TSTP Solution File: SYO470^6 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO470^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 08:46:19 EDT 2024
% Result : Theorem 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 33
% Syntax : Number of formulae : 91 ( 37 unt; 18 typ; 0 def)
% Number of atoms : 252 ( 26 equ; 0 cnn)
% Maximal formula atoms : 58 ( 3 avg)
% Number of connectives : 712 ( 135 ~; 126 |; 17 &; 428 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 133 ( 51 ^ 82 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_29,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_40,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(decl_42,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(decl_49,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_53,type,
rel_s5: $i > $i > $o ).
thf(decl_54,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(decl_55,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(decl_56,type,
p: $i > $o ).
thf(decl_57,type,
esk1_0: $i ).
thf(decl_58,type,
esk2_0: $i ).
thf(decl_59,type,
esk3_0: $i ).
thf(decl_60,type,
esk4_0: $i ).
thf(decl_61,type,
esk5_2: $i > $i > $i ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mand @ ( mimplies @ X6 @ X7 ) @ ( mimplies @ X7 @ X6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(mdia_s5,axiom,
( mdia_s5
= ( ^ [X6: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(mbox_s5,axiom,
( mbox_s5
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i] :
( ( X13 @ X15 @ X16 )
=> ( X13 @ X16 @ X15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(prove,conjecture,
mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(a3,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X16 @ X17 ) )
=> ( X13 @ X15 @ X17 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(a2,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(c_0_15,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_16,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_17,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_18,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_19,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_20,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_15,c_0_16]),c_0_17]) ).
thf(c_0_21,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_18,c_0_16]),c_0_17]) ).
thf(c_0_22,plain,
( mdia_s5
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X21: $i] :
( ~ ( rel_s5 @ Z1 @ X21 )
| ~ ( Z0 @ X21 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia_s5]) ).
thf(c_0_23,plain,
( mbox_s5
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s5]) ).
thf(c_0_24,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_19,c_0_20]),c_0_21]) ).
thf(c_0_25,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_26,plain,
( mdia_s5
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X21: $i] :
( ~ ( rel_s5 @ Z1 @ X21 )
| ~ ( Z0 @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_22,c_0_16]),c_0_23]) ).
thf(c_0_27,plain,
( msymmetric
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i] :
( ( Z0 @ X15 @ X16 )
=> ( Z0 @ X16 @ X15 ) ) ) ),
inference(fof_simplification,[status(thm)],[msymmetric]) ).
thf(c_0_28,negated_conjecture,
~ ! [X32: $i] :
~ ( ~ ( ~ ~ ! [X30: $i] :
( ~ ( rel_s5 @ X32 @ X30 )
| ~ ~ ! [X29: $i] :
( ~ ( rel_s5 @ X30 @ X29 )
| ~ ! [X28: $i] :
( ~ ( rel_s5 @ X29 @ X28 )
| ( p @ X28 ) ) ) )
| ! [X31: $i] :
( ~ ( rel_s5 @ X32 @ X31 )
| ( p @ X31 ) ) )
| ~ ( ~ ! [X31: $i] :
( ~ ( rel_s5 @ X32 @ X31 )
| ( p @ X31 ) )
| ~ ! [X30: $i] :
( ~ ( rel_s5 @ X32 @ X30 )
| ~ ~ ! [X29: $i] :
( ~ ( rel_s5 @ X30 @ X29 )
| ~ ! [X28: $i] :
( ~ ( rel_s5 @ X29 @ X28 )
| ( p @ X28 ) ) ) ) ) ),
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(assume_negation,[status(cth)],[prove]),c_0_24]),c_0_25]),c_0_23]),c_0_26])]) ).
thf(c_0_29,plain,
! [X26: $i,X27: $i] :
( ( rel_s5 @ X26 @ X27 )
=> ( rel_s5 @ X27 @ X26 ) ),
inference(apply_def,[status(thm)],[a3,c_0_27]) ).
thf(c_0_30,negated_conjecture,
! [X42: $i,X44: $i,X45: $i,X46: $i] :
( ( ~ ( rel_s5 @ esk1_0 @ X44 )
| ( p @ X44 )
| ( rel_s5 @ esk1_0 @ esk2_0 ) )
& ( ( rel_s5 @ X46 @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ( rel_s5 @ esk1_0 @ esk2_0 ) )
& ( ~ ( p @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ( rel_s5 @ esk1_0 @ esk2_0 ) )
& ( ~ ( rel_s5 @ esk1_0 @ X44 )
| ( p @ X44 )
| ( rel_s5 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s5 @ X46 @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ( rel_s5 @ esk2_0 @ esk3_0 ) )
& ( ~ ( p @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ( rel_s5 @ esk2_0 @ esk3_0 ) )
& ( ~ ( rel_s5 @ esk1_0 @ X44 )
| ( p @ X44 )
| ~ ( rel_s5 @ esk3_0 @ X42 )
| ( p @ X42 ) )
& ( ( rel_s5 @ X46 @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ~ ( rel_s5 @ esk3_0 @ X42 )
| ( p @ X42 ) )
& ( ~ ( p @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ~ ( rel_s5 @ esk3_0 @ X42 )
| ( p @ X42 ) )
& ( ~ ( rel_s5 @ esk1_0 @ X44 )
| ( p @ X44 )
| ( rel_s5 @ esk1_0 @ esk4_0 ) )
& ( ( rel_s5 @ X46 @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ( rel_s5 @ esk1_0 @ esk4_0 ) )
& ( ~ ( p @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ( rel_s5 @ esk1_0 @ esk4_0 ) )
& ( ~ ( rel_s5 @ esk1_0 @ X44 )
| ( p @ X44 )
| ~ ( p @ esk4_0 ) )
& ( ( rel_s5 @ X46 @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ~ ( p @ esk4_0 ) )
& ( ~ ( p @ ( esk5_2 @ X45 @ X46 ) )
| ~ ( rel_s5 @ X45 @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X45 )
| ~ ( p @ esk4_0 ) ) ),
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_28])])])])])]) ).
thf(c_0_31,plain,
! [X37: $i,X38: $i] :
( ~ ( rel_s5 @ X37 @ X38 )
| ( rel_s5 @ X38 @ X37 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
thf(c_0_32,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_33,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ( rel_s5 @ esk1_0 @ esk2_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s5 @ X3 @ ( esk5_2 @ X14 @ X3 ) )
| ( rel_s5 @ esk1_0 @ esk2_0 )
| ~ ( rel_s5 @ X14 @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_35,plain,
! [X3: $i,X14: $i] :
( ( rel_s5 @ X14 @ X3 )
| ~ ( rel_s5 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_36,plain,
! [X22: $i] : ( rel_s5 @ X22 @ X22 ),
inference(apply_def,[status(thm)],[a1,c_0_32]) ).
thf(c_0_37,plain,
( mtransitive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( Z0 @ X15 @ X16 )
& ( Z0 @ X16 @ X17 ) )
=> ( Z0 @ X15 @ X17 ) ) ) ),
inference(fof_simplification,[status(thm)],[mtransitive]) ).
thf(c_0_38,negated_conjecture,
! [X14: $i,X3: $i] :
( ( rel_s5 @ esk1_0 @ esk2_0 )
| ~ ( p @ ( esk5_2 @ X3 @ X14 ) )
| ~ ( rel_s5 @ X3 @ X14 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_39,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk5_2 @ X3 @ esk1_0 ) )
| ( rel_s5 @ esk1_0 @ esk2_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
thf(c_0_40,plain,
! [X33: $i] : ( rel_s5 @ X33 @ X33 ),
inference(variable_rename,[status(thm)],[c_0_36]) ).
thf(c_0_41,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_42,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s5 @ X3 @ ( esk5_2 @ X14 @ X3 ) )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ X14 @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_43,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ( rel_s5 @ esk1_0 @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_44,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s5 @ X3 @ ( esk5_2 @ X14 @ X3 ) )
| ( rel_s5 @ esk1_0 @ esk4_0 )
| ~ ( rel_s5 @ X14 @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_45,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( p @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_46,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s5 @ X3 @ ( esk5_2 @ X14 @ X3 ) )
| ~ ( rel_s5 @ X14 @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 )
| ~ ( p @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_47,plain,
! [X23: $i,X24: $i,X25: $i] :
( ( ( rel_s5 @ X23 @ X24 )
& ( rel_s5 @ X24 @ X25 ) )
=> ( rel_s5 @ X23 @ X25 ) ),
inference(apply_def,[status(thm)],[a2,c_0_37]) ).
thf(c_0_48,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk1_0 @ esk2_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35]) ).
thf(c_0_49,plain,
! [X3: $i] : ( rel_s5 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_50,negated_conjecture,
! [X14: $i,X3: $i] :
( ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( p @ ( esk5_2 @ X3 @ X14 ) )
| ~ ( rel_s5 @ X3 @ X14 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_51,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk5_2 @ X3 @ esk1_0 ) )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_35]) ).
thf(c_0_52,negated_conjecture,
! [X14: $i,X3: $i] :
( ( rel_s5 @ esk1_0 @ esk4_0 )
| ~ ( p @ ( esk5_2 @ X3 @ X14 ) )
| ~ ( rel_s5 @ X3 @ X14 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_53,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk5_2 @ X3 @ esk1_0 ) )
| ( rel_s5 @ esk1_0 @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_35]) ).
thf(c_0_54,negated_conjecture,
! [X14: $i,X3: $i] :
( ~ ( p @ ( esk5_2 @ X3 @ X14 ) )
| ~ ( rel_s5 @ X3 @ X14 )
| ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( p @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_55,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk5_2 @ X3 @ esk1_0 ) )
| ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( p @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_35]) ).
thf(c_0_56,plain,
! [X34: $i,X35: $i,X36: $i] :
( ~ ( rel_s5 @ X34 @ X35 )
| ~ ( rel_s5 @ X35 @ X36 )
| ( rel_s5 @ X34 @ X36 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
thf(c_0_57,negated_conjecture,
rel_s5 @ esk1_0 @ esk2_0,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_58,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_35]) ).
thf(c_0_59,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk1_0 @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_35]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( p @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_35]) ).
thf(c_0_61,plain,
! [X14: $i,X3: $i,X15: $i] :
( ( rel_s5 @ X3 @ X15 )
| ~ ( rel_s5 @ X3 @ X14 )
| ~ ( rel_s5 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
thf(c_0_62,negated_conjecture,
rel_s5 @ esk2_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_35,c_0_57]) ).
thf(c_0_63,negated_conjecture,
rel_s5 @ esk2_0 @ esk3_0,
inference(spm,[status(thm)],[c_0_58,c_0_49]) ).
thf(c_0_64,negated_conjecture,
! [X3: $i,X14: $i] :
( ( p @ X3 )
| ( p @ X14 )
| ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( rel_s5 @ esk3_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_65,negated_conjecture,
rel_s5 @ esk1_0 @ esk4_0,
inference(spm,[status(thm)],[c_0_59,c_0_49]) ).
thf(c_0_66,negated_conjecture,
~ ( p @ esk4_0 ),
inference(spm,[status(thm)],[c_0_60,c_0_49]) ).
thf(c_0_67,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk1_0 )
| ~ ( rel_s5 @ X3 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_68,negated_conjecture,
rel_s5 @ esk3_0 @ esk2_0,
inference(spm,[status(thm)],[c_0_35,c_0_63]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( rel_s5 @ esk3_0 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
thf(c_0_70,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk4_0 )
| ~ ( rel_s5 @ X3 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_65]) ).
thf(c_0_71,negated_conjecture,
rel_s5 @ esk3_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71])]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO470^6 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 08:44:53 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 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
% 0.21/0.50 # Version: 3.1.0-ho
% 0.21/0.50 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.50 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.50 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.50 # Starting post_as_ho1 with 300s (1) cores
% 0.21/0.50 # almost_fo_3_lam with pid 6302 completed with status 0
% 0.21/0.50 # Result found by almost_fo_3_lam
% 0.21/0.50 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.50 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.50 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.50 # No SInE strategy applied
% 0.21/0.50 # Search class: HGHNF-FFSF22-SHSSMFNN
% 0.21/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.50 # new_ho_10 with pid 6306 completed with status 0
% 0.21/0.50 # Result found by new_ho_10
% 0.21/0.50 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.50 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.50 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.50 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.50 # No SInE strategy applied
% 0.21/0.50 # Search class: HGHNF-FFSF22-SHSSMFNN
% 0.21/0.50 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.50 # Starting new_ho_10 with 163s (1) cores
% 0.21/0.50 # Preprocessing time : 0.001 s
% 0.21/0.50 # Presaturation interreduction done
% 0.21/0.50
% 0.21/0.50 # Proof found!
% 0.21/0.50 # SZS status Theorem
% 0.21/0.50 # SZS output start CNFRefutation
% See solution above
% 0.21/0.50 # Parsed axioms : 73
% 0.21/0.50 # Removed by relevancy pruning/SinE : 0
% 0.21/0.50 # Initial clauses : 54
% 0.21/0.50 # Removed in clause preprocessing : 36
% 0.21/0.50 # Initial clauses in saturation : 18
% 0.21/0.50 # Processed clauses : 111
% 0.21/0.50 # ...of these trivial : 1
% 0.21/0.50 # ...subsumed : 25
% 0.21/0.50 # ...remaining for further processing : 85
% 0.21/0.50 # Other redundant clauses eliminated : 0
% 0.21/0.50 # Clauses deleted for lack of memory : 0
% 0.21/0.50 # Backward-subsumed : 38
% 0.21/0.50 # Backward-rewritten : 11
% 0.21/0.50 # Generated clauses : 222
% 0.21/0.50 # ...of the previous two non-redundant : 201
% 0.21/0.50 # ...aggressively subsumed : 0
% 0.21/0.50 # Contextual simplify-reflections : 8
% 0.21/0.50 # Paramodulations : 222
% 0.21/0.50 # Factorizations : 0
% 0.21/0.50 # NegExts : 0
% 0.21/0.50 # Equation resolutions : 0
% 0.21/0.50 # Disequality decompositions : 0
% 0.21/0.50 # Total rewrite steps : 32
% 0.21/0.50 # ...of those cached : 17
% 0.21/0.50 # Propositional unsat checks : 0
% 0.21/0.50 # Propositional check models : 0
% 0.21/0.50 # Propositional check unsatisfiable : 0
% 0.21/0.50 # Propositional clauses : 0
% 0.21/0.50 # Propositional clauses after purity: 0
% 0.21/0.50 # Propositional unsat core size : 0
% 0.21/0.50 # Propositional preprocessing time : 0.000
% 0.21/0.50 # Propositional encoding time : 0.000
% 0.21/0.50 # Propositional solver time : 0.000
% 0.21/0.50 # Success case prop preproc time : 0.000
% 0.21/0.50 # Success case prop encoding time : 0.000
% 0.21/0.50 # Success case prop solver time : 0.000
% 0.21/0.50 # Current number of processed clauses : 18
% 0.21/0.50 # Positive orientable unit clauses : 11
% 0.21/0.50 # Positive unorientable unit clauses: 0
% 0.21/0.50 # Negative unit clauses : 1
% 0.21/0.50 # Non-unit-clauses : 6
% 0.21/0.50 # Current number of unprocessed clauses: 31
% 0.21/0.50 # ...number of literals in the above : 81
% 0.21/0.50 # Current number of archived formulas : 0
% 0.21/0.50 # Current number of archived clauses : 67
% 0.21/0.50 # Clause-clause subsumption calls (NU) : 549
% 0.21/0.50 # Rec. Clause-clause subsumption calls : 411
% 0.21/0.50 # Non-unit clause-clause subsumptions : 58
% 0.21/0.50 # Unit Clause-clause subsumption calls : 34
% 0.21/0.50 # Rewrite failures with RHS unbound : 0
% 0.21/0.50 # BW rewrite match attempts : 11
% 0.21/0.50 # BW rewrite match successes : 9
% 0.21/0.50 # Condensation attempts : 111
% 0.21/0.50 # Condensation successes : 0
% 0.21/0.50 # Termbank termtop insertions : 7139
% 0.21/0.50 # Search garbage collected termcells : 663
% 0.21/0.50
% 0.21/0.50 # -------------------------------------------------
% 0.21/0.50 # User time : 0.015 s
% 0.21/0.50 # System time : 0.001 s
% 0.21/0.50 # Total time : 0.016 s
% 0.21/0.50 # Maximum resident set size: 1896 pages
% 0.21/0.50
% 0.21/0.50 # -------------------------------------------------
% 0.21/0.50 # User time : 0.016 s
% 0.21/0.50 # System time : 0.004 s
% 0.21/0.50 # Total time : 0.020 s
% 0.21/0.50 # Maximum resident set size: 1800 pages
% 0.21/0.50 % E---3.1 exiting
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------