%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP179^1 : 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 : n017.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 1.95s 0.55s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 33 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 598 ( 14 ~; 10 |; 10 &; 564 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 9 con; 0-3 aty)
% Number of variables : 29 ( 0 ^; 29 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
standard_Constant_a: $tType ).
thf(decl_sort3,type,
labele431970251um_a_b: $tType ).
thf(decl_sort4,type,
set_Pr1647387645at_nat: $tType ).
thf(decl_sort5,type,
set_Pr409224873um_a_b: $tType ).
thf(decl_sort6,type,
set_Pr1174980151um_a_b: $tType ).
thf(decl_sort7,type,
labele935650037_a_nat: $tType ).
thf(decl_sort8,type,
set_nat: $tType ).
thf(decl_sort9,type,
product_prod_nat_nat: $tType ).
thf(decl_sort10,type,
produc1032616263at_nat: $tType ).
thf(decl_sort11,type,
produc1124793815um_a_b: $tType ).
thf(decl_sort12,type,
sum_sum_a_b: $tType ).
thf(decl_sort13,type,
set_Sum_sum_a_b: $tType ).
thf(decl_23,type,
zero_zero_nat: nat ).
thf(decl_25,type,
standard_S_Idt_a: standard_Constant_a ).
thf(decl_28,type,
edge_p1382426714tant_a: set_Pr1174980151um_a_b > set_Pr1647387645at_nat > set_Pr409224873um_a_b > $o ).
thf(decl_41,type,
labele16114835_a_nat: set_Pr1647387645at_nat > set_nat > labele935650037_a_nat ).
thf(decl_46,type,
labele195203296_a_nat: labele935650037_a_nat > set_Pr1647387645at_nat ).
thf(decl_47,type,
labele1939049654um_a_b: labele431970251um_a_b > set_Pr409224873um_a_b ).
thf(decl_48,type,
labele1810595089_a_nat: labele935650037_a_nat > set_nat ).
thf(decl_49,type,
labele577278695um_a_b: labele431970251um_a_b > set_Sum_sum_a_b ).
thf(decl_50,type,
restri572569417_a_nat: labele935650037_a_nat > labele935650037_a_nat ).
thf(decl_51,type,
restri1162247455um_a_b: labele431970251um_a_b > labele431970251um_a_b ).
thf(decl_54,type,
unival2092813468um_a_b: set_Pr1174980151um_a_b > $o ).
thf(decl_58,type,
bot_bot_set_nat: set_nat ).
thf(decl_59,type,
bot_bo810816657at_nat: set_Pr1647387645at_nat ).
thf(decl_65,type,
bot_bo575978147um_a_b: set_Pr1174980151um_a_b ).
thf(decl_83,type,
ord_le192794300um_a_b: set_Sum_sum_a_b > set_Sum_sum_a_b > $o ).
thf(decl_84,type,
produc407553657at_nat: standard_Constant_a > product_prod_nat_nat > produc1032616263at_nat ).
thf(decl_89,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(decl_91,type,
produc1808556047um_a_b: nat > sum_sum_a_b > produc1124793815um_a_b ).
thf(decl_104,type,
domain1368163076um_a_b: set_Pr1174980151um_a_b > set_nat ).
thf(decl_115,type,
image_256773707um_a_b: set_Pr1174980151um_a_b > set_nat > set_Sum_sum_a_b ).
thf(decl_135,type,
insert_nat: nat > set_nat > set_nat ).
thf(decl_136,type,
insert1625259895at_nat: produc1032616263at_nat > set_Pr1647387645at_nat > set_Pr1647387645at_nat ).
thf(decl_139,type,
insert983991207um_a_b: produc1124793815um_a_b > set_Pr1174980151um_a_b > set_Pr1174980151um_a_b ).
thf(decl_166,type,
g: labele431970251um_a_b ).
thf(decl_167,type,
f: set_Pr1174980151um_a_b ).
thf(decl_169,type,
v: sum_sum_a_b ).
thf(conj_0,conjecture,
( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
& ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
& ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',conj_0) ).
thf(fact_135_labeled__graph_Osel_I2_J,axiom,
! [X48: set_Pr1647387645at_nat,X49: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X48 @ X49 ) )
= X49 ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_135_labeled__graph_Osel_I2_J) ).
thf(fact_5_d,axiom,
( ( domain1368163076um_a_b @ f )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_5_d) ).
thf(fact_4_f,axiom,
( f
= ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_4_f) ).
thf(fact_9_u,axiom,
unival2092813468um_a_b @ f,
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_9_u) ).
thf(fact_137_labeled__graph_Osel_I1_J,axiom,
! [X48: set_Pr1647387645at_nat,X49: set_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X48 @ X49 ) )
= X48 ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_137_labeled__graph_Osel_I1_J) ).
thf(fact_3_r,axiom,
ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_3_r) ).
thf(fact_7_graph__single,axiom,
! [X1: standard_Constant_a,X4: nat,X5: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X5 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X5 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_7_graph__single) ).
thf(fact_252_insert__absorb2,axiom,
! [X517: nat,X61: set_nat] :
( ( insert_nat @ X517 @ ( insert_nat @ X517 @ X61 ) )
= ( insert_nat @ X517 @ X61 ) ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_252_insert__absorb2) ).
thf(fact_0_g,axiom,
( g
= ( restri1162247455um_a_b @ g ) ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_0_g) ).
thf(fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062,axiom,
edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
file('/export/starexec/sandbox/tmp/tmp.KpyEgSYN1r/E---3.1_827559.p',fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062) ).
thf(c_0_11,negated_conjecture,
~ ( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
& ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
& ( g
= ( restri1162247455um_a_b @ g ) )
& ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
& ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
& ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(c_0_12,negated_conjecture,
( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ~ ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
| ~ ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
| ~ ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
thf(c_0_13,plain,
! [X1944: set_Pr1647387645at_nat,X1945: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X1944 @ X1945 ) )
= X1945 ),
inference(variable_rename,[status(thm)],[fact_135_labeled__graph_Osel_I2_J]) ).
thf(c_0_14,plain,
( ( domain1368163076um_a_b @ f )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
inference(split_conjunct,[status(thm)],[fact_5_d]) ).
thf(c_0_15,plain,
( f
= ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ),
inference(split_conjunct,[status(thm)],[fact_4_f]) ).
thf(c_0_16,plain,
unival2092813468um_a_b @ f,
inference(split_conjunct,[status(thm)],[fact_9_u]) ).
thf(c_0_17,plain,
! [X1948: set_Pr1647387645at_nat,X1949: set_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X1948 @ X1949 ) )
= X1948 ),
inference(variable_rename,[status(thm)],[fact_137_labeled__graph_Osel_I1_J]) ).
thf(c_0_18,plain,
ord_le192794300um_a_b @ ( image_256773707um_a_b @ f @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
inference(split_conjunct,[status(thm)],[fact_3_r]) ).
thf(c_0_19,plain,
! [X1527: standard_Constant_a,X1528: nat,X1529: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1527 @ ( product_Pair_nat_nat @ X1528 @ X1529 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1528 @ ( insert_nat @ X1529 @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1527 @ ( product_Pair_nat_nat @ X1528 @ X1529 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X1528 @ ( insert_nat @ X1529 @ bot_bot_set_nat ) ) ) ) ),
inference(variable_rename,[status(thm)],[fact_7_graph__single]) ).
thf(c_0_20,plain,
! [X2233: nat,X2234: set_nat] :
( ( insert_nat @ X2233 @ ( insert_nat @ X2233 @ X2234 ) )
= ( insert_nat @ X2233 @ X2234 ) ),
inference(variable_rename,[status(thm)],[fact_252_insert__absorb2]) ).
thf(c_0_21,negated_conjecture,
( ( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
!= ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) ) )
| ( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
!= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) )
| ( g
!= ( restri1162247455um_a_b @ g ) )
| ~ ( ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele1810595089_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) @ ( labele577278695um_a_b @ g ) )
| ~ ( unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
| ~ ( edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( labele195203296_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) @ ( labele1939049654um_a_b @ g ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_22,plain,
( g
= ( restri1162247455um_a_b @ g ) ),
inference(split_conjunct,[status(thm)],[fact_0_g]) ).
thf(c_0_23,plain,
! [X8: set_Pr1647387645at_nat,X39: set_nat] :
( ( labele1810595089_a_nat @ ( labele16114835_a_nat @ X8 @ X39 ) )
= X39 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_24,plain,
( ( domain1368163076um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) )
= ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
thf(c_0_25,plain,
unival2092813468um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
thf(c_0_26,plain,
! [X39: set_nat,X8: set_Pr1647387645at_nat] :
( ( labele195203296_a_nat @ ( labele16114835_a_nat @ X8 @ X39 ) )
= X8 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
thf(c_0_27,plain,
edge_p1382426714tant_a @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( labele1939049654um_a_b @ g ),
inference(split_conjunct,[status(thm)],[fact_2__092_060open_062edge__preserving_A_123_I0_058_058_063_Hc1_M_Av_J_125_A_123_IS__Idt_M_A0_058_058_063_Hc1_M_A0_058_058_063_Hc1_J_125_A_Iedges_AG_J_092_060close_062]) ).
thf(c_0_28,plain,
ord_le192794300um_a_b @ ( image_256773707um_a_b @ ( insert983991207um_a_b @ ( produc1808556047um_a_b @ zero_zero_nat @ v ) @ bot_bo575978147um_a_b ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) @ ( labele577278695um_a_b @ g ),
inference(rw,[status(thm)],[c_0_18,c_0_15]) ).
thf(c_0_29,plain,
! [X1: standard_Constant_a,X4: nat,X5: nat] :
( ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X5 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
= ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X5 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_30,plain,
! [X4: nat,X39: set_nat] :
( ( insert_nat @ X4 @ ( insert_nat @ X4 @ X39 ) )
= ( insert_nat @ X4 @ X39 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_31,negated_conjecture,
( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
!= ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ standard_S_Idt_a @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ),
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)],[c_0_21,c_0_22]),c_0_23]),c_0_24]),c_0_25]),c_0_26]),c_0_27]),c_0_23]),c_0_28])]) ).
thf(c_0_32,plain,
! [X1: standard_Constant_a,X4: nat] :
( ( restri572569417_a_nat @ ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X4 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) )
= ( labele16114835_a_nat @ ( insert1625259895at_nat @ ( produc407553657at_nat @ X1 @ ( product_Pair_nat_nat @ X4 @ X4 ) ) @ bot_bo810816657at_nat ) @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP179^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n017.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 20:02:22 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.25 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.KpyEgSYN1r/E---3.1_827559.p
% 1.95/0.55 % Version: 3.5.1-ho
% 1.95/0.55 % Preprocessing class: HSLMSMSMSSMNSFA.
% 1.95/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.55 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.95/0.55 % Starting ehoh_best_sine_rwall with 300s (1) cores
% 1.95/0.55 % Starting full_lambda_6 with 300s (1) cores
% 1.95/0.55 % Starting ehoh_best_sine with 300s (1) cores
% 1.95/0.55 % ho_unfolding_3 with pid 827572 completed with status 0
% 1.95/0.55 % Result found by ho_unfolding_3
% 1.95/0.55 % Preprocessing class: HSLMSMSMSSMNSFA.
% 1.95/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.55 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.95/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.95/0.55 % No SInE strategy applied
% 1.95/0.55 % Search class: HGHSM-FSLM31-DSFFFFBN
% 1.95/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.95/0.55 % Starting SubtermCWHack with 136s (1) cores
% 1.95/0.55 % Starting ho_unfolding_3 with 151s (1) cores
% 1.95/0.55 % Starting lpo5_fix with 226s (1) cores
% 1.95/0.55 % Starting new_ho_2_cnf4 with 226s (1) cores
% 1.95/0.55 % Starting full_lambda_5 with 226s (1) cores
% 1.95/0.55 % full_lambda_5 with pid 827583 completed with status 0
% 1.95/0.55 % Result found by full_lambda_5
% 1.95/0.55 % Preprocessing class: HSLMSMSMSSMNSFA.
% 1.95/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.95/0.55 % Starting ho_unfolding_3 with 1500s (5) cores
% 1.95/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.95/0.55 % No SInE strategy applied
% 1.95/0.55 % Search class: HGHSM-FSLM31-DSFFFFBN
% 1.95/0.55 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.95/0.55 % Starting SubtermCWHack with 136s (1) cores
% 1.95/0.55 % Starting ho_unfolding_3 with 151s (1) cores
% 1.95/0.55 % Starting lpo5_fix with 226s (1) cores
% 1.95/0.55 % Starting new_ho_2_cnf4 with 226s (1) cores
% 1.95/0.55 % Starting full_lambda_5 with 226s (1) cores
% 1.95/0.55 % Preprocessing time : 0.009 s
% 1.95/0.55 % Presaturation interreduction done
% 1.95/0.55
% 1.95/0.55 % Proof found!
% 1.95/0.55 % SZS status Theorem
% 1.95/0.55 % SZS output start CNFRefutation
% See solution above
% 1.95/0.55 % Parsed axioms : 554
% 1.95/0.55 % Removed by relevancy pruning/SinE : 0
% 1.95/0.55 % Initial clauses : 779
% 1.95/0.55 % Removed in clause preprocessing : 205
% 1.95/0.55 % Initial clauses in saturation : 574
% 1.95/0.55 % Processed clauses : 2217
% 1.95/0.55 % ...of these trivial : 80
% 1.95/0.55 % ...subsumed : 855
% 1.95/0.55 % ...remaining for further processing : 1282
% 1.95/0.55 % Other redundant clauses eliminated : 200
% 1.95/0.55 % Clauses deleted for lack of memory : 0
% 1.95/0.55 % Backward-subsumed : 6
% 1.95/0.55 % Backward-rewritten : 26
% 1.95/0.55 % Generated clauses : 3847
% 1.95/0.55 % ...of the previous two non-redundant : 3129
% 1.95/0.55 % ...aggressively subsumed : 0
% 1.95/0.55 % Contextual simplify-reflections : 4
% 1.95/0.55 % Paramodulations : 3593
% 1.95/0.55 % Factorizations : 2
% 1.95/0.55 % NegExts : 0
% 1.95/0.55 % Equation resolutions : 244
% 1.95/0.55 % Disequality decompositions : 0
% 1.95/0.55 % Total rewrite steps : 1285
% 1.95/0.55 % ...of those cached : 1050
% 1.95/0.55 % Propositional unsat checks : 0
% 1.95/0.55 % Propositional check models : 0
% 1.95/0.55 % Propositional check unsatisfiable : 0
% 1.95/0.55 % Propositional clauses : 0
% 1.95/0.55 % Propositional clauses after purity: 0
% 1.95/0.55 % Propositional unsat core size : 0
% 1.95/0.55 % Propositional preprocessing time : 0.000
% 1.95/0.55 % Propositional encoding time : 0.000
% 1.95/0.55 % Propositional solver time : 0.000
% 1.95/0.55 % Success case prop preproc time : 0.000
% 1.95/0.55 % Success case prop encoding time : 0.000
% 1.95/0.55 % Success case prop solver time : 0.000
% 1.95/0.55 % Current number of processed clauses : 743
% 1.95/0.55 % Positive orientable unit clauses : 154
% 1.95/0.55 % Positive unorientable unit clauses: 0
% 1.95/0.55 % Negative unit clauses : 13
% 1.95/0.55 % Non-unit-clauses : 576
% 1.95/0.55 % Current number of unprocessed clauses: 1831
% 1.95/0.55 % ...number of literals in the above : 4468
% 1.95/0.55 % Current number of archived formulas : 0
% 1.95/0.55 % Current number of archived clauses : 452
% 1.95/0.55 % Clause-clause subsumption calls (NU) : 121806
% 1.95/0.55 % Rec. Clause-clause subsumption calls : 74668
% 1.95/0.55 % Non-unit clause-clause subsumptions : 681
% 1.95/0.55 % Unit Clause-clause subsumption calls : 11495
% 1.95/0.55 % Rewrite failures with RHS unbound : 0
% 1.95/0.55 % BW rewrite match attempts : 76
% 1.95/0.55 % BW rewrite match successes : 24
% 1.95/0.55 % Condensation attempts : 0
% 1.95/0.55 % Condensation successes : 0
% 1.95/0.55 % Termbank termtop insertions : 96543
% 1.95/0.55 % Search garbage collected termcells : 11397
% 1.95/0.55
% 1.95/0.55 % -------------------------------------------------
% 1.95/0.55 % User time : 0.242 s
% 1.95/0.55 % System time : 0.025 s
% 1.95/0.55 % Total time : 0.267 s
% 1.95/0.55 % Maximum resident set size: 6908 pages
% 1.95/0.55
% 1.95/0.55 % -------------------------------------------------
% 1.95/0.55 % User time : 1.106 s
% 1.95/0.55 % System time : 0.083 s
% 1.95/0.55 % Total time : 1.188 s
% 1.95/0.55 % Maximum resident set size: 5888 pages
% 1.95/0.55 % E exiting
%------------------------------------------------------------------------------