%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV073^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 08:39:41 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 70 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 321 ( 14 equ; 0 cnn)
% Maximal formula atoms : 73 ( 4 avg)
% Number of connectives : 1113 ( 138 ~; 169 |; 20 &; 786 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 13 con; 0-3 aty)
% Number of variables : 54 ( 32 ^; 22 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
mu: $tType ).
thf(decl_25,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_31,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_32,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_51,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_55,type,
rel_s4: $i > $i > $o ).
thf(decl_56,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_62,type,
leq: mu > mu > $i > $o ).
thf(decl_82,type,
minus: mu > mu > mu ).
thf(decl_83,type,
pv35: mu ).
thf(decl_84,type,
pv31: mu ).
thf(decl_86,type,
n135300: mu ).
thf(decl_88,type,
n5: mu ).
thf(decl_89,type,
n1: mu ).
thf(decl_92,type,
n0: mu ).
thf(decl_94,type,
esk1_0: $i ).
thf(decl_95,type,
esk2_0: $i ).
thf(decl_96,type,
esk3_0: $i ).
thf(decl_97,type,
esk4_0: $i ).
thf(decl_98,type,
esk5_0: $i ).
thf(decl_99,type,
esk6_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mor @ ( mnot @ X4 ) @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UaftfkNN8v/E---3.1_2849564.p',mimplies) ).
thf(mor,axiom,
( mor
= ( ^ [X4: $i > $o,X5: $i > $o,X3: $i] :
( ( X4 @ X3 )
| ( X5 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UaftfkNN8v/E---3.1_2849564.p',mor) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X3: $i] :
~ ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UaftfkNN8v/E---3.1_2849564.p',mnot) ).
thf(mand,axiom,
( mand
= ( ^ [X4: $i > $o,X5: $i > $o] : ( mnot @ ( mor @ ( mnot @ X4 ) @ ( mnot @ X5 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UaftfkNN8v/E---3.1_2849564.p',mand) ).
thf(cl5_nebula_array_0014,conjecture,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv31 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv35 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) @ ( mbox_s4 @ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv31 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv35 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) @ ( mbox_s4 @ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UaftfkNN8v/E---3.1_2849564.p',cl5_nebula_array_0014) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X4: $i > $o,X3: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ X3 @ X7 )
| ( X4 @ X7 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UaftfkNN8v/E---3.1_2849564.p',mbox_s4) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X4: $i > $o] :
! [X3: $i] : ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.UaftfkNN8v/E---3.1_2849564.p',mvalid) ).
thf(c_0_7,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_8,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_9,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_10,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_11,negated_conjecture,
~ ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv31 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv35 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) @ ( mbox_s4 @ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv31 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv35 ) ) @ ( mand @ ( mbox_s4 @ ( leq @ pv31 @ ( minus @ n5 @ n1 ) ) ) @ ( mbox_s4 @ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_array_0014]) ).
thf(c_0_12,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X7: $i] :
( ~ ( rel_s4 @ Z1 @ X7 )
| ( Z0 @ X7 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_13,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_14,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_7,c_0_8]),c_0_9]) ).
thf(c_0_15,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_10,c_0_8]),c_0_9]) ).
thf(c_0_16,negated_conjecture,
~ ! [X131: $i,X130: $i] :
( ~ ( rel_s4 @ X131 @ X130 )
| ~ ~ ( ~ ! [X122: $i] :
( ~ ( rel_s4 @ X130 @ X122 )
| ( leq @ n0 @ pv31 @ X122 ) )
| ~ ~ ( ~ ! [X123: $i] :
( ~ ( rel_s4 @ X130 @ X123 )
| ( leq @ n0 @ pv35 @ X123 ) )
| ~ ~ ( ~ ! [X124: $i] :
( ~ ( rel_s4 @ X130 @ X124 )
| ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ X124 ) )
| ~ ! [X125: $i] :
( ~ ( rel_s4 @ X130 @ X125 )
| ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ X125 ) ) ) ) )
| ~ ( ~ ! [X126: $i] :
( ~ ( rel_s4 @ X130 @ X126 )
| ( leq @ n0 @ pv31 @ X126 ) )
| ~ ~ ( ~ ! [X127: $i] :
( ~ ( rel_s4 @ X130 @ X127 )
| ( leq @ n0 @ pv35 @ X127 ) )
| ~ ~ ( ~ ! [X128: $i] :
( ~ ( rel_s4 @ X130 @ X128 )
| ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ X128 ) )
| ~ ! [X129: $i] :
( ~ ( rel_s4 @ X130 @ X129 )
| ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ X129 ) ) ) ) ) ),
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_11,c_0_12]),c_0_13]),c_0_14]),c_0_15])]) ).
thf(c_0_17,negated_conjecture,
! [X134: $i,X135: $i,X136: $i,X137: $i] :
( ( rel_s4 @ esk1_0 @ esk2_0 )
& ( ~ ( rel_s4 @ esk2_0 @ X134 )
| ( leq @ n0 @ pv31 @ X134 ) )
& ( ~ ( rel_s4 @ esk2_0 @ X135 )
| ( leq @ n0 @ pv35 @ X135 ) )
& ( ~ ( rel_s4 @ esk2_0 @ X136 )
| ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ X136 ) )
& ( ~ ( rel_s4 @ esk2_0 @ X137 )
| ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ X137 ) )
& ( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) )
& ( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) )
& ( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) )
& ( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) )
& ( ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) )
& ( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_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_16])])])])])]) ).
thf(c_0_18,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i] :
( ( leq @ n0 @ pv35 @ X3 )
| ~ ( rel_s4 @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_22,negated_conjecture,
! [X3: $i] :
( ( leq @ n0 @ pv31 @ X3 )
| ~ ( rel_s4 @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_23,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
thf(c_0_24,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_26,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23]) ).
thf(c_0_27,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i] :
( ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ X3 )
| ~ ( rel_s4 @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_29,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_26]) ).
thf(c_0_30,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_31,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_32,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_33,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_23]) ).
thf(c_0_34,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_35,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_28]),c_0_29]) ).
thf(c_0_36,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_19]),c_0_33]) ).
thf(c_0_37,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_29]) ).
thf(c_0_38,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_36]) ).
thf(c_0_39,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk5_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_36]) ).
thf(c_0_40,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_41,negated_conjecture,
! [X3: $i] :
( ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ X3 )
| ~ ( rel_s4 @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_42,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_43,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_44,negated_conjecture,
rel_s4 @ esk2_0 @ esk5_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_19]),c_0_39]) ).
thf(c_0_45,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_36]) ).
thf(c_0_46,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_41]),c_0_29]) ).
thf(c_0_47,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_48,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_44])]) ).
thf(c_0_49,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_19]),c_0_46]) ).
thf(c_0_50,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_41]),c_0_29]) ).
thf(c_0_51,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_52,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_22]),c_0_49]) ).
thf(c_0_53,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk6_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_22]),c_0_49]) ).
thf(c_0_54,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_55,negated_conjecture,
( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_56,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_41]),c_0_44])]) ).
thf(c_0_57,negated_conjecture,
rel_s4 @ esk2_0 @ esk6_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_19]),c_0_53]) ).
thf(c_0_58,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_41]),c_0_44])]) ).
thf(c_0_59,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ pv31 @ ( minus @ n5 @ n1 ) @ esk5_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_60,negated_conjecture,
( ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_41]),c_0_44])]) ).
thf(c_0_61,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk3_0 )
| ~ ( leq @ n0 @ pv35 @ esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_28]),c_0_57])]) ).
thf(c_0_62,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ( rel_s4 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_28]),c_0_49]) ).
thf(c_0_63,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ pv35 @ ( minus @ n135300 @ n1 ) @ esk6_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_41]),c_0_44])]) ).
thf(c_0_64,negated_conjecture,
( ~ ( leq @ n0 @ pv35 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_28]),c_0_57])]) ).
thf(c_0_65,negated_conjecture,
rel_s4 @ esk2_0 @ esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_19]),c_0_62]) ).
thf(c_0_66,negated_conjecture,
( ( rel_s4 @ esk2_0 @ esk4_0 )
| ~ ( leq @ n0 @ pv31 @ esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_28]),c_0_57])]) ).
thf(c_0_67,negated_conjecture,
~ ( leq @ n0 @ pv35 @ esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_22]),c_0_65])]) ).
thf(c_0_68,negated_conjecture,
rel_s4 @ esk2_0 @ esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_22]),c_0_65])]) ).
thf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_19]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV073^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.15 % Computer : n014.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % OS : Linux 6.8.0-71-generic
% 0.08/0.15 % CPULimit : 300
% 0.08/0.15 % WCLimit : 300
% 0.08/0.15 % DateTime : Tue Sep 29 15:59:44 UTC 2026
% 0.08/0.15 % CPUTime :
% 0.08/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.24 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.UaftfkNN8v/E---3.1_2849564.p
% 0.23/0.28 % Version: 3.5.1-ho
% 0.23/0.28 % Preprocessing class: HSLSSMSMMLLNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 900s (3) cores
% 0.23/0.28 % Starting ehoh_best8_lambda with 900s (3) cores
% 0.23/0.28 % Starting ho_unfolding_3 with 300s (1) cores
% 0.23/0.28 % Starting new_ho_16 with 300s (1) cores
% 0.23/0.28 % new_ho_16 with pid 2849580 completed with status 0
% 0.23/0.28 % Result found by new_ho_16
% 0.23/0.28 % Preprocessing class: HSLSSMSMMLLNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 900s (3) cores
% 0.23/0.28 % Starting ehoh_best8_lambda with 900s (3) cores
% 0.23/0.28 % Starting ho_unfolding_3 with 300s (1) cores
% 0.23/0.28 % Starting new_ho_16 with 300s (1) cores
% 0.23/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = LambdaDef)
% 0.23/0.28 % SinE strategy is LambdaDef
% 0.23/0.28 % Search class: HGHNF-FFMF22-SHSSMFNN
% 0.23/0.28 % partial match(1): HGHNF-FFSF22-SHSSMFNN
% 0.23/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.28 % SubtermCWHack with pid 2849581 completed with status 0
% 0.23/0.28 % Result found by SubtermCWHack
% 0.23/0.28 % Preprocessing class: HSLSSMSMMLLNHSN.
% 0.23/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.28 % Starting new_ho_10 with 900s (3) cores
% 0.23/0.28 % Starting ehoh_best8_lambda with 900s (3) cores
% 0.23/0.28 % Starting ho_unfolding_3 with 300s (1) cores
% 0.23/0.28 % Starting new_ho_16 with 300s (1) cores
% 0.23/0.28 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = LambdaDef)
% 0.23/0.28 % SinE strategy is LambdaDef
% 0.23/0.28 % Search class: HGHNF-FFMF22-SHSSMFNN
% 0.23/0.28 % partial match(1): HGHNF-FFSF22-SHSSMFNN
% 0.23/0.28 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.23/0.28 % Starting SubtermCWHack with 28s (1) cores
% 0.23/0.28 % Preprocessing time : 0.002 s
% 0.23/0.28
% 0.23/0.28 % Proof found!
% 0.23/0.28 % SZS status Theorem
% 0.23/0.28 % SZS output start CNFRefutation
% See solution above
% 0.23/0.28 % Parsed axioms : 280
% 0.23/0.28 % Removed by relevancy pruning/SinE : 247
% 0.23/0.28 % Initial clauses : 21
% 0.23/0.28 % Removed in clause preprocessing : 0
% 0.23/0.28 % Initial clauses in saturation : 21
% 0.23/0.28 % Processed clauses : 52
% 0.23/0.28 % ...of these trivial : 0
% 0.23/0.28 % ...subsumed : 0
% 0.23/0.28 % ...remaining for further processing : 52
% 0.23/0.28 % Other redundant clauses eliminated : 0
% 0.23/0.28 % Clauses deleted for lack of memory : 0
% 0.23/0.28 % Backward-subsumed : 36
% 0.23/0.28 % Backward-rewritten : 6
% 0.23/0.28 % Generated clauses : 32
% 0.23/0.28 % ...of the previous two non-redundant : 31
% 0.23/0.28 % ...aggressively subsumed : 0
% 0.23/0.28 % Contextual simplify-reflections : 21
% 0.23/0.28 % Paramodulations : 32
% 0.23/0.28 % Factorizations : 0
% 0.23/0.28 % NegExts : 0
% 0.23/0.28 % Equation resolutions : 0
% 0.23/0.28 % Disequality decompositions : 0
% 0.23/0.28 % Total rewrite steps : 17
% 0.23/0.28 % ...of those cached : 13
% 0.23/0.28 % Propositional unsat checks : 0
% 0.23/0.28 % Propositional check models : 0
% 0.23/0.28 % Propositional check unsatisfiable : 0
% 0.23/0.28 % Propositional clauses : 0
% 0.23/0.28 % Propositional clauses after purity: 0
% 0.23/0.28 % Propositional unsat core size : 0
% 0.23/0.28 % Propositional preprocessing time : 0.000
% 0.23/0.28 % Propositional encoding time : 0.000
% 0.23/0.28 % Propositional solver time : 0.000
% 0.23/0.28 % Success case prop preproc time : 0.000
% 0.23/0.28 % Success case prop encoding time : 0.000
% 0.23/0.28 % Success case prop solver time : 0.000
% 0.23/0.28 % Current number of processed clauses : 10
% 0.23/0.28 % Positive orientable unit clauses : 5
% 0.23/0.28 % Positive unorientable unit clauses: 0
% 0.23/0.28 % Negative unit clauses : 1
% 0.23/0.28 % Non-unit-clauses : 4
% 0.23/0.28 % Current number of unprocessed clauses: 0
% 0.23/0.28 % ...number of literals in the above : 0
% 0.23/0.28 % Current number of archived formulas : 0
% 0.23/0.28 % Current number of archived clauses : 42
% 0.23/0.28 % Clause-clause subsumption calls (NU) : 264
% 0.23/0.28 % Rec. Clause-clause subsumption calls : 172
% 0.23/0.28 % Non-unit clause-clause subsumptions : 52
% 0.23/0.28 % Unit Clause-clause subsumption calls : 5
% 0.23/0.28 % Rewrite failures with RHS unbound : 0
% 0.23/0.28 % BW rewrite match attempts : 4
% 0.23/0.28 % BW rewrite match successes : 4
% 0.23/0.28 % Condensation attempts : 0
% 0.23/0.28 % Condensation successes : 0
% 0.23/0.28 % Termbank termtop insertions : 9348
% 0.23/0.28 % Search garbage collected termcells : 3243
% 0.23/0.28
% 0.23/0.28 % -------------------------------------------------
% 0.23/0.28 % User time : 0.008 s
% 0.23/0.28 % System time : 0.004 s
% 0.23/0.28 % Total time : 0.012 s
% 0.23/0.28 % Maximum resident set size: 4128 pages
% 0.23/0.28
% 0.23/0.28 % -------------------------------------------------
% 0.23/0.28 % User time : 0.019 s
% 0.23/0.28 % System time : 0.008 s
% 0.23/0.28 % Total time : 0.027 s
% 0.23/0.28 % Maximum resident set size: 5376 pages
% 0.23/0.28 % E exiting
%------------------------------------------------------------------------------