%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET974+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 : n029.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 05:09:04 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 53 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 29 ~; 17 |; 13 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 66 ( 11 sgn 31 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t4_xboole_0,axiom,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(t104_zfmisc_1,axiom,
! [X1,X2,X3,X4,X5] :
~ ( in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5)))
& ! [X6,X7] :
~ ( X1 = ordered_pair(X6,X7)
& in(X6,set_intersection2(X2,X4))
& in(X7,set_intersection2(X3,X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
fof(t127_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ( disjoint(X1,X2)
| disjoint(X3,X4) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(c_0_3,plain,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_4,plain,
! [X65,X66,X68,X69,X70] :
( ( disjoint(X65,X66)
| in(esk9_2(X65,X66),set_intersection2(X65,X66)) )
& ( ~ in(X70,set_intersection2(X68,X69))
| ~ disjoint(X68,X69) ) ),
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_3])])])])]) ).
fof(c_0_5,plain,
! [X54,X55,X56,X57,X58] :
( ( X54 = ordered_pair(esk3_5(X54,X55,X56,X57,X58),esk4_5(X54,X55,X56,X57,X58))
| ~ in(X54,set_intersection2(cartesian_product2(X55,X56),cartesian_product2(X57,X58))) )
& ( in(esk3_5(X54,X55,X56,X57,X58),set_intersection2(X55,X57))
| ~ in(X54,set_intersection2(cartesian_product2(X55,X56),cartesian_product2(X57,X58))) )
& ( in(esk4_5(X54,X55,X56,X57,X58),set_intersection2(X56,X58))
| ~ in(X54,set_intersection2(cartesian_product2(X55,X56),cartesian_product2(X57,X58))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t104_zfmisc_1])])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( disjoint(X1,X2)
| disjoint(X3,X4) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(assume_negation,[status(cth)],[t127_zfmisc_1]) ).
cnf(c_0_7,plain,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( in(esk3_5(X1,X2,X3,X4,X5),set_intersection2(X2,X4))
| ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,negated_conjecture,
( ( disjoint(esk5_0,esk6_0)
| disjoint(esk7_0,esk8_0) )
& ~ disjoint(cartesian_product2(esk5_0,esk7_0),cartesian_product2(esk6_0,esk8_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_10,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(cartesian_product2(X1,X4),cartesian_product2(X2,X5))) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( disjoint(X1,X2)
| in(esk9_2(X1,X2),set_intersection2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,plain,
( in(esk4_5(X1,X2,X3,X4,X5),set_intersection2(X3,X5))
| ~ in(X1,set_intersection2(cartesian_product2(X2,X3),cartesian_product2(X4,X5))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
~ disjoint(cartesian_product2(esk5_0,esk7_0),cartesian_product2(esk6_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ disjoint(X1,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ disjoint(X1,X2)
| ~ in(X3,set_intersection2(cartesian_product2(X4,X1),cartesian_product2(X5,X2))) ),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( disjoint(esk5_0,esk6_0)
| disjoint(esk7_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
~ disjoint(esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ disjoint(X2,X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_19,negated_conjecture,
disjoint(esk7_0,esk8_0),
inference(sr,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET974+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 : n029.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 02:42:14 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 : 1.368s
%------------------------------------------------------------------------------