%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO049^1 : 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 : n026.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 08:42:13 AM UTC 2026
% Result : Theorem 0.31s 0.28s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 53 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 22 equ; 0 cnn)
% Maximal formula atoms : 90 ( 4 avg)
% Number of connectives : 627 ( 115 ~; 144 |; 23 &; 345 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 91 ( 58 ^; 33 !; 0 ?; 91 :)
% 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_33,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_39,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
epred1_0: $i > $i > $o ).
thf(decl_55,type,
esk1_0: $i ).
thf(decl_56,type,
epred2_0: $i > $o ).
thf(decl_57,type,
epred3_0: $i > $o ).
thf(decl_58,type,
esk2_0: $i ).
thf(decl_59,type,
esk3_0: $i ).
thf(decl_60,type,
esk4_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xZGFrLeO33/E---3.1_810652.p',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xZGFrLeO33/E---3.1_810652.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xZGFrLeO33/E---3.1_810652.p',mor) ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xZGFrLeO33/E---3.1_810652.p',mand) ).
thf(mdia,axiom,
( mdia
= ( ^ [X13: $i > $i > $o,X6: $i > $o] : ( mnot @ ( mbox @ X13 @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xZGFrLeO33/E---3.1_810652.p',mdia) ).
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.xZGFrLeO33/E---3.1_810652.p',mbox) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mand @ ( mimplies @ X6 @ X7 ) @ ( mimplies @ X7 @ X6 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xZGFrLeO33/E---3.1_810652.p',mequiv) ).
thf(conj,conjecture,
! [X13: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] :
( mforall_prop
@ ^ [X19: $i > $o] : ( mequiv @ ( mdia @ X13 @ ( mor @ X18 @ X19 ) ) @ ( mor @ ( mdia @ X13 @ X18 ) @ ( mdia @ X13 @ X19 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xZGFrLeO33/E---3.1_810652.p',conj) ).
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.xZGFrLeO33/E---3.1_810652.p',mforall_prop) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.xZGFrLeO33/E---3.1_810652.p',mvalid) ).
thf(c_0_10,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_11,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_12,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_13,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_14,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X22: $i] :
( ~ ( Z0 @ Z2 @ X22 )
| ~ ( Z1 @ X22 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia]) ).
thf(c_0_15,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_16,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_17,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_10,c_0_11]),c_0_12]) ).
thf(c_0_18,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_13,c_0_11]),c_0_12]) ).
thf(c_0_19,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [X18: $i > $o] :
( mforall_prop
@ ^ [X19: $i > $o] : ( mequiv @ ( mdia @ X13 @ ( mor @ X18 @ X19 ) ) @ ( mor @ ( mdia @ X13 @ X18 ) @ ( mdia @ X13 @ X19 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_20,plain,
( mdia
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
~ ! [X22: $i] :
( ~ ( Z0 @ Z2 @ X22 )
| ~ ( Z1 @ X22 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_11]) ).
thf(c_0_21,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_16,c_0_17]),c_0_18]) ).
thf(c_0_22,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_23,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_24,negated_conjecture,
~ ! [X13: $i > $i > $o,X28: $i,X27: $i > $o,X26: $i > $o] :
~ ( ~ ( ~ ~ ! [X23: $i] :
( ~ ( X13 @ X28 @ X23 )
| ~ ( ( X27 @ X23 )
| ( X26 @ X23 ) ) )
| ~ ! [X24: $i] :
( ~ ( X13 @ X28 @ X24 )
| ~ ( X27 @ X24 ) )
| ~ ! [X25: $i] :
( ~ ( X13 @ X28 @ X25 )
| ~ ( X26 @ X25 ) ) )
| ~ ( ~ ( ~ ! [X24: $i] :
( ~ ( X13 @ X28 @ X24 )
| ~ ( X27 @ X24 ) )
| ~ ! [X25: $i] :
( ~ ( X13 @ X28 @ X25 )
| ~ ( X26 @ X25 ) ) )
| ~ ! [X23: $i] :
( ~ ( X13 @ X28 @ X23 )
| ~ ( ( X27 @ X23 )
| ( X26 @ X23 ) ) ) ) ),
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)],[c_0_19]),c_0_20]),c_0_12]),c_0_21]),c_0_22]),c_0_23]) ).
thf(c_0_25,negated_conjecture,
! [X34: $i,X35: $i,X38: $i] :
( ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred3_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred3_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred2_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X38 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred3_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X38 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) )
& ( ( epred3_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) )
& ( ( epred3_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) )
& ( ~ ( epred2_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X38 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) )
& ( ~ ( epred3_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X38 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X34 )
| ~ ( epred2_0 @ X34 ) )
& ( ( epred3_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X34 )
| ~ ( epred2_0 @ X34 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X34 )
| ~ ( epred2_0 @ X34 ) )
& ( ( epred3_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X34 )
| ~ ( epred2_0 @ X34 ) )
& ( ~ ( epred2_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X34 )
| ~ ( epred2_0 @ X34 ) )
& ( ~ ( epred3_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X34 )
| ~ ( epred2_0 @ X34 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X35 )
| ~ ( epred3_0 @ X35 ) )
& ( ( epred3_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X35 )
| ~ ( epred3_0 @ X35 ) )
& ( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X35 )
| ~ ( epred3_0 @ X35 ) )
& ( ( epred3_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ X35 )
| ~ ( epred3_0 @ X35 ) )
& ( ~ ( epred2_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X35 )
| ~ ( epred3_0 @ X35 ) )
& ( ~ ( epred3_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X38 )
| ~ ( epred1_0 @ esk1_0 @ X35 )
| ~ ( epred3_0 @ X35 ) ) ),
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_24])])])])])]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred2_0 @ X3 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_27,negated_conjecture,
( ( epred3_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_28,negated_conjecture,
( ( epred3_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred3_0 @ X3 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_30,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_31,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ( epred3_0 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
thf(c_0_32,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 )
| ~ ( epred2_0 @ X3 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_33,negated_conjecture,
( ( epred3_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_34,negated_conjecture,
( ( epred3_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_35,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_36,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ( epred2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
thf(c_0_37,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 )
| ~ ( epred3_0 @ X3 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_38,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_39,negated_conjecture,
( ( epred3_0 @ esk4_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
thf(c_0_40,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_35]),c_0_36]) ).
thf(c_0_41,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_42,negated_conjecture,
( ( epred2_0 @ esk3_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
thf(c_0_43,negated_conjecture,
! [X3: $i,X14: $i] :
( ~ ( epred2_0 @ X3 )
| ~ ( epred1_0 @ esk1_0 @ X3 )
| ~ ( epred1_0 @ esk1_0 @ X14 )
| ~ ( epred2_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_44,negated_conjecture,
epred1_0 @ esk1_0 @ esk2_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_40]),c_0_31]) ).
thf(c_0_45,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk4_0 )
| ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_42]) ).
thf(c_0_46,negated_conjecture,
! [X3: $i] :
( ~ ( epred1_0 @ esk1_0 @ X3 )
| ~ ( epred2_0 @ esk2_0 )
| ~ ( epred2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_47,negated_conjecture,
( ( epred2_0 @ esk2_0 )
| ( epred3_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_45]),c_0_39]) ).
thf(c_0_48,negated_conjecture,
~ ( epred2_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_46,c_0_44]) ).
thf(c_0_49,negated_conjecture,
! [X3: $i,X14: $i] :
( ~ ( epred3_0 @ X3 )
| ~ ( epred1_0 @ esk1_0 @ X3 )
| ~ ( epred1_0 @ esk1_0 @ X14 )
| ~ ( epred3_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_50,negated_conjecture,
epred3_0 @ esk2_0,
inference(sr,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_51,negated_conjecture,
! [X3: $i] :
( ~ ( epred1_0 @ esk1_0 @ X3 )
| ~ ( epred3_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_50])]) ).
thf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_44]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO049^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n026.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 16:27:27 UTC 2026
% 0.12/0.20 % CPUTime :
% 0.12/0.20 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.24 Running higher-order theorem proving
% 0.12/0.25 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.xZGFrLeO33/E---3.1_810652.p
% 0.31/0.28 % Version: 3.5.1-ho
% 0.31/0.28 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.31/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.28 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.31/0.28 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.31/0.28 % Starting sh5l with 300s (1) cores
% 0.31/0.28 % Starting ho_unfolding_6 with 300s (1) cores
% 0.31/0.28 % lpo9_lambda_fix with pid 810687 completed with status 0
% 0.31/0.28 % Result found by lpo9_lambda_fix
% 0.31/0.28 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.31/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.28 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.31/0.28 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.31/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = gf500_gu_R04_F100_L20000)
% 0.31/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.31/0.28 % Search class: HGHNF-FFMM00-SHHSMFNN
% 0.31/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.31/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.31/0.28 % SubtermCWHack with pid 810691 completed with status 0
% 0.31/0.28 % Result found by SubtermCWHack
% 0.31/0.28 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.31/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.31/0.28 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.31/0.28 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.31/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = gf500_gu_R04_F100_L20000)
% 0.31/0.28 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.31/0.28 % Search class: HGHNF-FFMM00-SHHSMFNN
% 0.31/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.31/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.31/0.28 % Preprocessing time : 0.002 s
% 0.31/0.28
% 0.31/0.28 % Proof found!
% 0.31/0.28 % SZS status Theorem
% 0.31/0.28 % SZS output start CNFRefutation
% See solution above
% 0.31/0.28 % Parsed axioms : 64
% 0.31/0.28 % Removed by relevancy pruning/SinE : 51
% 0.31/0.28 % Initial clauses : 24
% 0.31/0.28 % Removed in clause preprocessing : 0
% 0.31/0.28 % Initial clauses in saturation : 24
% 0.31/0.28 % Processed clauses : 82
% 0.31/0.28 % ...of these trivial : 0
% 0.31/0.28 % ...subsumed : 27
% 0.31/0.28 % ...remaining for further processing : 55
% 0.31/0.28 % Other redundant clauses eliminated : 0
% 0.31/0.28 % Clauses deleted for lack of memory : 0
% 0.31/0.28 % Backward-subsumed : 37
% 0.31/0.28 % Backward-rewritten : 8
% 0.31/0.28 % Generated clauses : 144
% 0.31/0.28 % ...of the previous two non-redundant : 118
% 0.31/0.28 % ...aggressively subsumed : 0
% 0.31/0.28 % Contextual simplify-reflections : 12
% 0.31/0.28 % Paramodulations : 143
% 0.31/0.28 % Factorizations : 0
% 0.31/0.28 % NegExts : 0
% 0.31/0.28 % Equation resolutions : 0
% 0.31/0.28 % Disequality decompositions : 0
% 0.31/0.28 % Total rewrite steps : 14
% 0.31/0.28 % ...of those cached : 11
% 0.31/0.28 % Propositional unsat checks : 0
% 0.31/0.28 % Propositional check models : 0
% 0.31/0.28 % Propositional check unsatisfiable : 0
% 0.31/0.28 % Propositional clauses : 0
% 0.31/0.28 % Propositional clauses after purity: 0
% 0.31/0.28 % Propositional unsat core size : 0
% 0.31/0.28 % Propositional preprocessing time : 0.000
% 0.31/0.28 % Propositional encoding time : 0.000
% 0.31/0.28 % Propositional solver time : 0.000
% 0.31/0.28 % Success case prop preproc time : 0.000
% 0.31/0.28 % Success case prop encoding time : 0.000
% 0.31/0.28 % Success case prop solver time : 0.000
% 0.31/0.28 % Current number of processed clauses : 9
% 0.31/0.28 % Positive orientable unit clauses : 3
% 0.31/0.28 % Positive unorientable unit clauses: 0
% 0.31/0.28 % Negative unit clauses : 1
% 0.31/0.28 % Non-unit-clauses : 5
% 0.31/0.28 % Current number of unprocessed clauses: 33
% 0.31/0.28 % ...number of literals in the above : 160
% 0.31/0.28 % Current number of archived formulas : 0
% 0.31/0.28 % Current number of archived clauses : 46
% 0.31/0.28 % Clause-clause subsumption calls (NU) : 105
% 0.31/0.28 % Rec. Clause-clause subsumption calls : 82
% 0.31/0.28 % Non-unit clause-clause subsumptions : 66
% 0.31/0.28 % Unit Clause-clause subsumption calls : 13
% 0.31/0.28 % Rewrite failures with RHS unbound : 0
% 0.31/0.28 % BW rewrite match attempts : 3
% 0.31/0.28 % BW rewrite match successes : 3
% 0.31/0.28 % Condensation attempts : 0
% 0.31/0.28 % Condensation successes : 0
% 0.31/0.28 % Termbank termtop insertions : 4558
% 0.31/0.28 % Search garbage collected termcells : 938
% 0.31/0.28
% 0.31/0.28 % -------------------------------------------------
% 0.31/0.28 % User time : 0.007 s
% 0.31/0.28 % System time : 0.003 s
% 0.31/0.28 % Total time : 0.010 s
% 0.31/0.28 % Maximum resident set size: 3952 pages
% 0.31/0.28
% 0.31/0.28 % -------------------------------------------------
% 0.31/0.28 % User time : 0.009 s
% 0.31/0.28 % System time : 0.008 s
% 0.31/0.28 % Total time : 0.018 s
% 0.31/0.28 % Maximum resident set size: 4864 pages
% 0.31/0.28 % E exiting
%------------------------------------------------------------------------------