TSTP Solution File: SEU242+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU242+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 : Thu Aug 31 16:23:43 EDT 2023
% Result : Theorem 2.69s 2.85s
% Output : CNFRefutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 83 ( 13 unt; 27 typ; 0 def)
% Number of atoms : 213 ( 29 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 263 ( 106 ~; 119 |; 28 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 18 >; 8 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn; 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
one_to_one: $i > $o ).
tff(decl_27,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_29,type,
connected: $i > $o ).
tff(decl_30,type,
relation_field: $i > $i ).
tff(decl_31,type,
is_connected_in: ( $i * $i ) > $o ).
tff(decl_32,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_33,type,
singleton: $i > $i ).
tff(decl_34,type,
relation_dom: $i > $i ).
tff(decl_35,type,
relation_rng: $i > $i ).
tff(decl_36,type,
element: ( $i * $i ) > $o ).
tff(decl_37,type,
empty_set: $i ).
tff(decl_38,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk3_1: $i > $i ).
tff(decl_41,type,
esk4_0: $i ).
tff(decl_42,type,
esk5_0: $i ).
tff(decl_43,type,
esk6_0: $i ).
tff(decl_44,type,
esk7_0: $i ).
tff(decl_45,type,
esk8_0: $i ).
tff(decl_46,type,
esk9_0: $i ).
tff(decl_47,type,
esk10_0: $i ).
tff(decl_48,type,
esk11_0: $i ).
fof(l4_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,relation_field(X1))
& in(X3,relation_field(X1))
& X2 != X3
& ~ in(ordered_pair(X2,X3),X1)
& ~ in(ordered_pair(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
fof(d6_relat_2,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_connected_in(X1,X2)
<=> ! [X3,X4] :
~ ( in(X3,X2)
& in(X4,X2)
& X3 != X4
& ~ in(ordered_pair(X3,X4),X1)
& ~ in(ordered_pair(X4,X3),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
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(d14_relat_2,axiom,
! [X1] :
( relation(X1)
=> ( connected(X1)
<=> is_connected_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( connected(X1)
<=> ! [X2,X3] :
~ ( in(X2,relation_field(X1))
& in(X3,relation_field(X1))
& X2 != X3
& ~ in(ordered_pair(X2,X3),X1)
& ~ in(ordered_pair(X3,X2),X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l4_wellord1])]) ).
fof(c_0_6,plain,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_connected_in(X1,X2)
<=> ! [X3,X4] :
~ ( in(X3,X2)
& in(X4,X2)
& X3 != X4
& ~ in(ordered_pair(X3,X4),X1)
& ~ in(ordered_pair(X4,X3),X1) ) ) ),
inference(fof_simplification,[status(thm)],[d6_relat_2]) ).
fof(c_0_7,negated_conjecture,
! [X36,X37] :
( relation(esk4_0)
& ( in(esk5_0,relation_field(esk4_0))
| ~ connected(esk4_0) )
& ( in(esk6_0,relation_field(esk4_0))
| ~ connected(esk4_0) )
& ( esk5_0 != esk6_0
| ~ connected(esk4_0) )
& ( ~ in(ordered_pair(esk5_0,esk6_0),esk4_0)
| ~ connected(esk4_0) )
& ( ~ in(ordered_pair(esk6_0,esk5_0),esk4_0)
| ~ connected(esk4_0) )
& ( connected(esk4_0)
| ~ in(X36,relation_field(esk4_0))
| ~ in(X37,relation_field(esk4_0))
| X36 = X37
| in(ordered_pair(X36,X37),esk4_0)
| in(ordered_pair(X37,X36),esk4_0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
fof(c_0_8,plain,
! [X14,X15] : ordered_pair(X14,X15) = unordered_pair(unordered_pair(X14,X15),singleton(X14)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,plain,
! [X17,X18,X19,X20,X21] :
( ( ~ is_connected_in(X17,X18)
| ~ in(X19,X18)
| ~ in(X20,X18)
| X19 = X20
| in(ordered_pair(X19,X20),X17)
| in(ordered_pair(X20,X19),X17)
| ~ relation(X17) )
& ( in(esk1_2(X17,X21),X21)
| is_connected_in(X17,X21)
| ~ relation(X17) )
& ( in(esk2_2(X17,X21),X21)
| is_connected_in(X17,X21)
| ~ relation(X17) )
& ( esk1_2(X17,X21) != esk2_2(X17,X21)
| is_connected_in(X17,X21)
| ~ relation(X17) )
& ( ~ in(ordered_pair(esk1_2(X17,X21),esk2_2(X17,X21)),X17)
| is_connected_in(X17,X21)
| ~ relation(X17) )
& ( ~ in(ordered_pair(esk2_2(X17,X21),esk1_2(X17,X21)),X17)
| is_connected_in(X17,X21)
| ~ relation(X17) ) ),
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)],[c_0_6])])])])])]) ).
cnf(c_0_10,negated_conjecture,
( connected(esk4_0)
| X1 = X2
| in(ordered_pair(X1,X2),esk4_0)
| in(ordered_pair(X2,X1),esk4_0)
| ~ in(X1,relation_field(esk4_0))
| ~ in(X2,relation_field(esk4_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( in(esk1_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_14,plain,
! [X9,X10] : unordered_pair(X9,X10) = unordered_pair(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_15,plain,
( is_connected_in(X1,X2)
| ~ in(ordered_pair(esk2_2(X1,X2),esk1_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
( X1 = X2
| connected(esk4_0)
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),esk4_0)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk4_0)
| ~ in(X2,relation_field(esk4_0))
| ~ in(X1,relation_field(esk4_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( is_connected_in(esk4_0,X1)
| in(esk1_2(esk4_0,X1),X1) ),
inference(spm,[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,
( in(esk2_2(X1,X2),X2)
| is_connected_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,plain,
( is_connected_in(X1,X2)
| ~ in(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk2_2(X1,X2),esk1_2(X1,X2)),singleton(esk2_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( X1 = esk1_2(esk4_0,relation_field(esk4_0))
| is_connected_in(esk4_0,relation_field(esk4_0))
| connected(esk4_0)
| in(unordered_pair(unordered_pair(esk1_2(esk4_0,relation_field(esk4_0)),X1),singleton(esk1_2(esk4_0,relation_field(esk4_0)))),esk4_0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,esk1_2(esk4_0,relation_field(esk4_0)))),esk4_0)
| ~ in(X1,relation_field(esk4_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( is_connected_in(esk4_0,X1)
| in(esk2_2(esk4_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_24,plain,
( X3 = X4
| in(ordered_pair(X3,X4),X1)
| in(ordered_pair(X4,X3),X1)
| ~ is_connected_in(X1,X2)
| ~ in(X3,X2)
| ~ in(X4,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_25,plain,
! [X13] :
( ( ~ connected(X13)
| is_connected_in(X13,relation_field(X13))
| ~ relation(X13) )
& ( ~ is_connected_in(X13,relation_field(X13))
| connected(X13)
| ~ relation(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d14_relat_2])])]) ).
cnf(c_0_26,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),singleton(esk1_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_27,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk2_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_18]),c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( esk2_2(esk4_0,relation_field(esk4_0)) = esk1_2(esk4_0,relation_field(esk4_0))
| is_connected_in(esk4_0,relation_field(esk4_0))
| connected(esk4_0)
| in(unordered_pair(singleton(esk2_2(esk4_0,relation_field(esk4_0))),unordered_pair(esk1_2(esk4_0,relation_field(esk4_0)),esk2_2(esk4_0,relation_field(esk4_0)))),esk4_0)
| in(unordered_pair(singleton(esk1_2(esk4_0,relation_field(esk4_0))),unordered_pair(esk1_2(esk4_0,relation_field(esk4_0)),esk2_2(esk4_0,relation_field(esk4_0)))),esk4_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]),c_0_18]) ).
cnf(c_0_29,plain,
( X3 = X4
| in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X1)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X1)
| ~ relation(X1)
| ~ in(X4,X2)
| ~ in(X3,X2)
| ~ is_connected_in(X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_11]),c_0_11]) ).
cnf(c_0_30,plain,
( is_connected_in(X1,relation_field(X1))
| ~ connected(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( is_connected_in(X1,X2)
| ~ relation(X1)
| ~ in(unordered_pair(singleton(esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))),X1) ),
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_32,negated_conjecture,
( esk2_2(esk4_0,relation_field(esk4_0)) = esk1_2(esk4_0,relation_field(esk4_0))
| is_connected_in(esk4_0,relation_field(esk4_0))
| connected(esk4_0)
| in(unordered_pair(singleton(esk1_2(esk4_0,relation_field(esk4_0))),unordered_pair(esk1_2(esk4_0,relation_field(esk4_0)),esk2_2(esk4_0,relation_field(esk4_0)))),esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_13])]) ).
cnf(c_0_33,plain,
( X1 = X2
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),X3)
| ~ connected(X3)
| ~ relation(X3)
| ~ in(X2,relation_field(X3))
| ~ in(X1,relation_field(X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( is_connected_in(X1,X2)
| esk1_2(X1,X2) != esk2_2(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_35,negated_conjecture,
( esk2_2(esk4_0,relation_field(esk4_0)) = esk1_2(esk4_0,relation_field(esk4_0))
| is_connected_in(esk4_0,relation_field(esk4_0))
| connected(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_13])]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(ordered_pair(esk5_0,esk6_0),esk4_0)
| ~ connected(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_37,negated_conjecture,
( ~ in(ordered_pair(esk6_0,esk5_0),esk4_0)
| ~ connected(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_38,plain,
( X1 = X2
| in(unordered_pair(singleton(X2),unordered_pair(X2,X1)),X3)
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3)
| ~ connected(X3)
| ~ relation(X3)
| ~ in(X2,relation_field(X3))
| ~ in(X1,relation_field(X3)) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_39,negated_conjecture,
( in(esk5_0,relation_field(esk4_0))
| ~ connected(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_40,plain,
( connected(X1)
| ~ is_connected_in(X1,relation_field(X1))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_41,negated_conjecture,
( is_connected_in(esk4_0,relation_field(esk4_0))
| connected(esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_13])]) ).
cnf(c_0_42,negated_conjecture,
( ~ connected(esk4_0)
| ~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk5_0)),esk4_0) ),
inference(rw,[status(thm)],[c_0_36,c_0_11]) ).
cnf(c_0_43,negated_conjecture,
( ~ connected(esk4_0)
| ~ in(unordered_pair(unordered_pair(esk6_0,esk5_0),singleton(esk6_0)),esk4_0) ),
inference(rw,[status(thm)],[c_0_37,c_0_11]) ).
cnf(c_0_44,negated_conjecture,
( X1 = esk5_0
| in(unordered_pair(singleton(esk5_0),unordered_pair(esk5_0,X1)),esk4_0)
| in(unordered_pair(unordered_pair(X1,esk5_0),singleton(X1)),esk4_0)
| ~ connected(esk4_0)
| ~ in(X1,relation_field(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_13])]) ).
cnf(c_0_45,negated_conjecture,
connected(esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_13])]) ).
cnf(c_0_46,negated_conjecture,
( in(esk6_0,relation_field(esk4_0))
| ~ connected(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_47,negated_conjecture,
( esk5_0 != esk6_0
| ~ connected(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_48,negated_conjecture,
( ~ connected(esk4_0)
| ~ in(unordered_pair(singleton(esk5_0),unordered_pair(esk5_0,esk6_0)),esk4_0) ),
inference(rw,[status(thm)],[c_0_42,c_0_18]) ).
cnf(c_0_49,negated_conjecture,
( ~ connected(esk4_0)
| ~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk6_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_18]) ).
cnf(c_0_50,negated_conjecture,
( X1 = esk5_0
| in(unordered_pair(singleton(esk5_0),unordered_pair(esk5_0,X1)),esk4_0)
| in(unordered_pair(unordered_pair(X1,esk5_0),singleton(X1)),esk4_0)
| ~ in(X1,relation_field(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
cnf(c_0_51,negated_conjecture,
in(esk6_0,relation_field(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_45])]) ).
cnf(c_0_52,negated_conjecture,
esk6_0 != esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_45])]) ).
cnf(c_0_53,negated_conjecture,
~ in(unordered_pair(singleton(esk5_0),unordered_pair(esk5_0,esk6_0)),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_45])]) ).
cnf(c_0_54,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk5_0,esk6_0),singleton(esk6_0)),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_45])]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_18]),c_0_52]),c_0_53]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU242+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 18:54:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 2.69/2.85 % Version : CSE_E---1.5
% 2.69/2.85 % Problem : theBenchmark.p
% 2.69/2.85 % Proof found
% 2.69/2.85 % SZS status Theorem for theBenchmark.p
% 2.69/2.85 % SZS output start Proof
% See solution above
% 2.69/2.86 % Total time : 2.285000 s
% 2.69/2.86 % SZS output end Proof
% 2.69/2.86 % Total time : 2.288000 s
%------------------------------------------------------------------------------