%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP178^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 08:04:36 AM UTC 2026
% Result : Theorem 0.21s 0.36s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 22 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 704 ( 9 ~; 6 |; 12 &; 677 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 8 ( 7 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 3 ^; 39 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
set_nat: $tType ).
thf(decl_sort2,type,
set_Pr1986765409at_nat: $tType ).
thf(decl_sort3,type,
set_Pr9961929at_nat: $tType ).
thf(decl_sort4,type,
allegorical_term_b: $tType ).
thf(decl_sort5,type,
labeled_graph_b_nat: $tType ).
thf(decl_sort6,type,
produc1478835367term_b: $tType ).
thf(decl_sort7,type,
produc1235635379_b_nat: $tType ).
thf(decl_23,type,
finite_finite_nat: set_nat > $o ).
thf(decl_27,type,
finite1987068434at_nat: set_Pr9961929at_nat > $o ).
thf(decl_32,type,
allegorical_A_Int_b: allegorical_term_b > allegorical_term_b > allegorical_term_b ).
thf(decl_36,type,
graph_529870330at_nat: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).
thf(decl_41,type,
labeled_edges_b_nat: labeled_graph_b_nat > set_Pr9961929at_nat ).
thf(decl_44,type,
labele460410879_b_nat: labeled_graph_b_nat > set_nat ).
thf(decl_47,type,
restrict_b_nat: labeled_graph_b_nat > labeled_graph_b_nat ).
thf(decl_67,type,
produc1990145943term_b: allegorical_term_b > allegorical_term_b > produc1478835367term_b ).
thf(decl_70,type,
produc951298923_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).
thf(decl_77,type,
produc854192515term_b: produc1478835367term_b > allegorical_term_b ).
thf(decl_80,type,
produc1542243159_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(decl_83,type,
produc1223098053term_b: produc1478835367term_b > allegorical_term_b ).
thf(decl_86,type,
produc194497945_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).
thf(decl_97,type,
id_on_nat: set_nat > set_Pr1986765409at_nat ).
thf(decl_119,type,
translation_b: allegorical_term_b > labeled_graph_b_nat ).
thf(decl_164,type,
u: allegorical_term_b ).
thf(decl_165,type,
v: allegorical_term_b ).
thf(conj_0,conjecture,
( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',conj_0) ).
thf(fact_30_translation__graph,axiom,
( translation_b
= ( ^ [X28: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ X28 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',fact_30_translation__graph) ).
thf(fact_3_graph__rule__translation,axiom,
! [X5: allegorical_term_b,X6: allegorical_term_b] :
( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) ) )
& ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',fact_3_graph__rule__translation) ).
thf(fact_75_fst__conv,axiom,
! [X162: labeled_graph_b_nat,X163: labeled_graph_b_nat] :
( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X162 @ X163 ) )
= X162 ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',fact_75_fst__conv) ).
thf(fact_86_snd__conv,axiom,
! [X185: labeled_graph_b_nat,X186: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X185 @ X186 ) )
= X186 ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',fact_86_snd__conv) ).
thf(fact_76_fst__conv,axiom,
! [X164: allegorical_term_b,X165: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ X164 @ X165 ) )
= X164 ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',fact_76_fst__conv) ).
thf(fact_85_snd__conv,axiom,
! [X183: allegorical_term_b,X184: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X183 @ X184 ) )
= X184 ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',fact_85_snd__conv) ).
thf(fact_20_verts__in__translation__finite_I1_J,axiom,
! [X18: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X18 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',fact_20_verts__in__translation__finite_I1_J) ).
thf(fact_12_verts__in__translation__finite_I2_J,axiom,
! [X13: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X13 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aqD941YgCA/E---3.1_292103.p',fact_12_verts__in__translation__finite_I2_J) ).
thf(c_0_9,negated_conjecture,
~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
& ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_10,plain,
( translation_b
= ( ^ [Z0: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ Z0 ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_30_translation__graph]) ).
thf(c_0_11,plain,
! [X1041: allegorical_term_b,X1042: allegorical_term_b] :
( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1041 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1041 @ X1042 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1041 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1041 @ X1042 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1041 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1041 @ X1042 ) ) ) ) ) ) )
& ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1041 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1041 @ X1042 ) ) ) )
= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1041 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1041 @ X1042 ) ) ) ) ) )
& ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1041 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1041 @ X1042 ) ) ) ) ) )
& ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1041 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1041 @ X1042 ) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[fact_3_graph__rule__translation]) ).
thf(c_0_12,plain,
! [X1201: labeled_graph_b_nat,X1202: labeled_graph_b_nat] :
( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X1201 @ X1202 ) )
= X1201 ),
inference(variable_rename,[status(thm)],[fact_75_fst__conv]) ).
thf(c_0_13,plain,
! [X1047: labeled_graph_b_nat,X1048: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X1047 @ X1048 ) )
= X1048 ),
inference(variable_rename,[status(thm)],[fact_86_snd__conv]) ).
thf(c_0_14,negated_conjecture,
( ~ ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ~ ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
thf(c_0_15,plain,
! [X1175: allegorical_term_b,X1176: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ X1175 @ X1176 ) )
= X1175 ),
inference(variable_rename,[status(thm)],[fact_76_fst__conv]) ).
thf(c_0_16,plain,
! [X1110: allegorical_term_b,X1111: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X1110 @ X1111 ) )
= X1111 ),
inference(variable_rename,[status(thm)],[fact_85_snd__conv]) ).
thf(c_0_17,plain,
( translation_b
= ( ^ [Z0: allegorical_term_b] : ( restrict_b_nat @ ( translation_b @ Z0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
thf(c_0_18,plain,
! [X1108: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X1108 ) ) ),
inference(variable_rename,[status(thm)],[fact_20_verts__in__translation__finite_I1_J]) ).
thf(c_0_19,plain,
! [X1043: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X1043 ) ) ),
inference(variable_rename,[status(thm)],[fact_12_verts__in__translation__finite_I2_J]) ).
thf(c_0_20,plain,
! [X5: allegorical_term_b,X6: allegorical_term_b] : ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_21,plain,
! [X9: labeled_graph_b_nat,X8: labeled_graph_b_nat] :
( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X8 @ X9 ) )
= X8 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_22,plain,
! [X8: labeled_graph_b_nat,X9: labeled_graph_b_nat] :
( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X8 @ X9 ) )
= X9 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_23,negated_conjecture,
( ~ ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
| ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
!= ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) )
| ~ ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_24,plain,
! [X6: allegorical_term_b,X5: allegorical_term_b] :
( ( produc854192515term_b @ ( produc1990145943term_b @ X5 @ X6 ) )
= X5 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_25,plain,
! [X5: allegorical_term_b,X6: allegorical_term_b] :
( ( produc1223098053term_b @ ( produc1990145943term_b @ X5 @ X6 ) )
= X6 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_26,plain,
! [X5: allegorical_term_b] :
( ( restrict_b_nat @ ( translation_b @ X5 ) )
= ( translation_b @ X5 ) ),
inference(arg_cong,[status(thm)],[c_0_17]) ).
thf(c_0_27,plain,
! [X5: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_28,plain,
! [X5: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X5 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_29,plain,
! [X6: allegorical_term_b,X5: allegorical_term_b] : ( graph_529870330at_nat @ ( translation_b @ X5 ) @ ( translation_b @ ( allegorical_A_Int_b @ X5 @ X6 ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ X5 ) ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_21]) ).
thf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_22]),c_0_24]),c_0_25]),c_0_22]),c_0_26]),c_0_24]),c_0_25]),c_0_22]),c_0_27]),c_0_24]),c_0_25]),c_0_22]),c_0_28]),c_0_24]),c_0_25]),c_0_21]),c_0_24]),c_0_25]),c_0_22]),c_0_24]),c_0_25]),c_0_21]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP178^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n009.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 20:06:15 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.23 Running higher-order theorem proving
% 0.21/0.30 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.aqD941YgCA/E---3.1_292103.p
% 0.21/0.36 % Version: 3.5.1-ho
% 0.21/0.36 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.36 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.36 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.36 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.36 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.36 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.36 % Starting post_as_ho6 with 300s (1) cores
% 0.21/0.36 % full_lambda_3 with pid 292143 completed with status 0
% 0.21/0.36 % Result found by full_lambda_3
% 0.21/0.36 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.36 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.36 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.36 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.36 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.36 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.36 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,1.5,,2,20000,1.0))
% 0.21/0.36 % SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.21/0.36 % Search class: HHHSM-FFMS21-DHFFFSBN
% 0.21/0.36 % partial match(5): HGHSM-FFMS31-SHFSMSBN
% 0.21/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.36 % SubtermCWHack with pid 292145 completed with status 0
% 0.21/0.36 % Result found by SubtermCWHack
% 0.21/0.36 % Preprocessing class: HSLMSMSMSSMNHFA.
% 0.21/0.36 % Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.36 % Starting full_lambda_6 with 1200s (4) cores
% 0.21/0.36 % Starting additional_ho_6 with 300s (1) cores
% 0.21/0.36 % Starting new_ho_9 with 300s (1) cores
% 0.21/0.36 % Starting full_lambda_3 with 300s (1) cores
% 0.21/0.36 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountTerms,hypos,1.5,,2,20000,1.0))
% 0.21/0.36 % SinE strategy is GSinE(CountTerms,hypos,1.5,,2,20000,1.0)
% 0.21/0.36 % Search class: HHHSM-FFMS21-DHFFFSBN
% 0.21/0.36 % partial match(5): HGHSM-FFMS31-SHFSMSBN
% 0.21/0.36 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.36 % Starting SubtermCWHack with 28s (1) cores
% 0.21/0.36 % Preprocessing time : 0.004 s
% 0.21/0.36
% 0.21/0.36 % Proof found!
% 0.21/0.36 % SZS status Theorem
% 0.21/0.36 % SZS output start CNFRefutation
% See solution above
% 0.21/0.36 % Parsed axioms : 541
% 0.21/0.36 % Removed by relevancy pruning/SinE : 477
% 0.21/0.36 % Initial clauses : 87
% 0.21/0.36 % Removed in clause preprocessing : 5
% 0.21/0.36 % Initial clauses in saturation : 82
% 0.21/0.36 % Processed clauses : 132
% 0.21/0.36 % ...of these trivial : 19
% 0.21/0.36 % ...subsumed : 20
% 0.21/0.36 % ...remaining for further processing : 92
% 0.21/0.36 % Other redundant clauses eliminated : 54
% 0.21/0.36 % Clauses deleted for lack of memory : 0
% 0.21/0.36 % Backward-subsumed : 2
% 0.21/0.36 % Backward-rewritten : 12
% 0.21/0.36 % Generated clauses : 198
% 0.21/0.36 % ...of the previous two non-redundant : 88
% 0.21/0.36 % ...aggressively subsumed : 0
% 0.21/0.36 % Contextual simplify-reflections : 0
% 0.21/0.36 % Paramodulations : 116
% 0.21/0.36 % Factorizations : 0
% 0.21/0.36 % NegExts : 0
% 0.21/0.36 % Equation resolutions : 63
% 0.21/0.36 % Disequality decompositions : 0
% 0.21/0.36 % Total rewrite steps : 164
% 0.21/0.36 % ...of those cached : 119
% 0.21/0.36 % Propositional unsat checks : 0
% 0.21/0.36 % Propositional check models : 0
% 0.21/0.36 % Propositional check unsatisfiable : 0
% 0.21/0.36 % Propositional clauses : 0
% 0.21/0.36 % Propositional clauses after purity: 0
% 0.21/0.36 % Propositional unsat core size : 0
% 0.21/0.36 % Propositional preprocessing time : 0.000
% 0.21/0.36 % Propositional encoding time : 0.000
% 0.21/0.36 % Propositional solver time : 0.000
% 0.21/0.36 % Success case prop preproc time : 0.000
% 0.21/0.36 % Success case prop encoding time : 0.000
% 0.21/0.36 % Success case prop solver time : 0.000
% 0.21/0.36 % Current number of processed clauses : 60
% 0.21/0.36 % Positive orientable unit clauses : 35
% 0.21/0.36 % Positive unorientable unit clauses: 0
% 0.21/0.36 % Negative unit clauses : 0
% 0.21/0.36 % Non-unit-clauses : 25
% 0.21/0.36 % Current number of unprocessed clauses: 10
% 0.21/0.36 % ...number of literals in the above : 30
% 0.21/0.36 % Current number of archived formulas : 0
% 0.21/0.36 % Current number of archived clauses : 18
% 0.21/0.36 % Clause-clause subsumption calls (NU) : 168
% 0.21/0.36 % Rec. Clause-clause subsumption calls : 148
% 0.21/0.36 % Non-unit clause-clause subsumptions : 22
% 0.21/0.36 % Unit Clause-clause subsumption calls : 22
% 0.21/0.36 % Rewrite failures with RHS unbound : 0
% 0.21/0.36 % BW rewrite match attempts : 14
% 0.21/0.36 % BW rewrite match successes : 12
% 0.21/0.36 % Condensation attempts : 0
% 0.21/0.36 % Condensation successes : 0
% 0.21/0.36 % Termbank termtop insertions : 14545
% 0.21/0.36 % Search garbage collected termcells : 5439
% 0.21/0.36
% 0.21/0.36 % -------------------------------------------------
% 0.21/0.36 % User time : 0.016 s
% 0.21/0.36 % System time : 0.009 s
% 0.21/0.36 % Total time : 0.026 s
% 0.21/0.36 % Maximum resident set size: 5376 pages
% 0.21/0.36
% 0.21/0.36 % -------------------------------------------------
% 0.21/0.36 % User time : 0.037 s
% 0.21/0.36 % System time : 0.014 s
% 0.21/0.36 % Total time : 0.051 s
% 0.21/0.36 % Maximum resident set size: 6144 pages
% 0.21/0.36 % E exiting
%------------------------------------------------------------------------------