%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET995+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 : n008.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 05:09:06 PM UTC 2026
% Result : Theorem 1.16s 1.87s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 159 ( 66 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 204 ( 78 ~; 82 |; 29 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 30 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t17_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_dom(X2) = relation_dom(X3)
& relation_rng(X2) = singleton(X1)
& relation_rng(X3) = singleton(X1) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t9_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( ( relation_dom(X1) = relation_dom(X2)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_funct_1) ).
fof(c_0_4,plain,
! [X63,X64,X65,X66,X67,X68] :
( ( ~ in(X65,X64)
| X65 = X63
| X64 != singleton(X63) )
& ( X66 != X63
| in(X66,X64)
| X64 != singleton(X63) )
& ( ~ in(esk1_2(X67,X68),X68)
| esk1_2(X67,X68) != X67
| X68 = singleton(X67) )
& ( in(esk1_2(X67,X68),X68)
| esk1_2(X67,X68) = X67
| X68 = singleton(X67) ) ),
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)],[d1_tarski])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_dom(X2) = relation_dom(X3)
& relation_rng(X2) = singleton(X1)
& relation_rng(X3) = singleton(X1) )
=> X2 = X3 ) ) ),
inference(assume_negation,[status(cth)],[t17_funct_1]) ).
cnf(c_0_6,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
( relation(esk15_0)
& function(esk15_0)
& relation(esk16_0)
& function(esk16_0)
& relation_dom(esk15_0) = relation_dom(esk16_0)
& relation_rng(esk15_0) = singleton(esk14_0)
& relation_rng(esk16_0) = singleton(esk14_0)
& esk15_0 != esk16_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X70,X71,X72,X74,X75,X76,X78] :
( ( in(esk2_3(X70,X71,X72),relation_dom(X70))
| ~ in(X72,X71)
| X71 != relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( X72 = apply(X70,esk2_3(X70,X71,X72))
| ~ in(X72,X71)
| X71 != relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( ~ in(X75,relation_dom(X70))
| X74 != apply(X70,X75)
| in(X74,X71)
| X71 != relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( ~ in(esk3_2(X70,X76),X76)
| ~ in(X78,relation_dom(X70))
| esk3_2(X70,X76) != apply(X70,X78)
| X76 = relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( in(esk4_2(X70,X76),relation_dom(X70))
| in(esk3_2(X70,X76),X76)
| X76 = relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) )
& ( esk3_2(X70,X76) = apply(X70,esk4_2(X70,X76))
| in(esk3_2(X70,X76),X76)
| X76 = relation_rng(X70)
| ~ relation(X70)
| ~ function(X70) ) ),
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)],[d5_funct_1])])])])])]) ).
cnf(c_0_9,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
relation_rng(esk15_0) = singleton(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(X3,X4)
| ~ in(X1,relation_dom(X2))
| X3 != apply(X2,X1)
| X4 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X119,X120] :
( ( in(esk17_2(X119,X120),relation_dom(X119))
| relation_dom(X119) != relation_dom(X120)
| X119 = X120
| ~ relation(X120)
| ~ function(X120)
| ~ relation(X119)
| ~ function(X119) )
& ( apply(X119,esk17_2(X119,X120)) != apply(X120,esk17_2(X119,X120))
| relation_dom(X119) != relation_dom(X120)
| X119 = X120
| ~ relation(X120)
| ~ function(X120)
| ~ relation(X119)
| ~ function(X119) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_funct_1])])])])]) ).
cnf(c_0_13,negated_conjecture,
( X1 = esk14_0
| ~ in(X1,relation_rng(esk15_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( in(apply(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_11])]) ).
cnf(c_0_15,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
relation_rng(esk16_0) = singleton(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,plain,
( X1 = X2
| apply(X1,esk17_2(X1,X2)) != apply(X2,esk17_2(X1,X2))
| relation_dom(X1) != relation_dom(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( apply(esk15_0,X1) = esk14_0
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_20,plain,
( in(esk17_2(X1,X2),relation_dom(X1))
| X1 = X2
| relation_dom(X1) != relation_dom(X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
relation_dom(esk15_0) = relation_dom(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
relation_rng(esk16_0) = relation_rng(esk15_0),
inference(rw,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( X1 = esk15_0
| apply(X1,esk17_2(X1,esk15_0)) != esk14_0
| relation_dom(X1) != relation_dom(esk15_0)
| ~ relation(X1)
| ~ function(X1)
| ~ in(esk17_2(X1,esk15_0),relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15]),c_0_16])]) ).
cnf(c_0_26,negated_conjecture,
( esk16_0 = X1
| in(esk17_2(esk16_0,X1),relation_dom(esk15_0))
| relation_dom(esk15_0) != relation_dom(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_27,negated_conjecture,
esk15_0 != esk16_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( in(apply(esk16_0,X1),relation_rng(esk15_0))
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_24]),c_0_22]),c_0_23]),c_0_21])]) ).
cnf(c_0_29,negated_conjecture,
apply(esk16_0,esk17_2(esk16_0,esk15_0)) != esk14_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_21]),c_0_22]),c_0_23]),c_0_15]),c_0_16])]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( apply(esk16_0,X1) = esk14_0
| ~ in(X1,relation_dom(esk15_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
~ in(esk17_2(esk16_0,esk15_0),relation_dom(esk15_0)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_15]),c_0_16])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : SET995+1 : TPTP v9.2.1. Released v3.2.0.
% 0.02/0.21 % 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
% 0.13/0.44 % Computer : n008.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8042.1875MB
% 0.13/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Tue May 5 02:40:59 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 1.16/1.87 % Version : CSE_E---1.7
% 1.16/1.87 % Problem : theBenchmark.p
% 1.16/1.87 % SZS status Theorem for theBenchmark.p
% 1.16/1.87 % SZS output start CNFRefutation
% See solution above
% 1.16/1.88 % Total time : 1.385s
%------------------------------------------------------------------------------