TSTP Solution File: SWW101+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 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 : Fri Sep 1 00:16:19 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 50
% Syntax : Number of formulae : 100 ( 27 unt; 38 typ; 0 def)
% Number of atoms : 212 ( 79 equ)
% Maximal formula atoms : 75 ( 3 avg)
% Number of connectives : 235 ( 85 ~; 101 |; 43 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 32 >; 25 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 6 con; 0-3 aty)
% Number of variables : 46 ( 2 sgn; 23 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
bool: $i > $o ).
tff(decl_23,type,
false: $i ).
tff(decl_24,type,
true: $i ).
tff(decl_25,type,
err: $i ).
tff(decl_26,type,
d: $i > $o ).
tff(decl_27,type,
forallprefers: ( $i * $i ) > $o ).
tff(decl_28,type,
existsprefers: ( $i * $i ) > $o ).
tff(decl_29,type,
phi: $i > $i ).
tff(decl_30,type,
prop: $i > $i ).
tff(decl_31,type,
impl: ( $i * $i ) > $i ).
tff(decl_32,type,
lazy_impl: ( $i * $i ) > $i ).
tff(decl_33,type,
and1: ( $i * $i ) > $i ).
tff(decl_34,type,
f1: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
and2: ( $i * $i ) > $i ).
tff(decl_36,type,
lazy_and1: ( $i * $i ) > $i ).
tff(decl_37,type,
f2: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
lazy_and2: ( $i * $i ) > $i ).
tff(decl_39,type,
or1: ( $i * $i ) > $i ).
tff(decl_40,type,
f3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
or2: ( $i * $i ) > $i ).
tff(decl_42,type,
exists1: $i > $i ).
tff(decl_43,type,
apply: ( $i * $i ) > $i ).
tff(decl_44,type,
f4: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
f5: ( $i * $i ) > $i ).
tff(decl_46,type,
f6: ( $i * $i ) > $i ).
tff(decl_47,type,
exists2: $i > $i ).
tff(decl_48,type,
false1: $i ).
tff(decl_49,type,
f7: $i > $i ).
tff(decl_50,type,
false2: $i ).
tff(decl_51,type,
not1: $i > $i ).
tff(decl_52,type,
not2: $i > $i ).
tff(decl_53,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk4_1: $i > $i ).
tff(decl_57,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk6_1: $i > $i ).
tff(decl_59,type,
esk7_0: $i ).
fof(def_false2,axiom,
? [X5] :
( false2 = phi(f7(X5))
& ~ ? [X10] : forallprefers(f7(X10),f7(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false2) ).
fof(def_f7,axiom,
! [X5] : f7(X5) = lazy_impl(prop(X5),X5),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f7) ).
fof(prop_false,axiom,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_false) ).
fof(lazy_impl_axiom2,axiom,
! [X4] : lazy_impl(false,X4) = true,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom2) ).
fof(def_phi,axiom,
! [X1] :
( ( d(X1)
& phi(X1) = X1 )
| ( ~ d(X1)
& phi(X1) = err ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_phi) ).
fof(prop_true,axiom,
! [X1] :
( prop(X1) = true
<=> bool(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_true) ).
fof(lazy_impl_axiom3,axiom,
! [X4] : lazy_impl(true,X4) = phi(X4),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom3) ).
fof(def_forallprefers,axiom,
! [X1,X2] :
( forallprefers(X1,X2)
<=> ( ( ~ d(X1)
& d(X2) )
| ( d(X1)
& d(X2)
& ~ bool(X1)
& bool(X2) )
| ( X1 = false
& X2 = true ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).
fof(def_bool,axiom,
! [X1] :
( bool(X1)
<=> ( X1 = false
| X1 = true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_bool) ).
fof(false_true_err_in_d,axiom,
( d(true)
& d(false)
& d(err) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).
fof(false1_false2,conjecture,
false1 = false2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false1_false2) ).
fof(def_false1,axiom,
false1 = false,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false1) ).
fof(c_0_12,plain,
! [X83] :
( false2 = phi(f7(esk7_0))
& ~ forallprefers(f7(X83),f7(esk7_0)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_false2])])])]) ).
fof(c_0_13,plain,
! [X81] : f7(X81) = lazy_impl(prop(X81),X81),
inference(variable_rename,[status(thm)],[def_f7]) ).
fof(c_0_14,plain,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
inference(fof_simplification,[status(thm)],[prop_false]) ).
cnf(c_0_15,plain,
~ forallprefers(f7(X1),f7(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
f7(X1) = lazy_impl(prop(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X18] :
( ( prop(X18) != false
| ~ bool(X18) )
& ( bool(X18)
| prop(X18) = false ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
fof(c_0_18,plain,
! [X27] : lazy_impl(false,X27) = true,
inference(variable_rename,[status(thm)],[lazy_impl_axiom2]) ).
fof(c_0_19,plain,
! [X1] :
( ( d(X1)
& phi(X1) = X1 )
| ( ~ d(X1)
& phi(X1) = err ) ),
inference(fof_simplification,[status(thm)],[def_phi]) ).
cnf(c_0_20,plain,
~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk7_0),esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_21,plain,
( bool(X1)
| prop(X1) = false ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
lazy_impl(false,X1) = true,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X17] :
( ( prop(X17) != true
| bool(X17) )
& ( ~ bool(X17)
| prop(X17) = true ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[prop_true])]) ).
fof(c_0_24,plain,
! [X16] :
( ( ~ d(X16)
| d(X16) )
& ( phi(X16) = err
| d(X16) )
& ( ~ d(X16)
| phi(X16) = X16 )
& ( phi(X16) = err
| phi(X16) = X16 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_19])]) ).
fof(c_0_25,plain,
! [X28] : lazy_impl(true,X28) = phi(X28),
inference(variable_rename,[status(thm)],[lazy_impl_axiom3]) ).
fof(c_0_26,plain,
! [X1,X2] :
( forallprefers(X1,X2)
<=> ( ( ~ d(X1)
& d(X2) )
| ( d(X1)
& d(X2)
& ~ bool(X1)
& bool(X2) )
| ( X1 = false
& X2 = true ) ) ),
inference(fof_simplification,[status(thm)],[def_forallprefers]) ).
cnf(c_0_27,plain,
( bool(esk7_0)
| ~ forallprefers(lazy_impl(prop(X1),X1),true) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,plain,
( prop(X1) = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( phi(X1) = X1
| ~ d(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
lazy_impl(true,X1) = phi(X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X12,X13] :
( ( X12 = false
| d(X12)
| ~ d(X12)
| ~ forallprefers(X12,X13) )
& ( X13 = true
| d(X12)
| ~ d(X12)
| ~ forallprefers(X12,X13) )
& ( X12 = false
| d(X13)
| ~ d(X12)
| ~ forallprefers(X12,X13) )
& ( X13 = true
| d(X13)
| ~ d(X12)
| ~ forallprefers(X12,X13) )
& ( X12 = false
| ~ bool(X12)
| ~ d(X12)
| ~ forallprefers(X12,X13) )
& ( X13 = true
| ~ bool(X12)
| ~ d(X12)
| ~ forallprefers(X12,X13) )
& ( X12 = false
| bool(X13)
| ~ d(X12)
| ~ forallprefers(X12,X13) )
& ( X13 = true
| bool(X13)
| ~ d(X12)
| ~ forallprefers(X12,X13) )
& ( X12 = false
| d(X12)
| d(X13)
| ~ forallprefers(X12,X13) )
& ( X13 = true
| d(X12)
| d(X13)
| ~ forallprefers(X12,X13) )
& ( X12 = false
| d(X13)
| d(X13)
| ~ forallprefers(X12,X13) )
& ( X13 = true
| d(X13)
| d(X13)
| ~ forallprefers(X12,X13) )
& ( X12 = false
| ~ bool(X12)
| d(X13)
| ~ forallprefers(X12,X13) )
& ( X13 = true
| ~ bool(X12)
| d(X13)
| ~ forallprefers(X12,X13) )
& ( X12 = false
| bool(X13)
| d(X13)
| ~ forallprefers(X12,X13) )
& ( X13 = true
| bool(X13)
| d(X13)
| ~ forallprefers(X12,X13) )
& ( d(X12)
| ~ d(X13)
| forallprefers(X12,X13) )
& ( ~ d(X12)
| ~ d(X13)
| bool(X12)
| ~ bool(X13)
| forallprefers(X12,X13) )
& ( X12 != false
| X13 != true
| forallprefers(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
fof(c_0_32,plain,
! [X11] :
( ( ~ bool(X11)
| X11 = false
| X11 = true )
& ( X11 != false
| bool(X11) )
& ( X11 != true
| bool(X11) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_bool])])]) ).
cnf(c_0_33,plain,
false2 = phi(f7(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,plain,
( bool(esk7_0)
| ~ forallprefers(lazy_impl(true,X1),true)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
( lazy_impl(true,X1) = X1
| ~ d(X1) ),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
( forallprefers(X1,X2)
| X1 != false
| X2 != true ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
( bool(X1)
| X1 != false ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
false2 = lazy_impl(true,lazy_impl(prop(esk7_0),esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_30]),c_0_16]) ).
cnf(c_0_39,plain,
( bool(esk7_0)
| ~ forallprefers(X1,true)
| ~ d(X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
forallprefers(false,true),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_36])]) ).
cnf(c_0_41,plain,
d(false),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_42,plain,
bool(false),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
( lazy_impl(true,lazy_impl(true,esk7_0)) = false2
| ~ bool(esk7_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_28]) ).
cnf(c_0_44,plain,
bool(esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_42])]) ).
cnf(c_0_45,plain,
lazy_impl(true,lazy_impl(true,esk7_0)) = false2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_46,plain,
( X1 = false
| X1 = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_47,negated_conjecture,
false1 != false2,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[false1_false2])]) ).
cnf(c_0_48,plain,
( ~ forallprefers(lazy_impl(true,X1),lazy_impl(prop(esk7_0),esk7_0))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_49,plain,
( lazy_impl(true,esk7_0) = false2
| ~ d(esk7_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_35]) ).
cnf(c_0_50,plain,
( esk7_0 = true
| esk7_0 = false ),
inference(spm,[status(thm)],[c_0_46,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
false1 != false2,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,plain,
false1 = false,
inference(split_conjunct,[status(thm)],[def_false1]) ).
cnf(c_0_53,plain,
( ~ forallprefers(lazy_impl(true,X1),lazy_impl(true,esk7_0))
| ~ bool(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_28]),c_0_44])]) ).
cnf(c_0_54,plain,
( lazy_impl(true,false) = false2
| esk7_0 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_41])]) ).
cnf(c_0_55,negated_conjecture,
false2 != false,
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( ~ forallprefers(lazy_impl(true,X1),esk7_0)
| ~ d(esk7_0)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_35]) ).
cnf(c_0_57,plain,
esk7_0 = true,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_54]),c_0_41])]),c_0_55]) ).
cnf(c_0_58,plain,
d(true),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_59,plain,
( ~ forallprefers(lazy_impl(true,X1),true)
| ~ bool(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_57]),c_0_58])]) ).
cnf(c_0_60,plain,
( ~ forallprefers(X1,true)
| ~ d(X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_35]) ).
cnf(c_0_61,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_40]),c_0_41]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 19:43:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.025000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.029000 s
%------------------------------------------------------------------------------