%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU179+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 : n017.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 05:10:58 PM UTC 2026
% Result : Theorem 1.76s 1.88s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 12 unt; 0 def)
% Number of atoms : 150 ( 24 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 179 ( 75 ~; 77 |; 13 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 106 ( 6 sgn 40 !; 2 ?)
% 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/sandbox/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/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t25_relat_1,conjecture,
! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
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(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_6,plain,
! [X78,X79,X80,X82,X83,X84,X86] :
( ( ~ in(X80,X79)
| in(ordered_pair(esk5_3(X78,X79,X80),X80),X78)
| X79 != relation_rng(X78)
| ~ relation(X78) )
& ( ~ in(ordered_pair(X83,X82),X78)
| in(X82,X79)
| X79 != relation_rng(X78)
| ~ relation(X78) )
& ( ~ in(esk6_2(X78,X84),X84)
| ~ in(ordered_pair(X86,esk6_2(X78,X84)),X78)
| X84 = relation_rng(X78)
| ~ relation(X78) )
& ( in(esk6_2(X78,X84),X84)
| in(ordered_pair(esk7_2(X78,X84),esk6_2(X78,X84)),X78)
| X84 = relation_rng(X78)
| ~ relation(X78) ) ),
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,
! [X88,X89] : ordered_pair(X88,X89) = unordered_pair(unordered_pair(X88,X89),singleton(X88)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
cnf(c_0_8,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_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,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( subset(X1,X2)
=> ( subset(relation_dom(X1),relation_dom(X2))
& subset(relation_rng(X1),relation_rng(X2)) ) ) ) ),
inference(assume_negation,[status(cth)],[t25_relat_1]) ).
fof(c_0_11,plain,
! [X68,X69,X70,X72,X73,X74,X76] :
( ( ~ in(X70,X69)
| in(ordered_pair(X70,esk2_3(X68,X69,X70)),X68)
| X69 != relation_dom(X68)
| ~ relation(X68) )
& ( ~ in(ordered_pair(X72,X73),X68)
| in(X72,X69)
| X69 != relation_dom(X68)
| ~ relation(X68) )
& ( ~ in(esk3_2(X68,X74),X74)
| ~ in(ordered_pair(esk3_2(X68,X74),X76),X68)
| X74 = relation_dom(X68)
| ~ relation(X68) )
& ( in(esk3_2(X68,X74),X74)
| in(ordered_pair(esk3_2(X68,X74),esk4_2(X68,X74)),X68)
| X74 = relation_dom(X68)
| ~ relation(X68) ) ),
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)],[d4_relat_1])])])])])]) ).
cnf(c_0_12,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_8,c_0_9]) ).
fof(c_0_13,plain,
! [X60,X61] : unordered_pair(X60,X61) = unordered_pair(X61,X60),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_14,plain,
! [X62,X63,X64,X65,X66] :
( ( ~ subset(X62,X63)
| ~ in(X64,X62)
| in(X64,X63) )
& ( in(esk1_2(X65,X66),X65)
| subset(X65,X66) )
& ( ~ in(esk1_2(X65,X66),X66)
| subset(X65,X66) ) ),
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_15,negated_conjecture,
( relation(esk14_0)
& relation(esk15_0)
& subset(esk14_0,esk15_0)
& ( ~ subset(relation_dom(esk14_0),relation_dom(esk15_0))
| ~ subset(relation_rng(esk14_0),relation_rng(esk15_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_16,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
subset(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( in(ordered_pair(esk5_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_22,plain,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_23,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( in(X1,esk15_0)
| ~ in(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_26,plain,
( in(unordered_pair(unordered_pair(esk5_3(X3,X2,X1),X1),singleton(esk5_3(X3,X2,X1))),X3)
| X2 != relation_rng(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_27,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( in(ordered_pair(X1,esk2_3(X3,X2,X1)),X3)
| ~ in(X1,X2)
| X2 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_29,negated_conjecture,
( in(X1,relation_rng(esk15_0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X2)),esk14_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_30,plain,
( in(unordered_pair(unordered_pair(X1,esk5_3(X2,relation_rng(X2),X1)),singleton(esk5_3(X2,relation_rng(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_rng(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_18])]) ).
cnf(c_0_31,negated_conjecture,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_32,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X3)),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_33,plain,
( in(unordered_pair(unordered_pair(X1,esk2_3(X3,X2,X1)),singleton(X1)),X3)
| X2 != relation_dom(X3)
| ~ relation(X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_28,c_0_9]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,negated_conjecture,
( in(X1,relation_rng(esk15_0))
| ~ in(X1,relation_rng(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_36,negated_conjecture,
( in(X1,relation_dom(esk15_0))
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk14_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_25])]) ).
cnf(c_0_37,plain,
( in(unordered_pair(singleton(X1),unordered_pair(X1,esk2_3(X2,relation_dom(X2),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_18])]) ).
cnf(c_0_38,negated_conjecture,
( subset(X1,relation_rng(esk15_0))
| ~ in(esk1_2(X1,relation_rng(esk15_0)),relation_rng(esk14_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_40,negated_conjecture,
( in(X1,relation_dom(esk15_0))
| ~ in(X1,relation_dom(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_31])]) ).
cnf(c_0_41,negated_conjecture,
( ~ subset(relation_dom(esk14_0),relation_dom(esk15_0))
| ~ subset(relation_rng(esk14_0),relation_rng(esk15_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_42,negated_conjecture,
subset(relation_rng(esk14_0),relation_rng(esk15_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( subset(X1,relation_dom(esk15_0))
| ~ in(esk1_2(X1,relation_dom(esk15_0)),relation_dom(esk14_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
~ subset(relation_dom(esk14_0),relation_dom(esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU179+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:46:12 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.76/1.88 % Version : CSE_E---1.7
% 1.76/1.88 % Problem : theBenchmark.p
% 1.76/1.88 % SZS status Theorem for theBenchmark.p
% 1.76/1.88 % SZS output start CNFRefutation
% See solution above
% 1.76/1.88 % Total time : 1.371s
%------------------------------------------------------------------------------