%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SYO392^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:44:19 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 9
% Syntax : Number of formulae : 113 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 462 ( 20 equ; 0 cnn)
% Maximal formula atoms : 100 ( 4 avg)
% Number of connectives : 1557 ( 225 ~; 283 |; 24 &;1025 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 156 ( 45 ^; 111 !; 0 ?; 156 :)
% 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_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
rel_k: $i > $i > $o ).
thf(decl_55,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(decl_56,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(decl_57,type,
p: $i > $o ).
thf(decl_58,type,
esk1_0: $i ).
thf(decl_59,type,
esk2_0: $i ).
thf(decl_60,type,
esk3_1: $i > $i ).
thf(decl_61,type,
esk4_1: $i > $i ).
thf(decl_62,type,
esk5_0: $i ).
thf(decl_63,type,
esk6_1: $i > $i ).
thf(decl_64,type,
esk7_1: $i > $i ).
thf(mand,axiom,
( mand
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mnot @ ( mor @ ( mnot @ X6 ) @ ( mnot @ X7 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',mand) ).
thf(mnot,axiom,
( mnot
= ( ^ [X6: $i > $o,X3: $i] :
~ ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X3: $i] :
( ( X6 @ X3 )
| ( X7 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',mor) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mor @ ( mnot @ X6 ) @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',mimplies) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [X6: $i > $o,X7: $i > $o] : ( mand @ ( mimplies @ X6 @ X7 ) @ ( mimplies @ X7 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',mequiv) ).
thf(mdia_k,axiom,
( mdia_k
= ( ^ [X6: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',mdia_k) ).
thf(mbox_k,axiom,
( mbox_k
= ( ^ [X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( rel_k @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',mbox_k) ).
thf(prove,conjecture,
mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',prove) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.EIflV4No3V/E---3.1_366265.p',mvalid) ).
thf(c_0_9,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
~ ( ~ ( Z0 @ Z2 )
| ~ ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_10,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_11,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_12,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_13,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_14,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_9,c_0_10]),c_0_11]) ).
thf(c_0_15,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_12,c_0_10]),c_0_11]) ).
thf(c_0_16,plain,
( mdia_k
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X21: $i] :
( ~ ( rel_k @ Z1 @ X21 )
| ~ ( Z0 @ X21 ) ) ) ),
inference(fof_simplification,[status(thm)],[mdia_k]) ).
thf(c_0_17,plain,
( mbox_k
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X14: $i] :
( ~ ( rel_k @ Z1 @ X14 )
| ( Z0 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_k]) ).
thf(c_0_18,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove]) ).
thf(c_0_19,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_13,c_0_14]),c_0_15]) ).
thf(c_0_20,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_21,plain,
( mdia_k
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ! [X21: $i] :
( ~ ( rel_k @ Z1 @ X21 )
| ~ ( Z0 @ X21 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_16,c_0_10]),c_0_17]) ).
thf(c_0_22,negated_conjecture,
~ ! [X28: $i] :
~ ( ~ ( ~ ~ ! [X24: $i] :
( ~ ( rel_k @ X28 @ X24 )
| ~ ! [X23: $i] :
( ~ ( rel_k @ X24 @ X23 )
| ~ ! [X22: $i] :
( ~ ( rel_k @ X23 @ X22 )
| ( p @ X22 ) ) ) )
| ~ ! [X27: $i] :
( ~ ( rel_k @ X28 @ X27 )
| ~ ! [X26: $i] :
( ~ ( rel_k @ X27 @ X26 )
| ~ ! [X25: $i] :
( ~ ( rel_k @ X26 @ X25 )
| ( p @ X25 ) ) ) ) )
| ~ ( ~ ~ ! [X27: $i] :
( ~ ( rel_k @ X28 @ X27 )
| ~ ! [X26: $i] :
( ~ ( rel_k @ X27 @ X26 )
| ~ ! [X25: $i] :
( ~ ( rel_k @ X26 @ X25 )
| ( p @ X25 ) ) ) )
| ~ ! [X24: $i] :
( ~ ( rel_k @ X28 @ X24 )
| ~ ! [X23: $i] :
( ~ ( rel_k @ X24 @ X23 )
| ~ ! [X22: $i] :
( ~ ( rel_k @ X23 @ X22 )
| ( p @ X22 ) ) ) ) ) ),
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)],[c_0_18,c_0_10]),c_0_19]),c_0_20]),c_0_17]),c_0_21])]) ).
thf(c_0_23,negated_conjecture,
! [X31: $i,X33: $i,X35: $i,X37: $i,X39: $i,X41: $i] :
( ( ( rel_k @ esk1_0 @ esk5_0 )
| ( rel_k @ esk1_0 @ esk2_0 ) )
& ( ( rel_k @ X37 @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ( rel_k @ esk1_0 @ esk2_0 ) )
& ( ~ ( p @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ( rel_k @ esk1_0 @ esk2_0 ) )
& ( ( rel_k @ X39 @ ( esk7_1 @ X39 ) )
| ~ ( rel_k @ esk1_0 @ X39 )
| ( rel_k @ esk1_0 @ esk2_0 ) )
& ( ~ ( rel_k @ ( esk7_1 @ X39 ) @ X41 )
| ( p @ X41 )
| ~ ( rel_k @ esk1_0 @ X39 )
| ( rel_k @ esk1_0 @ esk2_0 ) )
& ( ( rel_k @ esk1_0 @ esk5_0 )
| ( rel_k @ X31 @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ( rel_k @ X37 @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ( rel_k @ X31 @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ~ ( p @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ( rel_k @ X31 @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ( rel_k @ X39 @ ( esk7_1 @ X39 ) )
| ~ ( rel_k @ esk1_0 @ X39 )
| ( rel_k @ X31 @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ~ ( rel_k @ ( esk7_1 @ X39 ) @ X41 )
| ( p @ X41 )
| ~ ( rel_k @ esk1_0 @ X39 )
| ( rel_k @ X31 @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ( rel_k @ esk1_0 @ esk5_0 )
| ~ ( p @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ( rel_k @ X37 @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ~ ( p @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ~ ( p @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ~ ( p @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ( rel_k @ X39 @ ( esk7_1 @ X39 ) )
| ~ ( rel_k @ esk1_0 @ X39 )
| ~ ( p @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ~ ( rel_k @ ( esk7_1 @ X39 ) @ X41 )
| ( p @ X41 )
| ~ ( rel_k @ esk1_0 @ X39 )
| ~ ( p @ ( esk3_1 @ X31 ) )
| ~ ( rel_k @ esk2_0 @ X31 ) )
& ( ( rel_k @ esk1_0 @ esk5_0 )
| ( rel_k @ X33 @ ( esk4_1 @ X33 ) )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ( rel_k @ X37 @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ( rel_k @ X33 @ ( esk4_1 @ X33 ) )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ~ ( p @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ( rel_k @ X33 @ ( esk4_1 @ X33 ) )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ( rel_k @ X39 @ ( esk7_1 @ X39 ) )
| ~ ( rel_k @ esk1_0 @ X39 )
| ( rel_k @ X33 @ ( esk4_1 @ X33 ) )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ~ ( rel_k @ ( esk7_1 @ X39 ) @ X41 )
| ( p @ X41 )
| ~ ( rel_k @ esk1_0 @ X39 )
| ( rel_k @ X33 @ ( esk4_1 @ X33 ) )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ( rel_k @ esk1_0 @ esk5_0 )
| ~ ( rel_k @ ( esk4_1 @ X33 ) @ X35 )
| ( p @ X35 )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ( rel_k @ X37 @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ~ ( rel_k @ ( esk4_1 @ X33 ) @ X35 )
| ( p @ X35 )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ~ ( p @ ( esk6_1 @ X37 ) )
| ~ ( rel_k @ esk5_0 @ X37 )
| ~ ( rel_k @ ( esk4_1 @ X33 ) @ X35 )
| ( p @ X35 )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ( rel_k @ X39 @ ( esk7_1 @ X39 ) )
| ~ ( rel_k @ esk1_0 @ X39 )
| ~ ( rel_k @ ( esk4_1 @ X33 ) @ X35 )
| ( p @ X35 )
| ~ ( rel_k @ esk1_0 @ X33 ) )
& ( ~ ( rel_k @ ( esk7_1 @ X39 ) @ X41 )
| ( p @ X41 )
| ~ ( rel_k @ esk1_0 @ X39 )
| ~ ( rel_k @ ( esk4_1 @ X33 ) @ X35 )
| ( p @ X35 )
| ~ ( rel_k @ esk1_0 @ X33 ) ) ),
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_22])])])])])]) ).
thf(c_0_24,negated_conjecture,
! [X14: $i,X3: $i] :
( ( p @ X14 )
| ( rel_k @ esk1_0 @ esk2_0 )
| ~ ( rel_k @ ( esk7_1 @ X3 ) @ X14 )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_25,negated_conjecture,
! [X3: $i] :
( ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ( rel_k @ esk1_0 @ esk2_0 )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk1_0 @ esk2_0 )
| ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_27,negated_conjecture,
! [X14: $i,X3: $i] :
( ( rel_k @ esk1_0 @ esk5_0 )
| ( p @ X14 )
| ~ ( rel_k @ ( esk4_1 @ X3 ) @ X14 )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk1_0 @ esk5_0 )
| ( rel_k @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk1_0 @ esk5_0 )
| ~ ( p @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_30,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk1_0 @ esk2_0 )
| ~ ( rel_k @ esk5_0 @ ( esk7_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
thf(c_0_31,negated_conjecture,
! [X3: $i] :
( ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ( rel_k @ esk1_0 @ esk2_0 )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_32,negated_conjecture,
( ( rel_k @ esk1_0 @ esk5_0 )
| ( rel_k @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_33,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk1_0 @ esk5_0 )
| ~ ( rel_k @ esk2_0 @ ( esk4_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk1_0 @ esk5_0 )
| ( rel_k @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_35,negated_conjecture,
rel_k @ esk1_0 @ esk2_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
thf(c_0_36,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ( rel_k @ X14 @ ( esk4_1 @ X14 ) )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_37,negated_conjecture,
rel_k @ esk1_0 @ esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
thf(c_0_38,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ( rel_k @ X14 @ ( esk4_1 @ X14 ) )
| ~ ( rel_k @ esk5_0 @ X3 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_39,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk5_0 @ ( esk4_1 @ esk5_0 ) )
| ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
thf(c_0_40,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk5_0 @ ( esk4_1 @ esk5_0 ) )
| ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_37]) ).
thf(c_0_41,negated_conjecture,
( ( rel_k @ esk5_0 @ ( esk7_1 @ esk5_0 ) )
| ( rel_k @ esk5_0 @ ( esk4_1 @ esk5_0 ) ) ),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
thf(c_0_42,negated_conjecture,
! [X3: $i,X14: $i,X15: $i] :
( ( p @ X14 )
| ( rel_k @ X15 @ ( esk4_1 @ X15 ) )
| ~ ( rel_k @ ( esk7_1 @ X3 ) @ X14 )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( rel_k @ esk1_0 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_43,negated_conjecture,
( ( rel_k @ ( esk7_1 @ esk5_0 ) @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ esk5_0 @ ( esk4_1 @ esk5_0 ) ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_44,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk5_0 @ ( esk4_1 @ esk5_0 ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_37])]) ).
thf(c_0_45,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ X14 @ ( esk4_1 @ X14 ) )
| ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_46,negated_conjecture,
( ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ esk5_0 @ ( esk4_1 @ esk5_0 ) ) ),
inference(spm,[status(thm)],[c_0_44,c_0_37]) ).
thf(c_0_47,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) )
| ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
thf(c_0_48,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk5_0 @ ( esk4_1 @ esk5_0 ) )
| ( rel_k @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41]) ).
thf(c_0_49,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) )
| ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_38,c_0_35]) ).
thf(c_0_50,negated_conjecture,
( ( rel_k @ esk5_0 @ ( esk7_1 @ esk5_0 ) )
| ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_47,c_0_37]) ).
thf(c_0_51,negated_conjecture,
rel_k @ esk5_0 @ ( esk4_1 @ esk5_0 ),
inference(spm,[status(thm)],[c_0_48,c_0_37]) ).
thf(c_0_52,negated_conjecture,
( ( rel_k @ ( esk7_1 @ esk5_0 ) @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
thf(c_0_53,negated_conjecture,
! [X15: $i,X3: $i,X14: $i] :
( ( p @ X15 )
| ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 )
| ~ ( rel_k @ ( esk4_1 @ X14 ) @ X15 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_54,negated_conjecture,
( ( rel_k @ ( esk4_1 @ esk5_0 ) @ ( esk6_1 @ ( esk4_1 @ esk5_0 ) ) )
| ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_49,c_0_51]) ).
thf(c_0_55,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_52]),c_0_37])]) ).
thf(c_0_56,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) )
| ( p @ ( esk6_1 @ ( esk4_1 @ esk5_0 ) ) )
| ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_37])]) ).
thf(c_0_57,negated_conjecture,
( ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_55,c_0_35]) ).
thf(c_0_58,negated_conjecture,
( ( p @ ( esk6_1 @ ( esk4_1 @ esk5_0 ) ) )
| ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_50]) ).
thf(c_0_59,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ( rel_k @ X14 @ ( esk3_1 @ X14 ) )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( rel_k @ esk2_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_60,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ) )
| ( rel_k @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_58]),c_0_51])]) ).
thf(c_0_61,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk5_0 @ ( esk7_1 @ esk5_0 ) )
| ( rel_k @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_37]) ).
thf(c_0_62,negated_conjecture,
rel_k @ esk2_0 @ ( esk4_1 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_60,c_0_35]) ).
thf(c_0_63,negated_conjecture,
! [X15: $i,X3: $i,X14: $i] :
( ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ( p @ X15 )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( rel_k @ ( esk4_1 @ X14 ) @ X15 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_64,negated_conjecture,
( ( rel_k @ ( esk4_1 @ esk2_0 ) @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ esk5_0 @ ( esk7_1 @ esk5_0 ) ) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_65,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk5_0 @ ( esk7_1 @ esk5_0 ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_35])]) ).
thf(c_0_66,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( p @ ( esk3_1 @ X14 ) )
| ~ ( rel_k @ esk2_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_67,negated_conjecture,
( ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ esk5_0 @ ( esk7_1 @ esk5_0 ) ) ),
inference(spm,[status(thm)],[c_0_65,c_0_37]) ).
thf(c_0_68,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ( rel_k @ X14 @ ( esk3_1 @ X14 ) )
| ~ ( rel_k @ esk5_0 @ X3 )
| ~ ( rel_k @ esk2_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk5_0 @ ( esk7_1 @ esk5_0 ) )
| ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_62])]) ).
thf(c_0_70,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) )
| ( rel_k @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_35]) ).
thf(c_0_71,negated_conjecture,
! [X3: $i] :
( ( rel_k @ ( esk4_1 @ esk2_0 ) @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_62]) ).
thf(c_0_72,negated_conjecture,
rel_k @ esk5_0 @ ( esk7_1 @ esk5_0 ),
inference(spm,[status(thm)],[c_0_69,c_0_37]) ).
thf(c_0_73,negated_conjecture,
! [X15: $i,X3: $i,X14: $i] :
( ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ( p @ X15 )
| ~ ( rel_k @ esk5_0 @ X3 )
| ~ ( rel_k @ ( esk4_1 @ X14 ) @ X15 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_74,negated_conjecture,
( ( rel_k @ ( esk4_1 @ esk2_0 ) @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_70,c_0_62]) ).
thf(c_0_75,negated_conjecture,
! [X3: $i,X14: $i,X15: $i] :
( ( p @ X14 )
| ( rel_k @ X15 @ ( esk3_1 @ X15 ) )
| ~ ( rel_k @ ( esk7_1 @ X3 ) @ X14 )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( rel_k @ esk2_0 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_76,negated_conjecture,
( ( rel_k @ ( esk7_1 @ esk5_0 ) @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ ( esk4_1 @ esk2_0 ) @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
thf(c_0_77,negated_conjecture,
! [X3: $i,X16: $i,X14: $i,X15: $i] :
( ( p @ X14 )
| ( p @ X16 )
| ~ ( rel_k @ ( esk7_1 @ X3 ) @ X14 )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( rel_k @ ( esk4_1 @ X15 ) @ X16 )
| ~ ( rel_k @ esk1_0 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_78,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_35])]) ).
thf(c_0_79,negated_conjecture,
! [X3: $i] :
( ( rel_k @ ( esk4_1 @ esk2_0 ) @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_37])]) ).
thf(c_0_80,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( p @ X3 )
| ~ ( rel_k @ ( esk7_1 @ X14 ) @ X3 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_74]),c_0_35])]) ).
thf(c_0_81,negated_conjecture,
( ( rel_k @ ( esk7_1 @ esk5_0 ) @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) ) ),
inference(spm,[status(thm)],[c_0_78,c_0_72]) ).
thf(c_0_82,negated_conjecture,
( ( rel_k @ ( esk4_1 @ esk2_0 ) @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_79,c_0_62]) ).
thf(c_0_83,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_74]),c_0_35])]) ).
thf(c_0_84,negated_conjecture,
( ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_37])]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_82]),c_0_35])]) ).
thf(c_0_86,negated_conjecture,
( ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_72])]) ).
thf(c_0_87,negated_conjecture,
! [X3: $i,X14: $i] :
( ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( p @ X3 )
| ~ ( rel_k @ ( esk7_1 @ X14 ) @ X3 )
| ~ ( rel_k @ esk1_0 @ X14 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_82]),c_0_35])]) ).
thf(c_0_88,negated_conjecture,
( ( rel_k @ ( esk7_1 @ esk5_0 ) @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_85,c_0_72]) ).
thf(c_0_89,negated_conjecture,
! [X3: $i] :
( ( rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ) )
| ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_86]),c_0_62])]) ).
thf(c_0_90,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ X14 @ ( esk3_1 @ X14 ) )
| ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 )
| ~ ( rel_k @ esk2_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_91,negated_conjecture,
( ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_37])]) ).
thf(c_0_92,negated_conjecture,
rel_k @ esk2_0 @ ( esk7_1 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_89,c_0_35]) ).
thf(c_0_93,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( rel_k @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_72])]) ).
thf(c_0_94,negated_conjecture,
! [X3: $i] :
( ( rel_k @ ( esk7_1 @ esk2_0 ) @ ( esk3_1 @ ( esk7_1 @ esk2_0 ) ) )
| ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_92]) ).
thf(c_0_95,negated_conjecture,
( ( rel_k @ ( esk4_1 @ esk2_0 ) @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_93,c_0_62]) ).
thf(c_0_96,negated_conjecture,
( ( rel_k @ ( esk7_1 @ esk5_0 ) @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ ( esk7_1 @ esk2_0 ) @ ( esk3_1 @ ( esk7_1 @ esk2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_94,c_0_72]) ).
thf(c_0_97,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ) )
| ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_95]),c_0_35])]) ).
thf(c_0_98,negated_conjecture,
! [X3: $i] :
( ( rel_k @ ( esk7_1 @ esk2_0 ) @ ( esk3_1 @ ( esk7_1 @ esk2_0 ) ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( rel_k @ X3 @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_96]),c_0_37])]) ).
thf(c_0_99,negated_conjecture,
! [X3: $i,X14: $i] :
( ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 )
| ~ ( p @ ( esk3_1 @ X14 ) )
| ~ ( rel_k @ esk2_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_100,negated_conjecture,
p @ ( esk3_1 @ ( esk4_1 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_91]),c_0_72])]) ).
thf(c_0_101,negated_conjecture,
! [X3: $i,X14: $i] :
( ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 )
| ~ ( p @ ( esk3_1 @ X14 ) )
| ~ ( rel_k @ esk2_0 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_102,negated_conjecture,
! [X3: $i,X14: $i,X15: $i] :
( ( p @ X14 )
| ~ ( rel_k @ ( esk7_1 @ X3 ) @ X14 )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( p @ ( esk3_1 @ X15 ) )
| ~ ( rel_k @ esk2_0 @ X15 ) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
thf(c_0_103,negated_conjecture,
( ( rel_k @ ( esk7_1 @ esk2_0 ) @ ( esk3_1 @ ( esk7_1 @ esk2_0 ) ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_98,c_0_92]) ).
thf(c_0_104,negated_conjecture,
! [X3: $i] :
( ( rel_k @ X3 @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_62])]) ).
thf(c_0_105,negated_conjecture,
! [X3: $i] :
( ~ ( p @ ( esk6_1 @ X3 ) )
| ~ ( rel_k @ esk5_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_100]),c_0_62])]) ).
thf(c_0_106,negated_conjecture,
! [X3: $i] :
( ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) )
| ( p @ ( esk3_1 @ ( esk7_1 @ esk2_0 ) ) )
| ~ ( p @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_35])]) ).
thf(c_0_107,negated_conjecture,
! [X3: $i,X14: $i] :
( ~ ( rel_k @ esk5_0 @ ( esk7_1 @ X3 ) )
| ~ ( p @ ( esk3_1 @ X14 ) )
| ~ ( rel_k @ esk1_0 @ X3 )
| ~ ( rel_k @ esk2_0 @ X14 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_104]),c_0_105]) ).
thf(c_0_108,negated_conjecture,
! [X3: $i] :
( ( rel_k @ X3 @ ( esk7_1 @ X3 ) )
| ~ ( rel_k @ esk1_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_100]),c_0_62])]) ).
thf(c_0_109,negated_conjecture,
( ( p @ ( esk3_1 @ ( esk7_1 @ esk2_0 ) ) )
| ( p @ ( esk6_1 @ ( esk7_1 @ esk5_0 ) ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_100]),c_0_62])]) ).
thf(c_0_110,negated_conjecture,
! [X3: $i] :
( ~ ( p @ ( esk3_1 @ X3 ) )
| ~ ( rel_k @ esk2_0 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_37])]) ).
thf(c_0_111,negated_conjecture,
p @ ( esk3_1 @ ( esk7_1 @ esk2_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_109]),c_0_72])]) ).
thf(c_0_112,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_92])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO392^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 16:49:48 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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.EIflV4No3V/E---3.1_366265.p
% 0.08/0.15 % Version: 3.5.1-ho
% 0.08/0.15 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.08/0.15 % Starting almost_fo_3_lam with 300s (1) cores
% 0.08/0.15 % Starting post_as_ho1 with 300s (1) cores
% 0.08/0.15 % ehoh_best2_full_lfho with pid 366279 completed with status 0
% 0.08/0.15 % Result found by ehoh_best2_full_lfho
% 0.08/0.15 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HGHNF-FFMF11-SHSSMFNN
% 0.08/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.15 % SubtermCWHack with pid 366283 completed with status 0
% 0.08/0.15 % Result found by SubtermCWHack
% 0.08/0.15 % Preprocessing class: HSMSSMSSMLMNHSN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting ho_unfolding_3 with 1500s (5) cores
% 0.08/0.15 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HGHNF-FFMF11-SHSSMFNN
% 0.08/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.15 % Preprocessing time : 0.001 s
% 0.08/0.15
% 0.08/0.15 % Proof found!
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15 % Parsed axioms : 70
% 0.08/0.15 % Removed by relevancy pruning/SinE : 0
% 0.08/0.15 % Initial clauses : 61
% 0.08/0.15 % Removed in clause preprocessing : 36
% 0.08/0.15 % Initial clauses in saturation : 25
% 0.08/0.15 % Processed clauses : 147
% 0.08/0.15 % ...of these trivial : 0
% 0.08/0.15 % ...subsumed : 13
% 0.08/0.15 % ...remaining for further processing : 134
% 0.08/0.15 % Other redundant clauses eliminated : 0
% 0.08/0.15 % Clauses deleted for lack of memory : 0
% 0.08/0.15 % Backward-subsumed : 58
% 0.08/0.15 % Backward-rewritten : 54
% 0.08/0.15 % Generated clauses : 269
% 0.08/0.15 % ...of the previous two non-redundant : 247
% 0.08/0.15 % ...aggressively subsumed : 0
% 0.08/0.15 % Contextual simplify-reflections : 7
% 0.08/0.15 % Paramodulations : 269
% 0.08/0.15 % Factorizations : 0
% 0.08/0.15 % NegExts : 0
% 0.08/0.15 % Equation resolutions : 0
% 0.08/0.15 % Disequality decompositions : 0
% 0.08/0.15 % Total rewrite steps : 192
% 0.08/0.15 % ...of those cached : 184
% 0.08/0.15 % Propositional unsat checks : 0
% 0.08/0.15 % Propositional check models : 0
% 0.08/0.15 % Propositional check unsatisfiable : 0
% 0.08/0.15 % Propositional clauses : 0
% 0.08/0.15 % Propositional clauses after purity: 0
% 0.08/0.15 % Propositional unsat core size : 0
% 0.08/0.15 % Propositional preprocessing time : 0.000
% 0.08/0.15 % Propositional encoding time : 0.000
% 0.08/0.15 % Propositional solver time : 0.000
% 0.08/0.15 % Success case prop preproc time : 0.000
% 0.08/0.15 % Success case prop encoding time : 0.000
% 0.08/0.15 % Success case prop solver time : 0.000
% 0.08/0.15 % Current number of processed clauses : 22
% 0.08/0.15 % Positive orientable unit clauses : 8
% 0.08/0.15 % Positive unorientable unit clauses: 0
% 0.08/0.15 % Negative unit clauses : 0
% 0.08/0.15 % Non-unit-clauses : 14
% 0.08/0.15 % Current number of unprocessed clauses: 31
% 0.08/0.15 % ...number of literals in the above : 143
% 0.08/0.15 % Current number of archived formulas : 0
% 0.08/0.15 % Current number of archived clauses : 112
% 0.08/0.15 % Clause-clause subsumption calls (NU) : 224
% 0.08/0.15 % Rec. Clause-clause subsumption calls : 124
% 0.08/0.15 % Non-unit clause-clause subsumptions : 77
% 0.08/0.15 % Unit Clause-clause subsumption calls : 18
% 0.08/0.15 % Rewrite failures with RHS unbound : 0
% 0.08/0.15 % BW rewrite match attempts : 8
% 0.08/0.15 % BW rewrite match successes : 8
% 0.08/0.15 % Condensation attempts : 0
% 0.08/0.15 % Condensation successes : 0
% 0.08/0.15 % Termbank termtop insertions : 10038
% 0.08/0.15 % Search garbage collected termcells : 776
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.009 s
% 0.08/0.15 % System time : 0.003 s
% 0.08/0.15 % Total time : 0.012 s
% 0.08/0.15 % Maximum resident set size: 3696 pages
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.012 s
% 0.08/0.15 % System time : 0.004 s
% 0.08/0.15 % Total time : 0.016 s
% 0.08/0.15 % Maximum resident set size: 4864 pages
% 0.08/0.15 % E exiting
%------------------------------------------------------------------------------