%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU469^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:23:53 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 409 ( 150 equ; 0 cnn)
% Maximal formula atoms : 212 ( 5 avg)
% Number of connectives : 1947 ( 202 ~; 406 |; 86 &;1223 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 85 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 5 con; 0-3 aty)
% Number of variables : 151 ( 30 ^; 121 !; 0 ?; 151 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_23,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(decl_28,type,
refl: ( $i > $i > $o ) > $o ).
thf(decl_30,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_35,type,
trans: ( $i > $i > $o ) > $o ).
thf(decl_36,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_37,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_52,type,
epred1_0: $i > $i > $o ).
thf(decl_53,type,
esk1_0: $i ).
thf(decl_54,type,
esk2_0: $i ).
thf(decl_55,type,
esk3_0: $i ).
thf(decl_56,type,
esk4_1: ( $i > $i > $o ) > $i ).
thf(decl_57,type,
esk5_1: ( $i > $i > $o ) > $i ).
thf(decl_58,type,
esk6_1: ( $i > $i > $o ) > $i ).
thf(decl_59,type,
esk7_1: ( $i > $i > $o ) > $i ).
thf(decl_60,type,
esk8_1: ( $i > $i > $o ) > $i ).
thf(decl_61,type,
esk9_1: ( $i > $i > $o ) > $i ).
thf(decl_62,type,
esk10_1: ( $i > $i > $o ) > $i ).
thf(decl_63,type,
esk11_1: ( $i > $i > $o ) > $i ).
thf(decl_64,type,
esk12_1: ( $i > $i > $o ) > $i ).
thf(decl_65,type,
esk13_1: ( $i > $i > $o ) > $i ).
thf(decl_66,type,
epred2_0: $i > $i > $o ).
thf(decl_67,type,
esk14_0: $i ).
thf(decl_68,type,
epred3_0: $i > $i > $o ).
thf(transitive_closure,axiom,
( tc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
! [X2: $i > $i > $o] :
( ( ( trans @ X2 )
& ( subrel @ X1 @ X2 ) )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1nlXkpbuwB/E---3.1_1304837.p',transitive_closure) ).
thf(subrel,axiom,
( subrel
= ( ^ [X1: $i > $i > $o,X2: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1nlXkpbuwB/E---3.1_1304837.p',subrel) ).
thf(transitive,axiom,
( trans
= ( ^ [X1: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X4 @ X6 ) )
=> ( X1 @ X3 @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1nlXkpbuwB/E---3.1_1304837.p',transitive) ).
thf(transitive_reflexive_closure,axiom,
( trc
= ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1nlXkpbuwB/E---3.1_1304837.p',transitive_reflexive_closure) ).
thf(reflexive_closure,axiom,
( rc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
( ( X3 = X4 )
| ( X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1nlXkpbuwB/E---3.1_1304837.p',reflexive_closure) ).
thf(transitive_reflexive_closure_is_transitive_reflexive,conjecture,
! [X1: $i > $i > $o] :
( ( trans @ ( trc @ X1 ) )
& ( refl @ ( trc @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1nlXkpbuwB/E---3.1_1304837.p',transitive_reflexive_closure_is_transitive_reflexive) ).
thf(reflexive,axiom,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X3: $i] : ( X1 @ X3 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1nlXkpbuwB/E---3.1_1304837.p',reflexive) ).
thf(c_0_7,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X16: $i,X17: $i,X18: $i] :
( ( ( X2 @ X16 @ X17 )
& ( X2 @ X17 @ X18 ) )
=> ( X2 @ X16 @ X18 ) )
& ! [X19: $i,X20: $i] :
( ( Z0 @ X19 @ X20 )
=> ( X2 @ X19 @ X20 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive_closure]) ).
thf(c_0_8,plain,
( subrel
= ( ^ [Z0: $i > $i > $o,Z1: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( Z0 @ X3 @ X4 )
=> ( Z1 @ X3 @ X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[subrel]) ).
thf(c_0_9,plain,
( trans
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i,X4: $i,X6: $i] :
( ( ( Z0 @ X3 @ X4 )
& ( Z0 @ X4 @ X6 ) )
=> ( Z0 @ X3 @ X6 ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive]) ).
thf(c_0_10,plain,
( trc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( ( Z1 = Z2 )
| ! [X21: $i > $i > $o] :
( ( ! [X22: $i,X23: $i,X24: $i] :
( ( ( X21 @ X22 @ X23 )
& ( X21 @ X23 @ X24 ) )
=> ( X21 @ X22 @ X24 ) )
& ! [X25: $i,X26: $i] :
( ( Z0 @ X25 @ X26 )
=> ( X21 @ X25 @ X26 ) ) )
=> ( X21 @ Z1 @ Z2 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[transitive_reflexive_closure]) ).
thf(c_0_11,plain,
( rc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( ( Z1 = Z2 )
| ( Z0 @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[reflexive_closure]) ).
thf(c_0_12,plain,
( tc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
! [X2: $i > $i > $o] :
( ( ! [X16: $i,X17: $i,X18: $i] :
( ( ( X2 @ X16 @ X17 )
& ( X2 @ X17 @ X18 ) )
=> ( X2 @ X16 @ X18 ) )
& ! [X19: $i,X20: $i] :
( ( Z0 @ X19 @ X20 )
=> ( X2 @ X19 @ X20 ) ) )
=> ( X2 @ Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
thf(c_0_13,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( trans @ ( trc @ X1 ) )
& ( refl @ ( trc @ X1 ) ) ),
inference(assume_negation,[status(cth)],[transitive_reflexive_closure_is_transitive_reflexive]) ).
thf(c_0_14,plain,
( refl
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i] : ( Z0 @ X3 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[reflexive]) ).
thf(c_0_15,plain,
( trc
= ( ^ [Z0: $i > $i > $o,Z1: $i,Z2: $i] :
( ( Z1 = Z2 )
| ! [X21: $i > $i > $o] :
( ( ! [X22: $i,X23: $i,X24: $i] :
( ( ( X21 @ X22 @ X23 )
& ( X21 @ X23 @ X24 ) )
=> ( X21 @ X22 @ X24 ) )
& ! [X25: $i,X26: $i] :
( ( Z0 @ X25 @ X26 )
=> ( X21 @ X25 @ X26 ) ) )
=> ( X21 @ Z1 @ Z2 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
thf(c_0_16,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ! [X164: $i,X165: $i,X166: $i] :
( ( ( ( X164 = X165 )
| ! [X158: $i > $i > $o] :
( ( ! [X159: $i,X160: $i,X161: $i] :
( ( ( X158 @ X159 @ X160 )
& ( X158 @ X160 @ X161 ) )
=> ( X158 @ X159 @ X161 ) )
& ! [X162: $i,X163: $i] :
( ( X1 @ X162 @ X163 )
=> ( X158 @ X162 @ X163 ) ) )
=> ( X158 @ X164 @ X165 ) ) )
& ( ( X165 = X166 )
| ! [X158: $i > $i > $o] :
( ( ! [X159: $i,X160: $i,X161: $i] :
( ( ( X158 @ X159 @ X160 )
& ( X158 @ X160 @ X161 ) )
=> ( X158 @ X159 @ X161 ) )
& ! [X162: $i,X163: $i] :
( ( X1 @ X162 @ X163 )
=> ( X158 @ X162 @ X163 ) ) )
=> ( X158 @ X165 @ X166 ) ) ) )
=> ( ( X164 = X166 )
| ! [X158: $i > $i > $o] :
( ( ! [X159: $i,X160: $i,X161: $i] :
( ( ( X158 @ X159 @ X160 )
& ( X158 @ X160 @ X161 ) )
=> ( X158 @ X159 @ X161 ) )
& ! [X162: $i,X163: $i] :
( ( X1 @ X162 @ X163 )
=> ( X158 @ X162 @ X163 ) ) )
=> ( X158 @ X164 @ X166 ) ) ) )
& ! [X173: $i] :
( ( X173 = X173 )
| ! [X167: $i > $i > $o] :
( ( ! [X168: $i,X169: $i,X170: $i] :
( ( ( X167 @ X168 @ X169 )
& ( X167 @ X169 @ X170 ) )
=> ( X167 @ X168 @ X170 ) )
& ! [X171: $i,X172: $i] :
( ( X1 @ X171 @ X172 )
=> ( X167 @ X171 @ X172 ) ) )
=> ( X167 @ X173 @ X173 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_13,c_0_14]),c_0_9]),c_0_15]) ).
thf(c_0_17,negated_conjecture,
! [X178: $i > $i > $o,X184: $i > $i > $o,X191: $i,X192: $i,X193: $i,X194: $i,X195: $i,X198: $i,X199: $i,X200: $i,X201: $i,X202: $i] :
( ( ( esk14_0 != esk14_0 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk4_1 @ X178 ) @ ( esk5_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk4_1 @ X178 ) @ ( esk5_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk4_1 @ X178 ) @ ( esk5_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk4_1 @ X178 ) @ ( esk5_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk4_1 @ X178 ) @ ( esk5_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk4_1 @ X178 ) @ ( esk5_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk4_1 @ X178 ) @ ( esk5_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk4_1 @ X178 ) @ ( esk5_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ( esk14_0 != esk14_0 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk5_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk5_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk5_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk5_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk5_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk5_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk5_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ( X178 @ ( esk5_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ( esk14_0 != esk14_0 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ~ ( X178 @ ( esk4_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ~ ( X178 @ ( esk4_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ~ ( X178 @ ( esk4_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ( epred1_0 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ~ ( X178 @ ( esk4_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ~ ( X178 @ ( esk4_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ~ ( X178 @ ( esk4_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ~ ( X178 @ ( esk4_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( X178 @ ( esk7_1 @ X178 ) @ ( esk8_1 @ X178 ) )
| ~ ( X178 @ ( esk4_1 @ X178 ) @ ( esk6_1 @ X178 ) )
| ( X178 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 ) )
& ( ( esk14_0 != esk14_0 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk9_1 @ X184 ) @ ( esk10_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk9_1 @ X184 ) @ ( esk10_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk9_1 @ X184 ) @ ( esk10_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk9_1 @ X184 ) @ ( esk10_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk9_1 @ X184 ) @ ( esk10_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk9_1 @ X184 ) @ ( esk10_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk9_1 @ X184 ) @ ( esk10_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk9_1 @ X184 ) @ ( esk10_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ( esk14_0 != esk14_0 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk10_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk10_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk10_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk10_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk10_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk10_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk10_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ( X184 @ ( esk10_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ( esk14_0 != esk14_0 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ~ ( X184 @ ( esk9_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ~ ( X184 @ ( esk9_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ~ ( X184 @ ( esk9_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ( epred1_0 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ~ ( X184 @ ( esk9_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ~ ( X184 @ ( esk9_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ~ ( X184 @ ( esk9_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ~ ( X184 @ ( esk9_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( X184 @ ( esk12_1 @ X184 ) @ ( esk13_1 @ X184 ) )
| ~ ( X184 @ ( esk9_1 @ X184 ) @ ( esk11_1 @ X184 ) )
| ( X184 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 ) )
& ( ( esk14_0 != esk14_0 )
| ( esk1_0 != esk3_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ( esk1_0 != esk3_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ( esk1_0 != esk3_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ( esk1_0 != esk3_0 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( epred2_0 @ X191 @ X192 )
| ~ ( epred2_0 @ X192 @ X193 )
| ( epred2_0 @ X191 @ X193 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( epred2_0 @ X191 @ X192 )
| ~ ( epred2_0 @ X192 @ X193 )
| ( epred2_0 @ X191 @ X193 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( epred2_0 @ X191 @ X192 )
| ~ ( epred2_0 @ X192 @ X193 )
| ( epred2_0 @ X191 @ X193 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( epred2_0 @ X191 @ X192 )
| ~ ( epred2_0 @ X192 @ X193 )
| ( epred2_0 @ X191 @ X193 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( epred1_0 @ X194 @ X195 )
| ( epred2_0 @ X194 @ X195 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( epred1_0 @ X194 @ X195 )
| ( epred2_0 @ X194 @ X195 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( epred1_0 @ X194 @ X195 )
| ( epred2_0 @ X194 @ X195 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( epred1_0 @ X194 @ X195 )
| ( epred2_0 @ X194 @ X195 ) )
& ( ( esk14_0 != esk14_0 )
| ~ ( epred2_0 @ esk1_0 @ esk3_0 ) )
& ( ~ ( epred3_0 @ X198 @ X199 )
| ~ ( epred3_0 @ X199 @ X200 )
| ( epred3_0 @ X198 @ X200 )
| ~ ( epred2_0 @ esk1_0 @ esk3_0 ) )
& ( ~ ( epred1_0 @ X201 @ X202 )
| ( epred3_0 @ X201 @ X202 )
| ~ ( epred2_0 @ esk1_0 @ esk3_0 ) )
& ( ~ ( epred3_0 @ esk14_0 @ esk14_0 )
| ~ ( epred2_0 @ esk1_0 @ 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,
! [X3: $i,X4: $i,X6: $i] :
( ( epred2_0 @ X3 @ X6 )
| ( esk14_0 != esk14_0 )
| ~ ( epred2_0 @ X3 @ X4 )
| ~ ( epred2_0 @ X4 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
| ( X1 @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ( X1 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 )
| ( esk14_0 != esk14_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_20,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ( X1 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 )
| ( esk14_0 != esk14_0 )
| ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_21,negated_conjecture,
! [X3: $i,X6: $i,X4: $i] :
( ( epred2_0 @ X3 @ X6 )
| ~ ( epred2_0 @ X4 @ X6 )
| ~ ( epred2_0 @ X3 @ X4 ) ),
inference(cn,[status(thm)],[c_0_18]) ).
thf(c_0_22,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk3_0 = esk2_0 )
| ( X1 @ esk2_0 @ esk3_0 )
| ( X1 @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_19]) ).
thf(c_0_23,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
| ( X1 @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( X1 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 )
| ( esk14_0 != esk14_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_24,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
| ( X1 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 )
| ( esk14_0 != esk14_0 )
| ~ ( X1 @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_25,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk3_0 = esk2_0 )
| ( X1 @ esk2_0 @ esk3_0 )
| ( X1 @ ( esk10_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_20]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred2_0 @ X3 @ X4 )
| ( esk14_0 != esk14_0 )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_27,negated_conjecture,
! [X3: $i] :
( ( esk3_0 = esk2_0 )
| ( epred1_0 @ ( esk12_1 @ epred2_0 ) @ ( esk13_1 @ epred2_0 ) )
| ( epred2_0 @ X3 @ ( esk11_1 @ epred2_0 ) )
| ( epred2_0 @ esk2_0 @ esk3_0 )
| ~ ( epred2_0 @ X3 @ ( esk10_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
thf(c_0_28,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk3_0 = esk2_0 )
| ( X1 @ esk2_0 @ esk3_0 )
| ( X1 @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_23]) ).
thf(c_0_29,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk3_0 = esk2_0 )
| ( X1 @ esk2_0 @ esk3_0 )
| ( epred1_0 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
| ~ ( X1 @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_24]) ).
thf(c_0_30,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
| ( X1 @ ( esk5_1 @ X1 ) @ ( esk6_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 )
| ( esk14_0 != esk14_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_31,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 )
| ( esk14_0 != esk14_0 )
| ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) )
| ~ ( X1 @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_32,negated_conjecture,
! [X3: $i] :
( ( esk3_0 = esk2_0 )
| ( epred2_0 @ X3 @ ( esk11_1 @ epred2_0 ) )
| ( epred2_0 @ esk2_0 @ esk3_0 )
| ~ ( epred2_0 @ ( esk12_1 @ epred2_0 ) @ ( esk13_1 @ epred2_0 ) )
| ~ ( epred2_0 @ X3 @ ( esk10_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
thf(c_0_33,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred2_0 @ X3 @ X4 )
| ~ ( epred1_0 @ X3 @ X4 ) ),
inference(cn,[status(thm)],[c_0_26]) ).
thf(c_0_34,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred1_0 @ ( esk12_1 @ epred2_0 ) @ ( esk13_1 @ epred2_0 ) )
| ( epred2_0 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
thf(c_0_35,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( X1 @ esk2_0 @ esk3_0 )
| ( esk2_0 = esk3_0 )
| ( esk14_0 != esk14_0 )
| ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_36,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk5_1 @ X1 ) @ ( esk6_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 )
| ( esk14_0 != esk14_0 )
| ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_37,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk2_0 = esk1_0 )
| ( X1 @ esk1_0 @ esk2_0 )
| ( X1 @ ( esk5_1 @ X1 ) @ ( esk6_1 @ X1 ) )
| ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_30]) ).
thf(c_0_38,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
| ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 )
| ( esk14_0 != esk14_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_39,negated_conjecture,
! [X1: $i > $i > $o] :
( ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 )
| ( esk14_0 != esk14_0 )
| ~ ( X1 @ ( esk4_1 @ X1 ) @ ( esk6_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_40,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk3_0 = esk2_0 )
| ( X1 @ esk2_0 @ esk3_0 )
| ~ ( X1 @ ( esk9_1 @ X1 ) @ ( esk11_1 @ X1 ) )
| ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_31]) ).
thf(c_0_41,negated_conjecture,
! [X3: $i] :
( ( esk3_0 = esk2_0 )
| ( epred2_0 @ X3 @ ( esk11_1 @ epred2_0 ) )
| ( epred2_0 @ esk2_0 @ esk3_0 )
| ~ ( epred2_0 @ X3 @ ( esk10_1 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
thf(c_0_42,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk3_0 = esk2_0 )
| ( X1 @ esk2_0 @ esk3_0 )
| ( X1 @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ~ ( X1 @ ( esk12_1 @ X1 ) @ ( esk13_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_35]) ).
thf(c_0_43,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk2_0 = esk1_0 )
| ( X1 @ esk1_0 @ esk2_0 )
| ( X1 @ ( esk5_1 @ X1 ) @ ( esk6_1 @ X1 ) )
| ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_36]) ).
thf(c_0_44,negated_conjecture,
! [X3: $i] :
( ( esk1_0 = esk2_0 )
| ( epred1_0 @ ( esk7_1 @ epred2_0 ) @ ( esk8_1 @ epred2_0 ) )
| ( epred2_0 @ X3 @ ( esk6_1 @ epred2_0 ) )
| ( epred2_0 @ esk1_0 @ esk2_0 )
| ~ ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
thf(c_0_45,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk2_0 = esk1_0 )
| ( X1 @ esk1_0 @ esk2_0 )
| ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_38]) ).
thf(c_0_46,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk2_0 = esk1_0 )
| ( X1 @ esk1_0 @ esk2_0 )
| ( epred1_0 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
| ~ ( X1 @ ( esk4_1 @ X1 ) @ ( esk6_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_39]) ).
thf(c_0_47,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred2_0 @ esk2_0 @ esk3_0 )
| ~ ( epred2_0 @ ( esk12_1 @ epred2_0 ) @ ( esk13_1 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
thf(c_0_48,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 )
| ( esk14_0 != esk14_0 )
| ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
| ~ ( X1 @ ( esk4_1 @ X1 ) @ ( esk6_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_49,negated_conjecture,
! [X3: $i] :
( ( esk1_0 = esk2_0 )
| ( epred2_0 @ X3 @ ( esk6_1 @ epred2_0 ) )
| ( epred2_0 @ esk1_0 @ esk2_0 )
| ~ ( epred2_0 @ ( esk7_1 @ epred2_0 ) @ ( esk8_1 @ epred2_0 ) )
| ~ ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
thf(c_0_50,negated_conjecture,
( ( esk1_0 = esk2_0 )
| ( epred1_0 @ ( esk7_1 @ epred2_0 ) @ ( esk8_1 @ epred2_0 ) )
| ( epred2_0 @ esk1_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
thf(c_0_51,negated_conjecture,
! [X1: $i > $i > $o] :
( ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ( X1 @ esk1_0 @ esk2_0 )
| ( esk1_0 = esk2_0 )
| ( esk14_0 != esk14_0 )
| ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_52,negated_conjecture,
( ( esk14_0 != esk14_0 )
| ~ ( epred2_0 @ esk1_0 @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_53,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred2_0 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_33]),c_0_34]) ).
thf(c_0_54,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk2_0 = esk1_0 )
| ( X1 @ esk1_0 @ esk2_0 )
| ~ ( X1 @ ( esk4_1 @ X1 ) @ ( esk6_1 @ X1 ) )
| ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_55,negated_conjecture,
! [X3: $i] :
( ( esk1_0 = esk2_0 )
| ( epred2_0 @ X3 @ ( esk6_1 @ epred2_0 ) )
| ( epred2_0 @ esk1_0 @ esk2_0 )
| ~ ( epred2_0 @ X3 @ ( esk5_1 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_33]),c_0_50]) ).
thf(c_0_56,negated_conjecture,
! [X1: $i > $i > $o] :
( ( esk2_0 = esk1_0 )
| ( X1 @ esk1_0 @ esk2_0 )
| ( X1 @ ( esk4_1 @ X1 ) @ ( esk5_1 @ X1 ) )
| ~ ( X1 @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) ) ),
inference(cn,[status(thm)],[c_0_51]) ).
thf(c_0_57,negated_conjecture,
~ ( epred2_0 @ esk1_0 @ esk3_0 ),
inference(cn,[status(thm)],[c_0_52]) ).
thf(c_0_58,negated_conjecture,
! [X3: $i] :
( ( esk3_0 = esk2_0 )
| ( epred2_0 @ X3 @ esk3_0 )
| ~ ( epred2_0 @ X3 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_53]) ).
thf(c_0_59,negated_conjecture,
( ( esk1_0 = esk2_0 )
| ( epred2_0 @ esk1_0 @ esk2_0 )
| ~ ( epred2_0 @ ( esk7_1 @ epred2_0 ) @ ( esk8_1 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
thf(c_0_60,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ~ ( epred2_0 @ esk1_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_61,negated_conjecture,
( ( esk1_0 = esk2_0 )
| ( epred2_0 @ esk1_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_33]),c_0_50]) ).
thf(c_0_62,negated_conjecture,
( ( esk14_0 != esk14_0 )
| ( esk1_0 != esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_63,negated_conjecture,
( ( esk1_0 = esk2_0 )
| ( esk3_0 = esk2_0 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
thf(c_0_64,negated_conjecture,
esk3_0 != esk1_0,
inference(cn,[status(thm)],[c_0_62]) ).
thf(c_0_65,negated_conjecture,
esk1_0 = esk2_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_63]),c_0_61]) ).
thf(c_0_66,negated_conjecture,
esk3_0 != esk2_0,
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_67,negated_conjecture,
~ ( epred2_0 @ esk2_0 @ esk3_0 ),
inference(rw,[status(thm)],[c_0_57,c_0_65]) ).
thf(c_0_68,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_53,c_0_66]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU469^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:45:07 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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.1nlXkpbuwB/E---3.1_1304837.p
% 0.22/0.29 % Version: 3.5.1-ho
% 0.22/0.29 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.29 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.29 % Starting sh1l with 300s (1) cores
% 0.22/0.29 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.29 % new_ho_9 with pid 1304868 completed with status 0
% 0.22/0.29 % Result found by new_ho_9
% 0.22/0.29 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.29 % No SInE strategy applied
% 0.22/0.29 % Search class: HGHSF-FFMF11-SHSSMMBN
% 0.22/0.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.29 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.29 % Starting new_ho_9 with 151s (1) cores
% 0.22/0.29 % Starting sh5l with 169s (1) cores
% 0.22/0.29 % Starting new_bool_2 with 169s (1) cores
% 0.22/0.29 % Starting ehoh_best_sine_rwall with 169s (1) cores
% 0.22/0.29 % SubtermCWHack with pid 1304875 completed with status 0
% 0.22/0.29 % Result found by SubtermCWHack
% 0.22/0.29 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.29 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.29 % No SInE strategy applied
% 0.22/0.29 % Search class: HGHSF-FFMF11-SHSSMMBN
% 0.22/0.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.29 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.29 % Preprocessing time : 0.001 s
% 0.22/0.29
% 0.22/0.29 % Proof found!
% 0.22/0.29 % SZS status Theorem
% 0.22/0.29 % SZS output start CNFRefutation
% See solution above
% 0.22/0.29 % Parsed axioms : 59
% 0.22/0.29 % Removed by relevancy pruning/SinE : 0
% 0.22/0.29 % Initial clauses : 93
% 0.22/0.29 % Removed in clause preprocessing : 29
% 0.22/0.29 % Initial clauses in saturation : 64
% 0.22/0.29 % Processed clauses : 128
% 0.22/0.29 % ...of these trivial : 0
% 0.22/0.29 % ...subsumed : 36
% 0.22/0.29 % ...remaining for further processing : 91
% 0.22/0.29 % Other redundant clauses eliminated : 0
% 0.22/0.29 % Clauses deleted for lack of memory : 0
% 0.22/0.29 % Backward-subsumed : 35
% 0.22/0.29 % Backward-rewritten : 33
% 0.22/0.29 % Generated clauses : 123
% 0.22/0.29 % ...of the previous two non-redundant : 126
% 0.22/0.29 % ...aggressively subsumed : 0
% 0.22/0.29 % Contextual simplify-reflections : 16
% 0.22/0.29 % Paramodulations : 120
% 0.22/0.29 % Factorizations : 0
% 0.22/0.29 % NegExts : 0
% 0.22/0.29 % Equation resolutions : 0
% 0.22/0.29 % Disequality decompositions : 0
% 0.22/0.29 % Total rewrite steps : 66
% 0.22/0.29 % ...of those cached : 65
% 0.22/0.29 % Propositional unsat checks : 0
% 0.22/0.29 % Propositional check models : 0
% 0.22/0.29 % Propositional check unsatisfiable : 0
% 0.22/0.29 % Propositional clauses : 0
% 0.22/0.29 % Propositional clauses after purity: 0
% 0.22/0.29 % Propositional unsat core size : 0
% 0.22/0.29 % Propositional preprocessing time : 0.000
% 0.22/0.29 % Propositional encoding time : 0.000
% 0.22/0.29 % Propositional solver time : 0.000
% 0.22/0.29 % Success case prop preproc time : 0.000
% 0.22/0.29 % Success case prop encoding time : 0.000
% 0.22/0.29 % Success case prop solver time : 0.000
% 0.22/0.29 % Current number of processed clauses : 20
% 0.22/0.29 % Positive orientable unit clauses : 1
% 0.22/0.29 % Positive unorientable unit clauses: 0
% 0.22/0.29 % Negative unit clauses : 3
% 0.22/0.29 % Non-unit-clauses : 16
% 0.22/0.29 % Current number of unprocessed clauses: 46
% 0.22/0.29 % ...number of literals in the above : 238
% 0.22/0.29 % Current number of archived formulas : 0
% 0.22/0.29 % Current number of archived clauses : 71
% 0.22/0.29 % Clause-clause subsumption calls (NU) : 1491
% 0.22/0.29 % Rec. Clause-clause subsumption calls : 561
% 0.22/0.29 % Non-unit clause-clause subsumptions : 81
% 0.22/0.29 % Unit Clause-clause subsumption calls : 40
% 0.22/0.29 % Rewrite failures with RHS unbound : 0
% 0.22/0.29 % BW rewrite match attempts : 1
% 0.22/0.29 % BW rewrite match successes : 1
% 0.22/0.29 % Condensation attempts : 0
% 0.22/0.29 % Condensation successes : 0
% 0.22/0.29 % Termbank termtop insertions : 10955
% 0.22/0.29 % Search garbage collected termcells : 1431
% 0.22/0.29
% 0.22/0.29 % -------------------------------------------------
% 0.22/0.29 % User time : 0.014 s
% 0.22/0.29 % System time : 0.004 s
% 0.22/0.29 % Total time : 0.018 s
% 0.22/0.29 % Maximum resident set size: 4200 pages
% 0.22/0.29
% 0.22/0.29 % -------------------------------------------------
% 0.22/0.29 % User time : 0.049 s
% 0.22/0.29 % System time : 0.016 s
% 0.22/0.29 % Total time : 0.065 s
% 0.22/0.29 % Maximum resident set size: 4608 pages
% 0.22/0.29 % E exiting
%------------------------------------------------------------------------------