TSTP Solution File: SET914^7 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET914^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n022.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 21 02:56:30 EDT 2024
% Result : Theorem 1.37s 0.65s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 47
% Syntax : Number of formulae : 122 ( 35 unt; 24 typ; 0 def)
% Number of atoms : 510 ( 17 equ; 0 cnn)
% Maximal formula atoms : 46 ( 5 avg)
% Number of connectives : 2122 ( 306 ~; 263 |; 25 &;1487 @)
% ( 2 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 6 con; 0-4 aty)
% Number of variables : 278 ( 68 ^ 210 !; 0 ?; 278 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_22,type,
qmltpeq: mu > mu > $i > $o ).
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_33,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_36,type,
exists_in_world: mu > $i > $o ).
thf(decl_37,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_58,type,
in: mu > mu > $i > $o ).
thf(decl_59,type,
disjoint: mu > mu > $i > $o ).
thf(decl_60,type,
empty_set: mu ).
thf(decl_61,type,
set_intersection2: mu > mu > mu ).
thf(decl_62,type,
unordered_pair: mu > mu > mu ).
thf(decl_63,type,
epred1_4: $i > mu > mu > mu > $o ).
thf(decl_64,type,
epred2_4: $i > mu > mu > mu > $o ).
thf(decl_66,type,
esk2_2: $i > mu > mu ).
thf(decl_69,type,
esk5_0: $i ).
thf(decl_70,type,
esk6_0: mu ).
thf(decl_71,type,
esk7_0: mu ).
thf(decl_72,type,
esk8_0: mu ).
thf(decl_73,type,
esk9_4: mu > mu > mu > $i > mu ).
thf(decl_74,type,
esk10_4: mu > mu > mu > $i > mu ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [X11: mu > $i > $o,X3: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ X3 )
=> ( X11 @ X12 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(idempotence_k3_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] : ( qmltpeq @ ( set_intersection2 @ X28 @ X28 ) @ X28 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mand @ ( mimplies @ X4 @ X5 ) @ ( mimplies @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mequiv) ).
thf(symmetry,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X23: mu] :
( mforall_ind
@ ^ [X24: mu] : ( mimplies @ ( qmltpeq @ X23 @ X24 ) @ ( qmltpeq @ X24 @ X23 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(in_substitution_2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] :
( mforall_ind
@ ^ [X30: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X28 @ X29 ) @ ( in @ X30 @ X28 ) ) @ ( in @ X30 @ X29 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_substitution_2) ).
thf(existence_of_set_intersection2_ax,axiom,
! [X7: $i,X20: mu,X21: mu] : ( exists_in_world @ ( set_intersection2 @ X20 @ X21 ) @ X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_set_intersection2_ax) ).
thf(d1_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mequiv @ ( qmltpeq @ X28 @ empty_set )
@ ( mforall_ind
@ ^ [X29: mu] : ( mnot @ ( in @ X29 @ X28 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(d7_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] : ( mequiv @ ( disjoint @ X28 @ X29 ) @ ( qmltpeq @ ( set_intersection2 @ X28 @ X29 ) @ empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(existence_of_empty_set_ax,axiom,
! [X7: $i] : ( exists_in_world @ empty_set @ X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_empty_set_ax) ).
thf(d3_xboole_0,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] :
( mforall_ind
@ ^ [X30: mu] :
( mequiv @ ( qmltpeq @ X30 @ ( set_intersection2 @ X28 @ X29 ) )
@ ( mforall_ind
@ ^ [X31: mu] : ( mequiv @ ( in @ X31 @ X30 ) @ ( mand @ ( in @ X31 @ X28 ) @ ( in @ X31 @ X29 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(disjoint_substitution_1,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] :
( mforall_ind
@ ^ [X30: mu] : ( mimplies @ ( mand @ ( qmltpeq @ X28 @ X29 ) @ ( disjoint @ X28 @ X30 ) ) @ ( disjoint @ X29 @ X30 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_substitution_1) ).
thf(commutativity_k2_tarski,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] : ( qmltpeq @ ( unordered_pair @ X28 @ X29 ) @ ( unordered_pair @ X29 @ X28 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(t55_zfmisc_1,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] :
( mforall_ind
@ ^ [X30: mu] : ( mnot @ ( mand @ ( disjoint @ ( unordered_pair @ X28 @ X29 ) @ X30 ) @ ( in @ X28 @ X30 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
thf(existence_of_unordered_pair_ax,axiom,
! [X7: $i,X20: mu,X21: mu] : ( exists_in_world @ ( unordered_pair @ X20 @ X21 ) @ X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_unordered_pair_ax) ).
thf(d2_tarski,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X28: mu] :
( mforall_ind
@ ^ [X29: mu] :
( mforall_ind
@ ^ [X30: mu] :
( mequiv @ ( qmltpeq @ X30 @ ( unordered_pair @ X28 @ X29 ) )
@ ( mforall_ind
@ ^ [X31: mu] : ( mequiv @ ( in @ X31 @ X30 ) @ ( mor @ ( qmltpeq @ X31 @ X28 ) @ ( qmltpeq @ X31 @ X29 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(reflexivity,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X22: mu] : ( qmltpeq @ X22 @ X22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(c_0_21,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_22,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_23,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_24,plain,
( mforall_ind
= ( ^ [Z0: mu > $i > $o,Z1: $i] :
! [X12: mu] :
( ( exists_in_world @ X12 @ Z1 )
=> ( Z0 @ X12 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[mforall_ind]) ).
thf(c_0_25,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_26,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_27,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_28,plain,
! [X124: $i,X123: mu] :
( ( exists_in_world @ X123 @ X124 )
=> ! [X122: mu] :
( ( exists_in_world @ X122 @ X124 )
=> ( qmltpeq @ ( set_intersection2 @ X123 @ X123 ) @ X123 @ X124 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0]),c_0_24]),c_0_25]) ).
thf(c_0_29,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[mequiv]) ).
thf(c_0_30,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_26,c_0_22]),c_0_23]) ).
thf(c_0_31,plain,
! [X56: $i,X55: mu] :
( ( exists_in_world @ X55 @ X56 )
=> ! [X54: mu] :
( ( exists_in_world @ X54 @ X56 )
=> ( ~ ( qmltpeq @ X55 @ X54 @ X56 )
| ( qmltpeq @ X54 @ X55 @ X56 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[symmetry]),c_0_27]),c_0_24]),c_0_25])]) ).
thf(c_0_32,plain,
! [X221: $i,X222: mu,X223: mu] :
( ~ ( exists_in_world @ X222 @ X221 )
| ~ ( exists_in_world @ X223 @ X221 )
| ( qmltpeq @ ( set_intersection2 @ X222 @ X222 ) @ X222 @ X221 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])]) ).
thf(c_0_33,plain,
( mequiv
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) )
| ~ ( ~ ( Z1 @ Z2 )
| ( Z0 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_30]),c_0_27]) ).
thf(c_0_34,plain,
! [X95: $i,X94: mu] :
( ( exists_in_world @ X94 @ X95 )
=> ! [X93: mu] :
( ( exists_in_world @ X93 @ X95 )
=> ! [X92: mu] :
( ( exists_in_world @ X92 @ X95 )
=> ( ~ ~ ( ~ ( qmltpeq @ X94 @ X93 @ X95 )
| ~ ( in @ X92 @ X94 @ X95 ) )
| ( in @ X92 @ X93 @ X95 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[in_substitution_2]),c_0_30]),c_0_27]),c_0_24]),c_0_25])]) ).
thf(c_0_35,plain,
! [X154: $i,X155: mu,X156: mu] :
( ~ ( exists_in_world @ X155 @ X154 )
| ~ ( exists_in_world @ X156 @ X154 )
| ~ ( qmltpeq @ X155 @ X156 @ X154 )
| ( qmltpeq @ X156 @ X155 @ X154 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
thf(c_0_36,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( qmltpeq @ ( set_intersection2 @ X10 @ X10 ) @ X10 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_37,plain,
! [X146: $i,X147: mu,X148: mu] : ( exists_in_world @ ( set_intersection2 @ X147 @ X148 ) @ X146 ),
inference(variable_rename,[status(thm)],[existence_of_set_intersection2_ax]) ).
thf(c_0_38,plain,
! [X107: $i,X106: mu] :
( ( exists_in_world @ X106 @ X107 )
=> ~ ( ~ ( ~ ( qmltpeq @ X106 @ empty_set @ X107 )
| ! [X105: mu] :
( ( exists_in_world @ X105 @ X107 )
=> ~ ( in @ X105 @ X106 @ X107 ) ) )
| ~ ( ~ ! [X105: mu] :
( ( exists_in_world @ X105 @ X107 )
=> ~ ( in @ X105 @ X106 @ X107 ) )
| ( qmltpeq @ X106 @ empty_set @ X107 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_xboole_0]),c_0_22]),c_0_33]),c_0_24]),c_0_25])]) ).
thf(c_0_39,plain,
! [X192: $i,X193: mu,X194: mu,X195: mu] :
( ~ ( exists_in_world @ X193 @ X192 )
| ~ ( exists_in_world @ X194 @ X192 )
| ~ ( exists_in_world @ X195 @ X192 )
| ~ ( qmltpeq @ X193 @ X194 @ X192 )
| ~ ( in @ X195 @ X193 @ X192 )
| ( in @ X195 @ X194 @ X192 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
thf(c_0_40,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( qmltpeq @ X12 @ X10 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( qmltpeq @ X10 @ X12 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_41,plain,
! [X10: mu,X3: $i] :
( ( qmltpeq @ ( set_intersection2 @ X10 @ X10 ) @ X10 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(condense,[status(thm)],[c_0_36]) ).
thf(c_0_42,plain,
! [X12: mu,X10: mu,X3: $i] : ( exists_in_world @ ( set_intersection2 @ X10 @ X12 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
thf(c_0_43,plain,
! [X114: mu,X115: mu,X116: mu,X117: $i] :
( ( epred2_4 @ X117 @ X116 @ X115 @ X114 )
<=> ~ ( ~ ( ~ ( qmltpeq @ X114 @ ( set_intersection2 @ X116 @ X115 ) @ X117 )
| ! [X113: mu] :
( ( exists_in_world @ X113 @ X117 )
=> ~ ( ~ ( ~ ( in @ X113 @ X114 @ X117 )
| ~ ( ~ ( in @ X113 @ X116 @ X117 )
| ~ ( in @ X113 @ X115 @ X117 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X113 @ X116 @ X117 )
| ~ ( in @ X113 @ X115 @ X117 ) )
| ( in @ X113 @ X114 @ X117 ) ) ) ) )
| ~ ( ~ ! [X113: mu] :
( ( exists_in_world @ X113 @ X117 )
=> ~ ( ~ ( ~ ( in @ X113 @ X114 @ X117 )
| ~ ( ~ ( in @ X113 @ X116 @ X117 )
| ~ ( in @ X113 @ X115 @ X117 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X113 @ X116 @ X117 )
| ~ ( in @ X113 @ X115 @ X117 ) )
| ( in @ X113 @ X114 @ X117 ) ) ) )
| ( qmltpeq @ X114 @ ( set_intersection2 @ X116 @ X115 ) @ X117 ) ) ) ),
introduced(definition) ).
thf(c_0_44,plain,
! [X120: $i,X119: mu] :
( ( exists_in_world @ X119 @ X120 )
=> ! [X118: mu] :
( ( exists_in_world @ X118 @ X120 )
=> ~ ( ~ ( ~ ( disjoint @ X119 @ X118 @ X120 )
| ( qmltpeq @ ( set_intersection2 @ X119 @ X118 ) @ empty_set @ X120 ) )
| ~ ( ~ ( qmltpeq @ ( set_intersection2 @ X119 @ X118 ) @ empty_set @ X120 )
| ( disjoint @ X119 @ X118 @ X120 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[d7_xboole_0]),c_0_33]),c_0_24]),c_0_25])]) ).
thf(c_0_45,plain,
! [X205: $i,X206: mu,X207: mu] :
( ( ~ ( qmltpeq @ X206 @ empty_set @ X205 )
| ~ ( exists_in_world @ X207 @ X205 )
| ~ ( in @ X207 @ X206 @ X205 )
| ~ ( exists_in_world @ X206 @ X205 ) )
& ( ( exists_in_world @ ( esk2_2 @ X205 @ X206 ) @ X205 )
| ( qmltpeq @ X206 @ empty_set @ X205 )
| ~ ( exists_in_world @ X206 @ X205 ) )
& ( ( in @ ( esk2_2 @ X205 @ X206 ) @ X206 @ X205 )
| ( qmltpeq @ X206 @ empty_set @ X205 )
| ~ ( exists_in_world @ X206 @ X205 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])])]) ).
thf(c_0_46,plain,
! [X12: mu,X14: mu,X10: mu,X3: $i] :
( ( in @ X14 @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( qmltpeq @ X10 @ X12 @ X3 )
| ~ ( in @ X14 @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_47,plain,
! [X10: mu,X3: $i] :
( ( qmltpeq @ X10 @ ( set_intersection2 @ X10 @ X10 ) @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
thf(c_0_48,plain,
! [X114: mu,X115: mu,X116: mu,X117: $i] :
( ( epred2_4 @ X117 @ X116 @ X115 @ X114 )
=> ~ ( ~ ( ~ ( qmltpeq @ X114 @ ( set_intersection2 @ X116 @ X115 ) @ X117 )
| ! [X113: mu] :
( ( exists_in_world @ X113 @ X117 )
=> ~ ( ~ ( ~ ( in @ X113 @ X114 @ X117 )
| ~ ( ~ ( in @ X113 @ X116 @ X117 )
| ~ ( in @ X113 @ X115 @ X117 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X113 @ X116 @ X117 )
| ~ ( in @ X113 @ X115 @ X117 ) )
| ( in @ X113 @ X114 @ X117 ) ) ) ) )
| ~ ( ~ ! [X113: mu] :
( ( exists_in_world @ X113 @ X117 )
=> ~ ( ~ ( ~ ( in @ X113 @ X114 @ X117 )
| ~ ( ~ ( in @ X113 @ X116 @ X117 )
| ~ ( in @ X113 @ X115 @ X117 ) ) )
| ~ ( ~ ~ ( ~ ( in @ X113 @ X116 @ X117 )
| ~ ( in @ X113 @ X115 @ X117 ) )
| ( in @ X113 @ X114 @ X117 ) ) ) )
| ( qmltpeq @ X114 @ ( set_intersection2 @ X116 @ X115 ) @ X117 ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_43]) ).
thf(c_0_49,plain,
! [X217: $i,X218: mu,X219: mu] :
( ( ~ ( disjoint @ X218 @ X219 @ X217 )
| ( qmltpeq @ ( set_intersection2 @ X218 @ X219 ) @ empty_set @ X217 )
| ~ ( exists_in_world @ X219 @ X217 )
| ~ ( exists_in_world @ X218 @ X217 ) )
& ( ~ ( qmltpeq @ ( set_intersection2 @ X218 @ X219 ) @ empty_set @ X217 )
| ( disjoint @ X218 @ X219 @ X217 )
| ~ ( exists_in_world @ X219 @ X217 )
| ~ ( exists_in_world @ X218 @ X217 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])])])]) ).
thf(c_0_50,plain,
! [X145: $i] : ( exists_in_world @ empty_set @ X145 ),
inference(variable_rename,[status(thm)],[existence_of_empty_set_ax]) ).
thf(c_0_51,plain,
! [X12: mu,X10: mu,X3: $i] :
( ~ ( qmltpeq @ X10 @ empty_set @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( in @ X12 @ X10 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_52,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( in @ X10 @ ( set_intersection2 @ X12 @ X12 ) @ X3 )
| ~ ( in @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42])]) ).
thf(c_0_53,plain,
! [X241: mu,X242: mu,X243: mu,X244: $i,X245: mu] :
( ( ( in @ X245 @ X243 @ X244 )
| ~ ( in @ X245 @ X241 @ X244 )
| ~ ( exists_in_world @ X245 @ X244 )
| ~ ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ( in @ X245 @ X242 @ X244 )
| ~ ( in @ X245 @ X241 @ X244 )
| ~ ( exists_in_world @ X245 @ X244 )
| ~ ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ~ ( in @ X245 @ X243 @ X244 )
| ~ ( in @ X245 @ X242 @ X244 )
| ( in @ X245 @ X241 @ X244 )
| ~ ( exists_in_world @ X245 @ X244 )
| ~ ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ( exists_in_world @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X244 )
| ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X243 @ X244 )
| ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X241 @ X244 )
| ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X242 @ X244 )
| ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X241 @ X244 )
| ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ~ ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X241 @ X244 )
| ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X241 @ X244 )
| ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X243 @ X244 )
| ~ ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X243 @ X244 )
| ~ ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X242 @ X244 )
| ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X242 @ X244 )
| ~ ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X243 @ X244 )
| ~ ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X242 @ X244 )
| ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) )
& ( ~ ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X241 @ X244 )
| ~ ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X243 @ X244 )
| ~ ( in @ ( esk10_4 @ X241 @ X242 @ X243 @ X244 ) @ X242 @ X244 )
| ( qmltpeq @ X241 @ ( set_intersection2 @ X243 @ X242 ) @ X244 )
| ~ ( epred2_4 @ X244 @ X243 @ X242 @ X241 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])])])]) ).
thf(c_0_54,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( qmltpeq @ ( set_intersection2 @ X10 @ X12 ) @ empty_set @ X3 )
| ~ ( disjoint @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_55,plain,
! [X3: $i] : ( exists_in_world @ empty_set @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_56,plain,
! [X12: mu,X10: mu,X3: $i] :
( ~ ( qmltpeq @ ( set_intersection2 @ X10 @ X10 ) @ empty_set @ X3 )
| ~ ( in @ X12 @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_42])]) ).
thf(c_0_57,plain,
! [X117: $i,X116: mu] :
( ( exists_in_world @ X116 @ X117 )
=> ! [X115: mu] :
( ( exists_in_world @ X115 @ X117 )
=> ! [X114: mu] :
( ( exists_in_world @ X114 @ X117 )
=> ( epred2_4 @ X117 @ X116 @ X115 @ X114 ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[d3_xboole_0]),c_0_30]),c_0_33]),c_0_24]),c_0_25])]),c_0_43]) ).
thf(c_0_58,plain,
! [X80: $i,X79: mu] :
( ( exists_in_world @ X79 @ X80 )
=> ! [X78: mu] :
( ( exists_in_world @ X78 @ X80 )
=> ! [X77: mu] :
( ( exists_in_world @ X77 @ X80 )
=> ( ~ ~ ( ~ ( qmltpeq @ X79 @ X78 @ X80 )
| ~ ( disjoint @ X79 @ X77 @ X80 ) )
| ( disjoint @ X78 @ X77 @ X80 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[disjoint_substitution_1]),c_0_30]),c_0_27]),c_0_24]),c_0_25])]) ).
thf(c_0_59,plain,
! [X101: $i,X100: mu] :
( ( exists_in_world @ X100 @ X101 )
=> ! [X99: mu] :
( ( exists_in_world @ X99 @ X101 )
=> ( qmltpeq @ ( unordered_pair @ X100 @ X99 ) @ ( unordered_pair @ X99 @ X100 ) @ X101 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[commutativity_k2_tarski]),c_0_24]),c_0_25]) ).
thf(c_0_60,plain,
! [X109: mu,X110: mu,X111: mu,X112: $i] :
( ( epred1_4 @ X112 @ X111 @ X110 @ X109 )
<=> ~ ( ~ ( ~ ( qmltpeq @ X109 @ ( unordered_pair @ X111 @ X110 ) @ X112 )
| ! [X108: mu] :
( ( exists_in_world @ X108 @ X112 )
=> ~ ( ~ ( ~ ( in @ X108 @ X109 @ X112 )
| ( qmltpeq @ X108 @ X111 @ X112 )
| ( qmltpeq @ X108 @ X110 @ X112 ) )
| ~ ( ~ ( ( qmltpeq @ X108 @ X111 @ X112 )
| ( qmltpeq @ X108 @ X110 @ X112 ) )
| ( in @ X108 @ X109 @ X112 ) ) ) ) )
| ~ ( ~ ! [X108: mu] :
( ( exists_in_world @ X108 @ X112 )
=> ~ ( ~ ( ~ ( in @ X108 @ X109 @ X112 )
| ( qmltpeq @ X108 @ X111 @ X112 )
| ( qmltpeq @ X108 @ X110 @ X112 ) )
| ~ ( ~ ( ( qmltpeq @ X108 @ X111 @ X112 )
| ( qmltpeq @ X108 @ X110 @ X112 ) )
| ( in @ X108 @ X109 @ X112 ) ) ) )
| ( qmltpeq @ X109 @ ( unordered_pair @ X111 @ X110 ) @ X112 ) ) ) ),
introduced(definition) ).
thf(c_0_61,plain,
! [X10: mu,X3: $i,X12: mu,X14: mu,X19: mu] :
( ( in @ X10 @ X19 @ X3 )
| ~ ( in @ X10 @ X12 @ X3 )
| ~ ( in @ X10 @ X14 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( qmltpeq @ X19 @ ( set_intersection2 @ X12 @ X14 ) @ X3 )
| ~ ( epred2_4 @ X3 @ X12 @ X14 @ X19 ) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
thf(c_0_62,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( qmltpeq @ empty_set @ ( set_intersection2 @ X10 @ X12 ) @ X3 )
| ~ ( disjoint @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_54]),c_0_55]),c_0_42])]) ).
thf(c_0_63,plain,
! [X10: mu,X3: $i] :
( ~ ( in @ X10 @ empty_set @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_41]),c_0_55])]) ).
thf(c_0_64,plain,
! [X213: $i,X214: mu,X215: mu,X216: mu] :
( ~ ( exists_in_world @ X214 @ X213 )
| ~ ( exists_in_world @ X215 @ X213 )
| ~ ( exists_in_world @ X216 @ X213 )
| ( epred2_4 @ X213 @ X214 @ X215 @ X216 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
thf(c_0_65,negated_conjecture,
~ ! [X135: $i,X134: mu] :
( ( exists_in_world @ X134 @ X135 )
=> ! [X133: mu] :
( ( exists_in_world @ X133 @ X135 )
=> ! [X132: mu] :
( ( exists_in_world @ X132 @ X135 )
=> ~ ~ ( ~ ( disjoint @ ( unordered_pair @ X134 @ X133 ) @ X132 @ X135 )
| ~ ( in @ X134 @ X132 @ X135 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t55_zfmisc_1])]),c_0_22]),c_0_30]),c_0_24]),c_0_25])]) ).
thf(c_0_66,plain,
! [X177: $i,X178: mu,X179: mu,X180: mu] :
( ~ ( exists_in_world @ X178 @ X177 )
| ~ ( exists_in_world @ X179 @ X177 )
| ~ ( exists_in_world @ X180 @ X177 )
| ~ ( qmltpeq @ X178 @ X179 @ X177 )
| ~ ( disjoint @ X178 @ X180 @ X177 )
| ( disjoint @ X179 @ X180 @ X177 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])]) ).
thf(c_0_67,plain,
! [X199: $i,X200: mu,X201: mu] :
( ~ ( exists_in_world @ X200 @ X199 )
| ~ ( exists_in_world @ X201 @ X199 )
| ( qmltpeq @ ( unordered_pair @ X200 @ X201 ) @ ( unordered_pair @ X201 @ X200 ) @ X199 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])]) ).
thf(c_0_68,plain,
! [X149: $i,X150: mu,X151: mu] : ( exists_in_world @ ( unordered_pair @ X150 @ X151 ) @ X149 ),
inference(variable_rename,[status(thm)],[existence_of_unordered_pair_ax]) ).
thf(c_0_69,plain,
! [X109: mu,X110: mu,X111: mu,X112: $i] :
( ( epred1_4 @ X112 @ X111 @ X110 @ X109 )
=> ~ ( ~ ( ~ ( qmltpeq @ X109 @ ( unordered_pair @ X111 @ X110 ) @ X112 )
| ! [X108: mu] :
( ( exists_in_world @ X108 @ X112 )
=> ~ ( ~ ( ~ ( in @ X108 @ X109 @ X112 )
| ( qmltpeq @ X108 @ X111 @ X112 )
| ( qmltpeq @ X108 @ X110 @ X112 ) )
| ~ ( ~ ( ( qmltpeq @ X108 @ X111 @ X112 )
| ( qmltpeq @ X108 @ X110 @ X112 ) )
| ( in @ X108 @ X109 @ X112 ) ) ) ) )
| ~ ( ~ ! [X108: mu] :
( ( exists_in_world @ X108 @ X112 )
=> ~ ( ~ ( ~ ( in @ X108 @ X109 @ X112 )
| ( qmltpeq @ X108 @ X111 @ X112 )
| ( qmltpeq @ X108 @ X110 @ X112 ) )
| ~ ( ~ ( ( qmltpeq @ X108 @ X111 @ X112 )
| ( qmltpeq @ X108 @ X110 @ X112 ) )
| ( in @ X108 @ X109 @ X112 ) ) ) )
| ( qmltpeq @ X109 @ ( unordered_pair @ X111 @ X110 ) @ X112 ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_60]) ).
thf(c_0_70,plain,
! [X112: $i,X111: mu] :
( ( exists_in_world @ X111 @ X112 )
=> ! [X110: mu] :
( ( exists_in_world @ X110 @ X112 )
=> ! [X109: mu] :
( ( exists_in_world @ X109 @ X112 )
=> ( epred1_4 @ X112 @ X111 @ X110 @ X109 ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_tarski]),c_0_23]),c_0_33]),c_0_24]),c_0_25])]),c_0_60]) ).
thf(c_0_71,plain,
! [X14: mu,X12: mu,X10: mu,X3: $i] :
( ~ ( epred2_4 @ X3 @ X10 @ X12 @ empty_set )
| ~ ( in @ X14 @ X12 @ X3 )
| ~ ( in @ X14 @ X10 @ X3 )
| ~ ( disjoint @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
thf(c_0_72,plain,
! [X12: mu,X14: mu,X10: mu,X3: $i] :
( ( epred2_4 @ X3 @ X10 @ X12 @ X14 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_73,negated_conjecture,
( ( exists_in_world @ esk6_0 @ esk5_0 )
& ( exists_in_world @ esk7_0 @ esk5_0 )
& ( exists_in_world @ esk8_0 @ esk5_0 )
& ( disjoint @ ( unordered_pair @ esk6_0 @ esk7_0 ) @ esk8_0 @ esk5_0 )
& ( in @ esk6_0 @ esk8_0 @ esk5_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])]) ).
thf(c_0_74,plain,
! [X10: mu,X14: mu,X12: mu,X3: $i] :
( ( disjoint @ X12 @ X14 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( qmltpeq @ X10 @ X12 @ X3 )
| ~ ( disjoint @ X10 @ X14 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
thf(c_0_75,plain,
! [X12: mu,X10: mu,X3: $i] :
( ( qmltpeq @ ( unordered_pair @ X10 @ X12 ) @ ( unordered_pair @ X12 @ X10 ) @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_76,plain,
! [X12: mu,X10: mu,X3: $i] : ( exists_in_world @ ( unordered_pair @ X10 @ X12 ) @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
thf(c_0_77,plain,
! [X235: mu,X236: mu,X237: mu,X238: $i,X239: mu] :
( ( ~ ( in @ X239 @ X235 @ X238 )
| ( qmltpeq @ X239 @ X237 @ X238 )
| ( qmltpeq @ X239 @ X236 @ X238 )
| ~ ( exists_in_world @ X239 @ X238 )
| ~ ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ~ ( qmltpeq @ X239 @ X237 @ X238 )
| ( in @ X239 @ X235 @ X238 )
| ~ ( exists_in_world @ X239 @ X238 )
| ~ ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ~ ( qmltpeq @ X239 @ X236 @ X238 )
| ( in @ X239 @ X235 @ X238 )
| ~ ( exists_in_world @ X239 @ X238 )
| ~ ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ( exists_in_world @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X238 )
| ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X237 @ X238 )
| ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X236 @ X238 )
| ( in @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X235 @ X238 )
| ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ~ ( in @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X235 @ X238 )
| ( in @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X235 @ X238 )
| ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X237 @ X238 )
| ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X236 @ X238 )
| ~ ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X237 @ X238 )
| ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ~ ( in @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X235 @ X238 )
| ~ ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X237 @ X238 )
| ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X237 @ X238 )
| ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X236 @ X238 )
| ~ ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X236 @ X238 )
| ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) )
& ( ~ ( in @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X235 @ X238 )
| ~ ( qmltpeq @ ( esk9_4 @ X235 @ X236 @ X237 @ X238 ) @ X236 @ X238 )
| ( qmltpeq @ X235 @ ( unordered_pair @ X237 @ X236 ) @ X238 )
| ~ ( epred1_4 @ X238 @ X237 @ X236 @ X235 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])])])]) ).
thf(c_0_78,plain,
! [X209: $i,X210: mu,X211: mu,X212: mu] :
( ~ ( exists_in_world @ X210 @ X209 )
| ~ ( exists_in_world @ X211 @ X209 )
| ~ ( exists_in_world @ X212 @ X209 )
| ( epred1_4 @ X209 @ X210 @ X211 @ X212 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_70])])])]) ).
thf(c_0_79,plain,
! [X53: $i,X52: mu] :
( ( exists_in_world @ X52 @ X53 )
=> ( qmltpeq @ X52 @ X52 @ X53 ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity]),c_0_24]),c_0_25]) ).
thf(c_0_80,plain,
! [X12: mu,X14: mu,X10: mu,X3: $i] :
( ~ ( in @ X10 @ X12 @ X3 )
| ~ ( in @ X10 @ X14 @ X3 )
| ~ ( disjoint @ X14 @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_55])]) ).
thf(c_0_81,negated_conjecture,
in @ esk6_0 @ esk8_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_82,negated_conjecture,
exists_in_world @ esk6_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_83,negated_conjecture,
exists_in_world @ esk8_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_84,plain,
! [X14: mu,X12: mu,X10: mu,X3: $i] :
( ( disjoint @ ( unordered_pair @ X10 @ X12 ) @ X14 @ X3 )
| ~ ( disjoint @ ( unordered_pair @ X12 @ X10 ) @ X14 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_76])]) ).
thf(c_0_85,negated_conjecture,
disjoint @ ( unordered_pair @ esk6_0 @ esk7_0 ) @ esk8_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_86,negated_conjecture,
exists_in_world @ esk7_0 @ esk5_0,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_87,plain,
! [X3: $i,X10: mu,X12: mu,X19: mu,X14: mu] :
( ( in @ X10 @ X14 @ X3 )
| ~ ( qmltpeq @ X10 @ X12 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( qmltpeq @ X14 @ ( unordered_pair @ X19 @ X12 ) @ X3 )
| ~ ( epred1_4 @ X3 @ X19 @ X12 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
thf(c_0_88,plain,
! [X12: mu,X14: mu,X10: mu,X3: $i] :
( ( epred1_4 @ X3 @ X10 @ X12 @ X14 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
thf(c_0_89,plain,
! [X152: $i,X153: mu] :
( ~ ( exists_in_world @ X153 @ X152 )
| ( qmltpeq @ X153 @ X153 @ X152 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])])]) ).
thf(c_0_90,negated_conjecture,
! [X10: mu] :
( ~ ( in @ esk6_0 @ X10 @ esk5_0 )
| ~ ( disjoint @ X10 @ esk8_0 @ esk5_0 )
| ~ ( exists_in_world @ X10 @ esk5_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_83])]) ).
thf(c_0_91,negated_conjecture,
disjoint @ ( unordered_pair @ esk7_0 @ esk6_0 ) @ esk8_0 @ esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_83]),c_0_86]),c_0_82])]) ).
thf(c_0_92,plain,
! [X12: mu,X19: mu,X14: mu,X10: mu,X3: $i] :
( ( in @ X10 @ X12 @ X3 )
| ~ ( qmltpeq @ X12 @ ( unordered_pair @ X14 @ X19 ) @ X3 )
| ~ ( qmltpeq @ X10 @ X19 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 )
| ~ ( exists_in_world @ X19 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
thf(c_0_93,plain,
! [X10: mu,X3: $i] :
( ( qmltpeq @ X10 @ X10 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
thf(c_0_94,negated_conjecture,
~ ( in @ esk6_0 @ ( unordered_pair @ esk7_0 @ esk6_0 ) @ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_76])]) ).
thf(c_0_95,plain,
! [X14: mu,X12: mu,X10: mu,X3: $i] :
( ( in @ X10 @ ( unordered_pair @ X12 @ X14 ) @ X3 )
| ~ ( qmltpeq @ X10 @ X14 @ X3 )
| ~ ( exists_in_world @ X10 @ X3 )
| ~ ( exists_in_world @ X14 @ X3 )
| ~ ( exists_in_world @ X12 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_76])]) ).
thf(c_0_96,plain,
~ ( qmltpeq @ esk6_0 @ esk6_0 @ esk5_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_82]),c_0_86])]) ).
thf(c_0_97,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_93]),c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET914^7 : TPTP v8.2.0. Released v5.5.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n022.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 : Mon May 20 11:04:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.37/0.65 # Version: 3.1.0-ho
% 1.37/0.65 # Preprocessing class: HSMSSMSSMLLNHSN.
% 1.37/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.37/0.65 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.37/0.65 # Starting post_as_ho3 with 300s (1) cores
% 1.37/0.65 # Starting new_ho_12 with 300s (1) cores
% 1.37/0.65 # Starting new_bool_2 with 300s (1) cores
% 1.37/0.65 # post_as_ho3 with pid 23525 completed with status 0
% 1.37/0.65 # Result found by post_as_ho3
% 1.37/0.65 # Preprocessing class: HSMSSMSSMLLNHSN.
% 1.37/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.37/0.65 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.37/0.65 # Starting post_as_ho3 with 300s (1) cores
% 1.37/0.65 # No SInE strategy applied
% 1.37/0.65 # Search class: HGHNM-FFMS32-SHSSMFNN
% 1.37/0.65 # partial match(2): HGUNM-FFMF32-SHSSMFNN
% 1.37/0.65 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.37/0.65 # Starting new_ho_10 with 163s (1) cores
% 1.37/0.65 # new_ho_10 with pid 23530 completed with status 0
% 1.37/0.65 # Result found by new_ho_10
% 1.37/0.65 # Preprocessing class: HSMSSMSSMLLNHSN.
% 1.37/0.65 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.37/0.65 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.37/0.65 # Starting post_as_ho3 with 300s (1) cores
% 1.37/0.65 # No SInE strategy applied
% 1.37/0.65 # Search class: HGHNM-FFMS32-SHSSMFNN
% 1.37/0.65 # partial match(2): HGUNM-FFMF32-SHSSMFNN
% 1.37/0.65 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.37/0.65 # Starting new_ho_10 with 163s (1) cores
% 1.37/0.65 # Preprocessing time : 0.003 s
% 1.37/0.65 # Presaturation interreduction done
% 1.37/0.65
% 1.37/0.65 # Proof found!
% 1.37/0.65 # SZS status Theorem
% 1.37/0.65 # SZS output start CNFRefutation
% See solution above
% 1.37/0.66 # Parsed axioms : 106
% 1.37/0.66 # Removed by relevancy pruning/SinE : 0
% 1.37/0.66 # Initial clauses : 103
% 1.37/0.66 # Removed in clause preprocessing : 48
% 1.37/0.66 # Initial clauses in saturation : 55
% 1.37/0.66 # Processed clauses : 611
% 1.37/0.66 # ...of these trivial : 5
% 1.37/0.66 # ...subsumed : 140
% 1.37/0.66 # ...remaining for further processing : 466
% 1.37/0.66 # Other redundant clauses eliminated : 0
% 1.37/0.66 # Clauses deleted for lack of memory : 0
% 1.37/0.66 # Backward-subsumed : 12
% 1.37/0.66 # Backward-rewritten : 1
% 1.37/0.66 # Generated clauses : 4148
% 1.37/0.66 # ...of the previous two non-redundant : 3963
% 1.37/0.66 # ...aggressively subsumed : 0
% 1.37/0.66 # Contextual simplify-reflections : 5
% 1.37/0.66 # Paramodulations : 4148
% 1.37/0.66 # Factorizations : 0
% 1.37/0.66 # NegExts : 0
% 1.37/0.66 # Equation resolutions : 0
% 1.37/0.66 # Disequality decompositions : 0
% 1.37/0.66 # Total rewrite steps : 5801
% 1.37/0.66 # ...of those cached : 5648
% 1.37/0.66 # Propositional unsat checks : 0
% 1.37/0.66 # Propositional check models : 0
% 1.37/0.66 # Propositional check unsatisfiable : 0
% 1.37/0.66 # Propositional clauses : 0
% 1.37/0.66 # Propositional clauses after purity: 0
% 1.37/0.66 # Propositional unsat core size : 0
% 1.37/0.66 # Propositional preprocessing time : 0.000
% 1.37/0.66 # Propositional encoding time : 0.000
% 1.37/0.66 # Propositional solver time : 0.000
% 1.37/0.66 # Success case prop preproc time : 0.000
% 1.37/0.66 # Success case prop encoding time : 0.000
% 1.37/0.66 # Success case prop solver time : 0.000
% 1.37/0.66 # Current number of processed clauses : 398
% 1.37/0.66 # Positive orientable unit clauses : 45
% 1.37/0.66 # Positive unorientable unit clauses: 0
% 1.37/0.66 # Negative unit clauses : 8
% 1.37/0.66 # Non-unit-clauses : 345
% 1.37/0.66 # Current number of unprocessed clauses: 3435
% 1.37/0.66 # ...number of literals in the above : 20482
% 1.37/0.66 # Current number of archived formulas : 0
% 1.37/0.66 # Current number of archived clauses : 68
% 1.37/0.66 # Clause-clause subsumption calls (NU) : 44676
% 1.37/0.66 # Rec. Clause-clause subsumption calls : 4085
% 1.37/0.66 # Non-unit clause-clause subsumptions : 149
% 1.37/0.66 # Unit Clause-clause subsumption calls : 357
% 1.37/0.66 # Rewrite failures with RHS unbound : 0
% 1.37/0.66 # BW rewrite match attempts : 9
% 1.37/0.66 # BW rewrite match successes : 1
% 1.37/0.66 # Condensation attempts : 611
% 1.37/0.66 # Condensation successes : 1
% 1.37/0.66 # Termbank termtop insertions : 133027
% 1.37/0.66 # Search garbage collected termcells : 5890
% 1.37/0.66
% 1.37/0.66 # -------------------------------------------------
% 1.37/0.66 # User time : 0.159 s
% 1.37/0.66 # System time : 0.009 s
% 1.37/0.66 # Total time : 0.169 s
% 1.37/0.66 # Maximum resident set size: 2852 pages
% 1.37/0.66
% 1.37/0.66 # -------------------------------------------------
% 1.37/0.66 # User time : 0.163 s
% 1.37/0.66 # System time : 0.011 s
% 1.37/0.66 # Total time : 0.174 s
% 1.37/0.66 # Maximum resident set size: 1920 pages
% 1.37/0.66 % E---3.1 exiting
% 1.37/0.66 % E exiting
%------------------------------------------------------------------------------