%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE120+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 : n006.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 04:35:45 PM UTC 2026
% Result : Theorem 1.90s 1.91s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 97 ( 97 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 136 ( 4 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(codomain3,axiom,
! [X4] : addition(coantidomain(coantidomain(X4)),coantidomain(X4)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain3) ).
fof(codomain1,axiom,
! [X4] : multiplication(X4,coantidomain(X4)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain1) ).
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(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(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(goals,conjecture,
! [X4] : addition(backward_diamond(one,domain(X4)),domain(X4)) = domain(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(backward_diamond,axiom,
! [X4,X5] : backward_diamond(X4,X5) = codomain(multiplication(codomain(X5),X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',backward_diamond) ).
fof(codomain4,axiom,
! [X4] : codomain(X4) = coantidomain(coantidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',codomain4) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(c_0_19,plain,
! [X65,X66,X67] : multiplication(addition(X65,X66),X67) = addition(multiplication(X65,X67),multiplication(X66,X67)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_20,plain,
! [X72] : multiplication(antidomain(X72),X72) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_21,plain,
! [X55] : addition(X55,zero) = X55,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_22,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,plain,
! [X50,X51] : addition(X50,X51) = addition(X51,X50),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_26,plain,
! [X75] : addition(antidomain(antidomain(X75)),antidomain(X75)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_27,plain,
! [X57,X58,X59] : multiplication(X57,multiplication(X58,X59)) = multiplication(multiplication(X57,X58),X59),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_28,plain,
! [X69] : multiplication(zero,X69) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_29,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X61] : multiplication(one,X61) = X61,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_33,plain,
! [X80] : addition(coantidomain(coantidomain(X80)),coantidomain(X80)) = one,
inference(variable_rename,[status(thm)],[codomain3]) ).
fof(c_0_34,plain,
! [X77] : multiplication(X77,coantidomain(X77)) = zero,
inference(variable_rename,[status(thm)],[codomain1]) ).
fof(c_0_35,plain,
! [X52,X53,X54] : addition(X54,addition(X53,X52)) = addition(addition(X54,X53),X52),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_36,plain,
! [X56] : addition(X56,X56) = X56,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_37,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_40,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_41,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
addition(coantidomain(coantidomain(X1)),coantidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
multiplication(X1,coantidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_46,plain,
! [X78,X79] : addition(coantidomain(multiplication(X78,X79)),coantidomain(multiplication(coantidomain(coantidomain(X78)),X79))) = coantidomain(multiplication(coantidomain(coantidomain(X78)),X79)),
inference(variable_rename,[status(thm)],[codomain2]) ).
cnf(c_0_47,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_23]),c_0_38]) ).
cnf(c_0_48,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_49,plain,
addition(coantidomain(X1),coantidomain(coantidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_42,c_0_30]) ).
cnf(c_0_50,plain,
coantidomain(one) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
cnf(c_0_51,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
cnf(c_0_52,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_53,plain,
! [X62,X63,X64] : multiplication(X62,addition(X63,X64)) = addition(multiplication(X62,X63),multiplication(X62,X64)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_54,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_46]) ).
cnf(c_0_55,plain,
multiplication(antidomain(antidomain(antidomain(X1))),X1) = zero,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_56,plain,
coantidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
cnf(c_0_57,plain,
addition(one,coantidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_49]),c_0_30]) ).
fof(c_0_58,plain,
! [X60] : multiplication(X60,one) = X60,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_59,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]) ).
cnf(c_0_61,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_62,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_23]),c_0_24]) ).
cnf(c_0_63,plain,
multiplication(X1,addition(X2,coantidomain(X1))) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_43]),c_0_24]) ).
cnf(c_0_64,plain,
multiplication(coantidomain(coantidomain(antidomain(antidomain(antidomain(X1))))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_60]),c_0_37]),c_0_61]) ).
cnf(c_0_65,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_40]),c_0_61]),c_0_48]) ).
cnf(c_0_66,plain,
multiplication(X1,addition(coantidomain(X1),X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_30]) ).
cnf(c_0_67,plain,
multiplication(coantidomain(coantidomain(antidomain(X1))),X1) = zero,
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
multiplication(addition(X1,X2),coantidomain(X2)) = multiplication(X1,coantidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_43]),c_0_24]) ).
cnf(c_0_69,plain,
multiplication(X1,coantidomain(coantidomain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_49]),c_0_61]) ).
fof(c_0_70,negated_conjecture,
~ ! [X4] : addition(backward_diamond(one,domain(X4)),domain(X4)) = domain(X4),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_71,plain,
! [X87,X88] : backward_diamond(X87,X88) = codomain(multiplication(codomain(X88),X87)),
inference(variable_rename,[status(thm)],[backward_diamond]) ).
fof(c_0_72,plain,
! [X81] : codomain(X81) = coantidomain(coantidomain(X81)),
inference(variable_rename,[status(thm)],[codomain4]) ).
cnf(c_0_73,plain,
multiplication(addition(coantidomain(coantidomain(antidomain(X1))),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_67]),c_0_51]) ).
cnf(c_0_74,plain,
coantidomain(coantidomain(coantidomain(X1))) = coantidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_49]),c_0_41]),c_0_69]) ).
fof(c_0_75,negated_conjecture,
addition(backward_diamond(one,domain(esk1_0)),domain(esk1_0)) != domain(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])]) ).
fof(c_0_76,plain,
! [X76] : domain(X76) = antidomain(antidomain(X76)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_77,plain,
backward_diamond(X1,X2) = codomain(multiplication(codomain(X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_78,plain,
codomain(X1) = coantidomain(coantidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_79,plain,
multiplication(coantidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_49]),c_0_41]),c_0_74]) ).
cnf(c_0_80,negated_conjecture,
addition(backward_diamond(one,domain(esk1_0)),domain(esk1_0)) != domain(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_81,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,plain,
backward_diamond(X1,X2) = coantidomain(coantidomain(multiplication(coantidomain(coantidomain(X2)),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78]),c_0_78]) ).
cnf(c_0_83,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_61]),c_0_30]) ).
cnf(c_0_84,plain,
multiplication(coantidomain(antidomain(X1)),antidomain(antidomain(X1))) = antidomain(antidomain(X1)),
inference(spm,[status(thm)],[c_0_79,c_0_65]) ).
cnf(c_0_85,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_40]),c_0_30]) ).
cnf(c_0_86,negated_conjecture,
addition(coantidomain(coantidomain(multiplication(coantidomain(coantidomain(antidomain(antidomain(esk1_0)))),one))),antidomain(antidomain(esk1_0))) != antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_81]),c_0_81]),c_0_81]),c_0_82]) ).
cnf(c_0_87,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_44,c_0_40]) ).
cnf(c_0_88,plain,
addition(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_30]),c_0_85]),c_0_61]),c_0_30]) ).
cnf(c_0_89,plain,
multiplication(addition(X1,X2),coantidomain(X1)) = multiplication(X2,coantidomain(X1)),
inference(spm,[status(thm)],[c_0_68,c_0_30]) ).
cnf(c_0_90,negated_conjecture,
addition(antidomain(antidomain(esk1_0)),coantidomain(coantidomain(coantidomain(coantidomain(antidomain(antidomain(esk1_0))))))) != antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_61]),c_0_30]) ).
cnf(c_0_91,plain,
multiplication(antidomain(X1),addition(X1,X2)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_23]),c_0_51]) ).
cnf(c_0_92,plain,
addition(antidomain(X1),coantidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_57]) ).
cnf(c_0_93,plain,
multiplication(antidomain(antidomain(X1)),coantidomain(antidomain(X1))) = coantidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_40]),c_0_41]) ).
cnf(c_0_94,negated_conjecture,
addition(antidomain(antidomain(esk1_0)),coantidomain(coantidomain(antidomain(antidomain(esk1_0))))) != antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[c_0_90,c_0_74]) ).
cnf(c_0_95,plain,
coantidomain(antidomain(X1)) = antidomain(antidomain(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_61]),c_0_93]) ).
cnf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_65]),c_0_95]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE120+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:30:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.90/1.91 % Version : CSE_E---1.7
% 1.90/1.91 % Problem : theBenchmark.p
% 1.90/1.91 % SZS status Theorem for theBenchmark.p
% 1.90/1.91 % SZS output start CNFRefutation
% See solution above
% 1.90/1.92 % Total time : 1.373s
%------------------------------------------------------------------------------