%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU197+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 : n021.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 8.85s 5.93s
% Output : CNFRefutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 198 ( 29 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 253 ( 109 ~; 118 |; 14 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 127 ( 7 sgn 40 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_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(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(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(t115_relat_1,conjecture,
! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_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(c_0_6,plain,
! [X63,X64,X65,X67,X68,X69,X71] :
( ( ~ in(X65,X64)
| in(ordered_pair(esk3_3(X63,X64,X65),X65),X63)
| X64 != relation_rng(X63)
| ~ relation(X63) )
& ( ~ in(ordered_pair(X68,X67),X63)
| in(X67,X64)
| X64 != relation_rng(X63)
| ~ relation(X63) )
& ( ~ in(esk4_2(X63,X69),X69)
| ~ in(ordered_pair(X71,esk4_2(X63,X69)),X63)
| X69 = relation_rng(X63)
| ~ relation(X63) )
& ( in(esk4_2(X63,X69),X69)
| in(ordered_pair(esk5_2(X63,X69),esk4_2(X63,X69)),X63)
| X69 = relation_rng(X63)
| ~ relation(X63) ) ),
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)],[d5_relat_1])])])])])]) ).
fof(c_0_7,plain,
! [X73,X74] : ordered_pair(X73,X74) = unordered_pair(unordered_pair(X73,X74),singleton(X73)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_8,plain,
( in(ordered_pair(esk3_3(X3,X2,X1),X1),X3)
| ~ in(X1,X2)
| X2 != relation_rng(X3)
| ~ 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,
! [X52,X53] : unordered_pair(X52,X53) = unordered_pair(X53,X52),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_11,plain,
! [X54,X55,X56,X57,X58,X59,X60] :
( ( in(X58,X54)
| ~ in(ordered_pair(X57,X58),X56)
| X56 != relation_rng_restriction(X54,X55)
| ~ relation(X56)
| ~ relation(X55) )
& ( in(ordered_pair(X57,X58),X55)
| ~ in(ordered_pair(X57,X58),X56)
| X56 != relation_rng_restriction(X54,X55)
| ~ relation(X56)
| ~ relation(X55) )
& ( ~ in(X60,X54)
| ~ in(ordered_pair(X59,X60),X55)
| in(ordered_pair(X59,X60),X56)
| X56 != relation_rng_restriction(X54,X55)
| ~ relation(X56)
| ~ relation(X55) )
& ( ~ in(ordered_pair(esk1_3(X54,X55,X56),esk2_3(X54,X55,X56)),X56)
| ~ in(esk2_3(X54,X55,X56),X54)
| ~ in(ordered_pair(esk1_3(X54,X55,X56),esk2_3(X54,X55,X56)),X55)
| X56 = relation_rng_restriction(X54,X55)
| ~ relation(X56)
| ~ relation(X55) )
& ( in(esk2_3(X54,X55,X56),X54)
| in(ordered_pair(esk1_3(X54,X55,X56),esk2_3(X54,X55,X56)),X56)
| X56 = relation_rng_restriction(X54,X55)
| ~ relation(X56)
| ~ relation(X55) )
& ( in(ordered_pair(esk1_3(X54,X55,X56),esk2_3(X54,X55,X56)),X55)
| in(ordered_pair(esk1_3(X54,X55,X56),esk2_3(X54,X55,X56)),X56)
| X56 = relation_rng_restriction(X54,X55)
| ~ relation(X56)
| ~ relation(X55) ) ),
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])])])])])]) ).
cnf(c_0_12,plain,
( in(unordered_pair(unordered_pair(esk3_3(X3,X2,X1),X1),singleton(esk3_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2,X3] :
( relation(X3)
=> ( in(X1,relation_rng(relation_rng_restriction(X2,X3)))
<=> ( in(X1,X2)
& in(X1,relation_rng(X3)) ) ) ),
inference(assume_negation,[status(cth)],[t115_relat_1]) ).
cnf(c_0_15,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_11]) ).
fof(c_0_16,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])]) ).
cnf(c_0_17,plain,
( in(unordered_pair(unordered_pair(X1,esk3_3(X2,X3,X1)),singleton(esk3_3(X2,X3,X1))),X2)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ in(X1,X3) ),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_18,negated_conjecture,
( relation(esk13_0)
& ( ~ in(esk11_0,relation_rng(relation_rng_restriction(esk12_0,esk13_0)))
| ~ in(esk11_0,esk12_0)
| ~ in(esk11_0,relation_rng(esk13_0)) )
& ( in(esk11_0,esk12_0)
| in(esk11_0,relation_rng(relation_rng_restriction(esk12_0,esk13_0))) )
& ( in(esk11_0,relation_rng(esk13_0))
| in(esk11_0,relation_rng(relation_rng_restriction(esk12_0,esk13_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_19,plain,
( in(X2,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_rng(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,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_15,c_0_9]),c_0_9]) ).
cnf(c_0_21,plain,
( relation(relation_rng_restriction(X2,X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( in(unordered_pair(unordered_pair(X1,esk3_3(X2,relation_rng(X2),X1)),singleton(esk3_3(X2,relation_rng(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( in(esk11_0,relation_rng(esk13_0))
| in(esk11_0,relation_rng(relation_rng_restriction(esk12_0,esk13_0))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( in(X2,X4)
| X4 != relation_rng(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_19,c_0_9]) ).
cnf(c_0_25,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_20]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( in(unordered_pair(unordered_pair(esk11_0,esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0)),singleton(esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0))),relation_rng_restriction(esk12_0,esk13_0))
| in(esk11_0,relation_rng(esk13_0))
| ~ relation(relation_rng_restriction(esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),X4)
| X4 != relation_rng_restriction(X2,X5)
| ~ relation(X4)
| ~ relation(X5) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,plain,
( in(ordered_pair(X3,X1),X5)
| ~ in(X1,X2)
| ~ in(ordered_pair(X3,X1),X4)
| X5 != relation_rng_restriction(X2,X4)
| ~ relation(X5)
| ~ relation(X4) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),relation_rng_restriction(X4,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_32,negated_conjecture,
( in(unordered_pair(unordered_pair(esk11_0,esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0)),singleton(esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0))),relation_rng_restriction(esk12_0,esk13_0))
| in(esk11_0,relation_rng(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_27])]) ).
cnf(c_0_33,plain,
( in(X1,X2)
| X4 != relation_rng_restriction(X2,X5)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X4) ),
inference(rw,[status(thm)],[c_0_28,c_0_9]) ).
cnf(c_0_34,negated_conjecture,
( in(esk11_0,esk12_0)
| in(esk11_0,relation_rng(relation_rng_restriction(esk12_0,esk13_0))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_35,plain,
( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X5)
| X5 != relation_rng_restriction(X2,X4)
| ~ relation(X5)
| ~ relation(X4)
| ~ in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_9]),c_0_9]) ).
cnf(c_0_36,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_37,negated_conjecture,
( in(unordered_pair(unordered_pair(esk11_0,esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0)),singleton(esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0))),esk13_0)
| in(esk11_0,relation_rng(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27])]) ).
cnf(c_0_38,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X4,X1),singleton(X4)),relation_rng_restriction(X2,X3)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_21]) ).
cnf(c_0_39,negated_conjecture,
( in(unordered_pair(unordered_pair(esk11_0,esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0)),singleton(esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0))),relation_rng_restriction(esk12_0,esk13_0))
| in(esk11_0,esk12_0)
| ~ relation(relation_rng_restriction(esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_40,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X4)
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_35]),c_0_21]) ).
cnf(c_0_41,negated_conjecture,
in(esk11_0,relation_rng(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_27])]) ).
cnf(c_0_42,plain,
( in(X1,X2)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X4),singleton(X4)),relation_rng_restriction(X2,X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_13]) ).
cnf(c_0_43,negated_conjecture,
( in(unordered_pair(unordered_pair(esk11_0,esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0)),singleton(esk3_3(relation_rng_restriction(esk12_0,esk13_0),relation_rng(relation_rng_restriction(esk12_0,esk13_0)),esk11_0))),relation_rng_restriction(esk12_0,esk13_0))
| in(esk11_0,esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_21]),c_0_27])]) ).
cnf(c_0_44,plain,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),relation_rng_restriction(X3,X4))
| ~ relation(X4)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),X4)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_13]) ).
cnf(c_0_45,negated_conjecture,
in(unordered_pair(unordered_pair(esk11_0,esk3_3(esk13_0,relation_rng(esk13_0),esk11_0)),singleton(esk3_3(esk13_0,relation_rng(esk13_0),esk11_0))),esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_41]),c_0_27])]) ).
cnf(c_0_46,negated_conjecture,
( ~ in(esk11_0,relation_rng(relation_rng_restriction(esk12_0,esk13_0)))
| ~ in(esk11_0,esk12_0)
| ~ in(esk11_0,relation_rng(esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_47,negated_conjecture,
in(esk11_0,esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_27])]) ).
cnf(c_0_48,negated_conjecture,
( in(unordered_pair(unordered_pair(esk11_0,esk3_3(esk13_0,relation_rng(esk13_0),esk11_0)),singleton(esk3_3(esk13_0,relation_rng(esk13_0),esk11_0))),relation_rng_restriction(X1,esk13_0))
| ~ in(esk11_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_27])]) ).
cnf(c_0_49,negated_conjecture,
( ~ in(esk11_0,relation_rng(relation_rng_restriction(esk12_0,esk13_0)))
| ~ in(esk11_0,relation_rng(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_50,negated_conjecture,
in(unordered_pair(unordered_pair(esk11_0,esk3_3(esk13_0,relation_rng(esk13_0),esk11_0)),singleton(esk3_3(esk13_0,relation_rng(esk13_0),esk11_0))),relation_rng_restriction(esk12_0,esk13_0)),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
~ in(esk11_0,relation_rng(relation_rng_restriction(esk12_0,esk13_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_41])]) ).
cnf(c_0_52,negated_conjecture,
~ relation(relation_rng_restriction(esk12_0,esk13_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_50]),c_0_51]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_21]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU197+1 : TPTP v9.2.1. Released v3.3.0.
% 0.11/0.13 % 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
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 5 02:48:55 EDT 2026
% 0.14/0.34 % CPUTime :
% 0.19/0.35 % start to proof: theBenchmark
% 8.85/5.93 % Version : CSE_E---1.7
% 8.85/5.93 % Problem : theBenchmark.p
% 8.85/5.93 % SZS status Theorem for theBenchmark.p
% 8.85/5.93 % SZS output start CNFRefutation
% See solution above
% 8.85/5.96 % Total time : 4.373s
%------------------------------------------------------------------------------