%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU204+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 : 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 05:11:03 PM UTC 2026
% Result : Theorem 137.70s 96.86s
% Output : CNFRefutation 138.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 113 ( 22 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 138 ( 55 ~; 61 |; 12 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 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; 0-4 aty)
% Number of variables : 86 ( 3 sgn 43 !; 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(d13_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(X5,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_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(t144_relat_1,conjecture,
! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t144_relat_1) ).
fof(c_0_6,plain,
! [X87,X88,X89,X91,X92,X93,X95] :
( ( ~ in(X89,X88)
| in(ordered_pair(esk5_3(X87,X88,X89),X89),X87)
| X88 != relation_rng(X87)
| ~ relation(X87) )
& ( ~ in(ordered_pair(X92,X91),X87)
| in(X91,X88)
| X88 != relation_rng(X87)
| ~ relation(X87) )
& ( ~ in(esk6_2(X87,X93),X93)
| ~ in(ordered_pair(X95,esk6_2(X87,X93)),X87)
| X93 = relation_rng(X87)
| ~ relation(X87) )
& ( in(esk6_2(X87,X93),X93)
| in(ordered_pair(esk7_2(X87,X93),esk6_2(X87,X93)),X87)
| X93 = relation_rng(X87)
| ~ relation(X87) ) ),
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,
! [X97,X98] : ordered_pair(X97,X98) = unordered_pair(unordered_pair(X97,X98),singleton(X97)),
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,plain,
! [X69,X70,X71,X72,X74,X75,X76,X77,X79] :
( ( in(ordered_pair(esk1_4(X69,X70,X71,X72),X72),X69)
| ~ in(X72,X71)
| X71 != relation_image(X69,X70)
| ~ relation(X69) )
& ( in(esk1_4(X69,X70,X71,X72),X70)
| ~ in(X72,X71)
| X71 != relation_image(X69,X70)
| ~ relation(X69) )
& ( ~ in(ordered_pair(X75,X74),X69)
| ~ in(X75,X70)
| in(X74,X71)
| X71 != relation_image(X69,X70)
| ~ relation(X69) )
& ( ~ in(esk2_3(X69,X76,X77),X77)
| ~ in(ordered_pair(X79,esk2_3(X69,X76,X77)),X69)
| ~ in(X79,X76)
| X77 = relation_image(X69,X76)
| ~ relation(X69) )
& ( in(ordered_pair(esk3_3(X69,X76,X77),esk2_3(X69,X76,X77)),X69)
| in(esk2_3(X69,X76,X77),X77)
| X77 = relation_image(X69,X76)
| ~ relation(X69) )
& ( in(esk3_3(X69,X76,X77),X76)
| in(esk2_3(X69,X76,X77),X77)
| X77 = relation_image(X69,X76)
| ~ relation(X69) ) ),
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)],[d13_relat_1])])])])])]) ).
cnf(c_0_11,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_12,plain,
! [X67,X68] : unordered_pair(X67,X68) = unordered_pair(X68,X67),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_13,plain,
( in(ordered_pair(esk1_4(X1,X2,X3,X4),X4),X1)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( in(unordered_pair(unordered_pair(esk1_4(X1,X2,X3,X4),X4),singleton(esk1_4(X1,X2,X3,X4))),X1)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ in(X4,X3) ),
inference(rw,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_17,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X3)),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( in(unordered_pair(unordered_pair(X1,esk1_4(X2,X3,relation_image(X2,X3),X1)),singleton(esk1_4(X2,X3,relation_image(X2,X3),X1))),X2)
| ~ relation(X2)
| ~ in(X1,relation_image(X2,X3)) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_15])]) ).
fof(c_0_19,plain,
! [X81,X82,X83,X84,X85] :
( ( ~ subset(X81,X82)
| ~ in(X83,X81)
| in(X83,X82) )
& ( in(esk4_2(X84,X85),X84)
| subset(X84,X85) )
& ( ~ in(esk4_2(X84,X85),X85)
| subset(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_tarski])])])])])]) ).
fof(c_0_20,negated_conjecture,
~ ! [X1,X2] :
( relation(X2)
=> subset(relation_image(X2,X1),relation_rng(X2)) ),
inference(assume_negation,[status(cth)],[t144_relat_1]) ).
cnf(c_0_21,plain,
( in(X1,relation_rng(X2))
| ~ relation(X2)
| ~ in(X1,relation_image(X2,X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( in(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,negated_conjecture,
( relation(esk16_0)
& ~ subset(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| ~ in(esk4_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( subset(relation_image(X1,X2),X3)
| in(esk4_2(relation_image(X1,X2),X3),relation_rng(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ subset(relation_image(esk16_0,esk15_0),relation_rng(esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( subset(relation_image(X1,X2),relation_rng(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU204+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.15/0.33 % Computer : n029.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 02:48:59 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 137.70/96.86 % Version : CSE_E---1.7
% 137.70/96.86 % Problem : theBenchmark.p
% 137.70/96.86 % SZS status Theorem for theBenchmark.p
% 137.70/96.86 % SZS output start CNFRefutation
% See solution above
% 138.39/97.59 % Total time : 70.559s
%------------------------------------------------------------------------------