%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ087^1 : 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 : n014.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 08:20:33 AM UTC 2026
% Result : Theorem 0.23s 0.36s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 89 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 313 ( 13 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 775 ( 112 ~; 124 |; 8 &; 531 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 176 ( 35 ^; 141 !; 0 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_28,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_33,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
a: $i > $i > $o ).
thf(decl_55,type,
b: $i > $i > $o ).
thf(decl_56,type,
c: $i > $i > $o ).
thf(decl_57,type,
fool: $i > $i > $o ).
thf(decl_58,type,
ws: ( $i > $i > $o ) > $i > $o ).
thf(decl_59,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_61,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_62,type,
esk4_2: $i > ( $i > $o ) > $i ).
thf(decl_74,type,
esk16_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_75,type,
esk17_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_76,type,
esk18_1: $i > $i ).
thf(decl_77,type,
esk19_1: $i > $i ).
thf(decl_78,type,
esk20_0: $i ).
thf(decl_79,type,
esk21_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',mor) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',mforall_prop) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',mvalid) ).
thf(t_axiom_for_fool,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] : ( mimplies @ ( mbox @ fool @ X18 ) @ X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',t_axiom_for_fool) ).
thf(conj,conjecture,
mvalid @ ( mbox @ c @ ( ws @ c ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',conj) ).
thf(axiom_1,axiom,
mvalid @ ( mbox @ fool @ ( mor @ ( ws @ a ) @ ( mor @ ( ws @ b ) @ ( ws @ c ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',axiom_1) ).
thf(i_axiom_for_fool_b,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mbox @ fool @ X6 ) @ ( mbox @ b @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',i_axiom_for_fool_b) ).
thf(axiom_5,axiom,
mvalid @ ( mnot @ ( mbox @ b @ ( ws @ b ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',axiom_5) ).
thf(a6_axiom_for_fool_c_b,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ X6 ) ) @ ( mbox @ b @ ( mnot @ ( mbox @ c @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',a6_axiom_for_fool_c_b) ).
thf(axiom_3_b_c,axiom,
mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ c @ ( mnot @ ( ws @ b ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',axiom_3_b_c) ).
thf(i_axiom_for_fool_a,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mbox @ fool @ X6 ) @ ( mbox @ a @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',i_axiom_for_fool_a) ).
thf(axiom_4,axiom,
mvalid @ ( mnot @ ( mbox @ a @ ( ws @ a ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',axiom_4) ).
thf(a6_axiom_for_fool_c_a,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ c @ X6 ) ) @ ( mbox @ a @ ( mnot @ ( mbox @ c @ X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',a6_axiom_for_fool_c_a) ).
thf(axiom_3_a_c,axiom,
mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ c @ ( mnot @ ( ws @ a ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Tvqyl0N48U/E---3.1_2637223.p',axiom_3_a_c) ).
thf(c_0_17,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_18,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_19,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_20,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_17,c_0_18]),c_0_19]) ).
thf(c_0_21,plain,
( mforall_prop
= ( ^ [Z0: ( $i > $o ) > $i > $o,Z1: $i] :
! [X10: $i > $o] : ( Z0 @ X10 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mforall_prop]) ).
thf(c_0_22,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_23,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_24,plain,
! [X62: $i,X61: $i > $o] :
( ~ ! [X60: $i] :
( ~ ( fool @ X62 @ X60 )
| ( X61 @ X60 ) )
| ( X61 @ X62 ) ),
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)],[t_axiom_for_fool]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
thf(c_0_25,negated_conjecture,
~ ( mvalid @ ( mbox @ c @ ( ws @ c ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_26,plain,
! [X23: $i,X22: $i] :
( ~ ( fool @ X23 @ X22 )
| ( ws @ a @ X22 )
| ( ws @ b @ X22 )
| ( ws @ c @ X22 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_1,c_0_19]),c_0_22]),c_0_23])]) ).
thf(c_0_27,plain,
! [X184: $i,X185: $i > $o] :
( ( ( fool @ X184 @ ( esk1_2 @ X184 @ X185 ) )
| ( X185 @ X184 ) )
& ( ~ ( X185 @ ( esk1_2 @ X184 @ X185 ) )
| ( X185 @ X184 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])])]) ).
thf(c_0_28,plain,
! [X75: $i,X74: $i > $o] :
( ~ ! [X72: $i] :
( ~ ( fool @ X75 @ X72 )
| ( X74 @ X72 ) )
| ! [X73: $i] :
( ~ ( b @ X75 @ X73 )
| ( X74 @ X73 ) ) ),
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)],[i_axiom_for_fool_b]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
thf(c_0_29,plain,
! [X143: $i] :
~ ! [X142: $i] :
( ~ ( b @ X143 @ X142 )
| ( ws @ b @ X142 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_5,c_0_18]),c_0_22]),c_0_23])]) ).
thf(c_0_30,negated_conjecture,
~ ! [X145: $i,X144: $i] :
( ~ ( c @ X145 @ X144 )
| ( ws @ c @ X144 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_25,c_0_22]),c_0_23])]) ).
thf(c_0_31,plain,
! [X146: $i,X147: $i] :
( ~ ( fool @ X146 @ X147 )
| ( ws @ a @ X147 )
| ( ws @ b @ X147 )
| ( ws @ c @ X147 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_26])]) ).
thf(c_0_32,plain,
! [X3: $i,X4: $i > $o] :
( ( X4 @ X3 )
| ~ ( X4 @ ( esk1_2 @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_33,plain,
! [X4: $i > $o,X3: $i] :
( ( fool @ X3 @ ( esk1_2 @ X3 @ X4 ) )
| ( X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_34,plain,
! [X196: $i,X197: $i > $o,X199: $i] :
( ( ( fool @ X196 @ ( esk4_2 @ X196 @ X197 ) )
| ~ ( b @ X196 @ X199 )
| ( X197 @ X199 ) )
& ( ~ ( X197 @ ( esk4_2 @ X196 @ X197 ) )
| ~ ( b @ X196 @ X199 )
| ( X197 @ X199 ) ) ),
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_35,plain,
! [X266: $i] :
( ( b @ X266 @ ( esk19_1 @ X266 ) )
& ~ ( ws @ b @ ( esk19_1 @ X266 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])]) ).
thf(c_0_36,plain,
! [X139: $i,X138: $i > $o] :
( ~ ~ ! [X135: $i] :
( ~ ( c @ X139 @ X135 )
| ( X138 @ X135 ) )
| ! [X137: $i] :
( ~ ( b @ X139 @ X137 )
| ~ ! [X136: $i] :
( ~ ( c @ X137 @ X136 )
| ( X138 @ X136 ) ) ) ),
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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[a6_axiom_for_fool_c_b]),c_0_18]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
thf(c_0_37,plain,
! [X53: $i,X52: $i] :
( ~ ( fool @ X53 @ X52 )
| ( ws @ b @ X52 )
| ! [X51: $i] :
( ~ ( c @ X52 @ X51 )
| ~ ( ws @ b @ X51 ) ) ),
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)],[axiom_3_b_c,c_0_18]),c_0_20]),c_0_22]),c_0_23])]) ).
thf(c_0_38,negated_conjecture,
( ( c @ esk20_0 @ esk21_0 )
& ~ ( ws @ c @ esk21_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])])]) ).
thf(c_0_39,plain,
! [X3: $i,X14: $i] :
( ( ws @ a @ X14 )
| ( ws @ b @ X14 )
| ( ws @ c @ X14 )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
thf(c_0_40,plain,
! [X3: $i] : ( fool @ X3 @ X3 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
thf(c_0_41,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( fool @ X3 @ ( esk4_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( b @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_42,plain,
! [X3: $i] : ( b @ X3 @ ( esk19_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_43,plain,
! [X259: $i,X260: $i > $o,X261: $i,X262: $i] :
( ( ( c @ X262 @ ( esk17_3 @ X259 @ X260 @ X262 ) )
| ~ ( b @ X259 @ X262 )
| ~ ( c @ X259 @ X261 )
| ( X260 @ X261 ) )
& ( ~ ( X260 @ ( esk17_3 @ X259 @ X260 @ X262 ) )
| ~ ( b @ X259 @ X262 )
| ~ ( c @ X259 @ X261 )
| ( X260 @ X261 ) ) ),
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_36])])])])])]) ).
thf(c_0_44,plain,
! [X175: $i,X176: $i,X177: $i] :
( ~ ( fool @ X175 @ X176 )
| ( ws @ b @ X176 )
| ~ ( c @ X176 @ X177 )
| ~ ( ws @ b @ X177 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_37])])]) ).
thf(c_0_45,negated_conjecture,
~ ( ws @ c @ esk21_0 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_46,plain,
! [X3: $i] :
( ( ws @ a @ X3 )
| ( ws @ b @ X3 )
| ( ws @ c @ X3 ) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_47,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ X14 )
| ~ ( X4 @ ( esk4_2 @ X3 @ X4 ) )
| ~ ( b @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_48,plain,
! [X4: $i > $o,X3: $i] :
( ( fool @ X3 @ ( esk4_2 @ X3 @ X4 ) )
| ( X4 @ ( esk19_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
thf(c_0_49,plain,
! [X4: $i > $o,X3: $i,X14: $i,X15: $i] :
( ( c @ X3 @ ( esk17_3 @ X14 @ X4 @ X3 ) )
| ( X4 @ X15 )
| ~ ( b @ X14 @ X3 )
| ~ ( c @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,negated_conjecture,
c @ esk20_0 @ esk21_0,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_51,plain,
! [X3: $i,X14: $i,X15: $i] :
( ( ws @ b @ X14 )
| ~ ( fool @ X3 @ X14 )
| ~ ( c @ X14 @ X15 )
| ~ ( ws @ b @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
thf(c_0_52,negated_conjecture,
( ( ws @ b @ esk21_0 )
| ( ws @ a @ esk21_0 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_53,plain,
! [X3: $i,X14: $i] :
( ( fool @ X3 @ ( esk19_1 @ X3 ) )
| ( fool @ X3 @ X14 )
| ~ ( b @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_54,plain,
! [X4: $i > $o,X3: $i,X14: $i,X15: $i] :
( ( X4 @ X15 )
| ~ ( X4 @ ( esk17_3 @ X3 @ X4 @ X14 ) )
| ~ ( b @ X3 @ X14 )
| ~ ( c @ X3 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_55,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( c @ X3 @ ( esk17_3 @ esk20_0 @ X4 @ X3 ) )
| ( X4 @ esk21_0 )
| ~ ( b @ esk20_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_56,plain,
! [X71: $i,X70: $i > $o] :
( ~ ! [X68: $i] :
( ~ ( fool @ X71 @ X68 )
| ( X70 @ X68 ) )
| ! [X69: $i] :
( ~ ( a @ X71 @ X69 )
| ( X70 @ X69 ) ) ),
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)],[i_axiom_for_fool_a]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
thf(c_0_57,plain,
! [X141: $i] :
~ ! [X140: $i] :
( ~ ( a @ X141 @ X140 )
| ( ws @ a @ X140 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom_4,c_0_18]),c_0_22]),c_0_23])]) ).
thf(c_0_58,negated_conjecture,
! [X14: $i,X3: $i] :
( ( ws @ a @ esk21_0 )
| ( ws @ b @ X3 )
| ~ ( c @ X3 @ esk21_0 )
| ~ ( fool @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_59,plain,
! [X3: $i] : ( fool @ X3 @ ( esk19_1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_42]) ).
thf(c_0_60,plain,
! [X3: $i] :
~ ( ws @ b @ ( esk19_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
thf(c_0_61,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ X3 @ esk21_0 )
| ( c @ X3 @ X14 )
| ~ ( b @ esk20_0 @ X3 )
| ~ ( c @ esk20_0 @ X14 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_62,plain,
! [X192: $i,X193: $i > $o,X195: $i] :
( ( ( fool @ X192 @ ( esk3_2 @ X192 @ X193 ) )
| ~ ( a @ X192 @ X195 )
| ( X193 @ X195 ) )
& ( ~ ( X193 @ ( esk3_2 @ X192 @ X193 ) )
| ~ ( a @ X192 @ X195 )
| ( X193 @ X195 ) ) ),
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_56])])])])])]) ).
thf(c_0_63,plain,
! [X264: $i] :
( ( a @ X264 @ ( esk18_1 @ X264 ) )
& ~ ( ws @ a @ ( esk18_1 @ X264 ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
thf(c_0_64,plain,
! [X134: $i,X133: $i > $o] :
( ~ ~ ! [X130: $i] :
( ~ ( c @ X134 @ X130 )
| ( X133 @ X130 ) )
| ! [X132: $i] :
( ~ ( a @ X134 @ X132 )
| ~ ! [X131: $i] :
( ~ ( c @ X132 @ X131 )
| ( X133 @ X131 ) ) ) ),
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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[a6_axiom_for_fool_c_a]),c_0_18]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
thf(c_0_65,plain,
! [X47: $i,X46: $i] :
( ~ ( fool @ X47 @ X46 )
| ( ws @ a @ X46 )
| ! [X45: $i] :
( ~ ( c @ X46 @ X45 )
| ~ ( ws @ a @ X45 ) ) ),
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)],[axiom_3_a_c,c_0_18]),c_0_20]),c_0_22]),c_0_23])]) ).
thf(c_0_66,negated_conjecture,
! [X3: $i] :
( ( ws @ a @ esk21_0 )
| ~ ( c @ ( esk19_1 @ X3 ) @ esk21_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
thf(c_0_67,negated_conjecture,
! [X3: $i] :
( ( c @ X3 @ esk21_0 )
| ~ ( b @ esk20_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_50]) ).
thf(c_0_68,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( fool @ X3 @ ( esk3_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_69,plain,
! [X3: $i] : ( a @ X3 @ ( esk18_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_70,plain,
! [X254: $i,X255: $i > $o,X256: $i,X257: $i] :
( ( ( c @ X257 @ ( esk16_3 @ X254 @ X255 @ X257 ) )
| ~ ( a @ X254 @ X257 )
| ~ ( c @ X254 @ X256 )
| ( X255 @ X256 ) )
& ( ~ ( X255 @ ( esk16_3 @ X254 @ X255 @ X257 ) )
| ~ ( a @ X254 @ X257 )
| ~ ( c @ X254 @ X256 )
| ( X255 @ X256 ) ) ),
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_64])])])])])]) ).
thf(c_0_71,plain,
! [X169: $i,X170: $i,X171: $i] :
( ~ ( fool @ X169 @ X170 )
| ( ws @ a @ X170 )
| ~ ( c @ X170 @ X171 )
| ~ ( ws @ a @ X171 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_65])])]) ).
thf(c_0_72,negated_conjecture,
! [X3: $i] :
( ( ws @ a @ esk21_0 )
| ~ ( b @ esk20_0 @ ( esk19_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_73,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ X14 )
| ~ ( X4 @ ( esk3_2 @ X3 @ X4 ) )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
thf(c_0_74,plain,
! [X4: $i > $o,X3: $i] :
( ( fool @ X3 @ ( esk3_2 @ X3 @ X4 ) )
| ( X4 @ ( esk18_1 @ X3 ) ) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
thf(c_0_75,plain,
! [X4: $i > $o,X3: $i,X14: $i,X15: $i] :
( ( c @ X3 @ ( esk16_3 @ X14 @ X4 @ X3 ) )
| ( X4 @ X15 )
| ~ ( a @ X14 @ X3 )
| ~ ( c @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_76,plain,
! [X3: $i,X14: $i,X15: $i] :
( ( ws @ a @ X14 )
| ~ ( fool @ X3 @ X14 )
| ~ ( c @ X14 @ X15 )
| ~ ( ws @ a @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
thf(c_0_77,negated_conjecture,
ws @ a @ esk21_0,
inference(spm,[status(thm)],[c_0_72,c_0_42]) ).
thf(c_0_78,plain,
! [X3: $i,X14: $i] :
( ( fool @ X3 @ ( esk18_1 @ X3 ) )
| ( fool @ X3 @ X14 )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
thf(c_0_79,plain,
! [X4: $i > $o,X3: $i,X14: $i,X15: $i] :
( ( X4 @ X15 )
| ~ ( X4 @ ( esk16_3 @ X3 @ X4 @ X14 ) )
| ~ ( a @ X3 @ X14 )
| ~ ( c @ X3 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
thf(c_0_80,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( c @ X3 @ ( esk16_3 @ esk20_0 @ X4 @ X3 ) )
| ( X4 @ esk21_0 )
| ~ ( a @ esk20_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_75,c_0_50]) ).
thf(c_0_81,negated_conjecture,
! [X14: $i,X3: $i] :
( ( ws @ a @ X3 )
| ~ ( c @ X3 @ esk21_0 )
| ~ ( fool @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_82,plain,
! [X3: $i] : ( fool @ X3 @ ( esk18_1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_69]) ).
thf(c_0_83,plain,
! [X3: $i] :
~ ( ws @ a @ ( esk18_1 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_84,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ X3 @ esk21_0 )
| ( c @ X3 @ X14 )
| ~ ( a @ esk20_0 @ X3 )
| ~ ( c @ esk20_0 @ X14 ) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i] :
~ ( c @ ( esk18_1 @ X3 ) @ esk21_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
thf(c_0_86,negated_conjecture,
! [X3: $i] :
( ( c @ X3 @ esk21_0 )
| ~ ( a @ esk20_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_84,c_0_50]) ).
thf(c_0_87,negated_conjecture,
! [X3: $i] :
~ ( a @ esk20_0 @ ( esk18_1 @ X3 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_88,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_87,c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ087^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:21:45 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.Tvqyl0N48U/E---3.1_2637223.p
% 0.23/0.36 % Version: 3.5.1-ho
% 0.23/0.36 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.23/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.36 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.36 % Starting new_ho_12 with 300s (1) cores
% 0.23/0.36 % Starting new_bool_2 with 300s (1) cores
% 0.23/0.36 % post_as_ho3 with pid 2637260 completed with status 0
% 0.23/0.36 % Result found by post_as_ho3
% 0.23/0.36 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.23/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.36 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.36 % No SInE strategy applied
% 0.23/0.36 % Search class: HGUNS-FFMF32-SHSSMMBN
% 0.23/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.36 % SubtermCWHack with pid 2637274 completed with status 0
% 0.23/0.36 % Result found by SubtermCWHack
% 0.23/0.36 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.23/0.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.36 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.23/0.36 % Starting post_as_ho3 with 300s (1) cores
% 0.23/0.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.36 % No SInE strategy applied
% 0.23/0.36 % Search class: HGUNS-FFMF32-SHSSMMBN
% 0.23/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.36 % Preprocessing time : 0.003 s
% 0.23/0.36
% 0.23/0.36 % Proof found!
% 0.23/0.36 % SZS status Theorem
% 0.23/0.36 % SZS output start CNFRefutation
% See solution above
% 0.23/0.36 % Parsed axioms : 101
% 0.23/0.36 % Removed by relevancy pruning/SinE : 0
% 0.23/0.36 % Initial clauses : 90
% 0.23/0.36 % Removed in clause preprocessing : 37
% 0.23/0.36 % Initial clauses in saturation : 53
% 0.23/0.36 % Processed clauses : 260
% 0.23/0.36 % ...of these trivial : 0
% 0.23/0.36 % ...subsumed : 40
% 0.23/0.36 % ...remaining for further processing : 220
% 0.23/0.36 % Other redundant clauses eliminated : 0
% 0.23/0.36 % Clauses deleted for lack of memory : 0
% 0.23/0.36 % Backward-subsumed : 39
% 0.23/0.36 % Backward-rewritten : 19
% 0.23/0.36 % Generated clauses : 3172
% 0.23/0.36 % ...of the previous two non-redundant : 2994
% 0.23/0.37 % ...aggressively subsumed : 0
% 0.23/0.37 % Contextual simplify-reflections : 0
% 0.23/0.37 % Paramodulations : 3160
% 0.23/0.37 % Factorizations : 12
% 0.23/0.37 % NegExts : 0
% 0.23/0.37 % Equation resolutions : 0
% 0.23/0.37 % Disequality decompositions : 0
% 0.23/0.37 % Total rewrite steps : 196
% 0.23/0.37 % ...of those cached : 171
% 0.23/0.37 % Propositional unsat checks : 0
% 0.23/0.37 % Propositional check models : 0
% 0.23/0.37 % Propositional check unsatisfiable : 0
% 0.23/0.37 % Propositional clauses : 0
% 0.23/0.37 % Propositional clauses after purity: 0
% 0.23/0.37 % Propositional unsat core size : 0
% 0.23/0.37 % Propositional preprocessing time : 0.000
% 0.23/0.37 % Propositional encoding time : 0.000
% 0.23/0.37 % Propositional solver time : 0.000
% 0.23/0.37 % Success case prop preproc time : 0.000
% 0.23/0.37 % Success case prop encoding time : 0.000
% 0.23/0.37 % Success case prop solver time : 0.000
% 0.23/0.37 % Current number of processed clauses : 162
% 0.23/0.37 % Positive orientable unit clauses : 14
% 0.23/0.37 % Positive unorientable unit clauses: 0
% 0.23/0.37 % Negative unit clauses : 5
% 0.23/0.37 % Non-unit-clauses : 143
% 0.23/0.37 % Current number of unprocessed clauses: 2733
% 0.23/0.37 % ...number of literals in the above : 10785
% 0.23/0.37 % Current number of archived formulas : 0
% 0.23/0.37 % Current number of archived clauses : 58
% 0.23/0.37 % Clause-clause subsumption calls (NU) : 2221
% 0.23/0.37 % Rec. Clause-clause subsumption calls : 1594
% 0.23/0.37 % Non-unit clause-clause subsumptions : 73
% 0.23/0.37 % Unit Clause-clause subsumption calls : 113
% 0.23/0.37 % Rewrite failures with RHS unbound : 0
% 0.23/0.37 % BW rewrite match attempts : 8
% 0.23/0.37 % BW rewrite match successes : 6
% 0.23/0.37 % Condensation attempts : 0
% 0.23/0.37 % Condensation successes : 0
% 0.23/0.37 % Termbank termtop insertions : 68885
% 0.23/0.37 % Search garbage collected termcells : 5614
% 0.23/0.37
% 0.23/0.37 % -------------------------------------------------
% 0.23/0.37 % User time : 0.076 s
% 0.23/0.37 % System time : 0.013 s
% 0.23/0.37 % Total time : 0.089 s
% 0.23/0.37 % Maximum resident set size: 4444 pages
% 0.23/0.37
% 0.23/0.37 % -------------------------------------------------
% 0.23/0.37 % User time : 0.078 s
% 0.23/0.37 % System time : 0.018 s
% 0.23/0.37 % Total time : 0.096 s
% 0.23/0.37 % Maximum resident set size: 4864 pages
% 0.23/0.37 % E exiting
%------------------------------------------------------------------------------