%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL877^2 : 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 : n007.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 08:13:59 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 76 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 300 ( 15 equ; 0 cnn)
% Maximal formula atoms : 38 ( 3 avg)
% Number of connectives : 1011 ( 137 ~; 213 |; 16 &; 639 @)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 190 ( 34 ^; 156 !; 0 ?; 190 :)
% 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_44,type,
meuclidean: ( $i > $i > $o ) > $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,
esk2_0: $i ).
thf(decl_58,type,
esk3_0: $i ).
thf(decl_59,type,
esk4_0: $i ).
thf(decl_60,type,
esk5_0: $i ).
thf(decl_61,type,
esk6_0: $i ).
thf(decl_62,type,
esk7_3: $i > ( $i > $o ) > $i > $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AtIpHTjm8g/E---3.1_3177030.p',mimplies) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AtIpHTjm8g/E---3.1_3177030.p',mor) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AtIpHTjm8g/E---3.1_3177030.p',mnot) ).
thf(conj,conjecture,
! [X13: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X13 @ X6 ) ) @ ( mbox @ X13 @ ( mnot @ ( mbox @ X13 @ X6 ) ) ) ) ) )
<=> ( meuclidean @ X13 ) ),
file('/export/starexec/sandbox/tmp/tmp.AtIpHTjm8g/E---3.1_3177030.p',conj) ).
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.AtIpHTjm8g/E---3.1_3177030.p',mbox) ).
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.AtIpHTjm8g/E---3.1_3177030.p',mforall_prop) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AtIpHTjm8g/E---3.1_3177030.p',mvalid) ).
thf(meuclidean,axiom,
( meuclidean
= ( ^ [X13: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( X13 @ X15 @ X16 )
& ( X13 @ X15 @ X17 ) )
=> ( X13 @ X16 @ X17 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.AtIpHTjm8g/E---3.1_3177030.p',meuclidean) ).
thf(c_0_8,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_9,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_10,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_11,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ( mvalid
@ ( mforall_prop
@ ^ [X6: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ X13 @ X6 ) ) @ ( mbox @ X13 @ ( mnot @ ( mbox @ X13 @ X6 ) ) ) ) ) )
<=> ( meuclidean @ X13 ) ),
inference(assume_negation,[status(cth)],[conj]) ).
thf(c_0_12,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_13,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_8,c_0_9]),c_0_10]) ).
thf(c_0_14,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_15,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_16,plain,
( meuclidean
= ( ^ [Z0: $i > $i > $o] :
! [X15: $i,X16: $i,X17: $i] :
( ( ( Z0 @ X15 @ X16 )
& ( Z0 @ X15 @ X17 ) )
=> ( Z0 @ X16 @ X17 ) ) ) ),
inference(fof_simplification,[status(thm)],[meuclidean]) ).
thf(c_0_17,negated_conjecture,
~ ! [X13: $i > $i > $o] :
( ! [X25: $i,X24: $i > $o] :
( ~ ~ ! [X21: $i] :
( ~ ( X13 @ X25 @ X21 )
| ( X24 @ X21 ) )
| ! [X23: $i] :
( ~ ( X13 @ X25 @ X23 )
| ~ ! [X22: $i] :
( ~ ( X13 @ X23 @ X22 )
| ( X24 @ X22 ) ) ) )
<=> ! [X26: $i,X27: $i,X28: $i] :
( ( ( X13 @ X26 @ X27 )
& ( X13 @ X26 @ X28 ) )
=> ( X13 @ X27 @ X28 ) ) ),
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(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_11]),c_0_10]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16]) ).
thf(c_0_18,negated_conjecture,
! [X34: $i,X38: $i,X39: $i > $o,X40: $i,X41: $i,X43: $i,X44: $i,X45: $i] :
( ( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk4_0 @ esk5_0 )
| ~ ( epred2_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred2_0 @ esk2_0 ) )
& ( ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred2_0 @ esk2_0 ) )
& ( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) )
& ( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) )
& ( ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) )
& ( ( epred1_0 @ esk4_0 @ esk5_0 )
| ~ ( epred1_0 @ esk3_0 @ X34 )
| ( epred2_0 @ X34 ) )
& ( ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred1_0 @ esk3_0 @ X34 )
| ( epred2_0 @ X34 ) )
& ( ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ esk3_0 @ X34 )
| ( epred2_0 @ X34 ) )
& ( ( epred1_0 @ X41 @ ( esk7_3 @ X38 @ X39 @ X41 ) )
| ~ ( epred1_0 @ X38 @ X41 )
| ~ ( epred1_0 @ X38 @ X40 )
| ( X39 @ X40 )
| ~ ( epred1_0 @ X43 @ X44 )
| ~ ( epred1_0 @ X43 @ X45 )
| ( epred1_0 @ X44 @ X45 ) )
& ( ~ ( X39 @ ( esk7_3 @ X38 @ X39 @ X41 ) )
| ~ ( epred1_0 @ X38 @ X41 )
| ~ ( epred1_0 @ X38 @ X40 )
| ( X39 @ X40 )
| ~ ( epred1_0 @ X43 @ X44 )
| ~ ( epred1_0 @ X43 @ X45 )
| ( epred1_0 @ X44 @ X45 ) ) ),
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_17])])])])])]) ).
thf(c_0_19,negated_conjecture,
! [X15: $i,X3: $i,X4: $i > $o,X14: $i,X16: $i,X17: $i,X20: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( X4 @ X15 )
| ( epred1_0 @ X17 @ X20 )
| ~ ( epred1_0 @ X14 @ X3 )
| ~ ( epred1_0 @ X14 @ X15 )
| ~ ( epred1_0 @ X16 @ X17 )
| ~ ( epred1_0 @ X16 @ X20 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_20,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X15: $i,X14: $i,X16: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( epred1_0 @ X15 @ esk6_0 )
| ( X4 @ X16 )
| ~ ( epred1_0 @ esk4_0 @ X15 )
| ~ ( epred1_0 @ X14 @ X16 )
| ~ ( epred1_0 @ X14 @ X3 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
thf(c_0_22,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_23,negated_conjecture,
( ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,negated_conjecture,
! [X15: $i,X14: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( X4 @ X15 )
| ~ ( epred1_0 @ X14 @ X15 )
| ~ ( epred1_0 @ X14 @ X3 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
thf(c_0_25,negated_conjecture,
! [X15: $i,X3: $i,X4: $i > $o,X14: $i,X16: $i,X17: $i,X20: $i] :
( ( X4 @ X15 )
| ( epred1_0 @ X17 @ X20 )
| ~ ( X4 @ ( esk7_3 @ X3 @ X4 @ X14 ) )
| ~ ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ X3 @ X15 )
| ~ ( epred1_0 @ X16 @ X17 )
| ~ ( epred1_0 @ X16 @ X20 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_26,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ esk4_0 @ X4 @ X3 ) )
| ( X4 @ esk6_0 )
| ~ ( epred1_0 @ esk4_0 @ X3 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
thf(c_0_27,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i,X14: $i,X17: $i,X16: $i,X15: $i] :
( ( epred1_0 @ X3 @ esk6_0 )
| ( epred1_0 @ X3 @ X14 )
| ( epred1_0 @ X15 @ X16 )
| ~ ( epred1_0 @ esk4_0 @ X14 )
| ~ ( epred1_0 @ esk4_0 @ X3 )
| ~ ( epred1_0 @ X17 @ X16 )
| ~ ( epred1_0 @ X17 @ X15 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_29,negated_conjecture,
! [X15: $i,X14: $i,X16: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ X15 @ esk2_0 )
| ( X4 @ X16 )
| ~ ( epred1_0 @ esk1_0 @ X15 )
| ~ ( epred1_0 @ X14 @ X16 )
| ~ ( epred1_0 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
thf(c_0_30,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_31,negated_conjecture,
! [X15: $i,X16: $i,X3: $i,X14: $i] :
( ( epred1_0 @ X3 @ esk6_0 )
| ( epred1_0 @ X14 @ X15 )
| ~ ( epred1_0 @ esk4_0 @ X3 )
| ~ ( epred1_0 @ X16 @ X15 )
| ~ ( epred1_0 @ X16 @ X14 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
thf(c_0_32,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_33,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk2_0 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_34,negated_conjecture,
! [X15: $i,X14: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk6_0 )
| ( X4 @ X15 )
| ~ ( epred1_0 @ X14 @ X15 )
| ~ ( epred1_0 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_35,negated_conjecture,
! [X15: $i,X14: $i,X3: $i] :
( ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ X15 @ X14 )
| ~ ( epred1_0 @ X15 @ X3 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_22]),c_0_23]) ).
thf(c_0_36,negated_conjecture,
! [X15: $i,X14: $i,X16: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ X15 @ esk2_0 )
| ( X4 @ X16 )
| ~ ( epred1_0 @ esk1_0 @ X15 )
| ~ ( epred1_0 @ X14 @ X16 )
| ~ ( epred1_0 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_32]) ).
thf(c_0_37,negated_conjecture,
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_38,negated_conjecture,
! [X15: $i,X14: $i,X16: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( epred1_0 @ X15 @ esk2_0 )
| ( X4 @ X16 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ esk1_0 @ X15 )
| ~ ( epred1_0 @ X14 @ X16 )
| ~ ( epred1_0 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
thf(c_0_39,negated_conjecture,
( ( epred1_0 @ esk1_0 @ esk3_0 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_40,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred2_0 @ X3 )
| ~ ( epred1_0 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_41,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ esk1_0 @ X4 @ X3 ) )
| ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( X4 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_34,c_0_27]) ).
thf(c_0_42,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ X3 @ esk6_0 )
| ~ ( epred1_0 @ esk4_0 @ X3 )
| ~ ( epred2_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_20]) ).
thf(c_0_43,negated_conjecture,
! [X15: $i,X14: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( X4 @ X15 )
| ~ ( epred1_0 @ X14 @ X15 )
| ~ ( epred1_0 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_44,negated_conjecture,
! [X15: $i,X14: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( X4 @ X15 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ X14 @ X15 )
| ~ ( epred1_0 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
thf(c_0_45,negated_conjecture,
! [X4: $i > $o] :
( ( epred2_0 @ ( esk7_3 @ esk1_0 @ X4 @ esk3_0 ) )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk6_0 )
| ( X4 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_30]) ).
thf(c_0_46,negated_conjecture,
~ ( epred2_0 @ esk2_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_22]),c_0_23]) ).
thf(c_0_47,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred2_0 @ X3 )
| ~ ( epred1_0 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_48,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ esk1_0 @ X4 @ X3 ) )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( X4 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_32]) ).
thf(c_0_49,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ X3 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ esk3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_50,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ esk1_0 @ X4 @ X3 ) )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( X4 @ esk2_0 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_33]) ).
thf(c_0_51,negated_conjecture,
! [X15: $i,X14: $i,X16: $i,X3: $i] :
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ X3 @ X14 )
| ( epred2_0 @ X15 )
| ~ ( epred1_0 @ esk1_0 @ X15 )
| ~ ( epred1_0 @ X16 @ X14 )
| ~ ( epred1_0 @ X16 @ X3 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_45]),c_0_46]),c_0_30]) ).
thf(c_0_52,negated_conjecture,
! [X4: $i > $o] :
( ( epred2_0 @ ( esk7_3 @ esk1_0 @ X4 @ esk3_0 ) )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( X4 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_37]) ).
thf(c_0_53,negated_conjecture,
! [X4: $i > $o] :
( ( epred2_0 @ ( esk7_3 @ esk1_0 @ X4 @ esk3_0 ) )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( X4 @ esk2_0 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_39]) ).
thf(c_0_54,negated_conjecture,
! [X15: $i,X14: $i,X3: $i] :
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ X15 @ X14 )
| ~ ( epred1_0 @ X15 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_27]),c_0_46]) ).
thf(c_0_55,negated_conjecture,
! [X15: $i,X14: $i,X16: $i,X3: $i] :
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ X3 @ X14 )
| ( epred2_0 @ X15 )
| ~ ( epred1_0 @ esk1_0 @ X15 )
| ~ ( epred1_0 @ X16 @ X14 )
| ~ ( epred1_0 @ X16 @ X3 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_52]),c_0_46]),c_0_37]) ).
thf(c_0_56,negated_conjecture,
! [X15: $i,X14: $i,X16: $i,X3: $i] :
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ X3 @ X14 )
| ( epred2_0 @ X15 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ esk1_0 @ X15 )
| ~ ( epred1_0 @ X16 @ X14 )
| ~ ( epred1_0 @ X16 @ X3 ) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_53]),c_0_46]),c_0_39]) ).
thf(c_0_57,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ esk4_0 @ esk6_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
thf(c_0_58,negated_conjecture,
! [X15: $i,X14: $i,X3: $i] :
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ X15 @ X14 )
| ~ ( epred1_0 @ X15 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_32]),c_0_46]) ).
thf(c_0_59,negated_conjecture,
! [X15: $i,X14: $i,X3: $i] :
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ X15 @ X14 )
| ~ ( epred1_0 @ X15 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_33]),c_0_46]) ).
thf(c_0_60,negated_conjecture,
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_30]) ).
thf(c_0_61,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_58,c_0_32]) ).
thf(c_0_62,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ X3 @ esk2_0 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 )
| ~ ( epred1_0 @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_33]) ).
thf(c_0_63,negated_conjecture,
epred1_0 @ esk4_0 @ esk6_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_60]),c_0_46]) ).
thf(c_0_64,negated_conjecture,
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_37]) ).
thf(c_0_65,negated_conjecture,
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_39]) ).
thf(c_0_66,negated_conjecture,
! [X15: $i,X14: $i,X16: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( epred1_0 @ X15 @ esk6_0 )
| ( X4 @ X16 )
| ~ ( epred1_0 @ esk4_0 @ X15 )
| ~ ( epred1_0 @ X14 @ X16 )
| ~ ( epred1_0 @ X14 @ X3 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_63]) ).
thf(c_0_67,negated_conjecture,
epred1_0 @ esk4_0 @ esk5_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_64]),c_0_46]) ).
thf(c_0_68,negated_conjecture,
~ ( epred1_0 @ esk5_0 @ esk6_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_65]),c_0_46]) ).
thf(c_0_69,negated_conjecture,
! [X15: $i,X14: $i,X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ X14 @ X4 @ X3 ) )
| ( X4 @ X15 )
| ~ ( epred1_0 @ X14 @ X15 )
| ~ ( epred1_0 @ X14 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
thf(c_0_70,negated_conjecture,
! [X4: $i > $o,X3: $i] :
( ( epred1_0 @ X3 @ ( esk7_3 @ esk4_0 @ X4 @ X3 ) )
| ( X4 @ esk6_0 )
| ~ ( epred1_0 @ esk4_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_63]) ).
thf(c_0_71,negated_conjecture,
! [X3: $i,X14: $i,X17: $i,X16: $i,X15: $i] :
( ( epred1_0 @ X3 @ esk6_0 )
| ( epred1_0 @ X3 @ X14 )
| ( epred1_0 @ X15 @ X16 )
| ~ ( epred1_0 @ esk4_0 @ X14 )
| ~ ( epred1_0 @ esk4_0 @ X3 )
| ~ ( epred1_0 @ X17 @ X16 )
| ~ ( epred1_0 @ X17 @ X15 ) ),
inference(spm,[status(thm)],[c_0_25,c_0_70]) ).
thf(c_0_72,negated_conjecture,
! [X15: $i,X16: $i,X3: $i,X14: $i] :
( ( epred1_0 @ X3 @ esk6_0 )
| ( epred1_0 @ X14 @ X15 )
| ~ ( epred1_0 @ esk4_0 @ X3 )
| ~ ( epred1_0 @ X16 @ X15 )
| ~ ( epred1_0 @ X16 @ X14 ) ),
inference(spm,[status(thm)],[c_0_71,c_0_63]) ).
thf(c_0_73,negated_conjecture,
! [X15: $i,X14: $i,X3: $i] :
( ( epred1_0 @ X3 @ X14 )
| ~ ( epred1_0 @ X15 @ X14 )
| ~ ( epred1_0 @ X15 @ X3 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_67]),c_0_68]) ).
thf(c_0_74,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ X3 @ esk6_0 )
| ~ ( epred1_0 @ esk4_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_73,c_0_63]) ).
thf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_67]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL877^2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.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 10:19:10 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 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.AtIpHTjm8g/E---3.1_3177030.p
% 0.22/0.33 % Version: 3.5.1-ho
% 0.22/0.33 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.22/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.33 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.22/0.33 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.22/0.33 % Starting sh5l with 300s (1) cores
% 0.22/0.33 % Starting ho_unfolding_6 with 300s (1) cores
% 0.22/0.33 % sh5l with pid 3177045 completed with status 0
% 0.22/0.33 % Result found by sh5l
% 0.22/0.33 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.22/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.33 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.22/0.33 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.22/0.33 % Starting sh5l with 300s (1) cores
% 0.22/0.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.22/0.33 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.22/0.33 % Search class: HGHNF-FFSS33-SHHSMSBN
% 0.22/0.33 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.33 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.33 % SubtermCWHack with pid 3177049 completed with status 0
% 0.22/0.33 % Result found by SubtermCWHack
% 0.22/0.33 % Preprocessing class: HSMSSMSSMLMNHHN.
% 0.22/0.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.33 % Starting ehoh_best2_full_lfho with 1500s (5) cores
% 0.22/0.33 % Starting lpo9_lambda_fix with 300s (1) cores
% 0.22/0.33 % Starting sh5l with 300s (1) cores
% 0.22/0.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.22/0.33 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.22/0.33 % Search class: HGHNF-FFSS33-SHHSMSBN
% 0.22/0.33 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.33 % Starting SubtermCWHack with 31s (1) cores
% 0.22/0.33 % Preprocessing time : 0.001 s
% 0.22/0.33
% 0.22/0.33 % Proof found!
% 0.22/0.33 % SZS status Theorem
% 0.22/0.33 % SZS output start CNFRefutation
% See solution above
% 0.22/0.33 % Parsed axioms : 64
% 0.22/0.33 % Removed by relevancy pruning/SinE : 50
% 0.22/0.33 % Initial clauses : 14
% 0.22/0.33 % Removed in clause preprocessing : 0
% 0.22/0.33 % Initial clauses in saturation : 14
% 0.22/0.33 % Processed clauses : 652
% 0.22/0.33 % ...of these trivial : 0
% 0.22/0.33 % ...subsumed : 372
% 0.22/0.33 % ...remaining for further processing : 280
% 0.22/0.33 % Other redundant clauses eliminated : 0
% 0.22/0.33 % Clauses deleted for lack of memory : 0
% 0.22/0.33 % Backward-subsumed : 230
% 0.22/0.33 % Backward-rewritten : 38
% 0.22/0.33 % Generated clauses : 4106
% 0.22/0.33 % ...of the previous two non-redundant : 4047
% 0.22/0.33 % ...aggressively subsumed : 0
% 0.22/0.33 % Contextual simplify-reflections : 63
% 0.22/0.33 % Paramodulations : 4106
% 0.22/0.33 % Factorizations : 0
% 0.22/0.33 % NegExts : 0
% 0.22/0.33 % Equation resolutions : 0
% 0.22/0.33 % Disequality decompositions : 0
% 0.22/0.33 % Total rewrite steps : 57
% 0.22/0.33 % ...of those cached : 55
% 0.22/0.33 % Propositional unsat checks : 0
% 0.22/0.33 % Propositional check models : 0
% 0.22/0.33 % Propositional check unsatisfiable : 0
% 0.22/0.33 % Propositional clauses : 0
% 0.22/0.33 % Propositional clauses after purity: 0
% 0.22/0.33 % Propositional unsat core size : 0
% 0.22/0.33 % Propositional preprocessing time : 0.000
% 0.22/0.33 % Propositional encoding time : 0.000
% 0.22/0.33 % Propositional solver time : 0.000
% 0.22/0.33 % Success case prop preproc time : 0.000
% 0.22/0.33 % Success case prop encoding time : 0.000
% 0.22/0.33 % Success case prop solver time : 0.000
% 0.22/0.33 % Current number of processed clauses : 12
% 0.22/0.33 % Positive orientable unit clauses : 2
% 0.22/0.33 % Positive unorientable unit clauses: 0
% 0.22/0.33 % Negative unit clauses : 2
% 0.22/0.33 % Non-unit-clauses : 8
% 0.22/0.33 % Current number of unprocessed clauses: 25
% 0.22/0.33 % ...number of literals in the above : 134
% 0.22/0.33 % Current number of archived formulas : 0
% 0.22/0.33 % Current number of archived clauses : 268
% 0.22/0.33 % Clause-clause subsumption calls (NU) : 5168
% 0.22/0.33 % Rec. Clause-clause subsumption calls : 1045
% 0.22/0.33 % Non-unit clause-clause subsumptions : 631
% 0.22/0.33 % Unit Clause-clause subsumption calls : 37
% 0.22/0.33 % Rewrite failures with RHS unbound : 0
% 0.22/0.33 % BW rewrite match attempts : 2
% 0.22/0.33 % BW rewrite match successes : 2
% 0.22/0.33 % Condensation attempts : 0
% 0.22/0.33 % Condensation successes : 0
% 0.22/0.33 % Termbank termtop insertions : 93241
% 0.22/0.33 % Search garbage collected termcells : 858
% 0.22/0.33
% 0.22/0.33 % -------------------------------------------------
% 0.22/0.33 % User time : 0.067 s
% 0.22/0.33 % System time : 0.004 s
% 0.22/0.33 % Total time : 0.071 s
% 0.22/0.33 % Maximum resident set size: 3640 pages
% 0.22/0.33
% 0.22/0.33 % -------------------------------------------------
% 0.22/0.33 % User time : 0.070 s
% 0.22/0.33 % System time : 0.008 s
% 0.22/0.33 % Total time : 0.078 s
% 0.22/0.33 % Maximum resident set size: 4608 pages
% 0.22/0.33 % E exiting
%------------------------------------------------------------------------------