%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU159+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n012.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 05:10:51 PM UTC 2026
% Result : Theorem 1.46s 1.72s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 90 ( 29 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 96 ( 35 ~; 44 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 58 ( 6 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_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(t38_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(c_0_3,plain,
! [X218,X219,X220,X221,X222,X223,X224,X225] :
( ( ~ in(X221,X220)
| X221 = X218
| X221 = X219
| X220 != unordered_pair(X218,X219) )
& ( X222 != X218
| in(X222,X220)
| X220 != unordered_pair(X218,X219) )
& ( X222 != X219
| in(X222,X220)
| X220 != unordered_pair(X218,X219) )
& ( esk4_3(X223,X224,X225) != X223
| ~ in(esk4_3(X223,X224,X225),X225)
| X225 = unordered_pair(X223,X224) )
& ( esk4_3(X223,X224,X225) != X224
| ~ in(esk4_3(X223,X224,X225),X225)
| X225 = unordered_pair(X223,X224) )
& ( in(esk4_3(X223,X224,X225),X225)
| esk4_3(X223,X224,X225) = X223
| esk4_3(X223,X224,X225) = X224
| X225 = unordered_pair(X223,X224) ) ),
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_tarski])])])])])]) ).
fof(c_0_4,plain,
! [X253,X254,X255,X256,X257] :
( ( ~ subset(X253,X254)
| ~ in(X255,X253)
| in(X255,X254) )
& ( in(esk11_2(X256,X257),X256)
| subset(X256,X257) )
& ( ~ in(esk11_2(X256,X257),X257)
| subset(X256,X257) ) ),
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_5,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[t38_zfmisc_1]) ).
cnf(c_0_7,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_5])]) ).
fof(c_0_9,negated_conjecture,
( ( ~ subset(unordered_pair(esk20_0,esk21_0),esk22_0)
| ~ in(esk20_0,esk22_0)
| ~ in(esk21_0,esk22_0) )
& ( in(esk20_0,esk22_0)
| subset(unordered_pair(esk20_0,esk21_0),esk22_0) )
& ( in(esk21_0,esk22_0)
| subset(unordered_pair(esk20_0,esk21_0),esk22_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_10,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X3,X1),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( in(esk21_0,esk22_0)
| subset(unordered_pair(esk20_0,esk21_0),esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_14,negated_conjecture,
( ~ subset(unordered_pair(esk20_0,esk21_0),esk22_0)
| ~ in(esk20_0,esk22_0)
| ~ in(esk21_0,esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
in(esk21_0,esk22_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( in(X1,X2)
| ~ subset(unordered_pair(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( in(esk20_0,esk22_0)
| subset(unordered_pair(esk20_0,esk21_0),esk22_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( ~ subset(unordered_pair(esk20_0,esk21_0),esk22_0)
| ~ in(esk20_0,esk22_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
in(esk20_0,esk22_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,negated_conjecture,
~ subset(unordered_pair(esk20_0,esk21_0),esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_22,plain,
( in(esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_23,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
in(esk11_2(unordered_pair(esk20_0,esk21_0),esk22_0),unordered_pair(esk20_0,esk21_0)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_26,negated_conjecture,
( esk11_2(unordered_pair(esk20_0,esk21_0),esk22_0) = esk21_0
| esk11_2(unordered_pair(esk20_0,esk21_0),esk22_0) = esk20_0 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
esk11_2(unordered_pair(esk20_0,esk21_0),esk22_0) = esk20_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_15])]),c_0_21]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_27]),c_0_19])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU159+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.06/0.25 % Computer : n012.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 5 02:46:16 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % start to proof: theBenchmark
% 1.46/1.72 % Version : CSE_E---1.7
% 1.46/1.72 % Problem : theBenchmark.p
% 1.46/1.72 % SZS status Theorem for theBenchmark.p
% 1.46/1.72 % SZS output start CNFRefutation
% See solution above
% 1.46/1.72 % Total time : 1.362s
%------------------------------------------------------------------------------