%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : PUZ087^2 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 0.28s 0.38s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 96 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 360 ( 13 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 957 ( 141 ~; 151 |; 11 &; 654 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 6 con; 0-3 aty)
% Number of variables : 196 ( 35 ^; 161 !; 0 ?; 196 :)
% 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,
priorG: $i > $i > $o ).
thf(decl_61,type,
esk1_2: $i > ( $i > $o ) > $i ).
thf(decl_63,type,
esk3_2: $i > ( $i > $o ) > $i ).
thf(decl_65,type,
esk5_2: $i > ( $i > $o ) > $i ).
thf(decl_76,type,
esk16_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_77,type,
esk17_3: $i > ( $i > $o ) > $i > $i ).
thf(decl_78,type,
esk18_2: $i > $i > $i ).
thf(decl_79,type,
esk19_3: $i > $i > $i > $i ).
thf(decl_80,type,
esk20_0: $i ).
thf(decl_81,type,
esk21_0: $i ).
thf(decl_82,type,
esk22_0: $i ).
thf(decl_83,type,
esk23_0: $i ).
thf(decl_84,type,
esk24_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',mor) ).
thf(mforall_prop,axiom,
( mforall_prop
= ( ^ [X9: ( $i > $o ) > $i > $o,X3: $i] :
! [X10: $i > $o] : ( X9 @ X10 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.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/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',mvalid) ).
thf(conj,conjecture,
mvalid @ ( mbox @ priorG @ ( mbox @ priorG @ ( mbox @ priorG @ ( mbox @ c @ ( ws @ c ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',conj) ).
thf(i_axiom_for_fool_c,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mbox @ fool @ X6 ) @ ( mbox @ c @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',i_axiom_for_fool_c) ).
thf(axiom_1,axiom,
mvalid @ ( mbox @ fool @ ( mor @ ( ws @ a ) @ ( mor @ ( ws @ b ) @ ( ws @ c ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',axiom_1) ).
thf(axiom_3_b_c,axiom,
mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ b ) ) @ ( mbox @ c @ ( mnot @ ( ws @ b ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',axiom_3_b_c) ).
thf(t_axiom_for_fool,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X19: $i > $o] : ( mimplies @ ( mbox @ fool @ X19 ) @ X19 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',t_axiom_for_fool) ).
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/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',a6_axiom_for_fool_c_b) ).
thf(axiom_5,axiom,
mvalid @ ( mbox @ priorG @ ( mbox @ priorG @ ( mnot @ ( mbox @ b @ ( ws @ b ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',axiom_5) ).
thf(i_axiom_for_fool_a,axiom,
( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mbox @ fool @ X6 ) @ ( mbox @ a @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',i_axiom_for_fool_a) ).
thf(axiom_4,axiom,
mvalid @ ( mbox @ priorG @ ( mnot @ ( mbox @ a @ ( ws @ a ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',axiom_4) ).
thf(axiom_3_a_c,axiom,
mvalid @ ( mbox @ fool @ ( mimplies @ ( mnot @ ( ws @ a ) ) @ ( mbox @ c @ ( mnot @ ( ws @ a ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',axiom_3_a_c) ).
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/sandbox/tmp/tmp.cOZdL3usB2/E---3.1_315762.p',a6_axiom_for_fool_c_a) ).
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,negated_conjecture,
~ ( mvalid @ ( mbox @ priorG @ ( mbox @ priorG @ ( mbox @ priorG @ ( mbox @ c @ ( ws @ c ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_25,plain,
! [X84: $i,X83: $i > $o] :
( ~ ! [X81: $i] :
( ~ ( fool @ X84 @ X81 )
| ( X83 @ X81 ) )
| ! [X82: $i] :
( ~ ( c @ X84 @ X82 )
| ( X83 @ X82 ) ) ),
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_c]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
thf(c_0_26,negated_conjecture,
~ ! [X156: $i,X155: $i] :
( ~ ( priorG @ X156 @ X155 )
| ! [X154: $i] :
( ~ ( priorG @ X155 @ X154 )
| ! [X153: $i] :
( ~ ( priorG @ X154 @ X153 )
| ! [X152: $i] :
( ~ ( c @ X153 @ X152 )
| ( ws @ c @ X152 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_24,c_0_22]),c_0_23])]) ).
thf(c_0_27,plain,
! [X215: $i,X216: $i > $o,X218: $i] :
( ( ( fool @ X215 @ ( esk5_2 @ X215 @ X216 ) )
| ~ ( c @ X215 @ X218 )
| ( X216 @ X218 ) )
& ( ~ ( X216 @ ( esk5_2 @ X215 @ X216 ) )
| ~ ( c @ X215 @ X218 )
| ( X216 @ X218 ) ) ),
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_25])])])])])]) ).
thf(c_0_28,negated_conjecture,
( ( priorG @ esk20_0 @ esk21_0 )
& ( priorG @ esk21_0 @ esk22_0 )
& ( priorG @ esk22_0 @ esk23_0 )
& ( c @ esk23_0 @ esk24_0 )
& ~ ( ws @ c @ esk24_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])]) ).
thf(c_0_29,plain,
! [X28: $i,X27: $i] :
( ~ ( fool @ X28 @ X27 )
| ( ws @ a @ X27 )
| ( ws @ b @ X27 )
| ( ws @ c @ X27 ) ),
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_30,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ X14 )
| ~ ( X4 @ ( esk5_2 @ X3 @ X4 ) )
| ~ ( c @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_31,negated_conjecture,
c @ esk23_0 @ esk24_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_32,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( fool @ X3 @ ( esk5_2 @ X3 @ X4 ) )
| ( X4 @ X14 )
| ~ ( c @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
thf(c_0_33,plain,
! [X58: $i,X57: $i] :
( ~ ( fool @ X58 @ X57 )
| ( ws @ b @ X57 )
| ! [X56: $i] :
( ~ ( c @ X57 @ X56 )
| ~ ( ws @ b @ X56 ) ) ),
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_34,plain,
! [X161: $i,X162: $i] :
( ~ ( fool @ X161 @ X162 )
| ( ws @ a @ X162 )
| ( ws @ b @ X162 )
| ( ws @ c @ X162 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
thf(c_0_35,negated_conjecture,
! [X4: $i > $o] :
( ( X4 @ esk24_0 )
| ~ ( X4 @ ( esk5_2 @ esk23_0 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_36,negated_conjecture,
! [X4: $i > $o] :
( ( fool @ esk23_0 @ ( esk5_2 @ esk23_0 @ X4 ) )
| ( X4 @ esk24_0 ) ),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
thf(c_0_37,plain,
! [X67: $i,X66: $i > $o] :
( ~ ! [X65: $i] :
( ~ ( fool @ X67 @ X65 )
| ( X66 @ X65 ) )
| ( X66 @ X67 ) ),
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_38,plain,
! [X144: $i,X143: $i > $o] :
( ~ ~ ! [X140: $i] :
( ~ ( c @ X144 @ X140 )
| ( X143 @ X140 ) )
| ! [X142: $i] :
( ~ ( b @ X144 @ X142 )
| ~ ! [X141: $i] :
( ~ ( c @ X142 @ X141 )
| ( X143 @ X141 ) ) ) ),
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_39,plain,
! [X190: $i,X191: $i,X192: $i] :
( ~ ( fool @ X190 @ X191 )
| ( ws @ b @ X191 )
| ~ ( c @ X191 @ X192 )
| ~ ( ws @ b @ X192 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_33])])]) ).
thf(c_0_40,plain,
! [X3: $i,X14: $i] :
( ( ws @ a @ X14 )
| ( ws @ b @ X14 )
| ( ws @ c @ X14 )
| ~ ( fool @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_41,negated_conjecture,
fool @ esk23_0 @ esk24_0,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
thf(c_0_42,negated_conjecture,
~ ( ws @ c @ esk24_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_43,plain,
! [X199: $i,X200: $i > $o] :
( ( ( fool @ X199 @ ( esk1_2 @ X199 @ X200 ) )
| ( X200 @ X199 ) )
& ( ~ ( X200 @ ( esk1_2 @ X199 @ X200 ) )
| ( X200 @ X199 ) ) ),
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_37])])])])]) ).
thf(c_0_44,plain,
! [X274: $i,X275: $i > $o,X276: $i,X277: $i] :
( ( ( c @ X277 @ ( esk17_3 @ X274 @ X275 @ X277 ) )
| ~ ( b @ X274 @ X277 )
| ~ ( c @ X274 @ X276 )
| ( X275 @ X276 ) )
& ( ~ ( X275 @ ( esk17_3 @ X274 @ X275 @ X277 ) )
| ~ ( b @ X274 @ X277 )
| ~ ( c @ X274 @ X276 )
| ( X275 @ X276 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])])]) ).
thf(c_0_45,plain,
! [X151: $i,X150: $i] :
( ~ ( priorG @ X151 @ X150 )
| ! [X149: $i] :
( ~ ( priorG @ X150 @ X149 )
| ~ ! [X148: $i] :
( ~ ( b @ X149 @ X148 )
| ( ws @ b @ X148 ) ) ) ),
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_46,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_39]) ).
thf(c_0_47,negated_conjecture,
( ( ws @ b @ esk24_0 )
| ( ws @ a @ esk24_0 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
thf(c_0_48,plain,
! [X3: $i,X4: $i > $o] :
( ( X4 @ X3 )
| ~ ( X4 @ ( esk1_2 @ X3 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_49,plain,
! [X4: $i > $o,X3: $i] :
( ( fool @ X3 @ ( esk1_2 @ X3 @ X4 ) )
| ( X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
thf(c_0_50,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_44]) ).
thf(c_0_51,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_44]) ).
thf(c_0_52,plain,
! [X282: $i,X283: $i,X284: $i] :
( ( ( b @ X284 @ ( esk19_3 @ X282 @ X283 @ X284 ) )
| ~ ( priorG @ X283 @ X284 )
| ~ ( priorG @ X282 @ X283 ) )
& ( ~ ( ws @ b @ ( esk19_3 @ X282 @ X283 @ X284 ) )
| ~ ( priorG @ X283 @ X284 )
| ~ ( priorG @ X282 @ X283 ) ) ),
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_45])])])])])]) ).
thf(c_0_53,negated_conjecture,
! [X14: $i,X3: $i] :
( ( ws @ a @ esk24_0 )
| ( ws @ b @ X3 )
| ~ ( c @ X3 @ esk24_0 )
| ~ ( fool @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
thf(c_0_54,plain,
! [X3: $i] : ( fool @ X3 @ X3 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_55,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( X4 @ esk24_0 )
| ~ ( X4 @ ( esk17_3 @ esk23_0 @ X4 @ X3 ) )
| ~ ( b @ esk23_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_50,c_0_31]) ).
thf(c_0_56,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( c @ X3 @ ( esk17_3 @ esk23_0 @ X4 @ X3 ) )
| ( X4 @ esk24_0 )
| ~ ( b @ esk23_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_31]) ).
thf(c_0_57,plain,
! [X76: $i,X75: $i > $o] :
( ~ ! [X73: $i] :
( ~ ( fool @ X76 @ X73 )
| ( X75 @ X73 ) )
| ! [X74: $i] :
( ~ ( a @ X76 @ X74 )
| ( X75 @ X74 ) ) ),
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_58,plain,
! [X147: $i,X146: $i] :
( ~ ( priorG @ X147 @ X146 )
| ~ ! [X145: $i] :
( ~ ( a @ X146 @ X145 )
| ( ws @ a @ X145 ) ) ),
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_59,plain,
! [X15: $i,X3: $i,X14: $i] :
( ~ ( ws @ b @ ( esk19_3 @ X3 @ X14 @ X15 ) )
| ~ ( priorG @ X14 @ X15 )
| ~ ( priorG @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i] :
( ( ws @ a @ esk24_0 )
| ( ws @ b @ X3 )
| ~ ( c @ X3 @ esk24_0 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_61,negated_conjecture,
! [X3: $i] :
( ( c @ X3 @ esk24_0 )
| ~ ( b @ esk23_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
thf(c_0_62,plain,
! [X3: $i,X14: $i,X15: $i] :
( ( b @ X3 @ ( esk19_3 @ X14 @ X15 @ X3 ) )
| ~ ( priorG @ X15 @ X3 )
| ~ ( priorG @ X14 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_63,plain,
! [X207: $i,X208: $i > $o,X210: $i] :
( ( ( fool @ X207 @ ( esk3_2 @ X207 @ X208 ) )
| ~ ( a @ X207 @ X210 )
| ( X208 @ X210 ) )
& ( ~ ( X208 @ ( esk3_2 @ X207 @ X208 ) )
| ~ ( a @ X207 @ X210 )
| ( X208 @ X210 ) ) ),
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_57])])])])])]) ).
thf(c_0_64,plain,
! [X279: $i,X280: $i] :
( ( ( a @ X280 @ ( esk18_2 @ X279 @ X280 ) )
| ~ ( priorG @ X279 @ X280 ) )
& ( ~ ( ws @ a @ ( esk18_2 @ X279 @ X280 ) )
| ~ ( priorG @ X279 @ X280 ) ) ),
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_58])])])])]) ).
thf(c_0_65,negated_conjecture,
! [X15: $i,X3: $i,X14: $i] :
( ( ws @ a @ esk24_0 )
| ~ ( c @ ( esk19_3 @ X3 @ X14 @ X15 ) @ esk24_0 )
| ~ ( priorG @ X14 @ X15 )
| ~ ( priorG @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_66,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk19_3 @ X3 @ X14 @ esk23_0 ) @ esk24_0 )
| ~ ( priorG @ X14 @ esk23_0 )
| ~ ( priorG @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_67,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_63]) ).
thf(c_0_68,plain,
! [X14: $i,X3: $i] :
( ( a @ X3 @ ( esk18_2 @ X14 @ X3 ) )
| ~ ( priorG @ X14 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_69,plain,
! [X52: $i,X51: $i] :
( ~ ( fool @ X52 @ X51 )
| ( ws @ a @ X51 )
| ! [X50: $i] :
( ~ ( c @ X51 @ X50 )
| ~ ( ws @ a @ X50 ) ) ),
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_70,negated_conjecture,
! [X14: $i,X3: $i] :
( ( ws @ a @ esk24_0 )
| ~ ( priorG @ X3 @ esk23_0 )
| ~ ( priorG @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
thf(c_0_71,negated_conjecture,
priorG @ esk22_0 @ esk23_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_72,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_63]) ).
thf(c_0_73,plain,
! [X14: $i,X4: $i > $o,X3: $i] :
( ( fool @ X3 @ ( esk3_2 @ X3 @ X4 ) )
| ( X4 @ ( esk18_2 @ X14 @ X3 ) )
| ~ ( priorG @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
thf(c_0_74,plain,
! [X139: $i,X138: $i > $o] :
( ~ ~ ! [X135: $i] :
( ~ ( c @ X139 @ X135 )
| ( X138 @ X135 ) )
| ! [X137: $i] :
( ~ ( a @ 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_a]),c_0_18]),c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
thf(c_0_75,plain,
! [X184: $i,X185: $i,X186: $i] :
( ~ ( fool @ X184 @ X185 )
| ( ws @ a @ X185 )
| ~ ( c @ X185 @ X186 )
| ~ ( ws @ a @ X186 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_69])])]) ).
thf(c_0_76,negated_conjecture,
! [X3: $i] :
( ( ws @ a @ esk24_0 )
| ~ ( priorG @ X3 @ esk22_0 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_77,negated_conjecture,
priorG @ esk21_0 @ esk22_0,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_78,plain,
! [X4: $i > $o,X3: $i,X14: $i] :
( ( X4 @ ( esk18_2 @ X3 @ X14 ) )
| ~ ( X4 @ ( esk3_2 @ X14 @ X4 ) )
| ~ ( priorG @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_68]) ).
thf(c_0_79,negated_conjecture,
! [X4: $i > $o] :
( ( fool @ esk23_0 @ ( esk3_2 @ esk23_0 @ X4 ) )
| ( X4 @ ( esk18_2 @ esk22_0 @ esk23_0 ) ) ),
inference(spm,[status(thm)],[c_0_73,c_0_71]) ).
thf(c_0_80,plain,
! [X269: $i,X270: $i > $o,X271: $i,X272: $i] :
( ( ( c @ X272 @ ( esk16_3 @ X269 @ X270 @ X272 ) )
| ~ ( a @ X269 @ X272 )
| ~ ( c @ X269 @ X271 )
| ( X270 @ X271 ) )
& ( ~ ( X270 @ ( esk16_3 @ X269 @ X270 @ X272 ) )
| ~ ( a @ X269 @ X272 )
| ~ ( c @ X269 @ X271 )
| ( X270 @ X271 ) ) ),
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_74])])])])])]) ).
thf(c_0_81,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_75]) ).
thf(c_0_82,negated_conjecture,
ws @ a @ esk24_0,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_83,negated_conjecture,
! [X3: $i] :
( ( fool @ esk23_0 @ ( esk18_2 @ esk22_0 @ esk23_0 ) )
| ( fool @ esk23_0 @ ( esk18_2 @ X3 @ esk23_0 ) )
| ~ ( priorG @ X3 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
thf(c_0_84,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_80]) ).
thf(c_0_85,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_80]) ).
thf(c_0_86,negated_conjecture,
! [X14: $i,X3: $i] :
( ( ws @ a @ X3 )
| ~ ( c @ X3 @ esk24_0 )
| ~ ( fool @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
thf(c_0_87,negated_conjecture,
fool @ esk23_0 @ ( esk18_2 @ esk22_0 @ esk23_0 ),
inference(spm,[status(thm)],[c_0_83,c_0_71]) ).
thf(c_0_88,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( X4 @ esk24_0 )
| ~ ( X4 @ ( esk16_3 @ esk23_0 @ X4 @ X3 ) )
| ~ ( a @ esk23_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_84,c_0_31]) ).
thf(c_0_89,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( c @ X3 @ ( esk16_3 @ esk23_0 @ X4 @ X3 ) )
| ( X4 @ esk24_0 )
| ~ ( a @ esk23_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_31]) ).
thf(c_0_90,plain,
! [X3: $i,X14: $i] :
( ~ ( ws @ a @ ( esk18_2 @ X3 @ X14 ) )
| ~ ( priorG @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
thf(c_0_91,negated_conjecture,
( ( ws @ a @ ( esk18_2 @ esk22_0 @ esk23_0 ) )
| ~ ( c @ ( esk18_2 @ esk22_0 @ esk23_0 ) @ esk24_0 ) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
thf(c_0_92,negated_conjecture,
! [X3: $i] :
( ( c @ X3 @ esk24_0 )
| ~ ( a @ esk23_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
thf(c_0_93,negated_conjecture,
~ ( c @ ( esk18_2 @ esk22_0 @ esk23_0 ) @ esk24_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_71])]) ).
thf(c_0_94,negated_conjecture,
! [X3: $i] :
( ( c @ ( esk18_2 @ X3 @ esk23_0 ) @ esk24_0 )
| ~ ( priorG @ X3 @ esk23_0 ) ),
inference(spm,[status(thm)],[c_0_92,c_0_68]) ).
thf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_71])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ087^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n017.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:17:37 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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/tmp/tmp.cOZdL3usB2/E---3.1_315762.p
% 0.28/0.38 % Version: 3.5.1-ho
% 0.28/0.38 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.38 % Starting post_as_ho3 with 300s (1) cores
% 0.28/0.38 % Starting new_ho_12 with 300s (1) cores
% 0.28/0.38 % Starting new_bool_2 with 300s (1) cores
% 0.28/0.38 % new_ho_10_cnf2 with pid 315775 completed with status 0
% 0.28/0.38 % Result found by new_ho_10_cnf2
% 0.28/0.38 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.38 % No SInE strategy applied
% 0.28/0.38 % Search class: HGHNF-FFMS32-SHSSMMBN
% 0.28/0.38 % partial match(2): HGUNF-FFSS32-SHSSMMBN
% 0.28/0.38 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.38 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.38 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.28/0.38 % Starting sh5l with 136s (1) cores
% 0.28/0.38 % Starting lpo1_def_fix with 136s (1) cores
% 0.28/0.38 % Starting ehoh_best8_lambda with 136s (1) cores
% 0.28/0.38 % new_ho_10_cnf2 with pid 315783 completed with status 0
% 0.28/0.38 % Result found by new_ho_10_cnf2
% 0.28/0.38 % Preprocessing class: HSMSSMSSMLLNHSN.
% 0.28/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.28/0.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.38 % No SInE strategy applied
% 0.28/0.38 % Search class: HGHNF-FFMS32-SHSSMMBN
% 0.28/0.38 % partial match(2): HGUNF-FFSS32-SHSSMMBN
% 0.28/0.38 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.38 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.38 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.28/0.38 % Preprocessing time : 0.003 s
% 0.28/0.38 % Presaturation interreduction done
% 0.28/0.38
% 0.28/0.38 % Proof found!
% 0.28/0.38 % SZS status Theorem
% 0.28/0.38 % SZS output start CNFRefutation
% See solution above
% 0.28/0.38 % Parsed axioms : 106
% 0.28/0.38 % Removed by relevancy pruning/SinE : 0
% 0.28/0.38 % Initial clauses : 97
% 0.28/0.38 % Removed in clause preprocessing : 39
% 0.28/0.38 % Initial clauses in saturation : 58
% 0.28/0.38 % Processed clauses : 374
% 0.28/0.38 % ...of these trivial : 0
% 0.28/0.38 % ...subsumed : 25
% 0.28/0.38 % ...remaining for further processing : 349
% 0.28/0.38 % Other redundant clauses eliminated : 0
% 0.28/0.38 % Clauses deleted for lack of memory : 0
% 0.28/0.38 % Backward-subsumed : 16
% 0.28/0.38 % Backward-rewritten : 21
% 0.28/0.38 % Generated clauses : 2049
% 0.28/0.38 % ...of the previous two non-redundant : 1955
% 0.28/0.38 % ...aggressively subsumed : 0
% 0.28/0.38 % Contextual simplify-reflections : 0
% 0.28/0.38 % Paramodulations : 2049
% 0.28/0.38 % Factorizations : 0
% 0.28/0.38 % NegExts : 0
% 0.28/0.38 % Equation resolutions : 0
% 0.28/0.38 % Disequality decompositions : 0
% 0.28/0.38 % Total rewrite steps : 155
% 0.28/0.38 % ...of those cached : 141
% 0.28/0.38 % Propositional unsat checks : 0
% 0.28/0.38 % Propositional check models : 0
% 0.28/0.38 % Propositional check unsatisfiable : 0
% 0.28/0.38 % Propositional clauses : 0
% 0.28/0.38 % Propositional clauses after purity: 0
% 0.28/0.38 % Propositional unsat core size : 0
% 0.28/0.38 % Propositional preprocessing time : 0.000
% 0.28/0.38 % Propositional encoding time : 0.000
% 0.28/0.38 % Propositional solver time : 0.000
% 0.28/0.38 % Success case prop preproc time : 0.000
% 0.28/0.38 % Success case prop encoding time : 0.000
% 0.28/0.38 % Success case prop solver time : 0.000
% 0.28/0.38 % Current number of processed clauses : 254
% 0.28/0.38 % Positive orientable unit clauses : 12
% 0.28/0.38 % Positive unorientable unit clauses: 0
% 0.28/0.38 % Negative unit clauses : 6
% 0.28/0.38 % Non-unit-clauses : 236
% 0.28/0.38 % Current number of unprocessed clauses: 1668
% 0.28/0.38 % ...number of literals in the above : 8426
% 0.28/0.38 % Current number of archived formulas : 0
% 0.28/0.38 % Current number of archived clauses : 95
% 0.28/0.38 % Clause-clause subsumption calls (NU) : 16364
% 0.28/0.38 % Rec. Clause-clause subsumption calls : 5802
% 0.28/0.38 % Non-unit clause-clause subsumptions : 38
% 0.28/0.38 % Unit Clause-clause subsumption calls : 159
% 0.28/0.38 % Rewrite failures with RHS unbound : 0
% 0.28/0.38 % BW rewrite match attempts : 7
% 0.28/0.38 % BW rewrite match successes : 6
% 0.28/0.38 % Condensation attempts : 374
% 0.28/0.38 % Condensation successes : 0
% 0.28/0.38 % Termbank termtop insertions : 74038
% 0.28/0.38 % Search garbage collected termcells : 5921
% 0.28/0.38
% 0.28/0.38 % -------------------------------------------------
% 0.28/0.38 % User time : 0.107 s
% 0.28/0.38 % System time : 0.009 s
% 0.28/0.38 % Total time : 0.117 s
% 0.28/0.38 % Maximum resident set size: 4704 pages
% 0.28/0.38
% 0.28/0.38 % -------------------------------------------------
% 0.28/0.38 % User time : 0.438 s
% 0.28/0.38 % System time : 0.028 s
% 0.28/0.38 % Total time : 0.465 s
% 0.28/0.38 % Maximum resident set size: 4864 pages
% 0.28/0.38 % E exiting
%------------------------------------------------------------------------------