%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 : Thu Sep 24 08:57:16 AM UTC 2026
% Result : Theorem 0.55s 0.82s
% Output : Proof 0.55s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('theBenchmark.p',p2) ).
fof(p3a,axiom,
empty(empty_set),
file('theBenchmark.p',p3a) ).
fof(p3b,axiom,
type(empty_set,set_type),
file('theBenchmark.p',p3b) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( member(ordered_pair(C,D),identity_relation_of(B))
<=> ( C = D
& member(C,B) ) ) ) ) ),
file('theBenchmark.p',p4) ).
fof(p5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),binary_relation_type) ),
file('theBenchmark.p',p5) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( B = C
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
<=> member(D,C) ) ) ) ) ),
file('theBenchmark.p',p6) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( not_equal(B,C)
<=> B != C ) ) ),
file('theBenchmark.p',p7) ).
fof(p8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p8) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(ordered_pair(B,C),set_type) ) ),
file('theBenchmark.p',p9) ).
fof(p10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p10) ).
fof(p11,axiom,
? [B] : ilf_type(B,binary_relation_type),
file('theBenchmark.p',p11) ).
fof(p12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( relation_like(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
=> ? [D] :
( ? [E] :
( C = ordered_pair(D,E)
& ilf_type(E,set_type) )
& ilf_type(D,set_type) ) ) ) ) ),
file('theBenchmark.p',p12) ).
fof(p13,axiom,
! [B] :
( ( ilf_type(B,set_type)
& empty(B) )
=> relation_like(B) ),
file('theBenchmark.p',p13) ).
fof(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('theBenchmark.p',p14) ).
fof(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),set_type) ) ),
file('theBenchmark.p',p15) ).
fof(p16,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('theBenchmark.p',p16) ).
fof(p17,axiom,
! [B] :
( ilf_type(B,set_type)
=> ? [C] : ilf_type(C,subset_type(B)) ),
file('theBenchmark.p',p17) ).
fof(p18,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('theBenchmark.p',p18) ).
fof(p19,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p19) ).
fof(p20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('theBenchmark.p',p20) ).
fof(p21,axiom,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ? [C] : ilf_type(C,member_type(B)) ),
file('theBenchmark.p',p21) ).
fof(p22,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p22) ).
fof(prove_relset_1_46,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> not_equal(identity_relation_of(B),empty_set) ),
file('theBenchmark.p',prove_relset_1_46) ).
fof(f_1_1,plain,
! [B] :
( ! [C] :
( ( ( member(C,B)
| ~ member(ordered_pair(C,C),identity_relation_of(B)) )
& ( member(ordered_pair(C,C),identity_relation_of(B))
| ~ member(C,B) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_1_2,plain,
! [U_1] :
( ! [U_0] :
( ( ( member(U_0,U_1)
| ~ member(ordered_pair(U_0,U_0),identity_relation_of(U_1)) )
& ( member(ordered_pair(U_0,U_0),identity_relation_of(U_1))
| ~ member(U_0,U_1) ) )
| ~ ilf_type(U_0,set_type) )
| ~ ilf_type(U_1,set_type) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( member(ordered_pair(U_0,U_0),identity_relation_of(U_1))
| ~ member(U_0,U_1)
| ~ ilf_type(U_0,set_type)
| ~ ilf_type(U_1,set_type) ),
inference(clausify,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( member(U_0,U_1)
| ~ member(ordered_pair(U_0,U_0),identity_relation_of(U_1))
| ~ ilf_type(U_0,set_type)
| ~ ilf_type(U_1,set_type) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B] :
( ~ member(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p2]) ).
fof(f_2_2,plain,
! [U_2] :
( ~ member(U_2,empty_set)
| ~ ilf_type(U_2,set_type) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ member(U_2,empty_set)
| ~ ilf_type(U_2,set_type) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[p3a]) ).
cnf(f_3_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
type(empty_set,set_type),
inference(fof_nnf,[status(thm)],[p3b]) ).
cnf(f_4_2,plain,
type(empty_set,set_type),
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( member(ordered_pair(C,D),identity_relation_of(B))
| C != D
| ~ member(C,B) )
& ( ( C = D
& member(C,B) )
| ~ member(ordered_pair(C,D),identity_relation_of(B)) ) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p4]) ).
fof(f_5_2,plain,
! [U_5] :
( ! [U_4] :
( ! [U_3] :
( ( ( member(ordered_pair(U_4,U_3),identity_relation_of(U_5))
| U_4 != U_3
| ~ member(U_4,U_5) )
& ( ( U_4 = U_3
& member(U_4,U_5) )
| ~ member(ordered_pair(U_4,U_3),identity_relation_of(U_5)) ) )
| ~ ilf_type(U_3,set_type) )
| ~ ilf_type(U_4,set_type) )
| ~ ilf_type(U_5,set_type) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( member(U_4,U_5)
| ~ member(ordered_pair(U_4,U_3),identity_relation_of(U_5))
| ~ ilf_type(U_3,set_type)
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( U_4 = U_3
| ~ member(ordered_pair(U_4,U_3),identity_relation_of(U_5))
| ~ ilf_type(U_3,set_type)
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( member(ordered_pair(U_4,U_3),identity_relation_of(U_5))
| U_4 != U_3
| ~ member(U_4,U_5)
| ~ ilf_type(U_3,set_type)
| ~ ilf_type(U_4,set_type)
| ~ ilf_type(U_5,set_type) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [B] :
( ilf_type(identity_relation_of(B),binary_relation_type)
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p5]) ).
fof(f_6_2,plain,
! [U_6] :
( ilf_type(identity_relation_of(U_6),binary_relation_type)
| ~ ilf_type(U_6,set_type) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ilf_type(identity_relation_of(U_6),binary_relation_type)
| ~ ilf_type(U_6,set_type) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [B] :
( ! [C] :
( ( ( B = C
| ? [D] :
( ( ( ~ member(D,B)
& member(D,C) )
| ( ~ member(D,C)
& member(D,B) ) )
& ilf_type(D,set_type) ) )
& ( ! [D] :
( ( ( member(D,B)
| ~ member(D,C) )
& ( member(D,C)
| ~ member(D,B) ) )
| ~ ilf_type(D,set_type) )
| B != C ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p6]) ).
fof(f_7_2,plain,
! [U_10] :
( ! [U_9] :
( ( ( U_10 = U_9
| ? [U_8] :
( ( ( ~ member(U_8,U_10)
& member(U_8,U_9) )
| ( ~ member(U_8,U_9)
& member(U_8,U_10) ) )
& ilf_type(U_8,set_type) ) )
& ( ! [U_7] :
( ( ( member(U_7,U_10)
| ~ member(U_7,U_9) )
& ( member(U_7,U_9)
| ~ member(U_7,U_10) ) )
| ~ ilf_type(U_7,set_type) )
| U_10 != U_9 ) )
| ~ ilf_type(U_9,set_type) )
| ~ ilf_type(U_10,set_type) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_10] :
( ! [U_9] :
( ( ( U_10 = U_9
| ( ( ( ~ member(sK1(U_10,U_9),U_10)
& member(sK1(U_10,U_9),U_9) )
| ( ~ member(sK1(U_10,U_9),U_9)
& member(sK1(U_10,U_9),U_10) ) )
& ilf_type(sK1(U_10,U_9),set_type) ) )
& ( ! [U_7] :
( ( ( member(U_7,U_10)
| ~ member(U_7,U_9) )
& ( member(U_7,U_9)
| ~ member(U_7,U_10) ) )
| ~ ilf_type(U_7,set_type) )
| U_10 != U_9 ) )
| ~ ilf_type(U_9,set_type) )
| ~ ilf_type(U_10,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_10,U_9))],[f_7_2]) ).
cnf(f_7_4,plain,
( member(U_7,U_9)
| ~ member(U_7,U_10)
| ~ ilf_type(U_7,set_type)
| U_10 != U_9
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( member(U_7,U_10)
| ~ member(U_7,U_9)
| ~ ilf_type(U_7,set_type)
| U_10 != U_9
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( ilf_type(sK1(U_10,U_9),set_type)
| U_10 = U_9
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( member(sK1(U_10,U_9),U_9)
| member(sK1(U_10,U_9),U_10)
| U_10 = U_9
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_8,plain,
( ~ member(sK1(U_10,U_9),U_10)
| member(sK1(U_10,U_9),U_10)
| U_10 = U_9
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_9,plain,
( member(sK1(U_10,U_9),U_9)
| ~ member(sK1(U_10,U_9),U_9)
| U_10 = U_9
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_10,plain,
( ~ member(sK1(U_10,U_9),U_10)
| ~ member(sK1(U_10,U_9),U_9)
| U_10 = U_9
| ~ ilf_type(U_9,set_type)
| ~ ilf_type(U_10,set_type) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [B] :
( ! [C] :
( ( ( not_equal(B,C)
| B = C )
& ( B != C
| ~ not_equal(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p7]) ).
fof(f_8_2,plain,
! [U_12] :
( ! [U_11] :
( ( ( not_equal(U_12,U_11)
| U_12 = U_11 )
& ( U_12 != U_11
| ~ not_equal(U_12,U_11) ) )
| ~ ilf_type(U_11,set_type) )
| ~ ilf_type(U_12,set_type) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( U_12 != U_11
| ~ not_equal(U_12,U_11)
| ~ ilf_type(U_11,set_type)
| ~ ilf_type(U_12,set_type) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( not_equal(U_12,U_11)
| U_12 = U_11
| ~ ilf_type(U_11,set_type)
| ~ ilf_type(U_12,set_type) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [B] :
( ( ( empty(B)
| ? [C] :
( member(C,B)
& ilf_type(C,set_type) ) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p8]) ).
fof(f_9_2,plain,
! [U_15] :
( ( ( empty(U_15)
| ? [U_14] :
( member(U_14,U_15)
& ilf_type(U_14,set_type) ) )
& ( ! [U_13] :
( ~ member(U_13,U_15)
| ~ ilf_type(U_13,set_type) )
| ~ empty(U_15) ) )
| ~ ilf_type(U_15,set_type) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_15] :
( ( ( empty(U_15)
| ( member(sK2(U_15),U_15)
& ilf_type(sK2(U_15),set_type) ) )
& ( ! [U_13] :
( ~ member(U_13,U_15)
| ~ ilf_type(U_13,set_type) )
| ~ empty(U_15) ) )
| ~ ilf_type(U_15,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_15))],[f_9_2]) ).
cnf(f_9_4,plain,
( ~ member(U_13,U_15)
| ~ ilf_type(U_13,set_type)
| ~ empty(U_15)
| ~ ilf_type(U_15,set_type) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( ilf_type(sK2(U_15),set_type)
| empty(U_15)
| ~ ilf_type(U_15,set_type) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( member(sK2(U_15),U_15)
| empty(U_15)
| ~ ilf_type(U_15,set_type) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [B] :
( ! [C] :
( ilf_type(ordered_pair(B,C),set_type)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p9]) ).
fof(f_10_2,plain,
! [U_17] :
( ! [U_16] :
( ilf_type(ordered_pair(U_17,U_16),set_type)
| ~ ilf_type(U_16,set_type) )
| ~ ilf_type(U_17,set_type) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ilf_type(ordered_pair(U_17,U_16),set_type)
| ~ ilf_type(U_16,set_type)
| ~ ilf_type(U_17,set_type) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [B] :
( ( ( ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ relation_like(B) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p10]) ).
fof(f_11_2,plain,
! [U_18] :
( ( ( ilf_type(U_18,binary_relation_type)
| ~ ilf_type(U_18,set_type)
| ~ relation_like(U_18) )
& ( ( ilf_type(U_18,set_type)
& relation_like(U_18) )
| ~ ilf_type(U_18,binary_relation_type) ) )
| ~ ilf_type(U_18,set_type) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation_like(U_18)
| ~ ilf_type(U_18,binary_relation_type)
| ~ ilf_type(U_18,set_type) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( ilf_type(U_18,set_type)
| ~ ilf_type(U_18,binary_relation_type)
| ~ ilf_type(U_18,set_type) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( ilf_type(U_18,binary_relation_type)
| ~ ilf_type(U_18,set_type)
| ~ relation_like(U_18)
| ~ ilf_type(U_18,set_type) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
? [B] : ilf_type(B,binary_relation_type),
inference(fof_nnf,[status(thm)],[p11]) ).
fof(f_12_2,plain,
? [U_19] : ilf_type(U_19,binary_relation_type),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
ilf_type(sK3,binary_relation_type),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3)],[f_12_2]) ).
cnf(f_12_4,plain,
ilf_type(sK3,binary_relation_type),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [B] :
( ( ( relation_like(B)
| ? [C] :
( ! [D] :
( ! [E] :
( C != ordered_pair(D,E)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
& member(C,B)
& ilf_type(C,set_type) ) )
& ( ! [C] :
( ? [D] :
( ? [E] :
( C = ordered_pair(D,E)
& ilf_type(E,set_type) )
& ilf_type(D,set_type) )
| ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ relation_like(B) ) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p12]) ).
fof(f_13_2,plain,
! [U_26] :
( ( ( relation_like(U_26)
| ? [U_25] :
( ! [U_24] :
( ! [U_23] :
( U_25 != ordered_pair(U_24,U_23)
| ~ ilf_type(U_23,set_type) )
| ~ ilf_type(U_24,set_type) )
& member(U_25,U_26)
& ilf_type(U_25,set_type) ) )
& ( ! [U_22] :
( ? [U_21] :
( ? [U_20] :
( U_22 = ordered_pair(U_21,U_20)
& ilf_type(U_20,set_type) )
& ilf_type(U_21,set_type) )
| ~ member(U_22,U_26)
| ~ ilf_type(U_22,set_type) )
| ~ relation_like(U_26) ) )
| ~ ilf_type(U_26,set_type) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_26] :
( ( ( relation_like(U_26)
| ? [U_25] :
( ! [U_24] :
( ! [U_23] :
( U_25 != ordered_pair(U_24,U_23)
| ~ ilf_type(U_23,set_type) )
| ~ ilf_type(U_24,set_type) )
& member(U_25,U_26)
& ilf_type(U_25,set_type) ) )
& ( ! [U_22] :
( ( ? [U_20] :
( U_22 = ordered_pair(sK4(U_26,U_22),U_20)
& ilf_type(U_20,set_type) )
& ilf_type(sK4(U_26,U_22),set_type) )
| ~ member(U_22,U_26)
| ~ ilf_type(U_22,set_type) )
| ~ relation_like(U_26) ) )
| ~ ilf_type(U_26,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4(U_26,U_22))],[f_13_2]) ).
fof(f_13_4,plain,
! [U_26] :
( ( ( relation_like(U_26)
| ? [U_25] :
( ! [U_24] :
( ! [U_23] :
( U_25 != ordered_pair(U_24,U_23)
| ~ ilf_type(U_23,set_type) )
| ~ ilf_type(U_24,set_type) )
& member(U_25,U_26)
& ilf_type(U_25,set_type) ) )
& ( ! [U_22] :
( ( U_22 = ordered_pair(sK4(U_26,U_22),sK5(U_26,U_22))
& ilf_type(sK5(U_26,U_22),set_type)
& ilf_type(sK4(U_26,U_22),set_type) )
| ~ member(U_22,U_26)
| ~ ilf_type(U_22,set_type) )
| ~ relation_like(U_26) ) )
| ~ ilf_type(U_26,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_20,sK5(U_26,U_22))],[f_13_3]) ).
fof(f_13_5,plain,
! [U_26] :
( ( ( relation_like(U_26)
| ( ! [U_24] :
( ! [U_23] :
( sK6(U_26) != ordered_pair(U_24,U_23)
| ~ ilf_type(U_23,set_type) )
| ~ ilf_type(U_24,set_type) )
& member(sK6(U_26),U_26)
& ilf_type(sK6(U_26),set_type) ) )
& ( ! [U_22] :
( ( U_22 = ordered_pair(sK4(U_26,U_22),sK5(U_26,U_22))
& ilf_type(sK5(U_26,U_22),set_type)
& ilf_type(sK4(U_26,U_22),set_type) )
| ~ member(U_22,U_26)
| ~ ilf_type(U_22,set_type) )
| ~ relation_like(U_26) ) )
| ~ ilf_type(U_26,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_25,sK6(U_26))],[f_13_4]) ).
cnf(f_13_6,plain,
( ilf_type(sK4(U_26,U_22),set_type)
| ~ member(U_22,U_26)
| ~ ilf_type(U_22,set_type)
| ~ relation_like(U_26)
| ~ ilf_type(U_26,set_type) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_7,plain,
( ilf_type(sK5(U_26,U_22),set_type)
| ~ member(U_22,U_26)
| ~ ilf_type(U_22,set_type)
| ~ relation_like(U_26)
| ~ ilf_type(U_26,set_type) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_8,plain,
( U_22 = ordered_pair(sK4(U_26,U_22),sK5(U_26,U_22))
| ~ member(U_22,U_26)
| ~ ilf_type(U_22,set_type)
| ~ relation_like(U_26)
| ~ ilf_type(U_26,set_type) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_9,plain,
( ilf_type(sK6(U_26),set_type)
| relation_like(U_26)
| ~ ilf_type(U_26,set_type) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_10,plain,
( member(sK6(U_26),U_26)
| relation_like(U_26)
| ~ ilf_type(U_26,set_type) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_11,plain,
( sK6(U_26) != ordered_pair(U_24,U_23)
| ~ ilf_type(U_23,set_type)
| ~ ilf_type(U_24,set_type)
| relation_like(U_26)
| ~ ilf_type(U_26,set_type) ),
inference(clausify,[status(thm)],[f_13_5]) ).
fof(f_14_1,plain,
! [B] :
( relation_like(B)
| ~ ilf_type(B,set_type)
| ~ empty(B) ),
inference(fof_nnf,[status(thm)],[p13]) ).
fof(f_14_2,plain,
! [U_27] :
( relation_like(U_27)
| ~ ilf_type(U_27,set_type)
| ~ empty(U_27) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( relation_like(U_27)
| ~ ilf_type(U_27,set_type)
| ~ empty(U_27) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [B] :
( ! [C] :
( ! [D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p14]) ).
fof(f_15_2,plain,
! [U_30] :
( ! [U_29] :
( ! [U_28] :
( relation_like(U_28)
| ~ ilf_type(U_28,subset_type(cross_product(U_30,U_29))) )
| ~ ilf_type(U_29,set_type) )
| ~ ilf_type(U_30,set_type) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( relation_like(U_28)
| ~ ilf_type(U_28,subset_type(cross_product(U_30,U_29)))
| ~ ilf_type(U_29,set_type)
| ~ ilf_type(U_30,set_type) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [B] :
( ! [C] :
( ilf_type(cross_product(B,C),set_type)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p15]) ).
fof(f_16_2,plain,
! [U_32] :
( ! [U_31] :
( ilf_type(cross_product(U_32,U_31),set_type)
| ~ ilf_type(U_31,set_type) )
| ~ ilf_type(U_32,set_type) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( ilf_type(cross_product(U_32,U_31),set_type)
| ~ ilf_type(U_31,set_type)
| ~ ilf_type(U_32,set_type) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [B] :
( ! [C] :
( ( ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p16]) ).
fof(f_17_2,plain,
! [U_34] :
( ! [U_33] :
( ( ( ilf_type(U_33,subset_type(U_34))
| ~ ilf_type(U_33,member_type(power_set(U_34))) )
& ( ilf_type(U_33,member_type(power_set(U_34)))
| ~ ilf_type(U_33,subset_type(U_34)) ) )
| ~ ilf_type(U_33,set_type) )
| ~ ilf_type(U_34,set_type) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( ilf_type(U_33,member_type(power_set(U_34)))
| ~ ilf_type(U_33,subset_type(U_34))
| ~ ilf_type(U_33,set_type)
| ~ ilf_type(U_34,set_type) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( ilf_type(U_33,subset_type(U_34))
| ~ ilf_type(U_33,member_type(power_set(U_34)))
| ~ ilf_type(U_33,set_type)
| ~ ilf_type(U_34,set_type) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [B] :
( ? [C] : ilf_type(C,subset_type(B))
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p17]) ).
fof(f_18_2,plain,
! [U_36] :
( ? [U_35] : ilf_type(U_35,subset_type(U_36))
| ~ ilf_type(U_36,set_type) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_36] :
( ilf_type(sK7(U_36),subset_type(U_36))
| ~ ilf_type(U_36,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_35,sK7(U_36))],[f_18_2]) ).
cnf(f_18_4,plain,
( ilf_type(sK7(U_36),subset_type(U_36))
| ~ ilf_type(U_36,set_type) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [B] :
( ! [C] :
( ( ( member(B,power_set(C))
| ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) ) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p18]) ).
fof(f_19_2,plain,
! [U_40] :
( ! [U_39] :
( ( ( member(U_40,power_set(U_39))
| ? [U_38] :
( ~ member(U_38,U_39)
& member(U_38,U_40)
& ilf_type(U_38,set_type) ) )
& ( ! [U_37] :
( member(U_37,U_39)
| ~ member(U_37,U_40)
| ~ ilf_type(U_37,set_type) )
| ~ member(U_40,power_set(U_39)) ) )
| ~ ilf_type(U_39,set_type) )
| ~ ilf_type(U_40,set_type) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_40] :
( ! [U_39] :
( ( ( member(U_40,power_set(U_39))
| ( ~ member(sK8(U_40,U_39),U_39)
& member(sK8(U_40,U_39),U_40)
& ilf_type(sK8(U_40,U_39),set_type) ) )
& ( ! [U_37] :
( member(U_37,U_39)
| ~ member(U_37,U_40)
| ~ ilf_type(U_37,set_type) )
| ~ member(U_40,power_set(U_39)) ) )
| ~ ilf_type(U_39,set_type) )
| ~ ilf_type(U_40,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_38,sK8(U_40,U_39))],[f_19_2]) ).
cnf(f_19_4,plain,
( member(U_37,U_39)
| ~ member(U_37,U_40)
| ~ ilf_type(U_37,set_type)
| ~ member(U_40,power_set(U_39))
| ~ ilf_type(U_39,set_type)
| ~ ilf_type(U_40,set_type) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( ilf_type(sK8(U_40,U_39),set_type)
| member(U_40,power_set(U_39))
| ~ ilf_type(U_39,set_type)
| ~ ilf_type(U_40,set_type) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( member(sK8(U_40,U_39),U_40)
| member(U_40,power_set(U_39))
| ~ ilf_type(U_39,set_type)
| ~ ilf_type(U_40,set_type) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_7,plain,
( ~ member(sK8(U_40,U_39),U_39)
| member(U_40,power_set(U_39))
| ~ ilf_type(U_39,set_type)
| ~ ilf_type(U_40,set_type) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p19]) ).
fof(f_20_2,plain,
! [U_41] :
( ( ilf_type(power_set(U_41),set_type)
& ~ empty(power_set(U_41)) )
| ~ ilf_type(U_41,set_type) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ~ empty(power_set(U_41))
| ~ ilf_type(U_41,set_type) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( ilf_type(power_set(U_41),set_type)
| ~ ilf_type(U_41,set_type) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [B] :
( ! [C] :
( ( ( ilf_type(B,member_type(C))
| ~ member(B,C) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p20]) ).
fof(f_21_2,plain,
! [U_43] :
( ! [U_42] :
( ( ( ilf_type(U_43,member_type(U_42))
| ~ member(U_43,U_42) )
& ( member(U_43,U_42)
| ~ ilf_type(U_43,member_type(U_42)) ) )
| ~ ilf_type(U_42,set_type)
| empty(U_42) )
| ~ ilf_type(U_43,set_type) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( member(U_43,U_42)
| ~ ilf_type(U_43,member_type(U_42))
| ~ ilf_type(U_42,set_type)
| empty(U_42)
| ~ ilf_type(U_43,set_type) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( ilf_type(U_43,member_type(U_42))
| ~ member(U_43,U_42)
| ~ ilf_type(U_42,set_type)
| empty(U_42)
| ~ ilf_type(U_43,set_type) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [B] :
( ? [C] : ilf_type(C,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B) ),
inference(fof_nnf,[status(thm)],[p21]) ).
fof(f_22_2,plain,
! [U_45] :
( ? [U_44] : ilf_type(U_44,member_type(U_45))
| ~ ilf_type(U_45,set_type)
| empty(U_45) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_45] :
( ilf_type(sK9(U_45),member_type(U_45))
| ~ ilf_type(U_45,set_type)
| empty(U_45) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_44,sK9(U_45))],[f_22_2]) ).
cnf(f_22_4,plain,
( ilf_type(sK9(U_45),member_type(U_45))
| ~ ilf_type(U_45,set_type)
| empty(U_45) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [B] : ilf_type(B,set_type),
inference(fof_nnf,[status(thm)],[p22]) ).
fof(f_23_2,plain,
! [U_46] : ilf_type(U_46,set_type),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
ilf_type(U_46,set_type),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> not_equal(identity_relation_of(B),empty_set) ),
inference(negate,[status(cth)],[prove_relset_1_46]) ).
fof(f_24_2,negated_conjecture,
? [B] :
( ~ not_equal(identity_relation_of(B),empty_set)
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(fof_nnf,[status(thm)],[f_24_1]) ).
fof(f_24_3,negated_conjecture,
? [U_47] :
( ~ not_equal(identity_relation_of(U_47),empty_set)
& ilf_type(U_47,set_type)
& ~ empty(U_47) ),
inference(variable_rename,[status(thm)],[f_24_2]) ).
fof(f_24_4,negated_conjecture,
( ~ not_equal(identity_relation_of(sK10),empty_set)
& ilf_type(sK10,set_type)
& ~ empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_47,sK10)],[f_24_3]) ).
fof(f_24_5,negated_conjecture,
( ~ not_equal(identity_relation_of(sK10),empty_set)
& ilf_type(sK10,set_type)
& ~ empty(sK10) ),
inference(definitional_conversion,[status(esa)],[f_24_4]) ).
cnf(f_24_6,negated_conjecture,
~ empty(sK10),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_7,negated_conjecture,
ilf_type(sK10,set_type),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_24_8,negated_conjecture,
~ not_equal(identity_relation_of(sK10),empty_set),
inference(clausify,[status(thm)],[f_24_5]) ).
cnf(f_7_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_8]) ).
cnf(f_7_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_9]) ).
cnf(f_11_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_4]) ).
cnf(f_11_5_simplified,plain,
( ilf_type(U_18,binary_relation_type)
| ~ ilf_type(U_18,set_type)
| ~ relation_like(U_18) ),
inference(simplify_clause,[status(thm)],[f_11_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( identity_relation_of(Eq_x_0) = identity_relation_of(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( cross_product(Eq_x_0,Eq_x_1) = cross_product(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( subset_type(Eq_x_0) = subset_type(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( power_set(Eq_x_0) = power_set(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( member_type(Eq_x_0) = member_type(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( ilf_type(Eq_y_0,Eq_y_1)
| ~ ilf_type(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( member(Eq_y_0,Eq_y_1)
| ~ member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( type(Eq_y_0,Eq_y_1)
| ~ type(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( not_equal(Eq_y_0,Eq_y_1)
| ~ not_equal(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( relation_like(Eq_y_0)
| ~ relation_like(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 19 22:45:37 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.55/0.82 % SZS status Theorem for theBenchmark
% 0.55/0.82 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------