%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU497^1 : 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 08:24:16 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 305 ( 156 equ; 0 cnn)
% Maximal formula atoms : 105 ( 4 avg)
% Number of connectives : 712 ( 105 ~; 181 |; 50 &; 355 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 84 ( 20 ^; 64 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_28,type,
refl: ( $i > $i > $o ) > $o ).
thf(decl_30,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(decl_32,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(decl_33,type,
asymm: ( $i > $i > $o ) > $o ).
thf(decl_35,type,
trans: ( $i > $i > $o ) > $o ).
thf(decl_39,type,
po: ( $i > $i > $o ) > $o ).
thf(decl_40,type,
so: ( $i > $i > $o ) > $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_0: $i ).
thf(decl_57,type,
esk5_0: $i ).
thf(decl_58,type,
esk6_0: $i ).
thf(partial_order,axiom,
( po
= ( ^ [X1: $i > $i > $o] :
( ( refl @ X1 )
& ( antisymm @ X1 )
& ( trans @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TOhTmyxuvy/E---3.1_375642.p',partial_order) ).
thf(reflexive,axiom,
( refl
= ( ^ [X1: $i > $i > $o] :
! [X3: $i] : ( X1 @ X3 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TOhTmyxuvy/E---3.1_375642.p',reflexive) ).
thf(antisymmetric,axiom,
( antisymm
= ( ^ [X1: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( ( X1 @ X3 @ X4 )
& ( X1 @ X4 @ X3 ) )
=> ( X3 = X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TOhTmyxuvy/E---3.1_375642.p',antisymmetric) ).
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.TOhTmyxuvy/E---3.1_375642.p',transitive) ).
thf(strict_order,axiom,
( so
= ( ^ [X1: $i > $i > $o] :
( ( asymm @ X1 )
& ( trans @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TOhTmyxuvy/E---3.1_375642.p',strict_order) ).
thf(asymmetric,axiom,
( asymm
= ( ^ [X1: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( X1 @ X3 @ X4 )
=> ~ ( X1 @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TOhTmyxuvy/E---3.1_375642.p',asymmetric) ).
thf(strict_order_induces_partial_order,conjecture,
! [X1: $i > $i > $o] :
( ( so @ X1 )
=> ( po @ ( rc @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TOhTmyxuvy/E---3.1_375642.p',strict_order_induces_partial_order) ).
thf(reflexive_closure,axiom,
( rc
= ( ^ [X1: $i > $i > $o,X3: $i,X4: $i] :
( ( X3 = X4 )
| ( X1 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.TOhTmyxuvy/E---3.1_375642.p',reflexive_closure) ).
thf(c_0_8,plain,
( po
= ( ^ [Z0: $i > $i > $o] :
( ! [X33: $i] : ( Z0 @ X33 @ X33 )
& ! [X34: $i,X35: $i] :
( ( ( Z0 @ X34 @ X35 )
& ( Z0 @ X35 @ X34 ) )
=> ( X34 = X35 ) )
& ! [X36: $i,X37: $i,X38: $i] :
( ( ( Z0 @ X36 @ X37 )
& ( Z0 @ X37 @ X38 ) )
=> ( Z0 @ X36 @ X38 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[partial_order]) ).
thf(c_0_9,plain,
( refl
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i] : ( Z0 @ X3 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[reflexive]) ).
thf(c_0_10,plain,
( antisymm
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( ( Z0 @ X3 @ X4 )
& ( Z0 @ X4 @ X3 ) )
=> ( X3 = X4 ) ) ) ),
inference(fof_simplification,[status(thm)],[antisymmetric]) ).
thf(c_0_11,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_12,plain,
( so
= ( ^ [Z0: $i > $i > $o] :
( ! [X39: $i,X40: $i] :
( ( Z0 @ X39 @ X40 )
=> ~ ( Z0 @ X40 @ X39 ) )
& ! [X41: $i,X42: $i,X43: $i] :
( ( ( Z0 @ X41 @ X42 )
& ( Z0 @ X42 @ X43 ) )
=> ( Z0 @ X41 @ X43 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[strict_order]) ).
thf(c_0_13,plain,
( asymm
= ( ^ [Z0: $i > $i > $o] :
! [X3: $i,X4: $i] :
( ( Z0 @ X3 @ X4 )
=> ~ ( Z0 @ X4 @ X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[asymmetric]) ).
thf(c_0_14,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( so @ X1 )
=> ( po @ ( rc @ X1 ) ) ),
inference(assume_negation,[status(cth)],[strict_order_induces_partial_order]) ).
thf(c_0_15,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_16,plain,
( po
= ( ^ [Z0: $i > $i > $o] :
( ! [X33: $i] : ( Z0 @ X33 @ X33 )
& ! [X34: $i,X35: $i] :
( ( ( Z0 @ X34 @ X35 )
& ( Z0 @ X35 @ X34 ) )
=> ( X34 = X35 ) )
& ! [X36: $i,X37: $i,X38: $i] :
( ( ( Z0 @ X36 @ X37 )
& ( Z0 @ X37 @ X38 ) )
=> ( Z0 @ X36 @ X38 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_8,c_0_9]),c_0_10]),c_0_11]) ).
thf(c_0_17,plain,
( so
= ( ^ [Z0: $i > $i > $o] :
( ! [X39: $i,X40: $i] :
( ( Z0 @ X39 @ X40 )
=> ~ ( Z0 @ X40 @ X39 ) )
& ! [X41: $i,X42: $i,X43: $i] :
( ( ( Z0 @ X41 @ X42 )
& ( Z0 @ X42 @ X43 ) )
=> ( Z0 @ X41 @ X43 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12,c_0_13]),c_0_11]) ).
thf(c_0_18,negated_conjecture,
~ ! [X1: $i > $i > $o] :
( ( ! [X158: $i,X159: $i] :
( ( X1 @ X158 @ X159 )
=> ~ ( X1 @ X159 @ X158 ) )
& ! [X160: $i,X161: $i,X162: $i] :
( ( ( X1 @ X160 @ X161 )
& ( X1 @ X161 @ X162 ) )
=> ( X1 @ X160 @ X162 ) ) )
=> ( ! [X163: $i] :
( ( X163 = X163 )
| ( X1 @ X163 @ X163 ) )
& ! [X164: $i,X165: $i] :
( ( ( ( X164 = X165 )
| ( X1 @ X164 @ X165 ) )
& ( ( X165 = X164 )
| ( X1 @ X165 @ X164 ) ) )
=> ( X164 = X165 ) )
& ! [X166: $i,X167: $i,X168: $i] :
( ( ( ( X166 = X167 )
| ( X1 @ X166 @ X167 ) )
& ( ( X167 = X168 )
| ( X1 @ X167 @ X168 ) ) )
=> ( ( X166 = X168 )
| ( X1 @ X166 @ X168 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17]) ).
thf(c_0_19,negated_conjecture,
! [X170: $i,X171: $i,X172: $i,X173: $i,X174: $i] :
( ( ~ ( epred1_0 @ X170 @ X171 )
| ~ ( epred1_0 @ X171 @ X170 ) )
& ( ~ ( epred1_0 @ X172 @ X173 )
| ~ ( epred1_0 @ X173 @ X174 )
| ( epred1_0 @ X172 @ X174 ) )
& ( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk4_0 != esk6_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk1_0 != esk1_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk4_0 != esk6_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( esk1_0 != esk1_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk2_0 != esk3_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk2_0 != esk3_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk4_0 != esk6_0 )
| ( esk2_0 != esk3_0 )
| ( esk1_0 != esk1_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk2_0 != esk3_0 )
| ( esk1_0 != esk1_0 ) )
& ( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ( esk4_0 != esk6_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ( esk4_0 != esk6_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk2_0 != esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk2_0 != esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ( esk4_0 != esk6_0 )
| ( esk2_0 != esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_0 ) )
& ( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk2_0 != esk3_0 )
| ~ ( epred1_0 @ esk1_0 @ esk1_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_18])])])])])]) ).
thf(c_0_20,negated_conjecture,
( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_21,negated_conjecture,
( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk2_0 != esk3_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_22,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( esk6_0 = esk5_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 ) ),
inference(cn,[status(thm)],[c_0_20]) ).
thf(c_0_23,negated_conjecture,
( ( esk6_0 = esk5_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk3_0 != esk2_0 ) ),
inference(cn,[status(thm)],[c_0_21]) ).
thf(c_0_24,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk2_0 != esk3_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_26,negated_conjecture,
( ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_27,negated_conjecture,
( ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk2_0 != esk3_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_28,negated_conjecture,
( ( esk5_0 = esk6_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_29,negated_conjecture,
! [X3: $i,X4: $i,X6: $i] :
( ( epred1_0 @ X3 @ X6 )
| ~ ( epred1_0 @ X3 @ X4 )
| ~ ( epred1_0 @ X4 @ X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_30,negated_conjecture,
( ( esk6_0 = esk5_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[c_0_22,c_0_23]) ).
thf(c_0_31,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( esk5_0 = esk4_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 ) ),
inference(cn,[status(thm)],[c_0_24]) ).
thf(c_0_32,negated_conjecture,
( ( esk5_0 = esk4_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk3_0 != esk2_0 ) ),
inference(cn,[status(thm)],[c_0_25]) ).
thf(c_0_33,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 ) ),
inference(cn,[status(thm)],[c_0_26]) ).
thf(c_0_34,negated_conjecture,
( ( esk3_0 != esk2_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 ) ),
inference(cn,[status(thm)],[c_0_27]) ).
thf(c_0_35,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( esk6_0 = esk5_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 ) ),
inference(cn,[status(thm)],[c_0_28]) ).
thf(c_0_36,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_37,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_38,negated_conjecture,
! [X3: $i] :
( ( esk6_0 = esk5_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( epred1_0 @ X3 @ esk6_0 )
| ~ ( epred1_0 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_39,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[c_0_31,c_0_32]) ).
thf(c_0_40,negated_conjecture,
( ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 ) ),
inference(csr,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_41,negated_conjecture,
( ( esk6_0 = esk5_0 )
| ( epred1_0 @ esk5_0 @ esk6_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[c_0_35,c_0_23]) ).
thf(c_0_42,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( esk5_0 = esk4_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 ) ),
inference(cn,[status(thm)],[c_0_36]) ).
thf(c_0_43,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 ) ),
inference(cn,[status(thm)],[c_0_37]) ).
thf(c_0_44,negated_conjecture,
! [X4: $i,X3: $i] :
( ~ ( epred1_0 @ X3 @ X4 )
| ~ ( epred1_0 @ X4 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_45,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ( esk6_0 = esk5_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
thf(c_0_46,negated_conjecture,
( ( esk2_0 = esk3_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk4_0 != esk6_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_47,negated_conjecture,
( ( esk4_0 != esk6_0 )
| ( esk2_0 != esk3_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_48,negated_conjecture,
! [X3: $i] :
( ( esk6_0 = esk5_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( epred1_0 @ X3 @ esk6_0 )
| ~ ( epred1_0 @ X3 @ esk5_0 ) ),
inference(spm,[status(thm)],[c_0_29,c_0_41]) ).
thf(c_0_49,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk4_0 @ esk5_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[c_0_42,c_0_32]) ).
thf(c_0_50,negated_conjecture,
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk4_0 @ esk6_0 ) ),
inference(csr,[status(thm)],[c_0_43,c_0_34]) ).
thf(c_0_51,negated_conjecture,
( ( esk6_0 = esk5_0 )
| ( esk4_0 = esk5_0 )
| ~ ( epred1_0 @ esk3_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_52,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk6_0 != esk4_0 ) ),
inference(cn,[status(thm)],[c_0_46]) ).
thf(c_0_53,negated_conjecture,
( ( esk3_0 != esk2_0 )
| ( esk6_0 != esk4_0 ) ),
inference(cn,[status(thm)],[c_0_47]) ).
thf(c_0_54,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ( esk6_0 = esk5_0 ) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]) ).
thf(c_0_55,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( esk4_0 != esk6_0 )
| ( esk1_0 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_56,negated_conjecture,
( ( epred1_0 @ esk2_0 @ esk3_0 )
| ( esk6_0 != esk4_0 ) ),
inference(csr,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_57,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_54]),c_0_49]) ).
thf(c_0_58,negated_conjecture,
( ( esk3_0 = esk2_0 )
| ( epred1_0 @ esk3_0 @ esk2_0 )
| ( esk6_0 != esk4_0 ) ),
inference(cn,[status(thm)],[c_0_55]) ).
thf(c_0_59,negated_conjecture,
( ( esk6_0 != esk4_0 )
| ~ ( epred1_0 @ esk3_0 @ esk2_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_56]) ).
thf(c_0_60,negated_conjecture,
( ( esk4_0 = esk5_0 )
| ~ ( epred1_0 @ esk2_0 @ esk3_0 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_57]) ).
thf(c_0_61,negated_conjecture,
esk6_0 != esk4_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_58,c_0_59]),c_0_53]) ).
thf(c_0_62,negated_conjecture,
esk4_0 = esk5_0,
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_54]),c_0_39]),c_0_60]) ).
thf(c_0_63,negated_conjecture,
esk6_0 != esk5_0,
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
thf(c_0_64,negated_conjecture,
( ( epred1_0 @ esk2_0 @ esk3_0 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 ) ),
inference(rw,[status(thm)],[c_0_40,c_0_62]) ).
thf(c_0_65,negated_conjecture,
epred1_0 @ esk2_0 @ esk3_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_30,c_0_63]),c_0_64]) ).
thf(c_0_66,negated_conjecture,
~ ( epred1_0 @ esk3_0 @ esk2_0 ),
inference(spm,[status(thm)],[c_0_44,c_0_65]) ).
thf(c_0_67,negated_conjecture,
( ( epred1_0 @ esk3_0 @ esk2_0 )
| ~ ( epred1_0 @ esk5_0 @ esk6_0 ) ),
inference(rw,[status(thm)],[c_0_50,c_0_62]) ).
thf(c_0_68,negated_conjecture,
epred1_0 @ esk5_0 @ esk6_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_41,c_0_63]),c_0_66]) ).
thf(c_0_69,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU497^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n016.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:51:19 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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.TOhTmyxuvy/E---3.1_375642.p
% 0.22/0.27 % Version: 3.5.1-ho
% 0.22/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.27 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.27 % Starting sh1l with 300s (1) cores
% 0.22/0.27 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.27 % new_ho_9 with pid 375666 completed with status 0
% 0.22/0.27 % Result found by new_ho_9
% 0.22/0.27 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.27 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.27 % No SInE strategy applied
% 0.22/0.27 % Search class: HGHSF-FFMS00-SHSSMFNN
% 0.22/0.27 % partial match(2): HGHNF-FFSS00-SHSSMFNN
% 0.22/0.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.27 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.27 % Starting new_ho_9 with 151s (1) cores
% 0.22/0.27 % Starting sh5l with 136s (1) cores
% 0.22/0.27 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.22/0.27 % Starting lpo1_def_fix with 136s (1) cores
% 0.22/0.27 % SubtermCWHack with pid 375671 completed with status 0
% 0.22/0.28 % Result found by SubtermCWHack
% 0.22/0.28 % Preprocessing class: HSSSSMSSMLSNHSN.
% 0.22/0.28 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.28 % Starting new_ho_9 with 1500s (5) cores
% 0.22/0.28 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.28 % No SInE strategy applied
% 0.22/0.28 % Search class: HGHSF-FFMS00-SHSSMFNN
% 0.22/0.28 % partial match(2): HGHNF-FFSS00-SHSSMFNN
% 0.22/0.28 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.28 % Starting SubtermCWHack with 136s (1) cores
% 0.22/0.28 % Preprocessing time : 0.001 s
% 0.22/0.28
% 0.22/0.28 % Proof found!
% 0.22/0.28 % SZS status Theorem
% 0.22/0.28 % SZS output start CNFRefutation
% See solution above
% 0.22/0.28 % Parsed axioms : 59
% 0.22/0.28 % Removed by relevancy pruning/SinE : 0
% 0.22/0.28 % Initial clauses : 55
% 0.22/0.28 % Removed in clause preprocessing : 29
% 0.22/0.28 % Initial clauses in saturation : 26
% 0.22/0.28 % Processed clauses : 56
% 0.22/0.28 % ...of these trivial : 1
% 0.22/0.28 % ...subsumed : 10
% 0.22/0.28 % ...remaining for further processing : 45
% 0.22/0.28 % Other redundant clauses eliminated : 0
% 0.22/0.28 % Clauses deleted for lack of memory : 0
% 0.22/0.28 % Backward-subsumed : 20
% 0.22/0.28 % Backward-rewritten : 13
% 0.22/0.28 % Generated clauses : 58
% 0.22/0.28 % ...of the previous two non-redundant : 57
% 0.22/0.28 % ...aggressively subsumed : 0
% 0.22/0.28 % Contextual simplify-reflections : 18
% 0.22/0.28 % Paramodulations : 56
% 0.22/0.28 % Factorizations : 0
% 0.22/0.28 % NegExts : 0
% 0.22/0.28 % Equation resolutions : 0
% 0.22/0.28 % Disequality decompositions : 0
% 0.22/0.28 % Total rewrite steps : 17
% 0.22/0.28 % ...of those cached : 14
% 0.22/0.28 % Propositional unsat checks : 0
% 0.22/0.28 % Propositional check models : 0
% 0.22/0.28 % Propositional check unsatisfiable : 0
% 0.22/0.28 % Propositional clauses : 0
% 0.22/0.28 % Propositional clauses after purity: 0
% 0.22/0.28 % Propositional unsat core size : 0
% 0.22/0.28 % Propositional preprocessing time : 0.000
% 0.22/0.28 % Propositional encoding time : 0.000
% 0.22/0.28 % Propositional solver time : 0.000
% 0.22/0.28 % Success case prop preproc time : 0.000
% 0.22/0.28 % Success case prop encoding time : 0.000
% 0.22/0.28 % Success case prop solver time : 0.000
% 0.22/0.28 % Current number of processed clauses : 10
% 0.22/0.28 % Positive orientable unit clauses : 3
% 0.22/0.28 % Positive unorientable unit clauses: 0
% 0.22/0.28 % Negative unit clauses : 3
% 0.22/0.28 % Non-unit-clauses : 4
% 0.22/0.28 % Current number of unprocessed clauses: 7
% 0.22/0.28 % ...number of literals in the above : 29
% 0.22/0.28 % Current number of archived formulas : 0
% 0.22/0.28 % Current number of archived clauses : 35
% 0.22/0.28 % Clause-clause subsumption calls (NU) : 181
% 0.22/0.28 % Rec. Clause-clause subsumption calls : 120
% 0.22/0.28 % Non-unit clause-clause subsumptions : 37
% 0.22/0.28 % Unit Clause-clause subsumption calls : 16
% 0.22/0.28 % Rewrite failures with RHS unbound : 0
% 0.22/0.28 % BW rewrite match attempts : 3
% 0.22/0.28 % BW rewrite match successes : 3
% 0.22/0.28 % Condensation attempts : 0
% 0.22/0.28 % Condensation successes : 0
% 0.22/0.28 % Termbank termtop insertions : 5012
% 0.22/0.28 % Search garbage collected termcells : 1075
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.008 s
% 0.22/0.28 % System time : 0.004 s
% 0.22/0.28 % Total time : 0.012 s
% 0.22/0.28 % Maximum resident set size: 3944 pages
% 0.22/0.28
% 0.22/0.28 % -------------------------------------------------
% 0.22/0.28 % User time : 0.019 s
% 0.22/0.28 % System time : 0.014 s
% 0.22/0.28 % Total time : 0.033 s
% 0.22/0.28 % Maximum resident set size: 4864 pages
% 0.22/0.28 % E exiting
%------------------------------------------------------------------------------