%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU072+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n031.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 05:10:35 PM UTC 2026
% Result : Theorem 173.44s 124.24s
% Output : CNFRefutation 174.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 11 unt; 0 def)
% Number of atoms : 191 ( 63 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 233 ( 91 ~; 103 |; 23 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 69 ( 1 sgn 40 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t153_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] : subset(relation_inverse_image(X1,relation_image(X1,X2)),X2)
=> one_to_one(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
fof(t39_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(t117_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(t142_funct_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( in(X1,relation_rng(X2))
<=> relation_inverse_image(X2,singleton(X1)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_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/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(d8_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
& in(X3,relation_dom(X1))
& apply(X1,X2) = apply(X1,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(t6_zfmisc_1,axiom,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] : subset(relation_inverse_image(X1,relation_image(X1,X2)),X2)
=> one_to_one(X1) ) ),
inference(assume_negation,[status(cth)],[t153_funct_1]) ).
fof(c_0_9,plain,
! [X117,X118] :
( ( ~ subset(X117,singleton(X118))
| X117 = empty_set
| X117 = singleton(X118) )
& ( X117 != empty_set
| subset(X117,singleton(X118)) )
& ( X117 != singleton(X118)
| subset(X117,singleton(X118)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
fof(c_0_10,negated_conjecture,
! [X112] :
( relation(esk17_0)
& function(esk17_0)
& subset(relation_inverse_image(esk17_0,relation_image(esk17_0,X112)),X112)
& ~ one_to_one(esk17_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_11,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
subset(relation_inverse_image(esk17_0,relation_image(esk17_0,X1)),X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( relation_inverse_image(esk17_0,relation_image(esk17_0,singleton(X1))) = singleton(X1)
| relation_inverse_image(esk17_0,relation_image(esk17_0,singleton(X1))) = empty_set ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_14,plain,
! [X107,X108] :
( ~ relation(X108)
| ~ function(X108)
| ~ in(X107,relation_dom(X108))
| relation_image(X108,singleton(X107)) = singleton(apply(X108,X107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t117_funct_1])]) ).
fof(c_0_15,plain,
! [X109,X110] :
( ( ~ in(X109,relation_rng(X110))
| relation_inverse_image(X110,singleton(X109)) != empty_set
| ~ relation(X110) )
& ( relation_inverse_image(X110,singleton(X109)) = empty_set
| in(X109,relation_rng(X110))
| ~ relation(X110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t142_funct_1])])]) ).
cnf(c_0_16,negated_conjecture,
( relation_inverse_image(esk17_0,relation_image(esk17_0,singleton(X1))) = empty_set
| singleton(X1) != empty_set ),
inference(ef,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( relation_image(X1,singleton(X2)) = singleton(apply(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_20,plain,
! [X71,X72,X73,X75,X76,X77,X79] :
( ( in(esk1_3(X71,X72,X73),relation_dom(X71))
| ~ in(X73,X72)
| X72 != relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( X73 = apply(X71,esk1_3(X71,X72,X73))
| ~ in(X73,X72)
| X72 != relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( ~ in(X76,relation_dom(X71))
| X75 != apply(X71,X76)
| in(X75,X72)
| X72 != relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( ~ in(esk2_2(X71,X77),X77)
| ~ in(X79,relation_dom(X71))
| esk2_2(X71,X77) != apply(X71,X79)
| X77 = relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( in(esk3_2(X71,X77),relation_dom(X71))
| in(esk2_2(X71,X77),X77)
| X77 = relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) )
& ( esk2_2(X71,X77) = apply(X71,esk3_2(X71,X77))
| in(esk2_2(X71,X77),X77)
| X77 = relation_rng(X71)
| ~ relation(X71)
| ~ function(X71) ) ),
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])])])])])]) ).
fof(c_0_21,plain,
! [X81,X82,X83] :
( ( ~ one_to_one(X81)
| ~ in(X82,relation_dom(X81))
| ~ in(X83,relation_dom(X81))
| apply(X81,X82) != apply(X81,X83)
| X82 = X83
| ~ relation(X81)
| ~ function(X81) )
& ( in(esk4_1(X81),relation_dom(X81))
| one_to_one(X81)
| ~ relation(X81)
| ~ function(X81) )
& ( in(esk5_1(X81),relation_dom(X81))
| one_to_one(X81)
| ~ relation(X81)
| ~ function(X81) )
& ( apply(X81,esk4_1(X81)) = apply(X81,esk5_1(X81))
| one_to_one(X81)
| ~ relation(X81)
| ~ function(X81) )
& ( esk4_1(X81) != esk5_1(X81)
| one_to_one(X81)
| ~ relation(X81)
| ~ function(X81) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_funct_1])])])])]) ).
cnf(c_0_22,plain,
( ~ in(X1,relation_rng(X2))
| relation_inverse_image(X2,singleton(X1)) != empty_set
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( relation_inverse_image(esk17_0,singleton(apply(esk17_0,X1))) = empty_set
| singleton(X1) != empty_set
| ~ in(X1,relation_dom(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_24,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_20]) ).
cnf(c_0_25,negated_conjecture,
( relation_inverse_image(esk17_0,singleton(apply(esk17_0,X1))) = singleton(X1)
| relation_inverse_image(esk17_0,singleton(apply(esk17_0,X1))) = empty_set
| ~ in(X1,relation_dom(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_17]),c_0_18]),c_0_19])]) ).
cnf(c_0_26,plain,
( in(esk5_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
~ one_to_one(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,negated_conjecture,
( singleton(X1) != empty_set
| ~ in(apply(esk17_0,X1),relation_rng(esk17_0))
| ~ in(X1,relation_dom(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18])]) ).
cnf(c_0_29,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_24])]) ).
cnf(c_0_30,plain,
( in(esk4_1(X1),relation_dom(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,negated_conjecture,
( relation_inverse_image(esk17_0,singleton(apply(esk17_0,esk5_1(esk17_0)))) = singleton(esk5_1(esk17_0))
| relation_inverse_image(esk17_0,singleton(apply(esk17_0,esk5_1(esk17_0)))) = empty_set ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18]),c_0_19])]),c_0_27]) ).
cnf(c_0_32,plain,
( apply(X1,esk4_1(X1)) = apply(X1,esk5_1(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,negated_conjecture,
( singleton(X1) != empty_set
| ~ in(X1,relation_dom(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_18]),c_0_19])]) ).
cnf(c_0_34,negated_conjecture,
( relation_inverse_image(esk17_0,singleton(apply(esk17_0,esk4_1(esk17_0)))) = singleton(esk4_1(esk17_0))
| relation_inverse_image(esk17_0,singleton(apply(esk17_0,esk4_1(esk17_0)))) = empty_set ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_18]),c_0_19])]),c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( relation_inverse_image(esk17_0,singleton(apply(esk17_0,esk4_1(esk17_0)))) = singleton(esk5_1(esk17_0))
| relation_inverse_image(esk17_0,singleton(apply(esk17_0,esk4_1(esk17_0)))) = empty_set ),
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_32]),c_0_18]),c_0_19])]),c_0_27]) ).
cnf(c_0_36,negated_conjecture,
singleton(esk5_1(esk17_0)) != empty_set,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_18]),c_0_19])]),c_0_27]) ).
cnf(c_0_37,negated_conjecture,
( relation_inverse_image(esk17_0,singleton(apply(esk17_0,esk4_1(esk17_0)))) = empty_set
| singleton(esk5_1(esk17_0)) = singleton(esk4_1(esk17_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
fof(c_0_38,plain,
! [X128,X129] :
( ~ subset(singleton(X128),singleton(X129))
| X128 = X129 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_zfmisc_1])]) ).
cnf(c_0_39,negated_conjecture,
( singleton(esk5_1(esk17_0)) = singleton(esk4_1(esk17_0))
| ~ in(apply(esk17_0,esk4_1(esk17_0)),relation_rng(esk17_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_37]),c_0_18])]) ).
cnf(c_0_40,plain,
( one_to_one(X1)
| in(apply(X1,esk4_1(X1)),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_26]) ).
cnf(c_0_41,plain,
( X1 = X2
| ~ subset(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
singleton(esk5_1(esk17_0)) = singleton(esk4_1(esk17_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_18]),c_0_19])]),c_0_27]) ).
fof(c_0_43,plain,
! [X106] : subset(X106,X106),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_44,negated_conjecture,
( esk5_1(esk17_0) = X1
| ~ subset(singleton(esk4_1(esk17_0)),singleton(X1)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_46,plain,
( one_to_one(X1)
| esk4_1(X1) != esk5_1(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_47,negated_conjecture,
esk5_1(esk17_0) = esk4_1(esk17_0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,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_46,c_0_47]),c_0_18]),c_0_19])]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU072+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.33 % Computer : n031.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 02:45:39 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 173.44/124.24 % Version : CSE_E---1.7
% 173.44/124.24 % Problem : theBenchmark.p
% 173.44/124.24 % SZS status Theorem for theBenchmark.p
% 173.44/124.24 % SZS output start CNFRefutation
% See solution above
% 174.37/125.17 % Total time : 90.237s
%------------------------------------------------------------------------------