%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET653+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n010.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 05:08:14 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 116 ( 44 ~; 41 |; 8 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 3 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(p22,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(prove_relset_1_15,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ( subset(X1,X2)
=> ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_15) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ( subset(domain_of(X4),X2)
=> ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(c_0_6,plain,
! [X59,X60,X61] :
( ~ ilf_type(X59,set_type)
| ~ ilf_type(X60,set_type)
| ~ ilf_type(X61,set_type)
| ~ subset(X59,X60)
| ~ subset(X60,X61)
| subset(X59,X61) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
fof(c_0_7,plain,
! [X114] : ilf_type(X114,set_type),
inference(variable_rename,[status(thm)],[p22]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ( subset(X1,X2)
=> ilf_type(X4,relation_type(X2,X3)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_15]) ).
cnf(c_0_9,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
( ilf_type(esk10_0,set_type)
& ilf_type(esk11_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,relation_type(esk10_0,esk12_0))
& subset(esk10_0,esk11_0)
& ~ ilf_type(esk13_0,relation_type(esk11_0,esk12_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X62,X63,X64] :
( ( subset(domain_of(X64),X62)
| ~ ilf_type(X64,relation_type(X62,X63))
| ~ ilf_type(X63,set_type)
| ~ ilf_type(X62,set_type) )
& ( subset(range_of(X64),X63)
| ~ ilf_type(X64,relation_type(X62,X63))
| ~ ilf_type(X63,set_type)
| ~ ilf_type(X62,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]),c_0_10])]) ).
cnf(c_0_14,negated_conjecture,
subset(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X65,X66,X67,X68] :
( ~ ilf_type(X65,set_type)
| ~ ilf_type(X66,set_type)
| ~ ilf_type(X67,set_type)
| ~ ilf_type(X68,relation_type(X65,X67))
| ~ subset(domain_of(X68),X66)
| ilf_type(X68,relation_type(X66,X67)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])]) ).
cnf(c_0_17,negated_conjecture,
( subset(X1,esk11_0)
| ~ subset(X1,esk10_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_10]),c_0_10])]) ).
cnf(c_0_19,negated_conjecture,
ilf_type(esk13_0,relation_type(esk10_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_20,plain,
! [X88] :
( ~ ilf_type(X88,set_type)
| subset(X88,X88) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])]) ).
cnf(c_0_21,plain,
( ilf_type(X4,relation_type(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,relation_type(X1,X3))
| ~ subset(domain_of(X4),X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( subset(X1,esk11_0)
| ~ subset(X2,esk10_0)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
subset(domain_of(esk13_0),esk10_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( subset(X1,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X4,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_10]),c_0_10]),c_0_10])]) ).
cnf(c_0_26,negated_conjecture,
( subset(X1,esk11_0)
| ~ subset(X1,domain_of(esk13_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
subset(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_10])]) ).
cnf(c_0_28,negated_conjecture,
~ ilf_type(esk13_0,relation_type(esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( ilf_type(esk13_0,relation_type(X1,esk12_0))
| ~ subset(domain_of(esk13_0),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_30,negated_conjecture,
subset(domain_of(esk13_0),esk11_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET653+3 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.15/0.32 % Computer : n010.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:30:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.369s
%------------------------------------------------------------------------------