%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET992+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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 : n002.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 1.38s 1.76s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 16 unt; 0 def)
% Number of atoms : 155 ( 56 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 182 ( 75 ~; 81 |; 16 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 77 ( 2 sgn 33 !; 2 ?)
% 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(t14_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_dom(X2) = singleton(X1)
=> relation_rng(X2) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_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(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(c_0_6,plain,
! [X62,X63,X64,X65,X66,X67] :
( ( ~ in(X64,X63)
| X64 = X62
| X63 != singleton(X62) )
& ( X65 != X62
| in(X65,X63)
| X63 != singleton(X62) )
& ( ~ in(esk1_2(X66,X67),X67)
| esk1_2(X66,X67) != X66
| X67 = singleton(X66) )
& ( in(esk1_2(X66,X67),X67)
| esk1_2(X66,X67) = X66
| X67 = singleton(X66) ) ),
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_7,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation_dom(X2) = singleton(X1)
=> relation_rng(X2) = singleton(apply(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t14_funct_1]) ).
cnf(c_0_8,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,negated_conjecture,
( relation(esk15_0)
& function(esk15_0)
& relation_dom(esk15_0) = singleton(esk14_0)
& relation_rng(esk15_0) != singleton(apply(esk15_0,esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X69,X70,X71,X73,X74,X75,X77] :
( ( in(esk2_3(X69,X70,X71),relation_dom(X69))
| ~ in(X71,X70)
| X70 != relation_rng(X69)
| ~ relation(X69)
| ~ function(X69) )
& ( X71 = apply(X69,esk2_3(X69,X70,X71))
| ~ in(X71,X70)
| X70 != relation_rng(X69)
| ~ relation(X69)
| ~ function(X69) )
& ( ~ in(X74,relation_dom(X69))
| X73 != apply(X69,X74)
| in(X73,X70)
| X70 != relation_rng(X69)
| ~ relation(X69)
| ~ function(X69) )
& ( ~ in(esk3_2(X69,X75),X75)
| ~ in(X77,relation_dom(X69))
| esk3_2(X69,X75) != apply(X69,X77)
| X75 = relation_rng(X69)
| ~ relation(X69)
| ~ function(X69) )
& ( in(esk4_2(X69,X75),relation_dom(X69))
| in(esk3_2(X69,X75),X75)
| X75 = relation_rng(X69)
| ~ relation(X69)
| ~ function(X69) )
& ( esk3_2(X69,X75) = apply(X69,esk4_2(X69,X75))
| in(esk3_2(X69,X75),X75)
| X75 = relation_rng(X69)
| ~ relation(X69)
| ~ function(X69) ) ),
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_11,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
relation_dom(esk15_0) = singleton(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( in(esk2_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( X1 = apply(X2,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( X1 = esk14_0
| ~ in(X1,relation_dom(esk15_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( in(esk2_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( apply(X1,esk2_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( esk2_3(esk15_0,relation_rng(esk15_0),X1) = esk14_0
| ~ in(X1,relation_rng(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_21,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_10]) ).
cnf(c_0_22,negated_conjecture,
( apply(esk15_0,esk14_0) = X1
| ~ in(X1,relation_rng(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]),c_0_18])]) ).
cnf(c_0_23,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_21])]) ).
cnf(c_0_24,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_25,negated_conjecture,
( apply(esk15_0,esk14_0) = apply(esk15_0,X1)
| ~ in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_17]),c_0_18])]) ).
cnf(c_0_26,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
fof(c_0_27,plain,
! [X102,X103] :
( ~ element(X102,X103)
| empty(X103)
| in(X102,X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_28,plain,
! [X79] : element(esk5_1(X79),X79),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_29,plain,
! [X116,X117] :
( ~ in(X116,X117)
| ~ empty(X117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_30,negated_conjecture,
( in(apply(esk15_0,esk14_0),relation_rng(esk15_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_23,c_0_25]),c_0_17]),c_0_18])]) ).
cnf(c_0_31,negated_conjecture,
in(esk14_0,relation_dom(esk15_0)),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_32,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
element(esk5_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
in(apply(esk15_0,esk14_0),relation_rng(esk15_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( empty(X1)
| in(esk5_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
~ empty(relation_rng(esk15_0)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
apply(esk15_0,esk14_0) = esk5_1(relation_rng(esk15_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_36]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
( esk5_1(relation_rng(esk15_0)) = X1
| ~ in(X1,relation_rng(esk15_0)) ),
inference(rw,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_40,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_41,negated_conjecture,
relation_rng(esk15_0) != singleton(apply(esk15_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_42,negated_conjecture,
( esk5_1(relation_rng(esk15_0)) = esk1_2(X1,relation_rng(esk15_0))
| esk1_2(X1,relation_rng(esk15_0)) = X1
| relation_rng(esk15_0) = singleton(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
singleton(esk5_1(relation_rng(esk15_0))) != relation_rng(esk15_0),
inference(rw,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_44,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_45,negated_conjecture,
esk1_2(esk5_1(relation_rng(esk15_0)),relation_rng(esk15_0)) = esk5_1(relation_rng(esk15_0)),
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_42])]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
in(esk5_1(relation_rng(esk15_0)),relation_rng(esk15_0)),
inference(rw,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET992+1 : TPTP v9.2.1. Bugfixed v4.0.0.
% 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
% 0.14/0.33 % Computer : n002.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:41:16 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.38/1.76 % Version : CSE_E---1.7
% 1.38/1.76 % Problem : theBenchmark.p
% 1.38/1.76 % SZS status Theorem for theBenchmark.p
% 1.38/1.76 % SZS output start CNFRefutation
% See solution above
% 1.38/1.76 % Total time : 1.370s
%------------------------------------------------------------------------------