%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE098+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 : n028.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 168.50s 84.76s
% Output : CNFRefutation 169.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 57 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 5 con; 0-2 aty)
% Number of variables : 87 ( 1 sgn 46 !; 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(goals,conjecture,
! [X4,X5,X6] :
( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
=> addition(multiplication(X4,domain(X5)),multiplication(domain(X6),X4)) = multiplication(domain(X6),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
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(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_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
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(c_0_13,plain,
! [X68,X69,X70] : multiplication(addition(X68,X69),X70) = addition(multiplication(X68,X70),multiplication(X69,X70)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_14,plain,
! [X75] : multiplication(antidomain(X75),X75) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_15,plain,
! [X58] : addition(X58,zero) = X58,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_16,negated_conjecture,
~ ! [X4,X5,X6] :
( addition(forward_diamond(X4,domain(X5)),domain(X6)) = domain(X6)
=> addition(multiplication(X4,domain(X5)),multiplication(domain(X6),X4)) = multiplication(domain(X6),X4) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_17,plain,
! [X88,X89] : forward_diamond(X88,X89) = domain(multiplication(X88,domain(X89))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_18,plain,
! [X79] : domain(X79) = antidomain(antidomain(X79)),
inference(variable_rename,[status(thm)],[domain4]) ).
cnf(c_0_19,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X53,X54] : addition(X53,X54) = addition(X54,X53),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_23,plain,
! [X78] : addition(antidomain(antidomain(X78)),antidomain(X78)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_24,negated_conjecture,
( addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0)
& addition(multiplication(esk1_0,domain(esk2_0)),multiplication(domain(esk3_0),esk1_0)) != multiplication(domain(esk3_0),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_25,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X65,X66,X67] : multiplication(X65,addition(X66,X67)) = addition(multiplication(X65,X66),multiplication(X65,X67)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_28,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X64] : multiplication(one,X64) = X64,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_32,negated_conjecture,
addition(forward_diamond(esk1_0,domain(esk2_0)),domain(esk3_0)) = domain(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).
cnf(c_0_34,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X63] : multiplication(X63,one) = X63,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_36,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_38,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_39,plain,
! [X55,X56,X57] : addition(X57,addition(X56,X55)) = addition(addition(X57,X56),X55),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_40,plain,
! [X59] : addition(X59,X59) = X59,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_41,negated_conjecture,
addition(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0))))))),antidomain(antidomain(esk3_0))) = antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_26]),c_0_26]),c_0_26]),c_0_33]) ).
cnf(c_0_42,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_20]),c_0_21]) ).
cnf(c_0_43,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_45,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_38]),c_0_29]) ).
cnf(c_0_48,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[c_0_41,c_0_29]) ).
cnf(c_0_49,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_37]),c_0_43]),c_0_44]) ).
cnf(c_0_50,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
multiplication(addition(X1,antidomain(antidomain(X2))),X2) = multiplication(addition(X1,one),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_44]),c_0_29]),c_0_47]) ).
cnf(c_0_52,negated_conjecture,
addition(antidomain(antidomain(esk3_0)),antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(esk2_0)))))) = antidomain(antidomain(esk3_0)),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_37]),c_0_29]) ).
cnf(c_0_54,negated_conjecture,
addition(multiplication(esk1_0,domain(esk2_0)),multiplication(domain(esk3_0),esk1_0)) != multiplication(domain(esk3_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_55,negated_conjecture,
multiplication(antidomain(antidomain(esk3_0)),multiplication(esk1_0,antidomain(antidomain(esk2_0)))) = multiplication(esk1_0,antidomain(antidomain(esk2_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_29]),c_0_53]),c_0_38]) ).
cnf(c_0_56,negated_conjecture,
addition(multiplication(esk1_0,antidomain(antidomain(esk2_0))),multiplication(antidomain(antidomain(esk3_0)),esk1_0)) != multiplication(antidomain(antidomain(esk3_0)),esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_57,negated_conjecture,
addition(multiplication(esk1_0,antidomain(antidomain(esk2_0))),multiplication(antidomain(antidomain(esk3_0)),X1)) = multiplication(antidomain(antidomain(esk3_0)),addition(multiplication(esk1_0,antidomain(antidomain(esk2_0))),X1)),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_58,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_43]),c_0_29]) ).
cnf(c_0_59,negated_conjecture,
$false,
inference(cn,[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_56,c_0_57]),c_0_29]),c_0_58]),c_0_29]),c_0_53]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE098+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
% 0.16/0.33 % Computer : n028.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 20:29:30 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 168.50/84.76 % Version : CSE_E---1.7
% 168.50/84.76 % Problem : theBenchmark.p
% 168.50/84.76 % SZS status Theorem for theBenchmark.p
% 168.50/84.76 % SZS output start CNFRefutation
% See solution above
% 169.09/85.36 % Total time : 59.469s
%------------------------------------------------------------------------------