%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE132+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 : n014.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 04:35:46 PM UTC 2026
% Result : Theorem 1.32s 1.74s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 58 unt; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 1 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(goals,conjecture,
! [X4] :
( ! [X5] : addition(forward_diamond(X4,domain(X5)),forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))) = forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))
=> ! [X6] :
( addition(domain(X6),forward_diamond(X4,domain(X6))) = forward_diamond(X4,domain(X6))
=> domain(X6) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(domain_difference,axiom,
! [X4,X5] : domain_difference(X4,X5) = multiplication(domain(X4),antidomain(X5)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',domain_difference) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(c_0_13,plain,
! [X72,X73,X74] : multiplication(addition(X72,X73),X74) = addition(multiplication(X72,X74),multiplication(X73,X74)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_14,plain,
! [X79] : multiplication(antidomain(X79),X79) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_15,plain,
! [X62] : addition(X62,zero) = X62,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_16,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X57,X58] : addition(X57,X58) = addition(X58,X57),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_20,plain,
! [X82] : addition(antidomain(antidomain(X82)),antidomain(X82)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_21,negated_conjecture,
~ ! [X4] :
( ! [X5] : addition(forward_diamond(X4,domain(X5)),forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))) = forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))
=> ! [X6] :
( addition(domain(X6),forward_diamond(X4,domain(X6))) = forward_diamond(X4,domain(X6))
=> domain(X6) = zero ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_22,plain,
! [X92,X93] : forward_diamond(X92,X93) = domain(multiplication(X92,domain(X93))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_23,plain,
! [X83] : domain(X83) = antidomain(antidomain(X83)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_24,plain,
! [X69,X70,X71] : multiplication(X69,addition(X70,X71)) = addition(multiplication(X69,X70),multiplication(X69,X71)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_25,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_26,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X68] : multiplication(one,X68) = X68,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_29,plain,
! [X90,X91] : domain_difference(X90,X91) = multiplication(domain(X90),antidomain(X91)),
inference(variable_rename,[status(thm)],[domain_difference]) ).
fof(c_0_30,negated_conjecture,
! [X105] :
( addition(forward_diamond(esk1_0,domain(X105)),forward_diamond(star(esk1_0),domain_difference(domain(X105),forward_diamond(esk1_0,domain(X105))))) = forward_diamond(star(esk1_0),domain_difference(domain(X105),forward_diamond(esk1_0,domain(X105))))
& addition(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))) = forward_diamond(esk1_0,domain(esk2_0))
& domain(esk2_0) != zero ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_31,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_34,plain,
! [X67] : multiplication(X67,one) = X67,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_35,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_37,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
domain_difference(X1,X2) = multiplication(domain(X1),antidomain(X2)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
addition(domain(esk2_0),forward_diamond(esk1_0,domain(esk2_0))) = forward_diamond(esk1_0,domain(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_41,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_18]) ).
cnf(c_0_42,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_44,negated_conjecture,
addition(forward_diamond(esk1_0,domain(X1)),forward_diamond(star(esk1_0),domain_difference(domain(X1),forward_diamond(esk1_0,domain(X1))))) = forward_diamond(star(esk1_0),domain_difference(domain(X1),forward_diamond(esk1_0,domain(X1)))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_45,plain,
domain_difference(X1,X2) = multiplication(antidomain(antidomain(X1)),antidomain(X2)),
inference(rw,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_46,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_32]),c_0_32]),c_0_32]),c_0_40]),c_0_40]) ).
cnf(c_0_47,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_42]),c_0_43]) ).
cnf(c_0_48,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1))))))),antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))) = antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_40]),c_0_45]),c_0_45]) ).
cnf(c_0_49,negated_conjecture,
addition(antidomain(antidomain(esk2_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))) = antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_47]) ).
cnf(c_0_50,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_42,c_0_17]) ).
cnf(c_0_51,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
fof(c_0_52,plain,
! [X75] : multiplication(X75,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_53,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(X1))))),antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),antidomain(multiplication(esk1_0,antidomain(antidomain(X1))))))))))) = antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(X1)),antidomain(multiplication(esk1_0,antidomain(antidomain(X1)))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]),c_0_47]) ).
cnf(c_0_54,negated_conjecture,
multiplication(antidomain(antidomain(esk2_0)),antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_49]),c_0_17]) ).
cnf(c_0_55,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_50]),c_0_51]) ).
cnf(c_0_56,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,negated_conjecture,
domain(esk2_0) != zero,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_58,negated_conjecture,
antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_50]),c_0_56]),c_0_55]),c_0_50]),c_0_18]),c_0_55]),c_0_50]),c_0_56]),c_0_55]),c_0_50]) ).
cnf(c_0_59,negated_conjecture,
antidomain(antidomain(esk2_0)) != zero,
inference(rw,[status(thm)],[c_0_57,c_0_32]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_58]),c_0_18]),c_0_58]),c_0_59]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE132+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n014.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 20:31:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.32/1.74 % Version : CSE_E---1.7
% 1.32/1.74 % Problem : theBenchmark.p
% 1.32/1.74 % SZS status Theorem for theBenchmark.p
% 1.32/1.74 % SZS output start CNFRefutation
% See solution above
% 1.32/1.74 % Total time : 1.369s
%------------------------------------------------------------------------------