%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU170+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n013.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 05:10:55 PM UTC 2026
% Result : Theorem 49.14s 33.80s
% Output : CNFRefutation 49.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 13 unt; 0 def)
% Number of atoms : 205 ( 21 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 215 ( 84 ~; 90 |; 24 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 155 ( 8 sgn 63 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t43_subset_1,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(t3_xboole_0,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(l3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t3_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(c_0_10,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,powerset(X1))
=> ( disjoint(X2,X3)
<=> subset(X2,subset_complement(X1,X3)) ) ) ),
inference(assume_negation,[status(cth)],[t43_subset_1]) ).
fof(c_0_12,plain,
! [X58,X59,X60,X61,X62,X63,X64,X65] :
( ( in(X61,X58)
| ~ in(X61,X60)
| X60 != set_difference(X58,X59) )
& ( ~ in(X61,X59)
| ~ in(X61,X60)
| X60 != set_difference(X58,X59) )
& ( ~ in(X62,X58)
| in(X62,X59)
| in(X62,X60)
| X60 != set_difference(X58,X59) )
& ( ~ in(esk2_3(X63,X64,X65),X65)
| ~ in(esk2_3(X63,X64,X65),X63)
| in(esk2_3(X63,X64,X65),X64)
| X65 = set_difference(X63,X64) )
& ( in(esk2_3(X63,X64,X65),X63)
| in(esk2_3(X63,X64,X65),X65)
| X65 = set_difference(X63,X64) )
& ( ~ in(esk2_3(X63,X64,X65),X64)
| in(esk2_3(X63,X64,X65),X65)
| X65 = set_difference(X63,X64) ) ),
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)],[c_0_10])])])])])]) ).
fof(c_0_13,plain,
! [X67,X68] :
( ~ element(X68,powerset(X67))
| subset_complement(X67,X68) = set_difference(X67,X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(c_0_14,plain,
! [X74,X75] :
( ~ element(X75,powerset(X74))
| subset_complement(X74,subset_complement(X74,X75)) = X75 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
fof(c_0_15,plain,
! [X69,X70] :
( ~ element(X70,powerset(X69))
| element(subset_complement(X69,X70),powerset(X69)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(c_0_16,plain,
! [X52,X53,X54,X55,X56] :
( ( ~ subset(X52,X53)
| ~ in(X54,X52)
| in(X54,X53) )
& ( in(esk1_2(X55,X56),X55)
| subset(X55,X56) )
& ( ~ in(esk1_2(X55,X56),X56)
| subset(X55,X56) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_17,negated_conjecture,
( element(esk10_0,powerset(esk9_0))
& element(esk11_0,powerset(esk9_0))
& ( ~ disjoint(esk10_0,esk11_0)
| ~ subset(esk10_0,subset_complement(esk9_0,esk11_0)) )
& ( disjoint(esk10_0,esk11_0)
| subset(esk10_0,subset_complement(esk9_0,esk11_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_18,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
cnf(c_0_19,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( disjoint(esk10_0,esk11_0)
| subset(esk10_0,subset_complement(esk9_0,esk11_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_25,plain,
! [X89,X90,X92,X93,X94] :
( ( in(esk8_2(X89,X90),X89)
| disjoint(X89,X90) )
& ( in(esk8_2(X89,X90),X90)
| disjoint(X89,X90) )
& ( ~ in(X94,X92)
| ~ in(X94,X93)
| ~ disjoint(X92,X93) ) ),
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)],[c_0_18])])])])])]) ).
fof(c_0_26,plain,
! [X76,X77,X78] :
( ~ element(X77,powerset(X76))
| ~ in(X78,X77)
| in(X78,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_subset_1])])]) ).
cnf(c_0_27,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( set_difference(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( disjoint(esk10_0,esk11_0)
| in(X1,subset_complement(esk9_0,esk11_0))
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( in(esk8_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( in(X3,X2)
| ~ element(X1,powerset(X2))
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
element(esk10_0,powerset(esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,plain,
( ~ element(X1,powerset(X2))
| ~ in(X3,subset_complement(X2,X1))
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( disjoint(esk10_0,esk11_0)
| disjoint(esk10_0,X1)
| in(esk8_2(esk10_0,X1),subset_complement(esk9_0,esk11_0)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
element(esk11_0,powerset(esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_37,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_38,negated_conjecture,
( in(X1,esk9_0)
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_41,negated_conjecture,
( disjoint(esk10_0,esk11_0)
| disjoint(esk10_0,X1)
| ~ in(esk8_2(esk10_0,X1),esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_42,plain,
( in(esk8_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_43,negated_conjecture,
( subset(X1,esk9_0)
| ~ in(esk1_2(X1,esk9_0),esk10_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( subset(set_difference(X1,X2),X3)
| in(esk1_2(set_difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_46,negated_conjecture,
disjoint(esk10_0,esk11_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,negated_conjecture,
subset(set_difference(esk10_0,X1),esk9_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( ~ in(X1,esk11_0)
| ~ in(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( subset(X1,esk9_0)
| ~ element(X1,powerset(esk10_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_28]) ).
cnf(c_0_50,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_51,negated_conjecture,
( disjoint(esk11_0,X1)
| ~ in(esk8_2(esk11_0,X1),esk10_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_30]) ).
cnf(c_0_52,plain,
( disjoint(X1,set_difference(X2,X3))
| in(esk8_2(X1,set_difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_42]) ).
cnf(c_0_53,negated_conjecture,
( in(X1,esk9_0)
| ~ element(X2,powerset(esk10_0))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_49]) ).
cnf(c_0_54,plain,
( element(set_difference(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_55,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_56,negated_conjecture,
disjoint(esk11_0,set_difference(esk10_0,X1)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( in(X1,esk9_0)
| ~ element(X2,powerset(esk10_0))
| ~ in(X1,set_difference(esk10_0,X2)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,plain,
( subset(X1,X2)
| in(esk1_2(X1,X2),set_difference(X1,X3))
| in(esk1_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_40]) ).
fof(c_0_59,plain,
! [X71] : element(esk3_1(X71),X71),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_60,negated_conjecture,
( ~ in(X1,set_difference(esk10_0,X2))
| ~ in(X1,esk11_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_56]) ).
fof(c_0_61,plain,
! [X88] : set_difference(X88,empty_set) = X88,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_62,plain,
( in(X1,subset_complement(X2,X3))
| in(X1,X3)
| ~ element(X3,powerset(X2))
| ~ in(X1,X2) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28])]) ).
cnf(c_0_63,negated_conjecture,
( subset(esk10_0,X1)
| in(esk1_2(esk10_0,X1),esk9_0)
| ~ element(X2,powerset(esk10_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_53]) ).
cnf(c_0_64,plain,
element(esk3_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_65,negated_conjecture,
( subset(set_difference(esk10_0,X1),X2)
| ~ in(esk1_2(set_difference(esk10_0,X1),X2),esk11_0) ),
inference(spm,[status(thm)],[c_0_60,c_0_40]) ).
cnf(c_0_66,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( in(X1,subset_complement(esk9_0,esk11_0))
| in(X1,esk11_0)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_62,c_0_36]) ).
cnf(c_0_68,negated_conjecture,
( subset(esk10_0,X1)
| in(esk1_2(esk10_0,X1),esk9_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
( subset(esk10_0,X1)
| ~ in(esk1_2(esk10_0,X1),esk11_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
( ~ disjoint(esk10_0,esk11_0)
| ~ subset(esk10_0,subset_complement(esk9_0,esk11_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_71,negated_conjecture,
( subset(esk10_0,X1)
| in(esk1_2(esk10_0,X1),subset_complement(esk9_0,esk11_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).
cnf(c_0_72,negated_conjecture,
~ subset(esk10_0,subset_complement(esk9_0,esk11_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_46])]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_71]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU170+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:50:26 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 49.14/33.80 % Version : CSE_E---1.7
% 49.14/33.80 % Problem : theBenchmark.p
% 49.14/33.80 % SZS status Theorem for theBenchmark.p
% 49.14/33.80 % SZS output start CNFRefutation
% See solution above
% 49.37/34.10 % Total time : 22.417s
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