%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU199+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 : n007.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 05:11:02 PM UTC 2026
% Result : Theorem 1.62s 1.85s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 123 ( 15 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 158 ( 66 ~; 72 |; 9 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 77 ( 6 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d12_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ! [X3] :
( relation(X3)
=> ( X3 = relation_rng_restriction(X1,X2)
<=> ! [X4,X5] :
( in(ordered_pair(X4,X5),X3)
<=> ( in(X5,X1)
& in(ordered_pair(X4,X5),X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
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(d3_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X1)
=> in(ordered_pair(X3,X4),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t117_relat_1,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
fof(c_0_6,plain,
! [X66,X67,X68,X69,X70,X71,X72] :
( ( in(X70,X66)
| ~ in(ordered_pair(X69,X70),X68)
| X68 != relation_rng_restriction(X66,X67)
| ~ relation(X68)
| ~ relation(X67) )
& ( in(ordered_pair(X69,X70),X67)
| ~ in(ordered_pair(X69,X70),X68)
| X68 != relation_rng_restriction(X66,X67)
| ~ relation(X68)
| ~ relation(X67) )
& ( ~ in(X72,X66)
| ~ in(ordered_pair(X71,X72),X67)
| in(ordered_pair(X71,X72),X68)
| X68 != relation_rng_restriction(X66,X67)
| ~ relation(X68)
| ~ relation(X67) )
& ( ~ in(ordered_pair(esk1_3(X66,X67,X68),esk2_3(X66,X67,X68)),X68)
| ~ in(esk2_3(X66,X67,X68),X66)
| ~ in(ordered_pair(esk1_3(X66,X67,X68),esk2_3(X66,X67,X68)),X67)
| X68 = relation_rng_restriction(X66,X67)
| ~ relation(X68)
| ~ relation(X67) )
& ( in(esk2_3(X66,X67,X68),X66)
| in(ordered_pair(esk1_3(X66,X67,X68),esk2_3(X66,X67,X68)),X68)
| X68 = relation_rng_restriction(X66,X67)
| ~ relation(X68)
| ~ relation(X67) )
& ( in(ordered_pair(esk1_3(X66,X67,X68),esk2_3(X66,X67,X68)),X67)
| in(ordered_pair(esk1_3(X66,X67,X68),esk2_3(X66,X67,X68)),X68)
| X68 = relation_rng_restriction(X66,X67)
| ~ relation(X68)
| ~ relation(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)],[d12_relat_1])])])])])]) ).
fof(c_0_7,plain,
! [X81,X82] : ordered_pair(X81,X82) = unordered_pair(unordered_pair(X81,X82),singleton(X81)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_8,plain,
( in(ordered_pair(X1,X2),X3)
| ~ in(ordered_pair(X1,X2),X4)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X83,X84] :
( ~ relation(X84)
| relation(relation_rng_restriction(X83,X84)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_relat_1])]) ).
fof(c_0_11,plain,
! [X75,X76,X77,X78] :
( ( ~ subset(X75,X76)
| ~ in(ordered_pair(X77,X78),X75)
| in(ordered_pair(X77,X78),X76)
| ~ relation(X76)
| ~ relation(X75) )
& ( in(ordered_pair(esk3_2(X75,X76),esk4_2(X75,X76)),X75)
| subset(X75,X76)
| ~ relation(X76)
| ~ relation(X75) )
& ( ~ in(ordered_pair(esk3_2(X75,X76),esk4_2(X75,X76)),X76)
| subset(X75,X76)
| ~ relation(X76)
| ~ relation(X75) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_relat_1])])])])]) ).
cnf(c_0_12,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| X4 != relation_rng_restriction(X5,X3)
| ~ relation(X4)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
cnf(c_0_13,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X64,X65] : unordered_pair(X64,X65) = unordered_pair(X65,X64),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_15,plain,
( in(ordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),X1)
| subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( subset(X1,X2)
| ~ in(ordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_rng_restriction(X4,X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| in(unordered_pair(unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),singleton(esk3_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_9]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_rng_restriction(X1,X2),X2) ),
inference(assume_negation,[status(cth)],[t117_relat_1]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2)),singleton(esk3_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_22,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),relation_rng_restriction(X4,X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( subset(X1,X2)
| in(unordered_pair(singleton(esk3_2(X1,X2)),unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2))),X1)
| ~ relation(X2)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
fof(c_0_24,negated_conjecture,
( relation(esk13_0)
& ~ subset(relation_rng_restriction(esk12_0,esk13_0),esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_25,plain,
( subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk3_2(X1,X2)),unordered_pair(esk3_2(X1,X2),esk4_2(X1,X2))),X2) ),
inference(rw,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_26,plain,
( subset(relation_rng_restriction(X1,X2),X3)
| in(unordered_pair(singleton(esk3_2(relation_rng_restriction(X1,X2),X3)),unordered_pair(esk3_2(relation_rng_restriction(X1,X2),X3),esk4_2(relation_rng_restriction(X1,X2),X3))),X2)
| ~ relation(X2)
| ~ relation(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_13]) ).
cnf(c_0_27,negated_conjecture,
~ subset(relation_rng_restriction(esk12_0,esk13_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( subset(relation_rng_restriction(X1,X2),X2)
| ~ relation(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_13]) ).
cnf(c_0_29,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU199+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:47:09 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.62/1.85 % Version : CSE_E---1.7
% 1.62/1.85 % Problem : theBenchmark.p
% 1.62/1.85 % SZS status Theorem for theBenchmark.p
% 1.62/1.85 % SZS output start CNFRefutation
% See solution above
% 1.62/1.85 % Total time : 1.370s
%------------------------------------------------------------------------------