%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE064+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 : 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 04:35:38 PM UTC 2026
% Result : Theorem 1.81s 1.90s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 64 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 1 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 10 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(goals,conjecture,
! [X4,X5] :
( addition(X4,multiplication(domain(X5),X4)) = multiplication(domain(X5),X4)
<= addition(domain(X4),domain(X5)) = domain(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain2,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(domain5,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
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(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(c_0_12,plain,
! [X61] : addition(domain(X61),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_13,plain,
! [X36,X37] : addition(X36,X37) = addition(X37,X36),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_14,negated_conjecture,
~ ! [X4,X5] :
( addition(domain(X4),domain(X5)) = domain(X5)
=> addition(X4,multiplication(domain(X5),X4)) = multiplication(domain(X5),X4) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(c_0_15,plain,
! [X58] : addition(X58,multiplication(domain(X58),X58)) = multiplication(domain(X58),X58),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_16,plain,
! [X46] : multiplication(X46,one) = X46,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_17,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X59,X60] : domain(multiplication(X59,X60)) = domain(multiplication(X59,domain(X60))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(c_0_20,plain,
! [X47] : multiplication(one,X47) = X47,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_21,negated_conjecture,
( addition(domain(esk1_0),domain(esk2_0)) = domain(esk2_0)
& addition(esk1_0,multiplication(domain(esk2_0),esk1_0)) != multiplication(domain(esk2_0),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_22,plain,
! [X62,X63] : domain(addition(X62,X63)) = addition(domain(X62),domain(X63)),
inference(variable_rename,[status(thm)],[domain5]) ).
cnf(c_0_23,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
! [X48,X49,X50] : multiplication(X48,addition(X49,X50)) = addition(multiplication(X48,X49),multiplication(X48,X50)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_29,plain,
! [X51,X52,X53] : multiplication(addition(X51,X52),X53) = addition(multiplication(X51,X53),multiplication(X52,X53)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_30,plain,
! [X38,X39,X40] : addition(X40,addition(X39,X38)) = addition(addition(X40,X39),X38),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_31,plain,
! [X42] : addition(X42,X42) = X42,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_32,negated_conjecture,
addition(domain(esk1_0),domain(esk2_0)) = domain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,plain,
domain(one) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_35,plain,
domain(domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).
cnf(c_0_36,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,negated_conjecture,
domain(addition(esk1_0,esk2_0)) = domain(esk2_0),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
domain(addition(X1,one)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_18]),c_0_25]) ).
cnf(c_0_42,plain,
addition(domain(X1),multiplication(domain(X1),domain(X1))) = multiplication(domain(X1),domain(X1)),
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_43,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_24]),c_0_18]) ).
cnf(c_0_44,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_18]) ).
cnf(c_0_45,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_36,c_0_24]) ).
cnf(c_0_46,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
addition(esk1_0,addition(esk2_0,multiplication(domain(esk2_0),addition(esk1_0,esk2_0)))) = multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_40]),c_0_38]) ).
cnf(c_0_48,plain,
domain(addition(domain(X1),X2)) = domain(addition(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_35]),c_0_33]) ).
cnf(c_0_49,plain,
domain(multiplication(X1,addition(X2,one))) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_41]),c_0_24]) ).
cnf(c_0_50,plain,
multiplication(domain(X1),domain(X1)) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_18]),c_0_25]),c_0_24]) ).
cnf(c_0_51,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_44]),c_0_18]),c_0_25]),c_0_27]) ).
cnf(c_0_52,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(one,X2),X1),
inference(spm,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_53,plain,
addition(X1,multiplication(X1,domain(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_25]),c_0_24]) ).
cnf(c_0_54,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),addition(esk1_0,esk2_0))) = multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,plain,
domain(addition(X1,multiplication(domain(X1),X2))) = domain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_43]),c_0_49]),c_0_35]) ).
cnf(c_0_56,plain,
domain(multiplication(domain(X1),X1)) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_50]),c_0_35]) ).
cnf(c_0_57,plain,
multiplication(addition(domain(X1),X2),X1) = addition(X1,multiplication(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_58,plain,
addition(X1,multiplication(domain(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_27]),c_0_27]) ).
cnf(c_0_59,negated_conjecture,
addition(esk1_0,addition(multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),X1)) = addition(multiplication(domain(esk2_0),addition(esk1_0,esk2_0)),X1),
inference(spm,[status(thm)],[c_0_38,c_0_54]) ).
cnf(c_0_60,plain,
domain(multiplication(domain(X1),addition(X1,X2))) = domain(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_36]) ).
cnf(c_0_61,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),esk1_0)) != multiplication(domain(esk2_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_62,plain,
multiplication(domain(addition(X1,X2)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_33]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
addition(esk1_0,multiplication(domain(esk2_0),addition(esk1_0,addition(esk2_0,X1)))) = multiplication(domain(esk2_0),addition(esk1_0,addition(esk2_0,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_36]),c_0_38]),c_0_38]) ).
cnf(c_0_64,negated_conjecture,
domain(multiplication(domain(esk2_0),addition(esk1_0,addition(esk2_0,X1)))) = domain(esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_40]),c_0_38]) ).
cnf(c_0_65,negated_conjecture,
multiplication(domain(esk2_0),esk1_0) != esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_44]),c_0_18]),c_0_25]),c_0_27]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE064+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
% 0.16/0.33 % Computer : n002.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 20:28:46 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.81/1.90 % Version : CSE_E---1.7
% 1.81/1.90 % Problem : theBenchmark.p
% 1.81/1.90 % SZS status Theorem for theBenchmark.p
% 1.81/1.90 % SZS output start CNFRefutation
% See solution above
% 1.81/1.91 % Total time : 1.368s
%------------------------------------------------------------------------------