%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE092+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 04:35:42 PM UTC 2026
% Result : Theorem 6.24s 4.45s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 86 ( 86 unt; 0 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 3 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
fof(codomain2,axiom,
! [X4,X5] : addition(coantidomain(multiplication(X4,X5)),coantidomain(multiplication(coantidomain(coantidomain(X4)),X5))) = coantidomain(multiplication(coantidomain(coantidomain(X4)),X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
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/sandbox/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(goals,conjecture,
! [X4] : domain(coantidomain(X4)) = coantidomain(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_16,plain,
! [X41,X42,X43] : addition(X43,addition(X42,X41)) = addition(addition(X43,X42),X41),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_17,plain,
! [X45] : addition(X45,X45) = X45,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_18,plain,
! [X69] : addition(coantidomain(coantidomain(X69)),coantidomain(X69)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_19,plain,
! [X39,X40] : addition(X39,X40) = addition(X40,X39),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_20,plain,
! [X44] : addition(X44,zero) = X44,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_21,plain,
! [X51,X52,X53] : multiplication(X51,addition(X52,X53)) = addition(multiplication(X51,X52),multiplication(X51,X53)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_22,plain,
! [X49] : multiplication(X49,one) = X49,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_23,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,plain,
! [X54,X55,X56] : multiplication(addition(X54,X55),X56) = addition(multiplication(X54,X56),multiplication(X55,X56)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_28,plain,
! [X61] : multiplication(antidomain(X61),X61) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_29,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_30,plain,
! [X64] : addition(antidomain(antidomain(X64)),antidomain(X64)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_31,plain,
! [X66] : multiplication(X66,coantidomain(X66)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_32,plain,
! [X67,X68] : addition(coantidomain(multiplication(X67,X68)),coantidomain(multiplication(coantidomain(coantidomain(X67)),X68))) = coantidomain(multiplication(coantidomain(coantidomain(X67)),X68)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_33,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_35,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_36,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_37,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_40,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_41,plain,
! [X50] : multiplication(one,X50) = X50,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_42,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
addition(coantidomain(multiplication(X1,X2)),coantidomain(multiplication(coantidomain(coantidomain(X1)),X2))) = coantidomain(multiplication(coantidomain(coantidomain(X1)),X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_45,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_26]) ).
cnf(c_0_46,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_47,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_48,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_49,plain,
! [X62,X63] : addition(antidomain(multiplication(X62,X63)),antidomain(multiplication(X62,antidomain(antidomain(X63))))) = antidomain(multiplication(X62,antidomain(antidomain(X63)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_50,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_42]),c_0_29]) ).
cnf(c_0_51,plain,
addition(coantidomain(X1),coantidomain(coantidomain(coantidomain(X1)))) = coantidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_34]),c_0_34]) ).
cnf(c_0_52,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_53,plain,
addition(X1,multiplication(X1,coantidomain(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_34]) ).
cnf(c_0_54,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_55,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_42]),c_0_39]) ).
cnf(c_0_56,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_49]) ).
cnf(c_0_57,plain,
multiplication(coantidomain(coantidomain(X1)),coantidomain(X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_42]) ).
cnf(c_0_58,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_52]),c_0_39]) ).
cnf(c_0_59,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_47]),c_0_26]) ).
cnf(c_0_60,plain,
addition(coantidomain(X1),addition(coantidomain(coantidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_23,c_0_36]) ).
cnf(c_0_61,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = antidomain(antidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_26]) ).
cnf(c_0_62,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_42]),c_0_29]) ).
cnf(c_0_63,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_36]),c_0_34]) ).
cnf(c_0_64,plain,
antidomain(multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59]) ).
cnf(c_0_65,plain,
addition(coantidomain(X1),antidomain(antidomain(coantidomain(coantidomain(X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_59]) ).
cnf(c_0_66,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_36]),c_0_48]),c_0_63]) ).
fof(c_0_67,negated_conjecture,
~ ! [X4] : domain(coantidomain(X4)) = coantidomain(X4),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_68,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(antidomain(coantidomain(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_64]),c_0_48]) ).
cnf(c_0_69,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_38]),c_0_29]) ).
cnf(c_0_70,plain,
addition(antidomain(antidomain(coantidomain(X1))),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_26]) ).
fof(c_0_71,negated_conjecture,
domain(coantidomain(esk1_0)) != coantidomain(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])]) ).
fof(c_0_72,plain,
! [X65] : domain(X65) = antidomain(antidomain(X65)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_73,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_29]) ).
cnf(c_0_74,plain,
multiplication(coantidomain(coantidomain(X1)),addition(antidomain(antidomain(coantidomain(X1))),X2)) = multiplication(coantidomain(coantidomain(X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_68]),c_0_39]) ).
cnf(c_0_75,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_47]),c_0_34]),c_0_54]) ).
cnf(c_0_76,plain,
multiplication(coantidomain(coantidomain(X1)),antidomain(coantidomain(X1))) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_70]),c_0_48]) ).
cnf(c_0_77,plain,
multiplication(X1,antidomain(antidomain(coantidomain(coantidomain(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_65]),c_0_34]) ).
cnf(c_0_78,negated_conjecture,
domain(coantidomain(esk1_0)) != coantidomain(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_79,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_80,plain,
multiplication(coantidomain(X1),antidomain(coantidomain(coantidomain(X1)))) = antidomain(coantidomain(coantidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_65]),c_0_48]) ).
cnf(c_0_81,plain,
coantidomain(coantidomain(X1)) = antidomain(coantidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_47]),c_0_34]),c_0_75]),c_0_76]) ).
cnf(c_0_82,plain,
multiplication(coantidomain(X1),antidomain(antidomain(coantidomain(X1)))) = coantidomain(X1),
inference(spm,[status(thm)],[c_0_77,c_0_66]) ).
cnf(c_0_83,negated_conjecture,
antidomain(antidomain(coantidomain(esk1_0))) != coantidomain(esk1_0),
inference(rw,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,plain,
antidomain(antidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE092+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n002.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:29:46 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.24/4.45 % Version : CSE_E---1.7
% 6.24/4.45 % Problem : theBenchmark.p
% 6.24/4.45 % SZS status Theorem for theBenchmark.p
% 6.24/4.45 % SZS output start CNFRefutation
% See solution above
% 6.24/4.47 % Total time : 3.373s
%------------------------------------------------------------------------------