4018,plain,
multiplication(one,antidomain(A)) = multiplication(antidomain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_23,c_63]) ).
cnf(c_4019,plain,
antidomain(A) = multiplication(antidomain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_36,c_4018]) ).
cnf(c_229,plain,
multiplication(antidomain(A),antidomain(A)) = antidomain(A),
inference(copy,[status(thm)],[c_4019]) ).
cnf(c_4020,plain,
addition(antidomain(A),multiplication(antidomain(A),B)) = multiplication(antidomain(A),addition(antidomain(A),B)),
inference(paramod,[status(thm)],[c_229,c_35]) ).
cnf(c_4021,plain,
multiplication(antidomain(A),addition(one,B)) = multiplication(antidomain(A),addition(antidomain(A),B)),
inference(paramod,[status(thm)],[c_76,c_4020]) ).
cnf(c_254,plain,
multiplication(antidomain(A),addition(antidomain(A),B)) = multiplication(antidomain(A),addition(one,B)),
inference(copy,[status(thm)],[c_4021]) ).
cnf(c_4022,plain,
multiplication(domain(zero),multiplication(domain(A),domain(antidomain(A)))) = multiplication(domain(A),domain(antidomain(A))),
inference(paramod,[status(thm)],[c_22,c_74]) ).
cnf(c_4023,plain,
multiplication(zero,multiplication(domain(A),domain(antidomain(A)))) = multiplication(domain(A),domain(antidomain(A))),
inference(paramod,[status(thm)],[c_25,c_4022]) ).
cnf(c_4024,plain,
zero = multiplication(domain(A),domain(antidomain(A))),
inference(paramod,[status(thm)],[c_30,c_4023]) ).
cnf(c_362,plain,
multiplication(domain(A),domain(antidomain(A))) = zero,
inference(copy,[status(thm)],[c_4024]) ).
cnf(c_4025,plain,
addition(zero,multiplication(A,domain(antidomain(B)))) = multiplication(addition(domain(B),A),domain(antidomain(B))),
inference(paramod,[status(thm)],[c_362,c_33]) ).
cnf(c_4026,plain,
multiplication(A,domain(antidomain(B))) = multiplication(addition(domain(B),A),domain(antidomain(B))),
inference(paramod,[status(thm)],[c_91,c_4025]) ).
cnf(c_428,plain,
multiplication(addition(domain(A),B),domain(antidomain(A))) = multiplication(B,domain(antidomain(A))),
inference(copy,[status(thm)],[c_4026]) ).
cnf(c_4027,plain,
addition(antidomain(A),one) = addition(domain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_23,c_88]) ).
cnf(c_4028,plain,
addition(one,antidomain(A)) = addition(domain(A),antidomain(A)),
inference(paramod,[status(thm)],[c_42,c_4027]) ).
cnf(c_437,plain,
addition(one,antidomain(A)) = one,
inference(paramod,[status(thm)],[c_23,c_4028]) ).
cnf(c_4029,plain,
multiplication(antidomain(A),multiplication(domain(antidomain(A)),addition(one,antidomain(A)))) = multiplication(antidomain(A),addition(one,domain(antidomain(A)))),
inference(paramod,[status(thm)],[c_210,c_254]) ).
cnf(c_4030,plain,
multiplication(antidomain(A),multiplication(domain(antidomain(A)),one)) = multiplication(antidomain(A),addition(one,domain(antidomain(A)))),
inference(paramod,[status(thm)],[c_437,c_4029]) ).
cnf(c_4031,plain,
multiplication(antidomain(A),domain(antidomain(A))) = multiplication(antidomain(A),addition(one,domain(antidomain(A)))),
inference(paramod,[status(thm)],[c_37,c_4030]) ).
cnf(c_4032,plain,
multiplication(antidomain(A),domain(antidomain(A))) = multiplication(antidomain(A),one),
inference(paramod,[status(thm)],[c_43,c_4031]) ).
cnf(c_3677,plain,
multiplication(antidomain(A),domain(antidomain(A))) = antidomain(A),
inference(paramod,[status(thm)],[c_37,c_4032]) ).
cnf(c_4033,plain,
multiplication(one,domain(antidomain(A))) = multiplication(antidomain(A),domain(antidomain(A))),
inference(paramod,[status(thm)],[c_23,c_428]) ).
cnf(c_4034,plain,
domain(antidomain(A)) = multiplication(antidomain(A),domain(antidomain(A))),
inference(paramod,[status(thm)],[c_36,c_4033]) ).
cnf(c_3999,plain,
domain(antidomain(A)) = antidomain(A),
inference(paramod,[status(thm)],[c_3677,c_4034]) ).
cnf(c_4000,plain,
$false,
inference(resolve,[status(thm)],[c_3999,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE078+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 19:20:54 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1671239 was started by sandbox2 on n008,
% 0.18/0.45 % Fri Sep 25 19:20:54 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 8.29/1.56
% 8.29/1.56 % SZS status Theorem for theBenchmark
% 8.29/1.56
% 8.29/1.56 % Proof 1 at 0.84 (+ 0.24) seconds.
% 8.29/1.56 % Length of proof is 55.
% 8.29/1.56 % Level of proof is 10.
% 8.29/1.56 % Maximum clause weight is 59.000.
% 8.29/1.56 % Given clauses 197.
% 8.29/1.56
% 8.29/1.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------