%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET958+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 : n014.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 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 53 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 51 ( 21 ~; 16 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t111_zfmisc_1,conjecture,
! [X1,X2] :
( ( ! [X3] :
~ ( in(X3,X1)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) )
=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t111_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(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_4,negated_conjecture,
~ ! [X1,X2] :
( ( ! [X3] :
~ ( in(X3,X1)
& ! [X4,X5] : X3 != ordered_pair(X4,X5) )
& ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) )
=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[t111_zfmisc_1]) ).
fof(c_0_5,negated_conjecture,
! [X47,X50,X51] :
( ( ~ in(X47,esk4_0)
| X47 = ordered_pair(esk6_1(X47),esk7_1(X47)) )
& ( ~ in(ordered_pair(X50,X51),esk4_0)
| in(ordered_pair(X50,X51),esk5_0) )
& ~ subset(esk4_0,esk5_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X38,X39] : ordered_pair(X38,X39) = unordered_pair(unordered_pair(X38,X39),singleton(X38)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_7,negated_conjecture,
( in(ordered_pair(X1,X2),esk5_0)
| ~ in(ordered_pair(X1,X2),esk4_0) ),
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]) ).
fof(c_0_9,plain,
! [X30,X31] : unordered_pair(X30,X31) = unordered_pair(X31,X30),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_10,negated_conjecture,
( X1 = ordered_pair(esk6_1(X1),esk7_1(X1))
| ~ in(X1,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk5_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( X1 = unordered_pair(unordered_pair(esk6_1(X1),esk7_1(X1)),singleton(esk6_1(X1)))
| ~ in(X1,esk4_0) ),
inference(rw,[status(thm)],[c_0_10,c_0_8]) ).
fof(c_0_14,plain,
! [X32,X33,X34,X35,X36] :
( ( ~ subset(X32,X33)
| ~ in(X34,X32)
| in(X34,X33) )
& ( in(esk1_2(X35,X36),X35)
| subset(X35,X36) )
& ( ~ in(esk1_2(X35,X36),X36)
| subset(X35,X36) ) ),
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_15,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk5_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk4_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( unordered_pair(singleton(esk6_1(X1)),unordered_pair(esk6_1(X1),esk7_1(X1))) = X1
| ~ in(X1,esk4_0) ),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( subset(X1,esk5_0)
| ~ in(esk1_2(X1,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
~ subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET958+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n014.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 02:57:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------