%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET956+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 05:09:02 PM UTC 2026
% Result : Theorem 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 72 ( 11 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 75 ( 30 ~; 27 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 72 ( 2 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t109_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,cartesian_product2(X2,X3))
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
=> in(ordered_pair(X5,X6),X4) ) )
=> subset(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t103_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
~ ( subset(X1,cartesian_product2(X2,X3))
& in(X4,X1)
& ! [X5,X6] :
~ ( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,cartesian_product2(X2,X3))
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
=> in(ordered_pair(X5,X6),X4) ) )
=> subset(X1,X4) ),
inference(assume_negation,[status(cth)],[t109_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
! [X61,X62] :
( subset(esk6_0,cartesian_product2(esk7_0,esk8_0))
& ( ~ in(ordered_pair(X61,X62),esk6_0)
| in(ordered_pair(X61,X62),esk9_0) )
& ~ subset(esk6_0,esk9_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X44,X45] : ordered_pair(X44,X45) = unordered_pair(unordered_pair(X44,X45),singleton(X44)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X51,X52,X53,X54] :
( ( in(esk4_4(X51,X52,X53,X54),X52)
| ~ subset(X51,cartesian_product2(X52,X53))
| ~ in(X54,X51) )
& ( in(esk5_4(X51,X52,X53,X54),X53)
| ~ subset(X51,cartesian_product2(X52,X53))
| ~ in(X54,X51) )
& ( X54 = ordered_pair(esk4_4(X51,X52,X53,X54),esk5_4(X51,X52,X53,X54))
| ~ subset(X51,cartesian_product2(X52,X53))
| ~ in(X54,X51) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t103_zfmisc_1])])])]) ).
cnf(c_0_9,negated_conjecture,
( in(ordered_pair(X1,X2),esk9_0)
| ~ in(ordered_pair(X1,X2),esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X36,X37] : unordered_pair(X36,X37) = unordered_pair(X37,X36),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( X1 = ordered_pair(esk4_4(X2,X3,X4,X1),esk5_4(X2,X3,X4,X1))
| ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk9_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk6_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( X1 = unordered_pair(unordered_pair(esk4_4(X2,X3,X4,X1),esk5_4(X2,X3,X4,X1)),singleton(esk4_4(X2,X3,X4,X1)))
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk9_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk6_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( unordered_pair(singleton(esk4_4(X1,X2,X3,X4)),unordered_pair(esk4_4(X1,X2,X3,X4),esk5_4(X1,X2,X3,X4))) = X4
| ~ subset(X1,cartesian_product2(X2,X3))
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
fof(c_0_18,plain,
! [X38,X39,X40,X41,X42] :
( ( ~ subset(X38,X39)
| ~ in(X40,X38)
| in(X40,X39) )
& ( in(esk1_2(X41,X42),X41)
| subset(X41,X42) )
& ( ~ in(esk1_2(X41,X42),X42)
| subset(X41,X42) ) ),
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])])])])])]) ).
cnf(c_0_19,negated_conjecture,
( in(X1,esk9_0)
| ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,esk6_0)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
subset(esk6_0,cartesian_product2(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( in(X1,esk9_0)
| ~ in(X1,esk6_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( subset(X1,esk9_0)
| ~ in(esk1_2(X1,esk9_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,negated_conjecture,
~ subset(esk6_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET956+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.32 % Computer : n005.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:39:45 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Theorem for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------