TSTP Solution File: LCL725^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : LCL725^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 : Mon May 20 23:53:15 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 30
% Syntax : Number of formulae : 116 ( 29 unt; 17 typ; 0 def)
% Number of atoms : 388 ( 20 equ; 0 cnn)
% Maximal formula atoms : 98 ( 3 avg)
% Number of connectives : 968 ( 161 ~; 220 |; 30 &; 551 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 124 ( 35 ^ 89 !; 0 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_24,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_25,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mimplies: ( $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,
phi: $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_0: $i ).
thf(decl_62,type,
esk6_0: $i ).
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(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(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(mreflexive,axiom,
( mreflexive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
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(conj,conjecture,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
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(a3,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(a2,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(c_0_13,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_14,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_15,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_16,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_17,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_18,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_13,c_0_14]),c_0_15]) ).
thf(c_0_19,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_20,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_16,c_0_14]),c_0_17]) ).
thf(c_0_21,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_22,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_23,negated_conjecture,
~ ( ! [X29: $i] :
( ~ ! [X28: $i] :
( ~ ( rel_s5 @ X29 @ X28 )
| ( phi @ X28 ) )
| ( phi @ X29 ) )
& ! [X33: $i] :
( ~ ! [X30: $i] :
( ~ ( rel_s5 @ X33 @ X30 )
| ( phi @ X30 ) )
| ! [X32: $i] :
( ~ ( rel_s5 @ X33 @ X32 )
| ! [X31: $i] :
( ~ ( rel_s5 @ X32 @ X31 )
| ( phi @ X31 ) ) ) )
& ! [X36: $i] :
( ~ ( phi @ X36 )
| ! [X35: $i] :
( ~ ( rel_s5 @ X36 @ X35 )
| ~ ! [X34: $i] :
( ~ ( rel_s5 @ X35 @ X34 )
| ~ ( phi @ X34 ) ) ) ) ),
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)],[conj]),c_0_18]),c_0_19]),c_0_17]),c_0_20])]) ).
thf(c_0_24,plain,
! [X22: $i] : ( rel_s5 @ X22 @ X22 ),
inference(apply_def,[status(thm)],[a1,c_0_21]) ).
thf(c_0_25,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_26,plain,
! [X26: $i,X27: $i] :
( ( rel_s5 @ X26 @ X27 )
=> ( rel_s5 @ X27 @ X26 ) ),
inference(apply_def,[status(thm)],[a3,c_0_22]) ).
thf(c_0_27,negated_conjecture,
! [X44: $i,X46: $i,X51: $i] :
( ( ( phi @ esk5_0 )
| ~ ( rel_s5 @ esk2_0 @ X46 )
| ( phi @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ( rel_s5 @ esk5_0 @ esk6_0 )
| ~ ( rel_s5 @ esk2_0 @ X46 )
| ( phi @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ~ ( rel_s5 @ esk6_0 @ X51 )
| ~ ( phi @ X51 )
| ~ ( rel_s5 @ esk2_0 @ X46 )
| ( phi @ X46 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ( phi @ esk5_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ~ ( rel_s5 @ esk6_0 @ X51 )
| ~ ( phi @ X51 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ( phi @ esk5_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ~ ( rel_s5 @ esk6_0 @ X51 )
| ~ ( phi @ X51 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ( phi @ esk5_0 )
| ~ ( phi @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ( rel_s5 @ esk5_0 @ esk6_0 )
| ~ ( phi @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ~ ( rel_s5 @ esk6_0 @ X51 )
| ~ ( phi @ X51 )
| ~ ( phi @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X44 )
| ( phi @ X44 ) )
& ( ( phi @ esk5_0 )
| ~ ( rel_s5 @ esk2_0 @ X46 )
| ( phi @ X46 )
| ~ ( phi @ esk1_0 ) )
& ( ( rel_s5 @ esk5_0 @ esk6_0 )
| ~ ( rel_s5 @ esk2_0 @ X46 )
| ( phi @ X46 )
| ~ ( phi @ esk1_0 ) )
& ( ~ ( rel_s5 @ esk6_0 @ X51 )
| ~ ( phi @ X51 )
| ~ ( rel_s5 @ esk2_0 @ X46 )
| ( phi @ X46 )
| ~ ( phi @ esk1_0 ) )
& ( ( phi @ esk5_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( phi @ esk1_0 ) )
& ( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( phi @ esk1_0 ) )
& ( ~ ( rel_s5 @ esk6_0 @ X51 )
| ~ ( phi @ X51 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( phi @ esk1_0 ) )
& ( ( phi @ esk5_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( phi @ esk1_0 ) )
& ( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( phi @ esk1_0 ) )
& ( ~ ( rel_s5 @ esk6_0 @ X51 )
| ~ ( phi @ X51 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( phi @ esk1_0 ) )
& ( ( phi @ esk5_0 )
| ~ ( phi @ esk4_0 )
| ~ ( phi @ esk1_0 ) )
& ( ( rel_s5 @ esk5_0 @ esk6_0 )
| ~ ( phi @ esk4_0 )
| ~ ( phi @ esk1_0 ) )
& ( ~ ( rel_s5 @ esk6_0 @ X51 )
| ~ ( phi @ X51 )
| ~ ( phi @ esk4_0 )
| ~ ( phi @ esk1_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_23])])])])])]) ).
thf(c_0_28,plain,
! [X37: $i] : ( rel_s5 @ X37 @ X37 ),
inference(variable_rename,[status(thm)],[c_0_24]) ).
thf(c_0_29,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_25]) ).
thf(c_0_30,plain,
! [X41: $i,X42: $i] :
( ~ ( rel_s5 @ X41 @ X42 )
| ( rel_s5 @ X42 @ X41 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
thf(c_0_31,negated_conjecture,
! [X3: $i] :
( ( phi @ esk5_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_32,plain,
! [X3: $i] : ( rel_s5 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_33,negated_conjecture,
( ( phi @ esk5_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_35,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_36,plain,
! [X38: $i,X39: $i,X40: $i] :
( ~ ( rel_s5 @ X38 @ X39 )
| ~ ( rel_s5 @ X39 @ X40 )
| ( rel_s5 @ X38 @ X40 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).
thf(c_0_37,plain,
! [X3: $i,X14: $i] :
( ( rel_s5 @ X14 @ X3 )
| ~ ( rel_s5 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_38,negated_conjecture,
( ( rel_s5 @ esk2_0 @ esk3_0 )
| ( phi @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
thf(c_0_39,negated_conjecture,
! [X3: $i] :
( ( phi @ esk5_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_40,negated_conjecture,
( ( phi @ esk5_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_41,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_32]),c_0_35]) ).
thf(c_0_42,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_43,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_44,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_36]) ).
thf(c_0_45,negated_conjecture,
( ( rel_s5 @ esk3_0 @ esk2_0 )
| ( phi @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_46,negated_conjecture,
( ( rel_s5 @ esk3_0 @ esk4_0 )
| ( phi @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_40]) ).
thf(c_0_47,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk3_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_41]) ).
thf(c_0_48,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk3_0 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_43]) ).
thf(c_0_49,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk2_0 )
| ( phi @ esk5_0 )
| ~ ( rel_s5 @ X3 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_50,negated_conjecture,
( ( rel_s5 @ esk4_0 @ esk3_0 )
| ( phi @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
thf(c_0_51,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ X3 @ esk2_0 )
| ~ ( rel_s5 @ X3 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_47]) ).
thf(c_0_52,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk4_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_48]) ).
thf(c_0_53,negated_conjecture,
! [X3: $i,X14: $i] :
( ( phi @ esk5_0 )
| ( phi @ X3 )
| ( phi @ X14 )
| ~ ( rel_s5 @ esk2_0 @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_54,negated_conjecture,
! [X3: $i] :
( ( phi @ esk5_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk2_0 @ X3 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_55,negated_conjecture,
( ( rel_s5 @ esk4_0 @ esk2_0 )
| ( phi @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_56,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ~ ( phi @ esk4_0 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_57,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( phi @ X3 )
| ( phi @ X14 )
| ~ ( rel_s5 @ esk2_0 @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_58,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk2_0 @ X3 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_59,negated_conjecture,
( ( rel_s5 @ esk4_0 @ esk2_0 )
| ( rel_s5 @ esk5_0 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i] :
( ( phi @ esk5_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk2_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_32]),c_0_54]) ).
thf(c_0_61,negated_conjecture,
( ( rel_s5 @ esk2_0 @ esk4_0 )
| ( phi @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_55]) ).
thf(c_0_62,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 )
| ~ ( phi @ esk4_0 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_63,negated_conjecture,
( ( rel_s5 @ esk6_0 @ esk5_0 )
| ~ ( phi @ esk1_0 )
| ~ ( phi @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_56]) ).
thf(c_0_64,negated_conjecture,
( ( phi @ esk5_0 )
| ~ ( phi @ esk4_0 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_65,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk2_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_32]),c_0_58]) ).
thf(c_0_66,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( rel_s5 @ esk2_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_59]) ).
thf(c_0_67,negated_conjecture,
! [X3: $i] :
( ( phi @ esk5_0 )
| ( phi @ X3 )
| ~ ( phi @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_68,negated_conjecture,
( ( phi @ esk4_0 )
| ( phi @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_69,negated_conjecture,
( ~ ( phi @ esk1_0 )
| ~ ( phi @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
thf(c_0_70,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s5 @ esk3_0 @ esk4_0 )
| ( phi @ X14 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_71,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_72,negated_conjecture,
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( phi @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_73,negated_conjecture,
! [X3: $i] :
( ( phi @ esk5_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_74,negated_conjecture,
( ( phi @ esk5_0 )
| ~ ( phi @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_68]) ).
thf(c_0_75,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk3_0 @ esk4_0 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_32]),c_0_71]) ).
thf(c_0_76,negated_conjecture,
( ( rel_s5 @ esk6_0 @ esk5_0 )
| ( phi @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_72]) ).
thf(c_0_77,negated_conjecture,
phi @ esk5_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_32]),c_0_74]) ).
thf(c_0_78,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_s5 @ esk2_0 @ esk3_0 )
| ( phi @ X14 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_79,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_80,negated_conjecture,
( ( rel_s5 @ esk3_0 @ esk4_0 )
| ( phi @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77])]) ).
thf(c_0_81,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_32]),c_0_79]) ).
thf(c_0_82,negated_conjecture,
! [X14: $i,X3: $i,X15: $i] :
( ( phi @ X14 )
| ( phi @ X15 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 )
| ~ ( rel_s5 @ esk2_0 @ X14 )
| ~ ( rel_s5 @ esk1_0 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_83,negated_conjecture,
! [X3: $i,X14: $i] :
( ( phi @ X14 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 )
| ~ ( rel_s5 @ esk2_0 @ X14 )
| ~ ( phi @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_84,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk4_0 )
| ( phi @ esk4_0 )
| ~ ( rel_s5 @ X3 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_80]) ).
thf(c_0_85,negated_conjecture,
( ( rel_s5 @ esk2_0 @ esk3_0 )
| ( phi @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_76]),c_0_77])]) ).
thf(c_0_86,negated_conjecture,
! [X3: $i,X14: $i] :
( ( phi @ X3 )
| ~ ( rel_s5 @ esk2_0 @ X3 )
| ~ ( rel_s5 @ esk6_0 @ X14 )
| ~ ( phi @ X14 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_32]),c_0_83]) ).
thf(c_0_87,negated_conjecture,
( ( rel_s5 @ esk2_0 @ esk4_0 )
| ( phi @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
thf(c_0_88,negated_conjecture,
! [X3: $i] :
( ( phi @ esk4_0 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 ) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
thf(c_0_89,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( phi @ X3 )
| ~ ( phi @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_90,negated_conjecture,
phi @ esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_76]),c_0_77])]) ).
thf(c_0_91,negated_conjecture,
! [X3: $i,X14: $i] :
( ( phi @ X14 )
| ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 )
| ~ ( phi @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_92,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk5_0 @ esk6_0 )
| ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90])]) ).
thf(c_0_93,negated_conjecture,
~ ( phi @ esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_90])]) ).
thf(c_0_94,negated_conjecture,
! [X3: $i,X14: $i] :
( ( phi @ X3 )
| ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( rel_s5 @ esk6_0 @ X14 )
| ~ ( phi @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_90])]) ).
thf(c_0_95,negated_conjecture,
rel_s5 @ esk5_0 @ esk6_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_32]),c_0_93]) ).
thf(c_0_96,negated_conjecture,
! [X3: $i] :
( ~ ( rel_s5 @ esk6_0 @ X3 )
| ~ ( phi @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_32]),c_0_93]) ).
thf(c_0_97,negated_conjecture,
rel_s5 @ esk6_0 @ esk5_0,
inference(spm,[status(thm)],[c_0_37,c_0_95]) ).
thf(c_0_98,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_77])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL725^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 03:03:53 EDT 2024
% 0.14/0.35 % 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
% 0.21/0.51 # Version: 3.1.0-ho
% 0.21/0.51 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.51 # Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.21/0.51 # Starting almost_fo_3_lam with 300s (1) cores
% 0.21/0.51 # Starting post_as_ho1 with 300s (1) cores
% 0.21/0.51 # ho_unfolding_3 with pid 13007 completed with status 0
% 0.21/0.51 # Result found by ho_unfolding_3
% 0.21/0.51 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.51 # No SInE strategy applied
% 0.21/0.51 # Search class: HGHNF-FFMF00-SHSSMFNN
% 0.21/0.51 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.51 # Starting new_ho_10 with 811s (1) cores
% 0.21/0.51 # Starting ho_unfolding_3 with 151s (1) cores
% 0.21/0.51 # Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.21/0.51 # Starting lpo1_def_fix with 136s (1) cores
% 0.21/0.51 # Starting ehoh_best8_lambda with 136s (1) cores
% 0.21/0.51 # ehoh_best_sine_rwall with pid 13020 completed with status 0
% 0.21/0.51 # Result found by ehoh_best_sine_rwall
% 0.21/0.51 # Preprocessing class: HSMSSMSSMLMNHSN.
% 0.21/0.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.51 # Starting ho_unfolding_3 with 1500s (5) cores
% 0.21/0.51 # No SInE strategy applied
% 0.21/0.51 # Search class: HGHNF-FFMF00-SHSSMFNN
% 0.21/0.51 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.21/0.51 # Starting new_ho_10 with 811s (1) cores
% 0.21/0.51 # Starting ho_unfolding_3 with 151s (1) cores
% 0.21/0.51 # Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.21/0.51 # Preprocessing time : 0.002 s
% 0.21/0.51 # Presaturation interreduction done
% 0.21/0.51
% 0.21/0.51 # Proof found!
% 0.21/0.51 # SZS status Theorem
% 0.21/0.51 # SZS output start CNFRefutation
% See solution above
% 0.21/0.51 # Parsed axioms : 73
% 0.21/0.51 # Removed by relevancy pruning/SinE : 0
% 0.21/0.51 # Initial clauses : 63
% 0.21/0.51 # Removed in clause preprocessing : 36
% 0.21/0.51 # Initial clauses in saturation : 27
% 0.21/0.51 # Processed clauses : 166
% 0.21/0.51 # ...of these trivial : 2
% 0.21/0.51 # ...subsumed : 35
% 0.21/0.51 # ...remaining for further processing : 129
% 0.21/0.51 # Other redundant clauses eliminated : 0
% 0.21/0.51 # Clauses deleted for lack of memory : 0
% 0.21/0.51 # Backward-subsumed : 46
% 0.21/0.51 # Backward-rewritten : 44
% 0.21/0.51 # Generated clauses : 200
% 0.21/0.51 # ...of the previous two non-redundant : 165
% 0.21/0.51 # ...aggressively subsumed : 0
% 0.21/0.51 # Contextual simplify-reflections : 11
% 0.21/0.51 # Paramodulations : 200
% 0.21/0.51 # Factorizations : 0
% 0.21/0.51 # NegExts : 0
% 0.21/0.51 # Equation resolutions : 0
% 0.21/0.51 # Disequality decompositions : 0
% 0.21/0.51 # Total rewrite steps : 95
% 0.21/0.51 # ...of those cached : 86
% 0.21/0.51 # Propositional unsat checks : 0
% 0.21/0.51 # Propositional check models : 0
% 0.21/0.51 # Propositional check unsatisfiable : 0
% 0.21/0.51 # Propositional clauses : 0
% 0.21/0.51 # Propositional clauses after purity: 0
% 0.21/0.51 # Propositional unsat core size : 0
% 0.21/0.51 # Propositional preprocessing time : 0.000
% 0.21/0.51 # Propositional encoding time : 0.000
% 0.21/0.51 # Propositional solver time : 0.000
% 0.21/0.51 # Success case prop preproc time : 0.000
% 0.21/0.51 # Success case prop encoding time : 0.000
% 0.21/0.51 # Success case prop solver time : 0.000
% 0.21/0.51 # Current number of processed clauses : 12
% 0.21/0.51 # Positive orientable unit clauses : 7
% 0.21/0.51 # Positive unorientable unit clauses: 0
% 0.21/0.51 # Negative unit clauses : 2
% 0.21/0.51 # Non-unit-clauses : 3
% 0.21/0.51 # Current number of unprocessed clauses: 27
% 0.21/0.51 # ...number of literals in the above : 87
% 0.21/0.51 # Current number of archived formulas : 0
% 0.21/0.51 # Current number of archived clauses : 117
% 0.21/0.51 # Clause-clause subsumption calls (NU) : 424
% 0.21/0.51 # Rec. Clause-clause subsumption calls : 369
% 0.21/0.51 # Non-unit clause-clause subsumptions : 77
% 0.21/0.51 # Unit Clause-clause subsumption calls : 21
% 0.21/0.51 # Rewrite failures with RHS unbound : 0
% 0.21/0.51 # BW rewrite match attempts : 5
% 0.21/0.51 # BW rewrite match successes : 5
% 0.21/0.51 # Condensation attempts : 0
% 0.21/0.51 # Condensation successes : 0
% 0.21/0.51 # Termbank termtop insertions : 7199
% 0.21/0.51 # Search garbage collected termcells : 738
% 0.21/0.51
% 0.21/0.51 # -------------------------------------------------
% 0.21/0.51 # User time : 0.016 s
% 0.21/0.51 # System time : 0.004 s
% 0.21/0.51 # Total time : 0.019 s
% 0.21/0.51 # Maximum resident set size: 1988 pages
% 0.21/0.51
% 0.21/0.51 # -------------------------------------------------
% 0.21/0.51 # User time : 0.067 s
% 0.21/0.51 # System time : 0.011 s
% 0.21/0.51 # Total time : 0.079 s
% 0.21/0.51 # Maximum resident set size: 1800 pages
% 0.21/0.51 % E---3.1 exiting
% 0.21/0.51 % E exiting
%------------------------------------------------------------------------------