%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL047+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 : n016.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 05:04:31 PM UTC 2026
% Result : Theorem 11.42s 7.43s
% Output : CNFRefutation 11.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 91 unt; 0 def)
% Number of atoms : 100 ( 99 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 145 ( 10 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(goals,conjecture,
! [X1,X2,X3] :
( ( join(X1,X2) = X2
& join(X1,X3) = X3 )
=> join(X1,meet(X2,X3)) = meet(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_11,plain,
! [X51,X52] : converse(composition(X51,X52)) = composition(converse(X52),converse(X51)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_12,plain,
! [X48] : converse(converse(X48)) = X48,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_13,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X44] : composition(X44,one) = X44,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_16,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X53,X54] : join(composition(converse(X53),complement(composition(X53,X54))),complement(X54)) = complement(X54),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_19,plain,
! [X32,X33] : join(X32,X33) = join(X33,X32),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_20,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
fof(c_0_21,plain,
! [X34,X35,X36] : join(X34,join(X35,X36)) = join(join(X34,X35),X36),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_22,plain,
! [X55] : top = join(X55,complement(X55)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_23,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_26,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_25]) ).
fof(c_0_30,plain,
! [X37,X38] : X37 = join(complement(join(complement(X37),complement(X38))),complement(join(complement(X37),X38))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_31,plain,
! [X39,X40] : meet(X39,X40) = complement(join(complement(X39),complement(X40))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_32,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_34,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]),c_0_29]) ).
fof(c_0_35,plain,
! [X56] : zero = meet(X56,complement(X56)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_36,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_39,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27]),c_0_24]) ).
cnf(c_0_40,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_40]) ).
cnf(c_0_44,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_24]) ).
cnf(c_0_45,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_24]),c_0_37]) ).
cnf(c_0_46,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_47,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_34]),c_0_40]) ).
cnf(c_0_48,plain,
join(zero,meet(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_50]) ).
cnf(c_0_52,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_51]) ).
cnf(c_0_53,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_54,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_52]) ).
cnf(c_0_55,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_37,c_0_51]) ).
cnf(c_0_56,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_53]) ).
fof(c_0_57,negated_conjecture,
~ ! [X1,X2,X3] :
( ( join(X1,X2) = X2
& join(X1,X3) = X3 )
=> join(X1,meet(X2,X3)) = meet(X2,X3) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_58,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_26]) ).
cnf(c_0_59,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_41]),c_0_24]) ).
cnf(c_0_60,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_55,c_0_24]) ).
cnf(c_0_61,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_24,c_0_42]) ).
cnf(c_0_62,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_53]),c_0_56]) ).
fof(c_0_63,negated_conjecture,
( join(esk1_0,esk2_0) = esk2_0
& join(esk1_0,esk3_0) = esk3_0
& join(esk1_0,meet(esk2_0,esk3_0)) != meet(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
cnf(c_0_64,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_60]) ).
cnf(c_0_66,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_32,c_0_61]) ).
cnf(c_0_67,plain,
join(X1,zero) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_62]),c_0_24]),c_0_27]),c_0_43]) ).
cnf(c_0_68,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_69,negated_conjecture,
join(esk1_0,esk3_0) = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_70,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,plain,
meet(X1,join(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_66]),c_0_51]),c_0_43]),c_0_67]) ).
cnf(c_0_72,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_68,c_0_52]) ).
cnf(c_0_73,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_59,c_0_45]) ).
cnf(c_0_74,negated_conjecture,
join(esk3_0,esk1_0) = esk3_0,
inference(rw,[status(thm)],[c_0_69,c_0_24]) ).
cnf(c_0_75,plain,
meet(X1,complement(meet(X2,X1))) = meet(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_70]),c_0_60]),c_0_45]) ).
cnf(c_0_76,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_55]) ).
cnf(c_0_77,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_73]) ).
cnf(c_0_79,negated_conjecture,
join(esk3_0,join(esk1_0,X1)) = join(esk3_0,X1),
inference(spm,[status(thm)],[c_0_26,c_0_74]) ).
cnf(c_0_80,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_51]) ).
cnf(c_0_81,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_73]),c_0_45]) ).
cnf(c_0_82,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_65]) ).
cnf(c_0_83,negated_conjecture,
meet(join(esk3_0,X1),join(esk1_0,X1)) = join(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_79]),c_0_45]) ).
cnf(c_0_84,negated_conjecture,
join(esk3_0,join(X1,esk1_0)) = join(esk3_0,X1),
inference(spm,[status(thm)],[c_0_79,c_0_24]) ).
cnf(c_0_85,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_70]),c_0_45]),c_0_81]) ).
cnf(c_0_86,plain,
join(X1,join(meet(complement(X1),X2),X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_82]),c_0_26]) ).
cnf(c_0_87,negated_conjecture,
meet(join(esk3_0,X1),join(X1,esk1_0)) = join(X1,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_72]),c_0_84]) ).
cnf(c_0_88,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(join(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_85]),c_0_51]),c_0_45]) ).
cnf(c_0_89,negated_conjecture,
join(esk1_0,esk2_0) = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_90,negated_conjecture,
meet(esk3_0,join(X1,esk1_0)) = join(esk1_0,meet(esk3_0,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_59]),c_0_88]),c_0_45]),c_0_24]) ).
cnf(c_0_91,negated_conjecture,
join(esk2_0,esk1_0) = esk2_0,
inference(rw,[status(thm)],[c_0_89,c_0_24]) ).
cnf(c_0_92,negated_conjecture,
join(esk1_0,meet(esk2_0,esk3_0)) != meet(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_93,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_45]),c_0_45]),c_0_92]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL047+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
% 0.14/0.31 % Computer : n016.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue May 5 01:45:06 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 11.42/7.43 % Version : CSE_E---1.7
% 11.42/7.43 % Problem : theBenchmark.p
% 11.42/7.43 % SZS status Theorem for theBenchmark.p
% 11.42/7.43 % SZS output start CNFRefutation
% See solution above
% 11.42/7.48 % Total time : 5.372s
%------------------------------------------------------------------------------