%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL026+2 : 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 : n007.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 05:04:20 PM UTC 2026
% Result : Theorem 4.62s 3.43s
% Output : CNFRefutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 81 ( 75 unt; 0 def)
% Number of atoms : 90 ( 89 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 4 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 126 ( 3 sgn 48 !; 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(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,X2] :
( join(X1,one) = one
=> ( join(meet(composition(X1,top),X2),composition(X1,X2)) = composition(X1,X2)
& join(composition(X1,X2),meet(composition(X1,top),X2)) = meet(composition(X1,top),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(c_0_13,plain,
! [X50,X51] : converse(composition(X50,X51)) = composition(converse(X51),converse(X50)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_14,plain,
! [X43] : composition(X43,one) = X43,
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,
! [X47] : converse(converse(X47)) = X47,
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,
! [X52,X53] : join(composition(converse(X52),complement(composition(X52,X53))),complement(X53)) = complement(X53),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_21,plain,
! [X31,X32] : join(X31,X32) = join(X32,X31),
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,
! [X55] : zero = meet(X55,complement(X55)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_24,plain,
! [X38,X39] : meet(X38,X39) = complement(join(complement(X38),complement(X39))),
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,
! [X54] : top = join(X54,complement(X54)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_31,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_32,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_33,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_35,plain,
! [X36,X37] : X36 = join(complement(join(complement(X36),complement(X37))),complement(join(complement(X36),X37))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_36,plain,
! [X33,X34,X35] : join(X33,join(X34,X35)) = join(join(X33,X34),X35),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_37,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27]),c_0_32]) ).
cnf(c_0_38,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_39,c_0_26]) ).
cnf(c_0_43,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,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_42,c_0_37]),c_0_34]),c_0_38]),c_0_26]) ).
cnf(c_0_45,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_47,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_48,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_47]) ).
fof(c_0_49,negated_conjecture,
~ ! [X1,X2] :
( join(X1,one) = one
=> ( join(meet(composition(X1,top),X2),composition(X1,X2)) = composition(X1,X2)
& join(composition(X1,X2),meet(composition(X1,top),X2)) = meet(composition(X1,top),X2) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_50,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_42]),c_0_26]) ).
cnf(c_0_51,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_48,c_0_26]) ).
fof(c_0_52,plain,
! [X44,X45,X46] : composition(join(X44,X45),X46) = join(composition(X44,X46),composition(X45,X46)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_53,plain,
! [X48,X49] : converse(join(X48,X49)) = join(converse(X48),converse(X49)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
fof(c_0_54,negated_conjecture,
( join(esk1_0,one) = one
& ( join(meet(composition(esk1_0,top),esk2_0),composition(esk1_0,esk2_0)) != composition(esk1_0,esk2_0)
| join(composition(esk1_0,esk2_0),meet(composition(esk1_0,top),esk2_0)) != meet(composition(esk1_0,top),esk2_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).
cnf(c_0_55,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_26]),c_0_40]) ).
cnf(c_0_60,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_55,c_0_46]) ).
cnf(c_0_61,plain,
composition(converse(X1),join(converse(X2),converse(X3))) = join(composition(converse(X1),converse(X2)),composition(converse(X1),converse(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_56]),c_0_57]),c_0_15]),c_0_15]),c_0_57]) ).
cnf(c_0_62,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_58,c_0_26]) ).
cnf(c_0_63,plain,
join(complement(X1),complement(join(complement(X1),complement(X2)))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_42]),c_0_46]),c_0_59]),c_0_26]),c_0_60]) ).
cnf(c_0_64,plain,
composition(X1,join(converse(X2),converse(X3))) = join(composition(X1,converse(X2)),composition(X1,converse(X3))),
inference(spm,[status(thm)],[c_0_61,c_0_19]) ).
cnf(c_0_65,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_62]),c_0_32]),c_0_32]) ).
cnf(c_0_66,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_46]) ).
cnf(c_0_67,plain,
composition(X1,join(converse(X2),X3)) = join(composition(X1,converse(X2)),composition(X1,X3)),
inference(spm,[status(thm)],[c_0_64,c_0_19]) ).
cnf(c_0_68,negated_conjecture,
join(X1,join(composition(esk1_0,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_65]) ).
cnf(c_0_69,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_66]),c_0_48]) ).
cnf(c_0_70,plain,
composition(X1,join(X2,X3)) = join(composition(X1,X2),composition(X1,X3)),
inference(spm,[status(thm)],[c_0_67,c_0_19]) ).
cnf(c_0_71,negated_conjecture,
join(complement(X1),complement(composition(esk1_0,X1))) = complement(composition(esk1_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_65]),c_0_26]) ).
cnf(c_0_72,negated_conjecture,
( join(meet(composition(esk1_0,top),esk2_0),composition(esk1_0,esk2_0)) != composition(esk1_0,esk2_0)
| join(composition(esk1_0,esk2_0),meet(composition(esk1_0,top),esk2_0)) != meet(composition(esk1_0,top),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_73,negated_conjecture,
join(X1,complement(join(composition(esk1_0,X1),X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_68]) ).
cnf(c_0_74,plain,
join(composition(X1,X2),composition(X1,complement(X2))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_70,c_0_34]) ).
cnf(c_0_75,negated_conjecture,
join(X1,complement(composition(esk1_0,complement(X1)))) = complement(composition(esk1_0,complement(X1))),
inference(spm,[status(thm)],[c_0_71,c_0_46]) ).
cnf(c_0_76,negated_conjecture,
( join(complement(join(complement(composition(esk1_0,top)),complement(esk2_0))),composition(esk1_0,esk2_0)) != composition(esk1_0,esk2_0)
| join(composition(esk1_0,esk2_0),complement(join(complement(composition(esk1_0,top)),complement(esk2_0)))) != complement(join(complement(composition(esk1_0,top)),complement(esk2_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_77,negated_conjecture,
complement(composition(esk1_0,complement(X1))) = join(X1,complement(composition(esk1_0,top))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]) ).
cnf(c_0_78,negated_conjecture,
( join(composition(esk1_0,esk2_0),complement(join(complement(esk2_0),complement(composition(esk1_0,top))))) != complement(join(complement(esk2_0),complement(composition(esk1_0,top))))
| join(composition(esk1_0,esk2_0),complement(join(complement(esk2_0),complement(composition(esk1_0,top))))) != composition(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_79,negated_conjecture,
complement(join(X1,complement(composition(esk1_0,top)))) = composition(esk1_0,complement(X1)),
inference(spm,[status(thm)],[c_0_46,c_0_77]) ).
cnf(c_0_80,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_46]),c_0_47]),c_0_79]),c_0_46]),c_0_79]),c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL026+2 : 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 : n007.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 01:40:39 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.62/3.43 % Version : CSE_E---1.7
% 4.62/3.43 % Problem : theBenchmark.p
% 4.62/3.43 % SZS status Theorem for theBenchmark.p
% 4.62/3.43 % SZS output start CNFRefutation
% See solution above
% 4.62/3.44 % Total time : 2.372s
%------------------------------------------------------------------------------