%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU477^1 : 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 : n016.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 08:23:54 AM UTC 2026
% Result : Theorem 1.12s 0.46s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
thf(decl_42,type,
term: ( $i > $i > $o ) > $o ).
thf(decl_52,type,
epred1_0: $i > $i > $o ).
thf(decl_53,type,
epred2_0: $i > $o ).
thf(decl_54,type,
esk1_0: $i ).
thf(decl_55,type,
esk2_1: $i > $i ).
thf(decl_56,type,
epred3_0: $i > $o ).
thf(decl_57,type,
esk3_0: $i ).
thf(decl_58,type,
esk4_1: $i > $i ).
thf(decl_59,type,
esk5_1: ( $i > $o ) > $i ).
thf(decl_60,type,
esk6_1: ( $i > $o ) > $i ).
thf(alternative_formulation_of_terminating,conjecture,
( term
= ( ^ [X1: $i > $i > $o] :
~ ? [X7: $i > $o] :
( ? [X3: $i] : ( X7 @ X3 )
& ! [X3: $i] :
( ( X7 @ X3 )
=> ? [X4: $i] :
( ( X7 @ X4 )
& ( X1 @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.F9M7ML2kjt/E---3.1_371789.p',alternative_formulation_of_terminating) ).
thf(terminating,axiom,
( term
= ( ^ [X1: $i > $i > $o] :
! [X7: $i > $o] :
( ? [X3: $i] : ( X7 @ X3 )
=> ? [X3: $i] :
( ( X7 @ X3 )
& ! [X4: $i] :
( ( X7 @ X4 )
=> ~ ( X1 @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.F9M7ML2kjt/E---3.1_371789.p',terminating) ).
thf(c_0_2,negated_conjecture,
( term
!= ( ^ [X1: $i > $i > $o] :
~ ? [X7: $i > $o] :
( ? [X3: $i] : ( X7 @ X3 )
& ! [X3: $i] :
( ( X7 @ X3 )
=> ? [X4: $i] :
( ( X7 @ X4 )
& ( X1 @ X3 @ X4 ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[alternative_formulation_of_terminating]) ).
thf(c_0_3,plain,
( term
= ( ^ [Z0: $i > $i > $o] :
! [X7: $i > $o] :
( ? [X3: $i] : ( X7 @ X3 )
=> ? [X3: $i] :
( ( X7 @ X3 )
& ! [X4: $i] :
( ( X7 @ X4 )
=> ~ ( Z0 @ X3 @ X4 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[terminating]) ).
thf(c_0_4,negated_conjecture,
~ ! [X161: $i > $i > $o] :
( ! [X157: $i > $o] :
( ? [X158: $i] : ( X157 @ X158 )
=> ? [X159: $i] :
( ( X157 @ X159 )
& ! [X160: $i] :
( ( X157 @ X160 )
=> ~ ( X161 @ X159 @ X160 ) ) ) )
<=> ~ ? [X7: $i > $o] :
( ? [X3: $i] : ( X7 @ X3 )
& ! [X3: $i] :
( ( X7 @ X3 )
=> ? [X4: $i] :
( ( X7 @ X4 )
& ( X161 @ X3 @ X4 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2]),c_0_3])]) ).
thf(c_0_5,negated_conjecture,
! [X165: $i,X169: $i,X171: $i > $o,X172: $i,X174: $i,X175: $i > $o,X176: $i,X178: $i] :
( ( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk1_0 ) )
& ( ( epred3_0 @ ( esk4_1 @ X169 ) )
| ~ ( epred3_0 @ X169 )
| ( epred2_0 @ esk1_0 ) )
& ( ( epred1_0 @ X169 @ ( esk4_1 @ X169 ) )
| ~ ( epred3_0 @ X169 )
| ( epred2_0 @ esk1_0 ) )
& ( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ ( esk2_1 @ X165 ) )
| ~ ( epred2_0 @ X165 ) )
& ( ( epred3_0 @ ( esk4_1 @ X169 ) )
| ~ ( epred3_0 @ X169 )
| ( epred2_0 @ ( esk2_1 @ X165 ) )
| ~ ( epred2_0 @ X165 ) )
& ( ( epred1_0 @ X169 @ ( esk4_1 @ X169 ) )
| ~ ( epred3_0 @ X169 )
| ( epred2_0 @ ( esk2_1 @ X165 ) )
| ~ ( epred2_0 @ X165 ) )
& ( ( epred3_0 @ esk3_0 )
| ( epred1_0 @ X165 @ ( esk2_1 @ X165 ) )
| ~ ( epred2_0 @ X165 ) )
& ( ( epred3_0 @ ( esk4_1 @ X169 ) )
| ~ ( epred3_0 @ X169 )
| ( epred1_0 @ X165 @ ( esk2_1 @ X165 ) )
| ~ ( epred2_0 @ X165 ) )
& ( ( epred1_0 @ X169 @ ( esk4_1 @ X169 ) )
| ~ ( epred3_0 @ X169 )
| ( epred1_0 @ X165 @ ( esk2_1 @ X165 ) )
| ~ ( epred2_0 @ X165 ) )
& ( ( X175 @ ( esk6_1 @ X175 ) )
| ~ ( X175 @ X176 )
| ( X171 @ ( esk5_1 @ X171 ) )
| ~ ( X171 @ X172 ) )
& ( ~ ( X175 @ X178 )
| ~ ( epred1_0 @ ( esk6_1 @ X175 ) @ X178 )
| ~ ( X175 @ X176 )
| ( X171 @ ( esk5_1 @ X171 ) )
| ~ ( X171 @ X172 ) )
& ( ( X175 @ ( esk6_1 @ X175 ) )
| ~ ( X175 @ X176 )
| ~ ( X171 @ X174 )
| ~ ( epred1_0 @ ( esk5_1 @ X171 ) @ X174 )
| ~ ( X171 @ X172 ) )
& ( ~ ( X175 @ X178 )
| ~ ( epred1_0 @ ( esk6_1 @ X175 ) @ X178 )
| ~ ( X175 @ X176 )
| ~ ( X171 @ X174 )
| ~ ( epred1_0 @ ( esk5_1 @ X171 ) @ X174 )
| ~ ( X171 @ X172 ) ) ),
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_4])])])])])]) ).
thf(c_0_6,negated_conjecture,
! [X3: $i,X4: $i,X8: $i > $o,X7: $i > $o,X6: $i] :
( ( X8 @ ( esk5_1 @ X8 ) )
| ~ ( X7 @ X3 )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( X7 @ X4 )
| ~ ( X8 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_7,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ X3 @ ( esk4_1 @ X3 ) )
| ( epred2_0 @ esk1_0 )
| ~ ( epred3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
! [X3: $i,X8: $i > $o,X7: $i > $o,X4: $i] :
( ( X7 @ ( esk6_1 @ X7 ) )
| ( X8 @ ( esk5_1 @ X8 ) )
| ~ ( X7 @ X3 )
| ~ ( X8 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_9,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_10,negated_conjecture,
! [X3: $i,X8: $i > $o,X7: $i > $o,X4: $i] :
( ( epred2_0 @ esk1_0 )
| ( X7 @ ( esk5_1 @ X7 ) )
| ~ ( X8 @ ( esk4_1 @ ( esk6_1 @ X8 ) ) )
| ~ ( epred3_0 @ ( esk6_1 @ X8 ) )
| ~ ( X7 @ X3 )
| ~ ( X8 @ X4 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
thf(c_0_11,negated_conjecture,
! [X3: $i] :
( ( epred3_0 @ ( esk4_1 @ X3 ) )
| ( epred2_0 @ esk1_0 )
| ~ ( epred3_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_12,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred3_0 @ ( esk5_1 @ epred3_0 ) )
| ( epred2_0 @ esk1_0 )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
thf(c_0_13,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( X7 @ ( esk5_1 @ X7 ) )
| ( epred2_0 @ esk1_0 )
| ~ ( epred3_0 @ ( esk6_1 @ epred3_0 ) )
| ~ ( X7 @ X3 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11])]) ).
thf(c_0_14,negated_conjecture,
( ( epred3_0 @ ( esk6_1 @ epred3_0 ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) )
| ( epred2_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
thf(c_0_15,negated_conjecture,
! [X3: $i,X4: $i,X8: $i > $o,X7: $i > $o,X6: $i] :
( ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 )
| ~ ( X8 @ X4 )
| ~ ( epred1_0 @ ( esk5_1 @ X8 ) @ X4 )
| ~ ( X8 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_16,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred3_0 @ ( esk5_1 @ epred3_0 ) )
| ( epred2_0 @ esk1_0 )
| ( X7 @ ( esk5_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
thf(c_0_17,negated_conjecture,
! [X3: $i,X8: $i > $o,X7: $i > $o,X4: $i] :
( ( epred2_0 @ esk1_0 )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X8 @ ( esk4_1 @ ( esk5_1 @ X8 ) ) )
| ~ ( epred3_0 @ ( esk5_1 @ X8 ) )
| ~ ( X8 @ X3 )
| ~ ( X7 @ X4 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
thf(c_0_18,negated_conjecture,
( ( epred3_0 @ ( esk5_1 @ epred3_0 ) )
| ( epred2_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
thf(c_0_19,negated_conjecture,
! [X3: $i,X4: $i,X6: $i,X7: $i > $o,X8: $i > $o,X9: $i] :
( ~ ( X7 @ X3 )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( X7 @ X4 )
| ~ ( X8 @ X6 )
| ~ ( epred1_0 @ ( esk5_1 @ X8 ) @ X6 )
| ~ ( X8 @ X9 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_20,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( X7 @ ( esk6_1 @ X7 ) )
| ( epred2_0 @ esk1_0 )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11])]),c_0_18]) ).
thf(c_0_21,negated_conjecture,
! [X4: $i,X8: $i > $o,X7: $i > $o,X6: $i,X3: $i] :
( ( epred2_0 @ esk1_0 )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( X8 @ ( esk4_1 @ ( esk5_1 @ X8 ) ) )
| ~ ( epred3_0 @ ( esk5_1 @ X8 ) )
| ~ ( X8 @ X4 )
| ~ ( X7 @ X6 )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_7]) ).
thf(c_0_22,negated_conjecture,
( ( epred3_0 @ ( esk6_1 @ epred3_0 ) )
| ( epred2_0 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
thf(c_0_23,negated_conjecture,
! [X3: $i,X8: $i > $o,X7: $i > $o,X4: $i] :
( ( epred2_0 @ esk1_0 )
| ~ ( X7 @ ( esk4_1 @ ( esk5_1 @ X7 ) ) )
| ~ ( X8 @ ( esk4_1 @ ( esk6_1 @ X8 ) ) )
| ~ ( epred3_0 @ ( esk5_1 @ X7 ) )
| ~ ( epred3_0 @ ( esk6_1 @ X8 ) )
| ~ ( X7 @ X3 )
| ~ ( X8 @ X4 ) ),
inference(spm,[status(thm)],[c_0_21,c_0_7]) ).
thf(c_0_24,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred2_0 @ esk1_0 )
| ( X7 @ ( esk5_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred2_0 @ esk1_0 )
| ~ ( X7 @ ( esk4_1 @ ( esk6_1 @ X7 ) ) )
| ~ ( epred3_0 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_11])]),c_0_24]) ).
thf(c_0_26,negated_conjecture,
! [X3: $i] :
( ( epred3_0 @ esk3_0 )
| ( epred1_0 @ X3 @ ( esk2_1 @ X3 ) )
| ~ ( epred2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_27,negated_conjecture,
epred2_0 @ esk1_0,
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_11])]),c_0_22]) ).
thf(c_0_28,negated_conjecture,
! [X3: $i,X8: $i > $o,X7: $i > $o,X4: $i] :
( ( epred3_0 @ esk3_0 )
| ( X7 @ ( esk5_1 @ X7 ) )
| ~ ( X8 @ ( esk2_1 @ ( esk6_1 @ X8 ) ) )
| ~ ( epred2_0 @ ( esk6_1 @ X8 ) )
| ~ ( X7 @ X3 )
| ~ ( X8 @ X4 ) ),
inference(spm,[status(thm)],[c_0_6,c_0_26]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i] :
( ( epred3_0 @ esk3_0 )
| ( epred2_0 @ ( esk2_1 @ X3 ) )
| ~ ( epred2_0 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_30,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_27]) ).
thf(c_0_31,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( X7 @ ( esk5_1 @ X7 ) )
| ( epred3_0 @ esk3_0 )
| ~ ( epred2_0 @ ( esk6_1 @ epred2_0 ) )
| ~ ( X7 @ X3 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29])]) ).
thf(c_0_32,negated_conjecture,
( ( epred2_0 @ ( esk6_1 @ epred2_0 ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
thf(c_0_33,negated_conjecture,
! [X4: $i,X8: $i > $o,X7: $i > $o,X6: $i,X3: $i] :
( ( epred3_0 @ esk3_0 )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( X8 @ ( esk2_1 @ ( esk5_1 @ X8 ) ) )
| ~ ( epred2_0 @ ( esk5_1 @ X8 ) )
| ~ ( X8 @ X4 )
| ~ ( X7 @ X6 )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
thf(c_0_34,negated_conjecture,
! [X3: $i,X8: $i > $o,X7: $i > $o,X4: $i] :
( ( epred3_0 @ esk3_0 )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X8 @ ( esk2_1 @ ( esk5_1 @ X8 ) ) )
| ~ ( epred2_0 @ ( esk5_1 @ X8 ) )
| ~ ( X8 @ X3 )
| ~ ( X7 @ X4 ) ),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
thf(c_0_35,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( epred3_0 @ esk3_0 )
| ( X7 @ ( esk5_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_36,negated_conjecture,
! [X3: $i,X8: $i > $o,X7: $i > $o,X4: $i] :
( ( epred3_0 @ esk3_0 )
| ~ ( X7 @ ( esk2_1 @ ( esk5_1 @ X7 ) ) )
| ~ ( X8 @ ( esk2_1 @ ( esk6_1 @ X8 ) ) )
| ~ ( epred2_0 @ ( esk5_1 @ X7 ) )
| ~ ( epred2_0 @ ( esk6_1 @ X8 ) )
| ~ ( X7 @ X3 )
| ~ ( X8 @ X4 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
thf(c_0_37,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( X7 @ ( esk6_1 @ X7 ) )
| ( epred3_0 @ esk3_0 )
| ~ ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ~ ( X7 @ X3 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29])]) ).
thf(c_0_38,negated_conjecture,
( ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( epred3_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
thf(c_0_39,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred3_0 @ esk3_0 )
| ~ ( X7 @ ( esk2_1 @ ( esk6_1 @ X7 ) ) )
| ~ ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ~ ( epred2_0 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_29])]) ).
thf(c_0_40,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred3_0 @ esk3_0 )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_41,negated_conjecture,
( ( epred3_0 @ esk3_0 )
| ~ ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ~ ( epred2_0 @ ( esk6_1 @ epred2_0 ) ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_29])]) ).
thf(c_0_42,negated_conjecture,
( ( epred2_0 @ ( esk6_1 @ epred2_0 ) )
| ( epred3_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
thf(c_0_43,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred3_0 @ ( esk4_1 @ X3 ) )
| ( epred1_0 @ X4 @ ( esk2_1 @ X4 ) )
| ~ ( epred3_0 @ X3 )
| ~ ( epred2_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_44,negated_conjecture,
epred3_0 @ esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_38]) ).
thf(c_0_45,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred3_0 @ ( esk4_1 @ X3 ) )
| ( epred2_0 @ ( esk2_1 @ X4 ) )
| ~ ( epred3_0 @ X3 )
| ~ ( epred2_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_46,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred1_0 @ X3 @ ( esk4_1 @ X3 ) )
| ( epred1_0 @ X4 @ ( esk2_1 @ X4 ) )
| ~ ( epred3_0 @ X3 )
| ~ ( epred2_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_47,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( epred3_0 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_32]) ).
thf(c_0_48,negated_conjecture,
( ( epred3_0 @ ( esk6_1 @ epred3_0 ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
thf(c_0_49,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( epred3_0 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_32]) ).
thf(c_0_50,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( epred1_0 @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_32]) ).
thf(c_0_51,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_52,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
thf(c_0_53,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_50,c_0_48]) ).
thf(c_0_54,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_51])]),c_0_52]) ).
thf(c_0_55,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred1_0 @ X3 @ ( esk4_1 @ X3 ) )
| ( epred2_0 @ ( esk2_1 @ X4 ) )
| ~ ( epred3_0 @ X3 )
| ~ ( epred2_0 @ X4 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_56,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( X7 @ ( esk5_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_53])]),c_0_54]) ).
thf(c_0_57,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( epred2_0 @ ( esk2_1 @ X3 ) )
| ~ ( epred2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_48]) ).
thf(c_0_58,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_56,c_0_32]) ).
thf(c_0_59,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk5_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_57,c_0_32]) ).
thf(c_0_60,negated_conjecture,
( ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ~ ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_58])]) ).
thf(c_0_61,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred3_0 @ ( esk5_1 @ epred3_0 ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_8,c_0_44]) ).
thf(c_0_62,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred2_0 @ ( esk5_1 @ epred2_0 ) )
| ( X7 @ ( esk5_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_59])]),c_0_54]),c_0_60]) ).
thf(c_0_63,negated_conjecture,
( ( epred2_0 @ ( esk6_1 @ epred2_0 ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_61,c_0_27]) ).
thf(c_0_64,negated_conjecture,
epred2_0 @ ( esk5_1 @ epred2_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_32]) ).
thf(c_0_65,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk5_1 @ epred3_0 ) @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) )
| ( epred2_0 @ ( esk2_1 @ X3 ) )
| ~ ( epred2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_63]) ).
thf(c_0_66,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_64]) ).
thf(c_0_67,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred3_0 ) @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_65,c_0_64]) ).
thf(c_0_68,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_63]) ).
thf(c_0_69,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_64]) ).
thf(c_0_70,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_67])]),c_0_68]) ).
thf(c_0_71,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred1_0 @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_64]) ).
thf(c_0_72,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_69,c_0_63]) ).
thf(c_0_73,negated_conjecture,
( ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_70,c_0_64]) ).
thf(c_0_74,negated_conjecture,
( ( epred3_0 @ ( esk6_1 @ epred3_0 ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_61,c_0_44]) ).
thf(c_0_75,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred3_0 ) @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_71,c_0_63]) ).
thf(c_0_76,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_72])]),c_0_73]) ).
thf(c_0_77,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) )
| ( epred2_0 @ ( esk2_1 @ X3 ) )
| ~ ( epred2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_74]) ).
thf(c_0_78,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_75])]),c_0_76]) ).
thf(c_0_79,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_71,c_0_74]) ).
thf(c_0_80,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_69,c_0_74]) ).
thf(c_0_81,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_77,c_0_64]) ).
thf(c_0_82,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_74]) ).
thf(c_0_83,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred2_0 @ ( esk6_1 @ epred2_0 ) ) ),
inference(spm,[status(thm)],[c_0_78,c_0_64]) ).
thf(c_0_84,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_79])]),c_0_80]) ).
thf(c_0_85,negated_conjecture,
( ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_81])]),c_0_82]) ).
thf(c_0_86,negated_conjecture,
epred2_0 @ ( esk6_1 @ epred2_0 ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_83])]),c_0_73]) ).
thf(c_0_87,negated_conjecture,
! [X7: $i > $o,X4: $i,X3: $i] :
( ( epred3_0 @ ( esk5_1 @ epred3_0 ) )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( X7 @ X4 )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_84])]),c_0_85]) ).
thf(c_0_88,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_77,c_0_86]) ).
thf(c_0_89,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_43,c_0_86]) ).
thf(c_0_90,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_86]) ).
thf(c_0_91,negated_conjecture,
( ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) )
| ~ ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) ) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88])]) ).
thf(c_0_92,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred1_0 @ X3 @ ( esk4_1 @ X3 ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_86]) ).
thf(c_0_93,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_89,c_0_74]) ).
thf(c_0_94,negated_conjecture,
( ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_74]),c_0_91]) ).
thf(c_0_95,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_74]) ).
thf(c_0_96,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_93])]),c_0_94]) ).
thf(c_0_97,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk5_1 @ epred3_0 ) ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_95])]),c_0_96]) ).
thf(c_0_98,negated_conjecture,
epred3_0 @ ( esk5_1 @ epred3_0 ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_97])]),c_0_94]) ).
thf(c_0_99,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_69,c_0_98]) ).
thf(c_0_100,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_98]) ).
thf(c_0_101,negated_conjecture,
! [X7: $i > $o,X4: $i,X3: $i] :
( ( epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( X7 @ X4 )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_99])]),c_0_100]) ).
thf(c_0_102,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_89,c_0_98]) ).
thf(c_0_103,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_90,c_0_98]) ).
thf(c_0_104,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred3_0 ) @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_71,c_0_98]) ).
thf(c_0_105,negated_conjecture,
epred3_0 @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102])]),c_0_103]) ).
thf(c_0_106,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk5_1 @ epred3_0 ) @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ X3 ) )
| ~ ( epred2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_98]) ).
thf(c_0_107,negated_conjecture,
! [X3: $i,X7: $i > $o,X4: $i] :
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( epred3_0 @ X3 )
| ~ ( X7 @ X4 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_104]),c_0_105])]) ).
thf(c_0_108,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred3_0 ) @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_106,c_0_64]) ).
thf(c_0_109,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_107,c_0_98]) ).
thf(c_0_110,negated_conjecture,
! [X3: $i,X7: $i > $o,X4: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( epred3_0 @ X3 )
| ~ ( X7 @ X4 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_108]),c_0_105])]) ).
thf(c_0_111,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk6_1 @ epred3_0 ) ) ),
inference(spm,[status(thm)],[c_0_109,c_0_98]) ).
thf(c_0_112,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(spm,[status(thm)],[c_0_110,c_0_98]) ).
thf(c_0_113,negated_conjecture,
! [X7: $i > $o,X3: $i] :
( ( epred3_0 @ ( esk6_1 @ epred3_0 ) )
| ( X7 @ ( esk6_1 @ X7 ) )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_111])]),c_0_112]) ).
thf(c_0_114,negated_conjecture,
epred3_0 @ ( esk6_1 @ epred3_0 ),
inference(spm,[status(thm)],[c_0_113,c_0_98]) ).
thf(c_0_115,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_69,c_0_114]) ).
thf(c_0_116,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_66,c_0_114]) ).
thf(c_0_117,negated_conjecture,
! [X7: $i > $o,X4: $i,X3: $i] :
( ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( X7 @ X4 )
| ~ ( X7 @ X3 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_115])]),c_0_116]) ).
thf(c_0_118,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_89,c_0_114]) ).
thf(c_0_119,negated_conjecture,
( ( epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_90,c_0_114]) ).
thf(c_0_120,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ X3 ) )
| ~ ( epred2_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_114]) ).
thf(c_0_121,negated_conjecture,
! [X4: $i,X7: $i > $o,X6: $i,X3: $i] :
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( epred3_0 @ X4 )
| ~ ( X7 @ X6 )
| ~ ( X7 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_104]),c_0_105])]) ).
thf(c_0_122,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_71,c_0_114]) ).
thf(c_0_123,negated_conjecture,
epred3_0 @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ),
inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118])]),c_0_119]) ).
thf(c_0_124,negated_conjecture,
! [X4: $i,X7: $i > $o,X6: $i,X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( epred3_0 @ X4 )
| ~ ( X7 @ X6 )
| ~ ( X7 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_108]),c_0_105])]) ).
thf(c_0_125,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_120,c_0_64]) ).
thf(c_0_126,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ~ ( epred3_0 @ X3 ) ),
inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])])]) ).
thf(c_0_127,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ) )
| ~ ( epred3_0 @ X3 ) ),
inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_123])])]) ).
thf(c_0_128,negated_conjecture,
epred1_0 @ ( esk5_1 @ epred2_0 ) @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_126,c_0_114]) ).
thf(c_0_129,negated_conjecture,
epred2_0 @ ( esk2_1 @ ( esk5_1 @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_127,c_0_114]) ).
thf(c_0_130,negated_conjecture,
! [X4: $i,X7: $i > $o,X6: $i,X3: $i] :
( ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( epred2_0 @ X4 )
| ~ ( X7 @ X6 )
| ~ ( X7 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_128]),c_0_129])]) ).
thf(c_0_131,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_92,c_0_114]) ).
thf(c_0_132,negated_conjecture,
( ( epred1_0 @ ( esk5_1 @ epred3_0 ) @ ( esk4_1 @ ( esk5_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_106,c_0_86]) ).
thf(c_0_133,negated_conjecture,
! [X3: $i,X4: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ~ ( epred2_0 @ X3 )
| ~ ( epred3_0 @ X4 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_123])]) ).
thf(c_0_134,negated_conjecture,
! [X4: $i,X7: $i > $o,X6: $i,X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ~ ( epred1_0 @ ( esk6_1 @ X7 ) @ X3 )
| ~ ( epred3_0 @ X4 )
| ~ ( X7 @ X6 )
| ~ ( X7 @ X3 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_132]),c_0_105])]) ).
thf(c_0_135,negated_conjecture,
( ( epred1_0 @ ( esk6_1 @ epred3_0 ) @ ( esk4_1 @ ( esk6_1 @ epred3_0 ) ) )
| ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) ) ),
inference(spm,[status(thm)],[c_0_120,c_0_86]) ).
thf(c_0_136,negated_conjecture,
! [X3: $i] :
( ( epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ~ ( epred3_0 @ X3 ) ),
inference(spm,[status(thm)],[c_0_133,c_0_86]) ).
thf(c_0_137,negated_conjecture,
! [X3: $i] :
( ( epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ) )
| ~ ( epred3_0 @ X3 ) ),
inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_123])])]) ).
thf(c_0_138,negated_conjecture,
epred1_0 @ ( esk6_1 @ epred2_0 ) @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_136,c_0_114]) ).
thf(c_0_139,negated_conjecture,
epred2_0 @ ( esk2_1 @ ( esk6_1 @ epred2_0 ) ),
inference(spm,[status(thm)],[c_0_137,c_0_114]) ).
thf(c_0_140,negated_conjecture,
! [X3: $i] :
~ ( epred2_0 @ X3 ),
inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_138]),c_0_139])])]) ).
thf(c_0_141,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_27,c_0_140]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU477^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:47:49 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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.F9M7ML2kjt/E---3.1_371789.p
% 1.12/0.46 % Version: 3.5.1-ho
% 1.12/0.46 % partial match(1): HSMSSMSSMLSNHSN
% 1.12/0.46 % Preprocessing class: HSMSSMSSMLSNHHN.
% 1.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.12/0.46 % Starting post_as_ho3 with 300s (1) cores
% 1.12/0.46 % Starting post_as_ho11 with 300s (1) cores
% 1.12/0.46 % Starting full_lambda_8 with 300s (1) cores
% 1.12/0.46 % new_ho_10_cnf2 with pid 371802 completed with status 0
% 1.12/0.46 % Result found by new_ho_10_cnf2
% 1.12/0.46 % partial match(1): HSMSSMSSMLSNHSN
% 1.12/0.46 % Preprocessing class: HSMSSMSSMLSNHHN.
% 1.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.12/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.12/0.46 % No SInE strategy applied
% 1.12/0.46 % Search class: HGHNF-FFSF11-SHHSMSBN
% 1.12/0.46 % partial match(2): HGHNF-FFSF33-SHHSMSBN
% 1.12/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.12/0.46 % Starting SubtermCWHack with 136s (1) cores
% 1.12/0.46 % Starting new_ho_10_cnf2 with 151s (1) cores
% 1.12/0.46 % Starting sh5l with 136s (1) cores
% 1.12/0.46 % Starting new_bool_1 with 136s (1) cores
% 1.12/0.46 % Starting new_bool_2 with 136s (1) cores
% 1.12/0.46 % new_ho_10_cnf2 with pid 371809 completed with status 0
% 1.12/0.46 % Result found by new_ho_10_cnf2
% 1.12/0.46 % partial match(1): HSMSSMSSMLSNHSN
% 1.12/0.46 % Preprocessing class: HSMSSMSSMLSNHHN.
% 1.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.46 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 1.12/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.12/0.46 % No SInE strategy applied
% 1.12/0.46 % Search class: HGHNF-FFSF11-SHHSMSBN
% 1.12/0.46 % partial match(2): HGHNF-FFSF33-SHHSMSBN
% 1.12/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.12/0.46 % Starting SubtermCWHack with 136s (1) cores
% 1.12/0.46 % Starting new_ho_10_cnf2 with 151s (1) cores
% 1.12/0.46 % Preprocessing time : 0.001 s
% 1.12/0.46 % Presaturation interreduction done
% 1.12/0.46
% 1.12/0.46 % Proof found!
% 1.12/0.46 % SZS status Theorem
% 1.12/0.46 % SZS output start CNFRefutation
% See solution above
% 1.12/0.46 % Parsed axioms : 59
% 1.12/0.46 % Removed by relevancy pruning/SinE : 0
% 1.12/0.46 % Initial clauses : 42
% 1.12/0.46 % Removed in clause preprocessing : 29
% 1.12/0.46 % Initial clauses in saturation : 13
% 1.12/0.46 % Processed clauses : 1907
% 1.12/0.46 % ...of these trivial : 34
% 1.12/0.46 % ...subsumed : 1026
% 1.12/0.46 % ...remaining for further processing : 847
% 1.12/0.46 % Other redundant clauses eliminated : 0
% 1.12/0.46 % Clauses deleted for lack of memory : 0
% 1.12/0.46 % Backward-subsumed : 327
% 1.12/0.46 % Backward-rewritten : 448
% 1.12/0.46 % Generated clauses : 11994
% 1.12/0.46 % ...of the previous two non-redundant : 11018
% 1.12/0.46 % ...aggressively subsumed : 0
% 1.12/0.46 % Contextual simplify-reflections : 79
% 1.12/0.46 % Paramodulations : 11984
% 1.12/0.46 % Factorizations : 0
% 1.12/0.46 % NegExts : 0
% 1.12/0.46 % Equation resolutions : 0
% 1.12/0.46 % Disequality decompositions : 0
% 1.12/0.46 % Total rewrite steps : 1515
% 1.12/0.46 % ...of those cached : 1487
% 1.12/0.46 % Propositional unsat checks : 0
% 1.12/0.46 % Propositional check models : 0
% 1.12/0.46 % Propositional check unsatisfiable : 0
% 1.12/0.46 % Propositional clauses : 0
% 1.12/0.46 % Propositional clauses after purity: 0
% 1.12/0.46 % Propositional unsat core size : 0
% 1.12/0.46 % Propositional preprocessing time : 0.000
% 1.12/0.46 % Propositional encoding time : 0.000
% 1.12/0.46 % Propositional solver time : 0.000
% 1.12/0.46 % Success case prop preproc time : 0.000
% 1.12/0.46 % Success case prop encoding time : 0.000
% 1.12/0.46 % Success case prop solver time : 0.000
% 1.12/0.46 % Current number of processed clauses : 49
% 1.12/0.46 % Positive orientable unit clauses : 21
% 1.12/0.46 % Positive unorientable unit clauses: 0
% 1.12/0.46 % Negative unit clauses : 1
% 1.12/0.46 % Non-unit-clauses : 27
% 1.12/0.46 % Current number of unprocessed clauses: 754
% 1.12/0.46 % ...number of literals in the above : 2393
% 1.12/0.46 % Current number of archived formulas : 0
% 1.12/0.46 % Current number of archived clauses : 798
% 1.12/0.46 % Clause-clause subsumption calls (NU) : 17768
% 1.12/0.46 % Rec. Clause-clause subsumption calls : 8248
% 1.12/0.46 % Non-unit clause-clause subsumptions : 1531
% 1.12/0.46 % Unit Clause-clause subsumption calls : 227
% 1.12/0.46 % Rewrite failures with RHS unbound : 0
% 1.12/0.46 % BW rewrite match attempts : 40
% 1.12/0.46 % BW rewrite match successes : 27
% 1.12/0.46 % Condensation attempts : 1907
% 1.12/0.46 % Condensation successes : 147
% 1.12/0.46 % Termbank termtop insertions : 320919
% 1.12/0.46 % Search garbage collected termcells : 891
% 1.12/0.46
% 1.12/0.46 % -------------------------------------------------
% 1.12/0.46 % User time : 0.193 s
% 1.12/0.46 % System time : 0.005 s
% 1.12/0.46 % Total time : 0.198 s
% 1.12/0.46 % Maximum resident set size: 3944 pages
% 1.12/0.46
% 1.12/0.46 % -------------------------------------------------
% 1.12/0.46 % User time : 0.935 s
% 1.12/0.46 % System time : 0.042 s
% 1.12/0.46 % Total time : 0.977 s
% 1.12/0.46 % Maximum resident set size: 4864 pages
% 1.12/0.46 % E exiting
%------------------------------------------------------------------------------