%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET994+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 : n007.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 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 22 unt; 0 def)
% Number of atoms : 131 ( 42 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 127 ( 49 ~; 40 |; 23 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 5 sgn 29 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(t16_funct_1,conjecture,
! [X1] :
( ! [X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_dom(X2) = X1
& relation_dom(X3) = X1 )
=> X2 = X3 ) ) )
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_funct_1) ).
fof(spc0_boole,axiom,
empty(n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc0_boole) ).
fof(s3_funct_1__e7_14__funct_1,axiom,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = n1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e7_14__funct_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(s3_funct_1__e4_14__funct_1,axiom,
! [X1] :
? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e4_14__funct_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_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(spc1_boole,axiom,
~ empty(n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',spc1_boole) ).
fof(c_0_10,plain,
! [X92] :
( ~ empty(X92)
| X92 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ! [X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( ( relation_dom(X2) = X1
& relation_dom(X3) = X1 )
=> X2 = X3 ) ) )
=> X1 = empty_set ),
inference(assume_negation,[status(cth)],[t16_funct_1]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
empty(n0),
inference(split_conjunct,[status(thm)],[spc0_boole]) ).
fof(c_0_14,negated_conjecture,
! [X78,X79] :
( ( ~ relation(X78)
| ~ function(X78)
| ~ relation(X79)
| ~ function(X79)
| relation_dom(X78) != esk12_0
| relation_dom(X79) != esk12_0
| X78 = X79 )
& esk12_0 != empty_set ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_15,plain,
! [X74,X76] :
( relation(esk11_1(X74))
& function(esk11_1(X74))
& relation_dom(esk11_1(X74)) = X74
& ( ~ in(X76,X74)
| apply(esk11_1(X74),X76) = n1 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e7_14__funct_1])])])]) ).
cnf(c_0_16,plain,
empty_set = n0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,plain,
! [X59] :
( ( empty(relation_dom(X59))
| ~ empty(X59) )
& ( relation(relation_dom(X59))
| ~ empty(X59) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
cnf(c_0_18,negated_conjecture,
( X1 = X2
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| relation_dom(X1) != esk12_0
| relation_dom(X2) != esk12_0 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
relation_dom(esk11_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
relation(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
function(esk11_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X71,X73] :
( relation(esk10_1(X71))
& function(esk10_1(X71))
& relation_dom(esk10_1(X71)) = X71
& ( ~ in(X73,X71)
| apply(esk10_1(X71),X73) = n0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s3_funct_1__e4_14__funct_1])])])]) ).
fof(c_0_23,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
cnf(c_0_24,plain,
( X1 = n0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_25,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( X1 = esk11_1(esk12_0)
| relation_dom(X1) != esk12_0
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])])]) ).
cnf(c_0_27,plain,
relation_dom(esk10_1(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
relation(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
function(esk10_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X58] :
( empty(X58)
| ~ relation(X58)
| ~ empty(relation_dom(X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_31,plain,
( relation_dom(X1) = n0
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
esk12_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_33,plain,
( apply(esk10_1(X2),X1) = n0
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_34,negated_conjecture,
esk10_1(esk12_0) = esk11_1(esk12_0),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])])]) ).
fof(c_0_35,plain,
! [X82,X83] :
( ~ element(X82,X83)
| empty(X83)
| in(X82,X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_36,plain,
! [X55] : element(esk1_1(X55),X55),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_37,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( n0 = X1
| ~ empty(esk10_1(X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
esk12_0 != n0,
inference(rw,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_40,plain,
( apply(esk11_1(X2),X1) = n1
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,negated_conjecture,
( apply(esk11_1(esk12_0),X1) = n0
| ~ in(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( empty(esk10_1(X1))
| ~ empty(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_28])]) ).
cnf(c_0_45,negated_conjecture,
~ empty(esk11_1(esk12_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_34]),c_0_39]) ).
fof(c_0_46,plain,
~ empty(n1),
inference(fof_simplification,[status(thm)],[spc1_boole]) ).
cnf(c_0_47,negated_conjecture,
( n1 = n0
| ~ in(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( empty(X1)
| in(esk1_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
~ empty(esk12_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_34]),c_0_45]) ).
cnf(c_0_50,plain,
~ empty(n1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,negated_conjecture,
n1 = n0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_52,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET994+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
% 0.15/0.32 % Computer : n007.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
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:40:24 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.368s
%------------------------------------------------------------------------------