%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU268+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n016.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 05:11:18 PM UTC 2026
% Result : Theorem 1.33s 1.70s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 20 unt; 0 def)
% Number of atoms : 123 ( 25 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 146 ( 61 ~; 65 |; 11 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 68 ( 3 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_reflexive_in(X1,X2)
<=> ! [X3] :
( in(X3,X2)
=> in(ordered_pair(X3,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(d1_wellord2,axiom,
! [X1,X2] :
( relation(X2)
=> ( X2 = inclusion_relation(X1)
<=> ( relation_field(X2) = X1
& ! [X3,X4] :
( ( in(X3,X1)
& in(X4,X1) )
=> ( in(ordered_pair(X3,X4),X2)
<=> subset(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(dt_k1_wellord2,axiom,
! [X1] : relation(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(d9_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( reflexive(X1)
<=> is_reflexive_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(t2_wellord2,conjecture,
! [X1] : reflexive(inclusion_relation(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
fof(c_0_8,plain,
! [X79,X80,X81,X82] :
( ( ~ is_reflexive_in(X79,X80)
| ~ in(X81,X80)
| in(ordered_pair(X81,X81),X79)
| ~ relation(X79) )
& ( in(esk1_2(X79,X82),X82)
| is_reflexive_in(X79,X82)
| ~ relation(X79) )
& ( ~ in(ordered_pair(esk1_2(X79,X82),esk1_2(X79,X82)),X79)
| is_reflexive_in(X79,X82)
| ~ relation(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)],[d1_relat_2])])])])])]) ).
fof(c_0_9,plain,
! [X90,X91] : ordered_pair(X90,X91) = unordered_pair(unordered_pair(X90,X91),singleton(X90)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_10,plain,
! [X84,X85,X86,X87] :
( ( relation_field(X85) = X84
| X85 != inclusion_relation(X84)
| ~ relation(X85) )
& ( ~ in(ordered_pair(X86,X87),X85)
| subset(X86,X87)
| ~ in(X86,X84)
| ~ in(X87,X84)
| X85 != inclusion_relation(X84)
| ~ relation(X85) )
& ( ~ subset(X86,X87)
| in(ordered_pair(X86,X87),X85)
| ~ in(X86,X84)
| ~ in(X87,X84)
| X85 != inclusion_relation(X84)
| ~ relation(X85) )
& ( in(esk2_2(X84,X85),X84)
| relation_field(X85) != X84
| X85 = inclusion_relation(X84)
| ~ relation(X85) )
& ( in(esk3_2(X84,X85),X84)
| relation_field(X85) != X84
| X85 = inclusion_relation(X84)
| ~ relation(X85) )
& ( ~ in(ordered_pair(esk2_2(X84,X85),esk3_2(X84,X85)),X85)
| ~ subset(esk2_2(X84,X85),esk3_2(X84,X85))
| relation_field(X85) != X84
| X85 = inclusion_relation(X84)
| ~ relation(X85) )
& ( in(ordered_pair(esk2_2(X84,X85),esk3_2(X84,X85)),X85)
| subset(esk2_2(X84,X85),esk3_2(X84,X85))
| relation_field(X85) != X84
| X85 = inclusion_relation(X84)
| ~ relation(X85) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_wellord2])])])])]) ).
cnf(c_0_11,plain,
( is_reflexive_in(X1,X2)
| ~ in(ordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X75,X76] : unordered_pair(X75,X76) = unordered_pair(X76,X75),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_14,plain,
( in(ordered_pair(X1,X2),X3)
| ~ subset(X1,X2)
| ~ in(X1,X4)
| ~ in(X2,X4)
| X3 != inclusion_relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X94] : relation(inclusion_relation(X94)),
inference(variable_rename,[status(thm)],[dt_k1_wellord2]) ).
cnf(c_0_16,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),singleton(esk1_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X3 != inclusion_relation(X4)
| ~ relation(X3)
| ~ in(X2,X4)
| ~ in(X1,X4)
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_19,plain,
relation(inclusion_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X113] : subset(X113,X113),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_21,plain,
! [X93] :
( ( ~ reflexive(X93)
| is_reflexive_in(X93,relation_field(X93))
| ~ relation(X93) )
& ( ~ is_reflexive_in(X93,relation_field(X93))
| reflexive(X93)
| ~ relation(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])]) ).
cnf(c_0_22,plain,
( relation_field(X1) = X2
| X1 != inclusion_relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( is_reflexive_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),inclusion_relation(X3))
| ~ subset(X1,X2)
| ~ in(X2,X3)
| ~ in(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_17])]),c_0_19])]) ).
cnf(c_0_25,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( in(esk1_2(X1,X2),X2)
| is_reflexive_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] : reflexive(inclusion_relation(X1)),
inference(assume_negation,[status(cth)],[t2_wellord2]) ).
cnf(c_0_28,plain,
( reflexive(X1)
| ~ is_reflexive_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
relation_field(inclusion_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_22]),c_0_19])]) ).
cnf(c_0_30,plain,
( is_reflexive_in(inclusion_relation(X1),X2)
| ~ in(esk1_2(inclusion_relation(X1),X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]),c_0_25])]) ).
cnf(c_0_31,plain,
( is_reflexive_in(inclusion_relation(X1),X2)
| in(esk1_2(inclusion_relation(X1),X2),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
fof(c_0_32,negated_conjecture,
~ reflexive(inclusion_relation(esk14_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_33,plain,
( reflexive(inclusion_relation(X1))
| ~ is_reflexive_in(inclusion_relation(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_19])]) ).
cnf(c_0_34,plain,
is_reflexive_in(inclusion_relation(X1),X1),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
~ reflexive(inclusion_relation(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
reflexive(inclusion_relation(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU268+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.10 % 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
% 0.11/0.30 % Computer : n016.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue May 5 02:53:21 EDT 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 % start to proof: theBenchmark
% 1.33/1.70 % Version : CSE_E---1.7
% 1.33/1.70 % Problem : theBenchmark.p
% 1.33/1.70 % SZS status Theorem for theBenchmark.p
% 1.33/1.70 % SZS output start CNFRefutation
% See solution above
% 1.33/1.70 % Total time : 1.368s
%------------------------------------------------------------------------------