%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU076+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 : n027.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 32.00s 19.47s
% Output : CNFRefutation 32.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 192 ( 30 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 264 ( 107 ~; 115 |; 30 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 84 ( 0 sgn 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d12_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_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(t157_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( subset(relation_image(X3,X1),relation_image(X3,X2))
& subset(X1,relation_dom(X3))
& one_to_one(X3) )
=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t157_funct_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_4,plain,
! [X66,X67,X68,X69,X71,X72,X73,X74,X76] :
( ( in(esk1_4(X66,X67,X68,X69),relation_dom(X66))
| ~ in(X69,X68)
| X68 != relation_image(X66,X67)
| ~ relation(X66)
| ~ function(X66) )
& ( in(esk1_4(X66,X67,X68,X69),X67)
| ~ in(X69,X68)
| X68 != relation_image(X66,X67)
| ~ relation(X66)
| ~ function(X66) )
& ( X69 = apply(X66,esk1_4(X66,X67,X68,X69))
| ~ in(X69,X68)
| X68 != relation_image(X66,X67)
| ~ relation(X66)
| ~ function(X66) )
& ( ~ in(X72,relation_dom(X66))
| ~ in(X72,X67)
| X71 != apply(X66,X72)
| in(X71,X68)
| X68 != relation_image(X66,X67)
| ~ relation(X66)
| ~ function(X66) )
& ( ~ in(esk2_3(X66,X73,X74),X74)
| ~ in(X76,relation_dom(X66))
| ~ in(X76,X73)
| esk2_3(X66,X73,X74) != apply(X66,X76)
| X74 = relation_image(X66,X73)
| ~ relation(X66)
| ~ function(X66) )
& ( in(esk3_3(X66,X73,X74),relation_dom(X66))
| in(esk2_3(X66,X73,X74),X74)
| X74 = relation_image(X66,X73)
| ~ relation(X66)
| ~ function(X66) )
& ( in(esk3_3(X66,X73,X74),X73)
| in(esk2_3(X66,X73,X74),X74)
| X74 = relation_image(X66,X73)
| ~ relation(X66)
| ~ function(X66) )
& ( esk2_3(X66,X73,X74) = apply(X66,esk3_3(X66,X73,X74))
| in(esk2_3(X66,X73,X74),X74)
| X74 = relation_image(X66,X73)
| ~ relation(X66)
| ~ function(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)],[d12_funct_1])])])])])]) ).
fof(c_0_5,plain,
! [X84,X85,X86] :
( ( ~ one_to_one(X84)
| ~ in(X85,relation_dom(X84))
| ~ in(X86,relation_dom(X84))
| apply(X84,X85) != apply(X84,X86)
| X85 = X86
| ~ relation(X84)
| ~ function(X84) )
& ( in(esk5_1(X84),relation_dom(X84))
| one_to_one(X84)
| ~ relation(X84)
| ~ function(X84) )
& ( in(esk6_1(X84),relation_dom(X84))
| one_to_one(X84)
| ~ relation(X84)
| ~ function(X84) )
& ( apply(X84,esk5_1(X84)) = apply(X84,esk6_1(X84))
| one_to_one(X84)
| ~ relation(X84)
| ~ function(X84) )
& ( esk5_1(X84) != esk6_1(X84)
| one_to_one(X84)
| ~ relation(X84)
| ~ function(X84) ) ),
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_6,plain,
( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( in(esk1_4(X1,X2,X3,X4),relation_dom(X1))
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( subset(relation_image(X3,X1),relation_image(X3,X2))
& subset(X1,relation_dom(X3))
& one_to_one(X3) )
=> subset(X1,X2) ) ),
inference(assume_negation,[status(cth)],[t157_funct_1]) ).
cnf(c_0_9,plain,
( in(esk1_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,plain,
( X2 = X3
| ~ one_to_one(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X3,relation_dom(X1))
| apply(X1,X2) != apply(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( apply(X1,esk1_4(X1,X2,relation_image(X1,X2),X3)) = X3
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( in(esk1_4(X1,X2,relation_image(X1,X2),X3),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_7]) ).
fof(c_0_13,plain,
! [X78,X79,X80,X81,X82] :
( ( ~ subset(X78,X79)
| ~ in(X80,X78)
| in(X80,X79) )
& ( in(esk4_2(X81,X82),X81)
| subset(X81,X82) )
& ( ~ in(esk4_2(X81,X82),X82)
| subset(X81,X82) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_14,negated_conjecture,
( relation(esk20_0)
& function(esk20_0)
& subset(relation_image(esk20_0,esk18_0),relation_image(esk20_0,esk19_0))
& subset(esk18_0,relation_dom(esk20_0))
& one_to_one(esk20_0)
& ~ subset(esk18_0,esk19_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_15,plain,
( in(esk1_4(X1,X2,relation_image(X1,X2),X3),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( esk1_4(X1,X2,relation_image(X1,X2),apply(X1,X3)) = X3
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(apply(X1,X3),relation_image(X1,X2))
| ~ in(X3,relation_dom(X1)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11])]),c_0_12]) ).
cnf(c_0_17,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
subset(relation_image(esk20_0,esk18_0),relation_image(esk20_0,esk19_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( in(X1,X2)
| ~ one_to_one(X3)
| ~ relation(X3)
| ~ function(X3)
| ~ in(apply(X3,X1),relation_image(X3,X2))
| ~ in(X1,relation_dom(X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( in(X1,relation_image(esk20_0,esk19_0))
| ~ in(X1,relation_image(esk20_0,esk18_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
one_to_one(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
relation(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
function(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( in(X4,X5)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X4 != apply(X2,X1)
| X5 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_25,negated_conjecture,
subset(esk18_0,relation_dom(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( in(X1,esk19_0)
| ~ in(apply(esk20_0,X1),relation_image(esk20_0,esk18_0))
| ~ in(X1,relation_dom(esk20_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
( in(apply(X1,X2),relation_image(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,relation_dom(esk20_0))
| ~ in(X1,esk18_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_29,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,esk19_0)
| ~ in(X1,esk18_0) ),
inference(csr,[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_22]),c_0_23])]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( subset(X1,esk19_0)
| ~ in(esk4_2(X1,esk19_0),esk18_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
( in(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_33,negated_conjecture,
~ subset(esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU076+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
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % 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 02:43:20 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 32.00/19.47 % Version : CSE_E---1.7
% 32.00/19.47 % Problem : theBenchmark.p
% 32.00/19.47 % SZS status Theorem for theBenchmark.p
% 32.00/19.47 % SZS output start CNFRefutation
% See solution above
% 32.19/19.60 % Total time : 14.396s
%------------------------------------------------------------------------------