%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL027+4 : 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 : n023.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 05:04:22 PM UTC 2026
% Result : Theorem 4.17s 3.33s
% Output : CNFRefutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 74 ( 67 unt; 0 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 5 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
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/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(goals,conjecture,
! [X1] :
( join(X1,one) = one
=> ( join(meet(complement(composition(X1,top)),one),meet(complement(X1),one)) = meet(complement(X1),one)
& join(meet(complement(X1),one),meet(complement(composition(X1,top)),one)) = meet(complement(composition(X1,top)),one) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_13,plain,
! [X58,X59] : converse(composition(X58,X59)) = composition(converse(X59),converse(X58)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_14,plain,
! [X51] : composition(X51,one) = X51,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_15,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X55] : converse(converse(X55)) = X55,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_18,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X60,X61] : join(composition(converse(X60),complement(composition(X60,X61))),complement(X61)) = complement(X61),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_21,plain,
! [X39,X40] : join(X39,X40) = join(X40,X39),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_22,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_23,plain,
! [X63] : zero = meet(X63,complement(X63)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_24,plain,
! [X46,X47] : meet(X46,X47) = complement(join(complement(X46),complement(X47))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_25,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_28,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,plain,
! [X62] : top = join(X62,complement(X62)),
inference(variable_rename,[status(thm)],[def_top]) ).
fof(c_0_31,plain,
! [X52,X53,X54] : composition(join(X52,X53),X54) = join(composition(X52,X54),composition(X53,X54)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_32,plain,
! [X56,X57] : converse(join(X56,X57)) = join(converse(X56),converse(X57)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_33,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_35,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_37,plain,
! [X44,X45] : X44 = join(complement(join(complement(X44),complement(X45))),complement(join(complement(X44),X45))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_38,plain,
! [X41,X42,X43] : join(X41,join(X42,X43)) = join(join(X41,X42),X43),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_39,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_40,negated_conjecture,
~ ! [X1] :
( join(X1,one) = one
=> ( join(meet(complement(composition(X1,top)),one),meet(complement(X1),one)) = meet(complement(X1),one)
& join(meet(complement(X1),one),meet(complement(composition(X1,top)),one)) = meet(complement(composition(X1,top)),one) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_41,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_27]),c_0_34]) ).
cnf(c_0_43,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_34]),c_0_26]) ).
fof(c_0_47,negated_conjecture,
( join(esk1_0,one) = one
& ( join(meet(complement(composition(esk1_0,top)),one),meet(complement(esk1_0),one)) != meet(complement(esk1_0),one)
| join(meet(complement(esk1_0),one),meet(complement(composition(esk1_0,top)),one)) != meet(complement(composition(esk1_0,top)),one) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
cnf(c_0_48,plain,
join(composition(converse(X1),converse(X2)),composition(converse(X1),converse(X3))) = composition(converse(X1),join(converse(X2),converse(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_39]),c_0_15]),c_0_41]),c_0_15]),c_0_15]) ).
cnf(c_0_49,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_26]) ).
cnf(c_0_51,plain,
join(composition(join(X1,one),X2),X3) = join(X2,join(composition(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,plain,
join(converse(X1),composition(converse(X1),converse(X2))) = composition(converse(X1),join(one,converse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_27]),c_0_16]),c_0_26]),c_0_26]) ).
cnf(c_0_54,negated_conjecture,
( join(meet(complement(composition(esk1_0,top)),one),meet(complement(esk1_0),one)) != meet(complement(esk1_0),one)
| join(meet(complement(esk1_0),one),meet(complement(composition(esk1_0,top)),one)) != meet(complement(composition(esk1_0,top)),one) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_45,c_0_49]) ).
cnf(c_0_56,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_42]),c_0_36]),c_0_43]),c_0_26]) ).
cnf(c_0_57,plain,
join(composition(join(one,X1),X2),X3) = join(X2,join(composition(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_51,c_0_26]) ).
cnf(c_0_58,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_52,c_0_26]) ).
cnf(c_0_59,plain,
join(converse(X1),composition(converse(X1),X2)) = composition(converse(X1),join(one,X2)),
inference(spm,[status(thm)],[c_0_53,c_0_19]) ).
cnf(c_0_60,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_39,c_0_34]) ).
cnf(c_0_61,negated_conjecture,
( join(complement(join(complement(complement(composition(esk1_0,top))),complement(one))),complement(join(complement(complement(esk1_0)),complement(one)))) != complement(join(complement(complement(esk1_0)),complement(one)))
| join(complement(join(complement(complement(esk1_0)),complement(one))),complement(join(complement(complement(composition(esk1_0,top))),complement(one)))) != complement(join(complement(complement(composition(esk1_0,top))),complement(one))) ),
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_54,c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_62,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
join(X1,join(composition(esk1_0,X1),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_34]) ).
cnf(c_0_64,plain,
join(X1,composition(X1,X2)) = composition(X1,join(one,X2)),
inference(spm,[status(thm)],[c_0_59,c_0_19]) ).
cnf(c_0_65,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_60,c_0_36]) ).
cnf(c_0_66,negated_conjecture,
( join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(one),complement(complement(composition(esk1_0,top)))))
| join(complement(join(complement(one),complement(complement(esk1_0)))),complement(join(complement(one),complement(complement(composition(esk1_0,top)))))) != complement(join(complement(one),complement(complement(esk1_0)))) ),
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_61,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_67,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_56,c_0_62]) ).
cnf(c_0_68,negated_conjecture,
join(X1,join(X2,composition(esk1_0,X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_26]) ).
cnf(c_0_69,plain,
join(X1,composition(X1,complement(one))) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_16]),c_0_16]) ).
cnf(c_0_70,negated_conjecture,
( join(complement(join(complement(one),esk1_0)),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(complement(one),composition(esk1_0,top)))
| join(complement(join(complement(one),esk1_0)),complement(join(complement(one),composition(esk1_0,top)))) != complement(join(complement(one),esk1_0)) ),
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_66,c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]),c_0_67]) ).
cnf(c_0_71,negated_conjecture,
join(complement(one),composition(esk1_0,top)) = join(complement(one),esk1_0),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_67]) ).
cnf(c_0_73,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)],[c_0_70,c_0_71]),c_0_72]),c_0_71]),c_0_71]),c_0_72])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL027+4 : 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 : n023.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 : Tue May 5 01:43:09 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.17/3.33 % Version : CSE_E---1.7
% 4.17/3.33 % Problem : theBenchmark.p
% 4.17/3.33 % SZS status Theorem for theBenchmark.p
% 4.17/3.33 % SZS output start CNFRefutation
% See solution above
% 4.17/3.34 % Total time : 2.371s
%------------------------------------------------------------------------------