%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE090+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:35:41 PM UTC 2026
% Result : Theorem 4.44s 3.35s
% Output : CNFRefutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 55 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 77 ( 1 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(goals,conjecture,
! [X4,X5] :
( addition(X4,X5) = X5
=> addition(antidomain(X5),antidomain(X4)) = antidomain(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(c_0_12,plain,
! [X65] : addition(antidomain(antidomain(X65)),antidomain(X65)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_13,plain,
! [X40,X41] : addition(X40,X41) = addition(X41,X40),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_14,plain,
! [X50] : multiplication(X50,one) = X50,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_15,plain,
! [X62] : multiplication(antidomain(X62),X62) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_16,plain,
! [X52,X53,X54] : multiplication(X52,addition(X53,X54)) = addition(multiplication(X52,X53),multiplication(X52,X54)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_17,plain,
! [X45] : addition(X45,zero) = X45,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_18,negated_conjecture,
~ ! [X4,X5] :
( addition(X4,X5) = X5
=> addition(antidomain(X5),antidomain(X4)) = antidomain(X4) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_19,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,plain,
! [X42,X43,X44] : addition(X44,addition(X43,X42)) = addition(addition(X44,X43),X42),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_24,plain,
! [X46] : addition(X46,X46) = X46,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_25,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_27,negated_conjecture,
( addition(esk1_0,esk2_0) = esk2_0
& addition(antidomain(esk2_0),antidomain(esk1_0)) != antidomain(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_28,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_32,plain,
! [X55,X56,X57] : multiplication(addition(X55,X56),X57) = addition(multiplication(X55,X57),multiplication(X56,X57)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_33,plain,
! [X63,X64] : addition(antidomain(multiplication(X63,X64)),antidomain(multiplication(X63,antidomain(antidomain(X64))))) = antidomain(multiplication(X63,antidomain(antidomain(X64)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_34,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_26]) ).
cnf(c_0_35,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_38,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,negated_conjecture,
multiplication(antidomain(esk2_0),esk1_0) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_22]) ).
cnf(c_0_42,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_28]),c_0_20]) ).
fof(c_0_44,plain,
! [X51] : multiplication(one,X51) = X51,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_45,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_22]),c_0_26]) ).
cnf(c_0_46,negated_conjecture,
antidomain(multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]) ).
cnf(c_0_47,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_48,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_45,c_0_20]) ).
cnf(c_0_49,negated_conjecture,
multiplication(antidomain(esk2_0),antidomain(antidomain(esk1_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_46]),c_0_47]) ).
cnf(c_0_50,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_28]),c_0_47]) ).
cnf(c_0_51,negated_conjecture,
multiplication(antidomain(esk2_0),addition(antidomain(antidomain(esk1_0)),X1)) = multiplication(antidomain(esk2_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_49]),c_0_37]) ).
cnf(c_0_52,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_21]),c_0_50]) ).
cnf(c_0_53,negated_conjecture,
addition(antidomain(esk2_0),antidomain(esk1_0)) != antidomain(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_54,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_47]),c_0_20]) ).
cnf(c_0_55,negated_conjecture,
multiplication(antidomain(esk2_0),antidomain(esk1_0)) = antidomain(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_28]),c_0_21]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
addition(antidomain(esk1_0),antidomain(esk2_0)) != antidomain(esk1_0),
inference(rw,[status(thm)],[c_0_53,c_0_20]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_20]),c_0_43]),c_0_47]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE090+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.11/0.31 % Computer : n005.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 4 20:30:00 EDT 2026
% 0.11/0.31 % CPUTime :
% 0.11/0.32 % start to proof: theBenchmark
% 4.44/3.35 % Version : CSE_E---1.7
% 4.44/3.35 % Problem : theBenchmark.p
% 4.44/3.35 % SZS status Theorem for theBenchmark.p
% 4.44/3.35 % SZS output start CNFRefutation
% See solution above
% 4.44/3.37 % Total time : 2.369s
%------------------------------------------------------------------------------