%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE082+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 : n004.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 04:35:40 PM UTC 2026
% Result : Theorem 1.67s 1.85s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 66 unt; 0 def)
% Number of atoms : 75 ( 74 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 3 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 9 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5] :
( ! [X6] :
( addition(domain(X6),antidomain(X6)) = one
& multiplication(domain(X6),antidomain(X6)) = zero )
=> addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,domain(X5)))) = antidomain(multiplication(X4,domain(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(domain(X4),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
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(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain5,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).
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(domain2,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
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(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(c_0_13,negated_conjecture,
~ ! [X4,X5] :
( ! [X6] :
( addition(domain(X6),antidomain(X6)) = one
& multiplication(domain(X6),antidomain(X6)) = zero )
=> addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,domain(X5)))) = antidomain(multiplication(X4,domain(X5))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_14,negated_conjecture,
! [X68] :
( addition(domain(X68),antidomain(X68)) = one
& multiplication(domain(X68),antidomain(X68)) = zero
& addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(multiplication(esk1_0,domain(esk2_0)))) != antidomain(multiplication(esk1_0,domain(esk2_0))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])]) ).
fof(c_0_15,plain,
! [X38,X39] : addition(X38,X39) = addition(X39,X38),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_16,plain,
! [X63] : addition(domain(X63),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_17,plain,
! [X40,X41,X42] : addition(X42,addition(X41,X40)) = addition(addition(X42,X41),X40),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_18,negated_conjecture,
addition(domain(X1),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X44] : addition(X44,X44) = X44,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_21,plain,
! [X60] : addition(X60,multiplication(domain(X60),X60)) = multiplication(domain(X60),X60),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_22,plain,
! [X48] : multiplication(X48,one) = X48,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_23,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
addition(antidomain(X1),domain(X1)) = one,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_26,plain,
! [X64,X65] : domain(addition(X64,X65)) = addition(domain(X64),domain(X65)),
inference(variable_rename,[status(thm)],[domain5]) ).
cnf(c_0_27,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_31,negated_conjecture,
addition(antidomain(X1),addition(domain(X1),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
fof(c_0_34,plain,
! [X50,X51,X52] : multiplication(X50,addition(X51,X52)) = addition(multiplication(X50,X51),multiplication(X50,X52)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_35,plain,
! [X61,X62] : domain(multiplication(X61,X62)) = domain(multiplication(X61,domain(X62))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_36,plain,
domain(one) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
fof(c_0_37,plain,
! [X53,X54,X55] : multiplication(addition(X53,X54),X55) = addition(multiplication(X53,X55),multiplication(X54,X55)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_38,plain,
! [X43] : addition(X43,zero) = X43,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_39,negated_conjecture,
addition(antidomain(X1),domain(addition(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_30]) ).
cnf(c_0_40,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_41,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
domain(addition(X1,one)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_36]),c_0_19]),c_0_30]) ).
fof(c_0_44,plain,
! [X49] : multiplication(one,X49) = X49,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_45,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,negated_conjecture,
multiplication(domain(X1),antidomain(X1)) = zero,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_47,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,negated_conjecture,
addition(antidomain(X1),domain(addition(X2,X1))) = one,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_19]) ).
cnf(c_0_50,plain,
domain(multiplication(X1,addition(X2,one))) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_29]) ).
cnf(c_0_51,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,negated_conjecture,
multiplication(addition(X1,domain(X2)),antidomain(X2)) = multiplication(X1,antidomain(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_53,negated_conjecture,
addition(antidomain(multiplication(X1,X2)),domain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
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_45,c_0_51]),c_0_19]) ).
cnf(c_0_55,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_19]) ).
cnf(c_0_56,plain,
domain(domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_51]),c_0_51]) ).
cnf(c_0_57,negated_conjecture,
multiplication(antidomain(multiplication(X1,X2)),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_51]) ).
cnf(c_0_58,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_54]),c_0_19]),c_0_30]),c_0_51]) ).
cnf(c_0_59,negated_conjecture,
multiplication(addition(domain(X1),X2),antidomain(X1)) = multiplication(X2,antidomain(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_55]) ).
cnf(c_0_60,negated_conjecture,
addition(domain(X1),antidomain(domain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_56]),c_0_19]) ).
cnf(c_0_61,negated_conjecture,
multiplication(antidomain(X1),antidomain(domain(X1))) = antidomain(domain(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_19]) ).
cnf(c_0_63,negated_conjecture,
multiplication(antidomain(domain(X1)),antidomain(X1)) = antidomain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_51]) ).
cnf(c_0_64,negated_conjecture,
addition(antidomain(X1),antidomain(domain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_61]),c_0_19]),c_0_62]),c_0_29]) ).
cnf(c_0_65,negated_conjecture,
antidomain(domain(X1)) = antidomain(X1),
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_49,c_0_63]),c_0_19]),c_0_64]),c_0_19]),c_0_62]),c_0_29]) ).
cnf(c_0_66,negated_conjecture,
addition(antidomain(multiplication(esk1_0,esk2_0)),antidomain(multiplication(esk1_0,domain(esk2_0)))) != antidomain(multiplication(esk1_0,domain(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_67,negated_conjecture,
antidomain(multiplication(X1,domain(X2))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_42]),c_0_65]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67]),c_0_27]),c_0_67])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE082+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
% 0.16/0.32 % Computer : n004.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 20:28:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.67/1.85 % Version : CSE_E---1.7
% 1.67/1.85 % Problem : theBenchmark.p
% 1.67/1.85 % SZS status Theorem for theBenchmark.p
% 1.67/1.85 % SZS output start CNFRefutation
% See solution above
% 1.67/1.86 % Total time : 1.371s
%------------------------------------------------------------------------------