%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO470^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:43:11 AM UTC 2026
% Result : Theorem 0.32s 0.28s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 302 ( 26 equ; 0 cnn)
% Maximal formula atoms : 58 ( 3 avg)
% Number of connectives : 880 ( 142 ~; 151 |; 17 &; 564 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 140 ( 51 ^; 89 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_30,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_40,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(decl_41,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(decl_43,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_s5: $i > $i > $o ).
thf(decl_55,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(decl_56,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
p: $i > $o ).
thf(decl_58,type,
esk1_0: $i ).
thf(decl_59,type,
esk2_0: $i ).
thf(decl_60,type,
esk3_0: $i ).
thf(decl_61,type,
esk4_0: $i ).
thf(decl_62,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/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mimplies) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mand @ ( mimplies @ X6 @ X7 ) @ ( mimplies @ X7 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mequiv) ).
thf(mdia_s5,axiom,
( mdia_s5
= ( ^ [X6: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mdia_s5) ).
thf(mbox_s5,axiom,
( mbox_s5
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_s5 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mbox_s5) ).
thf(prove,conjecture,
mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',prove) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mvalid) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [X13: $i > $i > $o] :
! [X15: $i] : ( X13 @ X15 @ X15 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mreflexive) ).
thf(a1,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',a1) ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i] :
( ( X13 @ X15 @ X16 )
=> ( X13 @ X16 @ X15 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',msymmetric) ).
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/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',mtransitive) ).
thf(a3,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',a3) ).
thf(a2,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p',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,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(c_0_25,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_26,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_27,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_28,plain,
( mreflexive
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i] : ( Z0 @ X15 @ X15 ) ) ),
inference(fof_simplification,[status(thm)],[mreflexive]) ).
thf(c_0_29,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)],[c_0_24,c_0_25]),c_0_26]),c_0_23]),c_0_27])]) ).
thf(c_0_30,plain,
! [X22: $i] : ( rel_s5 @ X22 @ X22 ),
inference(apply_def,[status(thm)],[a1,c_0_28]) ).
thf(c_0_31,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_32,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_29])])])])])]) ).
thf(c_0_33,plain,
! [X33: $i] : ( rel_s5 @ X33 @ X33 ),
inference(variable_rename,[status(thm)],[c_0_30]) ).
thf(c_0_34,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_35,plain,
! [X26: $i,X27: $i] :
( ( rel_s5 @ X26 @ X27 )
=> ( rel_s5 @ X27 @ X26 ) ),
inference(apply_def,[status(thm)],[a3,c_0_31]) ).
thf(c_0_36,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_32]) ).
thf(c_0_37,plain,
! [X3: $i] : ( rel_s5 @ X3 @ X3 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_38,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_34]) ).
thf(c_0_39,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_35])])]) ).
thf(c_0_40,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ ( esk5_2 @ esk1_0 @ X3 ) )
| ( rel_s5 @ esk1_0 @ esk2_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_41,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_32]) ).
thf(c_0_42,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_32]) ).
thf(c_0_43,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_38])])]) ).
thf(c_0_44,plain,
! [X3: $i,X14: $i] :
( ( rel_s5 @ X14 @ X3 )
| ~ ( rel_s5 @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_45,negated_conjecture,
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk1_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
thf(c_0_46,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ ( esk5_2 @ esk1_0 @ X3 ) )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_37]) ).
thf(c_0_47,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ ( esk5_2 @ esk1_0 @ X3 ) )
| ( rel_s5 @ esk1_0 @ esk4_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
thf(c_0_48,plain,
! [X3: $i,X14: $i,X15: $i] :
( ( rel_s5 @ X3 @ X15 )
| ~ ( rel_s5 @ X3 @ X14 )
| ~ ( rel_s5 @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_49,negated_conjecture,
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk2_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_50,negated_conjecture,
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_37]) ).
thf(c_0_51,negated_conjecture,
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk1_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_37]) ).
thf(c_0_52,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ X3 @ esk1_0 )
| ~ ( rel_s5 @ X3 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_53,negated_conjecture,
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk3_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_50]) ).
thf(c_0_54,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_32]) ).
thf(c_0_55,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ X3 @ esk4_0 )
| ~ ( rel_s5 @ X3 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_51]) ).
thf(c_0_56,negated_conjecture,
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk3_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_57,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( p @ esk4_0 )
| ( p @ X3 )
| ~ ( rel_s5 @ esk3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
thf(c_0_58,negated_conjecture,
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk3_0 @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_59,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_32]) ).
thf(c_0_60,negated_conjecture,
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( p @ esk4_0 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_61,negated_conjecture,
! [X14: $i,X3: $i] :
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ X3 @ ( esk5_2 @ X14 @ X3 ) )
| ~ ( rel_s5 @ esk1_0 @ X14 )
| ~ ( rel_s5 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_62,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ X3 @ ( esk5_2 @ esk1_0 @ X3 ) )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_37]) ).
thf(c_0_63,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ( rel_s5 @ esk2_0 @ esk3_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_64,negated_conjecture,
rel_s5 @ esk1_0 @ ( esk5_2 @ esk1_0 @ esk1_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_37]) ).
thf(c_0_65,negated_conjecture,
( ( p @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
thf(c_0_66,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ( rel_s5 @ esk1_0 @ esk2_0 )
| ~ ( rel_s5 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_67,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ X3 @ esk3_0 )
| ~ ( rel_s5 @ X3 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_65]) ).
thf(c_0_68,negated_conjecture,
( ( p @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk1_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_64]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( p @ X3 )
| ~ ( rel_s5 @ esk3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_64]) ).
thf(c_0_70,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ~ ( rel_s5 @ X3 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_64]) ).
thf(c_0_71,negated_conjecture,
( ( p @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ( rel_s5 @ esk1_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_72,negated_conjecture,
( ( p @ ( esk5_2 @ esk1_0 @ esk1_0 ) )
| ~ ( rel_s5 @ esk3_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_73,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_32]) ).
thf(c_0_74,negated_conjecture,
p @ ( esk5_2 @ esk1_0 @ esk1_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_71]),c_0_72]) ).
thf(c_0_75,negated_conjecture,
rel_s5 @ esk1_0 @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_37])]) ).
thf(c_0_76,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_32]) ).
thf(c_0_77,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_32]) ).
thf(c_0_78,negated_conjecture,
rel_s5 @ esk2_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_44,c_0_75]) ).
thf(c_0_79,negated_conjecture,
rel_s5 @ esk2_0 @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_74]),c_0_37])]) ).
thf(c_0_80,negated_conjecture,
! [X3: $i,X14: $i,X15: $i] :
( ( p @ X15 )
| ~ ( p @ ( esk5_2 @ X3 @ X14 ) )
| ~ ( rel_s5 @ X3 @ X14 )
| ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( rel_s5 @ esk3_0 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
thf(c_0_81,negated_conjecture,
rel_s5 @ esk1_0 @ esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_74]),c_0_37])]) ).
thf(c_0_82,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk1_0 )
| ~ ( rel_s5 @ X3 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_78]) ).
thf(c_0_83,negated_conjecture,
rel_s5 @ esk3_0 @ esk2_0,
inference(spm,[status(thm)],[c_0_44,c_0_79]) ).
thf(c_0_84,negated_conjecture,
! [X3: $i] :
( ( p @ X3 )
| ~ ( rel_s5 @ esk3_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_74]),c_0_37])]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i] :
( ( rel_s5 @ X3 @ esk4_0 )
| ~ ( rel_s5 @ X3 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_48,c_0_81]) ).
thf(c_0_86,negated_conjecture,
rel_s5 @ esk3_0 @ esk1_0,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
thf(c_0_87,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_32]) ).
thf(c_0_88,negated_conjecture,
p @ esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
thf(c_0_89,negated_conjecture,
! [X3: $i,X14: $i] :
( ~ ( p @ ( esk5_2 @ X3 @ X14 ) )
| ~ ( rel_s5 @ esk1_0 @ X3 )
| ~ ( rel_s5 @ X3 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88])]) ).
thf(c_0_90,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_74]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO470^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n003.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 17:05:14 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.25 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.x0QN9B7ojI/E---3.1_2773630.p
% 0.32/0.28 % Version: 3.5.1-ho
% 0.32/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.32/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.32/0.28 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.32/0.28 % Starting almost_fo_3_lam with 300s (1) cores
% 0.32/0.28 % Starting post_as_ho1 with 300s (1) cores
% 0.32/0.28 % ho_unfolding_3 with pid 2773643 completed with status 0
% 0.32/0.28 % Result found by ho_unfolding_3
% 0.32/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.32/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.32/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.32/0.28 % No SInE strategy applied
% 0.32/0.28 % Search class: HGHNF-FFSF22-SHSSMFNN
% 0.32/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.32/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.32/0.28 % Starting ho_unfolding_3 with 151s (1) cores
% 0.32/0.28 % Starting sh5l with 136s (1) cores
% 0.32/0.28 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.32/0.28 % Starting lpo1_def_fix with 136s (1) cores
% 0.32/0.28 % ho_unfolding_3 with pid 2773649 completed with status 0
% 0.32/0.28 % Result found by ho_unfolding_3
% 0.32/0.28 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.32/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.28 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.32/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.32/0.28 % No SInE strategy applied
% 0.32/0.28 % Search class: HGHNF-FFSF22-SHSSMFNN
% 0.32/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.32/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.32/0.28 % Starting ho_unfolding_3 with 151s (1) cores
% 0.32/0.28 % Preprocessing time : 0.001 s
% 0.32/0.28 % Presaturation interreduction done
% 0.32/0.28
% 0.32/0.28 % Proof found!
% 0.32/0.28 % SZS status Theorem
% 0.32/0.28 % SZS output start CNFRefutation
% See solution above
% 0.32/0.28 % Parsed axioms : 73
% 0.32/0.28 % Removed by relevancy pruning/SinE : 0
% 0.32/0.28 % Initial clauses : 54
% 0.32/0.28 % Removed in clause preprocessing : 36
% 0.32/0.28 % Initial clauses in saturation : 18
% 0.32/0.28 % Processed clauses : 239
% 0.32/0.28 % ...of these trivial : 0
% 0.32/0.28 % ...subsumed : 96
% 0.32/0.28 % ...remaining for further processing : 143
% 0.32/0.28 % Other redundant clauses eliminated : 0
% 0.32/0.28 % Clauses deleted for lack of memory : 0
% 0.32/0.28 % Backward-subsumed : 10
% 0.32/0.28 % Backward-rewritten : 81
% 0.32/0.28 % Generated clauses : 420
% 0.32/0.28 % ...of the previous two non-redundant : 369
% 0.32/0.28 % ...aggressively subsumed : 0
% 0.32/0.28 % Contextual simplify-reflections : 1
% 0.32/0.28 % Paramodulations : 420
% 0.32/0.28 % Factorizations : 0
% 0.32/0.28 % NegExts : 0
% 0.32/0.28 % Equation resolutions : 0
% 0.32/0.28 % Disequality decompositions : 0
% 0.32/0.28 % Total rewrite steps : 147
% 0.32/0.28 % ...of those cached : 125
% 0.32/0.28 % Propositional unsat checks : 0
% 0.32/0.28 % Propositional check models : 0
% 0.32/0.28 % Propositional check unsatisfiable : 0
% 0.32/0.28 % Propositional clauses : 0
% 0.32/0.28 % Propositional clauses after purity: 0
% 0.32/0.28 % Propositional unsat core size : 0
% 0.32/0.28 % Propositional preprocessing time : 0.000
% 0.32/0.28 % Propositional encoding time : 0.000
% 0.32/0.28 % Propositional solver time : 0.000
% 0.32/0.28 % Success case prop preproc time : 0.000
% 0.32/0.28 % Success case prop encoding time : 0.000
% 0.32/0.28 % Success case prop solver time : 0.000
% 0.32/0.28 % Current number of processed clauses : 34
% 0.32/0.28 % Positive orientable unit clauses : 22
% 0.32/0.28 % Positive unorientable unit clauses: 0
% 0.32/0.28 % Negative unit clauses : 0
% 0.32/0.28 % Non-unit-clauses : 12
% 0.32/0.28 % Current number of unprocessed clauses: 21
% 0.32/0.28 % ...number of literals in the above : 46
% 0.32/0.28 % Current number of archived formulas : 0
% 0.32/0.28 % Current number of archived clauses : 109
% 0.32/0.28 % Clause-clause subsumption calls (NU) : 727
% 0.32/0.28 % Rec. Clause-clause subsumption calls : 581
% 0.32/0.28 % Non-unit clause-clause subsumptions : 103
% 0.32/0.28 % Unit Clause-clause subsumption calls : 10
% 0.32/0.28 % Rewrite failures with RHS unbound : 0
% 0.32/0.28 % BW rewrite match attempts : 8
% 0.32/0.28 % BW rewrite match successes : 8
% 0.32/0.28 % Condensation attempts : 239
% 0.32/0.28 % Condensation successes : 0
% 0.32/0.28 % Termbank termtop insertions : 9314
% 0.32/0.28 % Search garbage collected termcells : 662
% 0.32/0.28
% 0.32/0.28 % -------------------------------------------------
% 0.32/0.28 % User time : 0.014 s
% 0.32/0.28 % System time : 0.002 s
% 0.32/0.28 % Total time : 0.016 s
% 0.32/0.28 % Maximum resident set size: 3648 pages
% 0.32/0.28
% 0.32/0.28 % -------------------------------------------------
% 0.32/0.28 % User time : 0.039 s
% 0.32/0.28 % System time : 0.012 s
% 0.32/0.28 % Total time : 0.051 s
% 0.32/0.28 % Maximum resident set size: 4864 pages
% 0.32/0.28 % E exiting
%------------------------------------------------------------------------------