%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU046+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 : n019.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 05:10:33 PM UTC 2026
% Result : Theorem 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 4 unt; 0 def)
% Number of atoms : 164 ( 17 equ)
% Maximal formula atoms : 79 ( 6 avg)
% Number of connectives : 228 ( 91 ~; 101 |; 24 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 57 ( 6 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t85_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_rng_restriction(X1,X3)
<=> ( ! [X4] :
( in(X4,relation_dom(X2))
<=> ( in(X4,relation_dom(X3))
& in(apply(X3,X4),X1) ) )
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
fof(fc5_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( relation(relation_rng_restriction(X1,X2))
& function(relation_rng_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(dt_k8_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> relation(relation_rng_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(t89_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
& subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t89_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(t118_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
fof(c_0_6,plain,
! [X116,X117,X118,X119,X120,X121] :
( ( in(X119,relation_dom(X118))
| ~ in(X119,relation_dom(X117))
| X117 != relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( in(apply(X118,X119),X116)
| ~ in(X119,relation_dom(X117))
| X117 != relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( ~ in(X120,relation_dom(X118))
| ~ in(apply(X118,X120),X116)
| in(X120,relation_dom(X117))
| X117 != relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( ~ in(X121,relation_dom(X117))
| apply(X117,X121) = apply(X118,X121)
| X117 != relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( in(esk14_3(X116,X117,X118),relation_dom(X117))
| ~ in(esk13_3(X116,X117,X118),relation_dom(X117))
| ~ in(esk13_3(X116,X117,X118),relation_dom(X118))
| ~ in(apply(X118,esk13_3(X116,X117,X118)),X116)
| X117 = relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( apply(X117,esk14_3(X116,X117,X118)) != apply(X118,esk14_3(X116,X117,X118))
| ~ in(esk13_3(X116,X117,X118),relation_dom(X117))
| ~ in(esk13_3(X116,X117,X118),relation_dom(X118))
| ~ in(apply(X118,esk13_3(X116,X117,X118)),X116)
| X117 = relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( in(esk14_3(X116,X117,X118),relation_dom(X117))
| in(esk13_3(X116,X117,X118),relation_dom(X118))
| in(esk13_3(X116,X117,X118),relation_dom(X117))
| X117 = relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( apply(X117,esk14_3(X116,X117,X118)) != apply(X118,esk14_3(X116,X117,X118))
| in(esk13_3(X116,X117,X118),relation_dom(X118))
| in(esk13_3(X116,X117,X118),relation_dom(X117))
| X117 = relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( in(esk14_3(X116,X117,X118),relation_dom(X117))
| in(apply(X118,esk13_3(X116,X117,X118)),X116)
| in(esk13_3(X116,X117,X118),relation_dom(X117))
| X117 = relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) )
& ( apply(X117,esk14_3(X116,X117,X118)) != apply(X118,esk14_3(X116,X117,X118))
| in(apply(X118,esk13_3(X116,X117,X118)),X116)
| in(esk13_3(X116,X117,X118),relation_dom(X117))
| X117 = relation_rng_restriction(X116,X118)
| ~ relation(X118)
| ~ function(X118)
| ~ relation(X117)
| ~ function(X117) ) ),
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)],[t85_funct_1])])])])])]) ).
fof(c_0_7,plain,
! [X80,X81] :
( ( relation(relation_rng_restriction(X80,X81))
| ~ relation(X81)
| ~ function(X81) )
& ( function(relation_rng_restriction(X80,X81))
| ~ relation(X81)
| ~ function(X81) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc5_funct_1])])]) ).
fof(c_0_8,plain,
! [X75,X76] :
( ~ relation(X76)
| relation(relation_rng_restriction(X75,X76)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
& subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2)) ) ),
inference(assume_negation,[status(cth)],[t89_funct_1]) ).
cnf(c_0_10,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(X3))
| X3 != relation_rng_restriction(X4,X2)
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( function(relation_rng_restriction(X1,X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X69,X70,X71,X72,X73] :
( ( ~ subset(X69,X70)
| ~ in(X71,X69)
| in(X71,X70) )
& ( in(esk1_2(X72,X73),X72)
| subset(X72,X73) )
& ( ~ in(esk1_2(X72,X73),X73)
| subset(X72,X73) ) ),
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(esk16_0)
& function(esk16_0)
& ( ~ subset(relation_dom(relation_rng_restriction(esk15_0,esk16_0)),relation_dom(esk16_0))
| ~ subset(relation_rng(relation_rng_restriction(esk15_0,esk16_0)),relation_rng(esk16_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_15,plain,
! [X99,X100] :
( ~ relation(X100)
| subset(relation_rng(relation_rng_restriction(X99,X100)),relation_rng(X100)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_relat_1])]) ).
cnf(c_0_16,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_dom(relation_rng_restriction(X3,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_10]),c_0_11]),c_0_12]) ).
cnf(c_0_17,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( ~ subset(relation_dom(relation_rng_restriction(esk15_0,esk16_0)),relation_dom(esk16_0))
| ~ subset(relation_rng(relation_rng_restriction(esk15_0,esk16_0)),relation_rng(esk16_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( subset(relation_rng(relation_rng_restriction(X2,X1)),relation_rng(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
( subset(relation_dom(relation_rng_restriction(X1,X2)),X3)
| in(esk1_2(relation_dom(relation_rng_restriction(X1,X2)),X3),relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
~ subset(relation_dom(relation_rng_restriction(esk15_0,esk16_0)),relation_dom(esk16_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,plain,
( subset(relation_dom(relation_rng_restriction(X1,X2)),relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
function(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU046+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.17/0.32 % Computer : n019.cluster.edu
% 0.17/0.32 % Model : x86_64 x86_64
% 0.17/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.32 % Memory : 8042.1875MB
% 0.17/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.32 % CPULimit : 300
% 0.17/0.32 % WCLimit : 300
% 0.17/0.32 % DateTime : Tue May 5 02:42:14 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Theorem for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------