%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU166+3 : TPTP v9.2.1. Released v3.2.0.
% 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 : n031.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 05:10:54 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 133 ( 31 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 156 ( 66 ~; 70 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-4 aty)
% Number of variables : 126 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_zfmisc_1,axiom,
! [X1,X2,X3] :
( X3 = cartesian_product2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5,X6] :
( in(X5,X1)
& in(X6,X2)
& X4 = ordered_pair(X5,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t118_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_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(c_0_5,plain,
! [X35,X36,X37,X38,X41,X42,X43,X44,X45,X46,X48,X49] :
( ( in(esk1_4(X35,X36,X37,X38),X35)
| ~ in(X38,X37)
| X37 != cartesian_product2(X35,X36) )
& ( in(esk2_4(X35,X36,X37,X38),X36)
| ~ in(X38,X37)
| X37 != cartesian_product2(X35,X36) )
& ( X38 = ordered_pair(esk1_4(X35,X36,X37,X38),esk2_4(X35,X36,X37,X38))
| ~ in(X38,X37)
| X37 != cartesian_product2(X35,X36) )
& ( ~ in(X42,X35)
| ~ in(X43,X36)
| X41 != ordered_pair(X42,X43)
| in(X41,X37)
| X37 != cartesian_product2(X35,X36) )
& ( ~ in(esk3_3(X44,X45,X46),X46)
| ~ in(X48,X44)
| ~ in(X49,X45)
| esk3_3(X44,X45,X46) != ordered_pair(X48,X49)
| X46 = cartesian_product2(X44,X45) )
& ( in(esk4_3(X44,X45,X46),X44)
| in(esk3_3(X44,X45,X46),X46)
| X46 = cartesian_product2(X44,X45) )
& ( in(esk5_3(X44,X45,X46),X45)
| in(esk3_3(X44,X45,X46),X46)
| X46 = cartesian_product2(X44,X45) )
& ( esk3_3(X44,X45,X46) = ordered_pair(esk4_3(X44,X45,X46),esk5_3(X44,X45,X46))
| in(esk3_3(X44,X45,X46),X46)
| X46 = cartesian_product2(X44,X45) ) ),
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)],[d2_zfmisc_1])])])])])]) ).
fof(c_0_6,plain,
! [X58,X59] : ordered_pair(X58,X59) = unordered_pair(unordered_pair(X58,X59),singleton(X58)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_7,plain,
( in(X5,X6)
| ~ in(X1,X2)
| ~ in(X3,X4)
| X5 != ordered_pair(X1,X3)
| X6 != cartesian_product2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( in(X5,X6)
| X6 != cartesian_product2(X2,X4)
| X5 != unordered_pair(unordered_pair(X1,X3),singleton(X1))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_10,plain,
! [X33,X34] : unordered_pair(X33,X34) = unordered_pair(X34,X33),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_11,plain,
( X1 = ordered_pair(esk1_4(X2,X3,X4,X1),esk2_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != cartesian_product2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( X1 = unordered_pair(unordered_pair(esk1_4(X2,X3,X4,X1),esk2_4(X2,X3,X4,X1)),singleton(esk1_4(X2,X3,X4,X1)))
| X4 != cartesian_product2(X2,X3)
| ~ in(X1,X4) ),
inference(rw,[status(thm)],[c_0_11,c_0_8]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
inference(assume_negation,[status(cth)],[t118_zfmisc_1]) ).
cnf(c_0_16,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),cartesian_product2(X3,X4))
| ~ in(X2,X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( unordered_pair(singleton(esk1_4(X1,X2,cartesian_product2(X1,X2),X3)),unordered_pair(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),esk2_4(X1,X2,cartesian_product2(X1,X2),X3))) = X3
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_13])]) ).
cnf(c_0_18,plain,
( in(esk2_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_19,plain,
! [X52,X53,X54,X55,X56] :
( ( ~ subset(X52,X53)
| ~ in(X54,X52)
| in(X54,X53) )
& ( in(esk6_2(X55,X56),X55)
| subset(X55,X56) )
& ( ~ in(esk6_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_20,negated_conjecture,
( subset(esk9_0,esk10_0)
& ( ~ subset(cartesian_product2(esk9_0,esk11_0),cartesian_product2(esk10_0,esk11_0))
| ~ subset(cartesian_product2(esk11_0,esk9_0),cartesian_product2(esk11_0,esk10_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_21,plain,
( in(X1,cartesian_product2(X2,X3))
| ~ in(esk2_4(X4,X5,cartesian_product2(X4,X5),X1),X3)
| ~ in(esk1_4(X4,X5,cartesian_product2(X4,X5),X1),X2)
| ~ in(X1,cartesian_product2(X4,X5)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( in(esk2_4(X1,X2,cartesian_product2(X1,X2),X3),X2)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
subset(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( in(X1,cartesian_product2(X2,X3))
| ~ in(esk1_4(X4,X3,cartesian_product2(X4,X3),X1),X2)
| ~ in(X1,cartesian_product2(X4,X3)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( in(X1,esk10_0)
| ~ in(X1,esk9_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
( in(esk1_4(X1,X2,X3,X4),X1)
| ~ in(X4,X3)
| X3 != cartesian_product2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,cartesian_product2(esk10_0,X2))
| ~ in(esk1_4(X3,X2,cartesian_product2(X3,X2),X1),esk9_0)
| ~ in(X1,cartesian_product2(X3,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( in(esk1_4(X1,X2,cartesian_product2(X1,X2),X3),X1)
| ~ in(X3,cartesian_product2(X1,X2)) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,cartesian_product2(X2,esk10_0))
| ~ in(esk2_4(X3,X4,cartesian_product2(X3,X4),X1),esk9_0)
| ~ in(esk1_4(X3,X4,cartesian_product2(X3,X4),X1),X2)
| ~ in(X1,cartesian_product2(X3,X4)) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_31,plain,
( subset(X1,X2)
| ~ in(esk6_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( in(X1,cartesian_product2(esk10_0,X2))
| ~ in(X1,cartesian_product2(esk9_0,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
( in(X1,cartesian_product2(X2,esk10_0))
| ~ in(esk1_4(X3,esk9_0,cartesian_product2(X3,esk9_0),X1),X2)
| ~ in(X1,cartesian_product2(X3,esk9_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
( subset(X1,cartesian_product2(esk10_0,X2))
| ~ in(esk6_2(X1,cartesian_product2(esk10_0,X2)),cartesian_product2(esk9_0,X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( in(esk6_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_36,negated_conjecture,
( in(X1,cartesian_product2(X2,esk10_0))
| ~ in(X1,cartesian_product2(X2,esk9_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
( ~ subset(cartesian_product2(esk9_0,esk11_0),cartesian_product2(esk10_0,esk11_0))
| ~ subset(cartesian_product2(esk11_0,esk9_0),cartesian_product2(esk11_0,esk10_0)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_38,negated_conjecture,
subset(cartesian_product2(esk9_0,X1),cartesian_product2(esk10_0,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( subset(X1,cartesian_product2(X2,esk10_0))
| ~ in(esk6_2(X1,cartesian_product2(X2,esk10_0)),cartesian_product2(X2,esk9_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
~ subset(cartesian_product2(esk11_0,esk9_0),cartesian_product2(esk11_0,esk10_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
subset(cartesian_product2(X1,esk9_0),cartesian_product2(X1,esk10_0)),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU166+3 : TPTP v9.2.1. Released v3.2.0.
% 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 : n031.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 02:47:54 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------