%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU226+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n010.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 05:11:09 PM UTC 2026
% Result : Theorem 1.42s 1.78s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 158 ( 27 equ)
% Maximal formula atoms : 44 ( 6 avg)
% Number of connectives : 225 ( 91 ~; 101 |; 23 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 73 ( 0 sgn 36 !; 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/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
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(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(t145_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).
fof(c_0_4,plain,
! [X78,X79,X80,X81,X82,X83,X84] :
( ( in(X81,relation_dom(X78))
| ~ in(X81,X80)
| X80 != relation_inverse_image(X78,X79)
| ~ relation(X78)
| ~ function(X78) )
& ( in(apply(X78,X81),X79)
| ~ in(X81,X80)
| X80 != relation_inverse_image(X78,X79)
| ~ relation(X78)
| ~ function(X78) )
& ( ~ in(X82,relation_dom(X78))
| ~ in(apply(X78,X82),X79)
| in(X82,X80)
| X80 != relation_inverse_image(X78,X79)
| ~ relation(X78)
| ~ function(X78) )
& ( ~ in(esk4_3(X78,X83,X84),X84)
| ~ in(esk4_3(X78,X83,X84),relation_dom(X78))
| ~ in(apply(X78,esk4_3(X78,X83,X84)),X83)
| X84 = relation_inverse_image(X78,X83)
| ~ relation(X78)
| ~ function(X78) )
& ( in(esk4_3(X78,X83,X84),relation_dom(X78))
| in(esk4_3(X78,X83,X84),X84)
| X84 = relation_inverse_image(X78,X83)
| ~ relation(X78)
| ~ function(X78) )
& ( in(apply(X78,esk4_3(X78,X83,X84)),X83)
| in(esk4_3(X78,X83,X84),X84)
| X84 = relation_inverse_image(X78,X83)
| ~ relation(X78)
| ~ function(X78) ) ),
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])])])])])]) ).
cnf(c_0_5,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]) ).
fof(c_0_6,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])])])])])]) ).
cnf(c_0_7,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_8,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_6]) ).
cnf(c_0_9,plain,
( in(apply(X1,esk1_4(X2,relation_inverse_image(X1,X3),X4,X5)),X3)
| X4 != relation_image(X2,relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ relation(X2)
| ~ function(X1)
| ~ function(X2)
| ~ in(X5,X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,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_6]) ).
cnf(c_0_11,plain,
( in(X1,X2)
| X3 != relation_image(X4,relation_inverse_image(X4,X2))
| ~ relation(X4)
| ~ function(X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_12,plain,
! [X86,X87,X88,X89,X90] :
( ( ~ subset(X86,X87)
| ~ in(X88,X86)
| in(X88,X87) )
& ( in(esk5_2(X89,X90),X89)
| subset(X89,X90) )
& ( ~ in(esk5_2(X89,X90),X90)
| subset(X89,X90) ) ),
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_13,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> subset(relation_image(X2,relation_inverse_image(X2,X1)),X1) ),
inference(assume_negation,[status(cth)],[t145_funct_1]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ function(X3)
| ~ in(X1,relation_image(X3,relation_inverse_image(X3,X2))) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,negated_conjecture,
( relation(esk18_0)
& function(esk18_0)
& ~ subset(relation_image(esk18_0,relation_inverse_image(esk18_0,esk17_0)),esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X3)
| in(esk5_2(relation_image(X1,relation_inverse_image(X1,X2)),X3),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
~ subset(relation_image(esk18_0,relation_inverse_image(esk18_0,esk17_0)),esk17_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
relation(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
function(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[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])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU226+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n010.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
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:49:51 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.42/1.78 % Version : CSE_E---1.7
% 1.42/1.78 % Problem : theBenchmark.p
% 1.42/1.78 % SZS status Theorem for theBenchmark.p
% 1.42/1.78 % SZS output start CNFRefutation
% See solution above
% 1.42/1.79 % Total time : 1.371s
%------------------------------------------------------------------------------