%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU077+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 : n001.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 3.32s 3.05s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 6 unt; 0 def)
% Number of atoms : 173 ( 25 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 237 ( 97 ~; 104 |; 24 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_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(t158_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2))
& subset(X1,relation_rng(X3)) )
=> subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t158_funct_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_4,plain,
! [X67,X68,X69,X70,X71,X72,X73] :
( ( in(X70,relation_dom(X67))
| ~ in(X70,X69)
| X69 != relation_inverse_image(X67,X68)
| ~ relation(X67)
| ~ function(X67) )
& ( in(apply(X67,X70),X68)
| ~ in(X70,X69)
| X69 != relation_inverse_image(X67,X68)
| ~ relation(X67)
| ~ function(X67) )
& ( ~ in(X71,relation_dom(X67))
| ~ in(apply(X67,X71),X68)
| in(X71,X69)
| X69 != relation_inverse_image(X67,X68)
| ~ relation(X67)
| ~ function(X67) )
& ( ~ in(esk1_3(X67,X72,X73),X73)
| ~ in(esk1_3(X67,X72,X73),relation_dom(X67))
| ~ in(apply(X67,esk1_3(X67,X72,X73)),X72)
| X73 = relation_inverse_image(X67,X72)
| ~ relation(X67)
| ~ function(X67) )
& ( in(esk1_3(X67,X72,X73),relation_dom(X67))
| in(esk1_3(X67,X72,X73),X73)
| X73 = relation_inverse_image(X67,X72)
| ~ relation(X67)
| ~ function(X67) )
& ( in(apply(X67,esk1_3(X67,X72,X73)),X72)
| in(esk1_3(X67,X72,X73),X73)
| X73 = relation_inverse_image(X67,X72)
| ~ relation(X67)
| ~ function(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)],[d13_funct_1])])])])])]) ).
fof(c_0_5,plain,
! [X81,X82,X83,X85,X86,X87,X89] :
( ( in(esk3_3(X81,X82,X83),relation_dom(X81))
| ~ in(X83,X82)
| X82 != relation_rng(X81)
| ~ relation(X81)
| ~ function(X81) )
& ( X83 = apply(X81,esk3_3(X81,X82,X83))
| ~ in(X83,X82)
| X82 != relation_rng(X81)
| ~ relation(X81)
| ~ function(X81) )
& ( ~ in(X86,relation_dom(X81))
| X85 != apply(X81,X86)
| in(X85,X82)
| X82 != relation_rng(X81)
| ~ relation(X81)
| ~ function(X81) )
& ( ~ in(esk4_2(X81,X87),X87)
| ~ in(X89,relation_dom(X81))
| esk4_2(X81,X87) != apply(X81,X89)
| X87 = relation_rng(X81)
| ~ relation(X81)
| ~ function(X81) )
& ( in(esk5_2(X81,X87),relation_dom(X81))
| in(esk4_2(X81,X87),X87)
| X87 = relation_rng(X81)
| ~ relation(X81)
| ~ function(X81) )
& ( esk4_2(X81,X87) = apply(X81,esk5_2(X81,X87))
| in(esk4_2(X81,X87),X87)
| X87 = relation_rng(X81)
| ~ relation(X81)
| ~ function(X81) ) ),
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_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( ( subset(relation_inverse_image(X3,X1),relation_inverse_image(X3,X2))
& subset(X1,relation_rng(X3)) )
=> subset(X1,X2) ) ),
inference(assume_negation,[status(cth)],[t158_funct_1]) ).
cnf(c_0_7,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( X1 = apply(X2,esk3_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X75,X76,X77,X78,X79] :
( ( ~ subset(X75,X76)
| ~ in(X77,X75)
| in(X77,X76) )
& ( in(esk2_2(X78,X79),X78)
| subset(X78,X79) )
& ( ~ in(esk2_2(X78,X79),X79)
| subset(X78,X79) ) ),
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_10,negated_conjecture,
( relation(esk19_0)
& function(esk19_0)
& subset(relation_inverse_image(esk19_0,esk17_0),relation_inverse_image(esk19_0,esk18_0))
& subset(esk17_0,relation_rng(esk19_0))
& ~ subset(esk17_0,esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_11,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( apply(X1,esk3_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
subset(relation_inverse_image(esk19_0,esk17_0),relation_inverse_image(esk19_0,esk18_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,plain,
( in(esk3_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_5]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ function(X3)
| ~ in(esk3_3(X3,relation_rng(X3),X1),relation_inverse_image(X3,X2))
| ~ in(X1,relation_rng(X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( in(X1,relation_inverse_image(esk19_0,esk18_0))
| ~ in(X1,relation_inverse_image(esk19_0,esk17_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( in(esk3_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
subset(esk17_0,relation_rng(esk19_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( in(X1,esk18_0)
| ~ in(esk3_3(esk19_0,relation_rng(esk19_0),X1),relation_inverse_image(esk19_0,esk17_0))
| ~ in(X1,relation_rng(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_25,plain,
( in(esk3_3(X1,relation_rng(X1),X2),relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_12]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( in(X1,relation_rng(esk19_0))
| ~ in(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_27,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,esk18_0)
| ~ in(X1,esk17_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19]),c_0_20])]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( subset(X1,esk18_0)
| ~ in(esk2_2(X1,esk18_0),esk17_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,negated_conjecture,
~ subset(esk17_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU077+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
% 0.14/0.32 % Computer : n001.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:44:03 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 3.32/3.05 % Version : CSE_E---1.7
% 3.32/3.05 % Problem : theBenchmark.p
% 3.32/3.05 % SZS status Theorem for theBenchmark.p
% 3.32/3.05 % SZS output start CNFRefutation
% See solution above
% 3.32/3.06 % Total time : 2.373s
%------------------------------------------------------------------------------