%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU008+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 : n029.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 05:10:29 PM UTC 2026
% Result : Theorem 1.32s 1.72s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 16 unt; 0 def)
% Number of atoms : 117 ( 38 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 135 ( 51 ~; 52 |; 20 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 59 ( 4 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t38_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_funct_1) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,set_intersection2(relation_dom(X3),X1))
=> apply(X3,X2) = apply(relation_composition(identity_relation(X1),X3),X2) ) ),
inference(assume_negation,[status(cth)],[t38_funct_1]) ).
fof(c_0_8,plain,
! [X79,X80,X81,X82,X83,X84,X85,X86] :
( ( in(X82,X79)
| ~ in(X82,X81)
| X81 != set_intersection2(X79,X80) )
& ( in(X82,X80)
| ~ in(X82,X81)
| X81 != set_intersection2(X79,X80) )
& ( ~ in(X83,X79)
| ~ in(X83,X80)
| in(X83,X81)
| X81 != set_intersection2(X79,X80) )
& ( ~ in(esk1_3(X84,X85,X86),X86)
| ~ in(esk1_3(X84,X85,X86),X84)
| ~ in(esk1_3(X84,X85,X86),X85)
| X86 = set_intersection2(X84,X85) )
& ( in(esk1_3(X84,X85,X86),X84)
| in(esk1_3(X84,X85,X86),X86)
| X86 = set_intersection2(X84,X85) )
& ( in(esk1_3(X84,X85,X86),X85)
| in(esk1_3(X84,X85,X86),X86)
| X86 = set_intersection2(X84,X85) ) ),
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_xboole_0])])])])])]) ).
fof(c_0_9,negated_conjecture,
( relation(esk14_0)
& function(esk14_0)
& in(esk13_0,set_intersection2(relation_dom(esk14_0),esk12_0))
& apply(esk14_0,esk13_0) != apply(relation_composition(identity_relation(esk12_0),esk14_0),esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X77,X78] : set_intersection2(X77,X78) = set_intersection2(X78,X77),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_11,plain,
! [X125,X126,X127] :
( ( relation_dom(X126) = X125
| X126 != identity_relation(X125)
| ~ relation(X126)
| ~ function(X126) )
& ( ~ in(X127,X125)
| apply(X126,X127) = X127
| X126 != identity_relation(X125)
| ~ relation(X126)
| ~ function(X126) )
& ( in(esk11_2(X125,X126),X125)
| relation_dom(X126) != X125
| X126 = identity_relation(X125)
| ~ relation(X126)
| ~ function(X126) )
& ( apply(X126,esk11_2(X125,X126)) != esk11_2(X125,X126)
| relation_dom(X126) != X125
| X126 = identity_relation(X125)
| ~ relation(X126)
| ~ function(X126) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(c_0_12,plain,
! [X90] : relation(identity_relation(X90)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_13,plain,
! [X100] :
( relation(identity_relation(X100))
& function(identity_relation(X100)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
in(esk13_0,set_intersection2(relation_dom(esk14_0),esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X119,X120,X121] :
( ~ relation(X120)
| ~ function(X120)
| ~ relation(X121)
| ~ function(X121)
| ~ in(X119,relation_dom(X120))
| apply(relation_composition(X120,X121),X119) = apply(X121,apply(X120,X119)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
cnf(c_0_18,plain,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
in(esk13_0,set_intersection2(esk12_0,relation_dom(esk14_0))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
apply(esk14_0,esk13_0) != apply(relation_composition(identity_relation(esk12_0),esk14_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,negated_conjecture,
function(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_28,negated_conjecture,
in(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
apply(esk14_0,apply(identity_relation(esk12_0),esk13_0)) != apply(esk14_0,esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_19]),c_0_26]),c_0_20])]),c_0_27]),c_0_28])]) ).
cnf(c_0_31,negated_conjecture,
( apply(X1,esk13_0) = esk13_0
| X1 != identity_relation(esk12_0)
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU008+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
% 0.15/0.32 % Computer : n029.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 02:40:59 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.32/1.72 % Version : CSE_E---1.7
% 1.32/1.72 % Problem : theBenchmark.p
% 1.32/1.72 % SZS status Theorem for theBenchmark.p
% 1.32/1.72 % SZS output start CNFRefutation
% See solution above
% 1.32/1.72 % Total time : 1.369s
%------------------------------------------------------------------------------