%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET595+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n006.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 05:08:04 PM UTC 2026
% Result : Theorem 16.85s 10.49s
% Output : CNFRefutation 16.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 73 ( 25 unt; 0 def)
% Number of atoms : 153 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 127 ( 47 ~; 60 |; 12 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 163 ( 18 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th54,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> X2 = union(X1,difference(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th54) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> X2 = union(X1,difference(X2,X1)) ),
inference(assume_negation,[status(cth)],[prove_th54]) ).
fof(c_0_7,plain,
! [X35,X36,X37,X38,X39] :
( ( ~ subset(X35,X36)
| ~ member(X37,X35)
| member(X37,X36) )
& ( member(esk2_2(X38,X39),X38)
| subset(X38,X39) )
& ( ~ member(esk2_2(X38,X39),X39)
| subset(X38,X39) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subset_defn])])])])])]) ).
fof(c_0_8,negated_conjecture,
( subset(esk4_0,esk5_0)
& esk5_0 != union(esk4_0,difference(esk5_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
cnf(c_0_10,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X32,X33,X34] :
( ( member(X34,X32)
| ~ member(X34,difference(X32,X33)) )
& ( ~ member(X34,X33)
| ~ member(X34,difference(X32,X33)) )
& ( ~ member(X34,X32)
| member(X34,X33)
| member(X34,difference(X32,X33)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( subset(X1,esk5_0)
| ~ member(esk2_2(X1,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( subset(difference(X1,X2),X3)
| member(esk2_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
subset(difference(esk4_0,X1),esk5_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_21,plain,
! [X29,X30,X31] :
( ( ~ member(X31,union(X29,X30))
| member(X31,X29)
| member(X31,X30) )
& ( ~ member(X31,X29)
| member(X31,union(X29,X30)) )
& ( ~ member(X31,X30)
| member(X31,union(X29,X30)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_22,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_23,plain,
! [X41,X42] :
( ( subset(X41,X42)
| X41 != X42 )
& ( subset(X42,X41)
| X41 != X42 )
& ( ~ subset(X41,X42)
| ~ subset(X42,X41)
| X41 = X42 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_24,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,difference(esk4_0,X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_25,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk2_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_26,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( subset(X1,difference(X2,X3))
| member(esk2_2(X1,difference(X2,X3)),X3)
| ~ member(esk2_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( subset(difference(esk4_0,X1),X2)
| member(esk2_2(difference(esk4_0,X1),X2),esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_31,plain,
( subset(difference(difference(X1,X2),X3),X4)
| ~ member(esk2_2(difference(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_32,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk2_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk2_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
( subset(difference(difference(esk4_0,X1),X2),X3)
| member(esk2_2(difference(difference(esk4_0,X1),X2),X3),esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_35,plain,
( subset(difference(X1,union(X2,X3)),X4)
| ~ member(esk2_2(difference(X1,union(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_36,plain,
( subset(X1,difference(X1,X2))
| member(esk2_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_37,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,negated_conjecture,
subset(difference(esk4_0,esk5_0),X1),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_39,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_40,plain,
( subset(difference(difference(X1,union(X2,X3)),X4),X5)
| ~ member(esk2_2(difference(difference(X1,union(X2,X3)),X4),X5),X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( subset(difference(difference(esk4_0,X1),difference(esk5_0,X2)),X3)
| member(esk2_2(difference(difference(esk4_0,X1),difference(esk5_0,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
subset(difference(X1,union(X2,X3)),difference(difference(X1,union(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_43,plain,
! [X43,X44] : union(X43,X44) = union(X44,X43),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_44,plain,
( subset(difference(difference(X1,X2),X3),X4)
| member(esk2_2(difference(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_45,negated_conjecture,
difference(difference(esk4_0,esk5_0),X1) = difference(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
( subset(union(X1,X2),X3)
| member(esk2_2(union(X1,X2),X3),X1)
| member(esk2_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_16]) ).
cnf(c_0_47,negated_conjecture,
( subset(difference(esk4_0,X1),difference(esk5_0,X2))
| member(esk2_2(difference(esk4_0,X1),difference(esk5_0,X2)),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_48,negated_conjecture,
subset(difference(difference(esk4_0,union(X1,X2)),difference(esk5_0,X2)),X3),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
difference(difference(X1,union(X2,X3)),X2) = difference(X1,union(X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_42]),c_0_29])]) ).
cnf(c_0_50,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,plain,
( subset(difference(difference(X1,X2),difference(X1,X3)),X4)
| member(esk2_2(difference(difference(X1,X2),difference(X1,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( ~ member(X1,difference(esk4_0,esk5_0))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( subset(union(X1,esk4_0),esk5_0)
| member(esk2_2(union(X1,esk4_0),esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
subset(difference(esk4_0,X1),difference(esk5_0,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_47]) ).
cnf(c_0_55,negated_conjecture,
( X1 = difference(esk4_0,esk5_0)
| ~ subset(X1,difference(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_28,c_0_38]) ).
cnf(c_0_56,negated_conjecture,
subset(difference(esk4_0,union(X1,difference(esk5_0,X1))),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_57,plain,
subset(difference(difference(X1,union(X2,X3)),difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
~ member(X1,difference(esk4_0,esk5_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_38]),c_0_52]) ).
cnf(c_0_59,negated_conjecture,
( subset(union(esk4_0,difference(X1,X2)),esk5_0)
| member(esk2_2(union(esk4_0,difference(X1,X2)),esk5_0),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_53]),c_0_50]),c_0_50]) ).
cnf(c_0_60,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk2_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_61,negated_conjecture,
( difference(esk5_0,X1) = difference(esk4_0,X1)
| ~ subset(difference(esk5_0,X1),difference(esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_28,c_0_54]) ).
cnf(c_0_62,negated_conjecture,
difference(esk4_0,union(X1,difference(esk5_0,X1))) = difference(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,plain,
subset(difference(X1,union(X2,difference(X1,X2))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_49]),c_0_50]) ).
cnf(c_0_64,negated_conjecture,
subset(X1,difference(X1,difference(esk4_0,esk5_0))),
inference(spm,[status(thm)],[c_0_58,c_0_36]) ).
cnf(c_0_65,negated_conjecture,
subset(union(esk4_0,difference(esk5_0,X1)),esk5_0),
inference(spm,[status(thm)],[c_0_13,c_0_59]) ).
cnf(c_0_66,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_13,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
difference(esk5_0,union(X1,difference(esk5_0,X1))) = difference(esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_68,negated_conjecture,
difference(X1,difference(esk4_0,esk5_0)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_64]),c_0_29])]) ).
cnf(c_0_69,negated_conjecture,
( union(esk4_0,difference(esk5_0,X1)) = esk5_0
| ~ subset(esk5_0,union(esk4_0,difference(esk5_0,X1))) ),
inference(spm,[status(thm)],[c_0_28,c_0_65]) ).
cnf(c_0_70,negated_conjecture,
subset(esk5_0,union(X1,difference(esk5_0,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_71,negated_conjecture,
esk5_0 != union(esk4_0,difference(esk5_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET595+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n006.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 02:28:46 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 16.85/10.49 % Version : CSE_E---1.7
% 16.85/10.49 % Problem : theBenchmark.p
% 16.85/10.49 % SZS status Theorem for theBenchmark.p
% 16.85/10.49 % SZS output start CNFRefutation
% See solution above
% 16.96/10.57 % Total time : 7.382s
%------------------------------------------------------------------------------