%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU190+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 08:58:24 AM UTC 2026
% Result : Theorem 257.87s 263.18s
% Output : Proof 259.29s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d10_relat_1,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('theBenchmark.p',d10_relat_1) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t71_relat_1,conjecture,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('theBenchmark.p',t71_relat_1) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_2_2,plain,
! [U_2] :
( relation(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( relation(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_3_2,plain,
! [U_4,U_3] : unordered_pair(U_4,U_3) = unordered_pair(U_3,U_4),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
unordered_pair(U_4,U_3) = unordered_pair(U_3,U_4),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] :
( ( ( B = identity_relation(A)
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),B)
& C = D
& in(C,A) )
| ( ( C != D
| ~ in(C,A) )
& in(ordered_pair(C,D),B) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),B)
| C != D
| ~ in(C,A) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d10_relat_1]) ).
fof(f_4_2,plain,
! [U_10,U_9] :
( ( ( U_9 = identity_relation(U_10)
| ? [U_8,U_7] :
( ( ~ in(ordered_pair(U_8,U_7),U_9)
& U_8 = U_7
& in(U_8,U_10) )
| ( ( U_8 != U_7
| ~ in(U_8,U_10) )
& in(ordered_pair(U_8,U_7),U_9) ) ) )
& ( ! [U_6,U_5] :
( ( in(ordered_pair(U_6,U_5),U_9)
| U_6 != U_5
| ~ in(U_6,U_10) )
& ( ( U_6 = U_5
& in(U_6,U_10) )
| ~ in(ordered_pair(U_6,U_5),U_9) ) )
| U_9 != identity_relation(U_10) ) )
| ~ relation(U_9) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_10,U_9] :
( ( ( U_9 = identity_relation(U_10)
| ? [U_18,U_16] :
( ~ in(ordered_pair(U_18,U_16),U_9)
& U_18 = U_16
& in(U_18,U_10) )
| ? [U_17,U_15] :
( ( U_17 != U_15
| ~ in(U_17,U_10) )
& in(ordered_pair(U_17,U_15),U_9) ) )
& ( ( ! [U_14,U_12] :
( in(ordered_pair(U_14,U_12),U_9)
| U_14 != U_12
| ~ in(U_14,U_10) )
& ! [U_13,U_11] :
( ( U_13 = U_11
& in(U_13,U_10) )
| ~ in(ordered_pair(U_13,U_11),U_9) ) )
| U_9 != identity_relation(U_10) ) )
| ~ relation(U_9) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
! [U_10,U_9] :
( ( ( U_9 = identity_relation(U_10)
| ? [U_18,U_16] :
( ~ in(ordered_pair(U_18,U_16),U_9)
& U_18 = U_16
& in(U_18,U_10) )
| ? [U_15] :
( ( sK1(U_10,U_9) != U_15
| ~ in(sK1(U_10,U_9),U_10) )
& in(ordered_pair(sK1(U_10,U_9),U_15),U_9) ) )
& ( ( ! [U_14,U_12] :
( in(ordered_pair(U_14,U_12),U_9)
| U_14 != U_12
| ~ in(U_14,U_10) )
& ! [U_13,U_11] :
( ( U_13 = U_11
& in(U_13,U_10) )
| ~ in(ordered_pair(U_13,U_11),U_9) ) )
| U_9 != identity_relation(U_10) ) )
| ~ relation(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_17,sK1(U_10,U_9))],[f_4_3]) ).
fof(f_4_5,plain,
! [U_10,U_9] :
( ( ( U_9 = identity_relation(U_10)
| ? [U_18,U_16] :
( ~ in(ordered_pair(U_18,U_16),U_9)
& U_18 = U_16
& in(U_18,U_10) )
| ( ( sK1(U_10,U_9) != sK2(U_10,U_9)
| ~ in(sK1(U_10,U_9),U_10) )
& in(ordered_pair(sK1(U_10,U_9),sK2(U_10,U_9)),U_9) ) )
& ( ( ! [U_14,U_12] :
( in(ordered_pair(U_14,U_12),U_9)
| U_14 != U_12
| ~ in(U_14,U_10) )
& ! [U_13,U_11] :
( ( U_13 = U_11
& in(U_13,U_10) )
| ~ in(ordered_pair(U_13,U_11),U_9) ) )
| U_9 != identity_relation(U_10) ) )
| ~ relation(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_10,U_9))],[f_4_4]) ).
fof(f_4_6,plain,
! [U_10,U_9] :
( ( ( U_9 = identity_relation(U_10)
| ? [U_16] :
( ~ in(ordered_pair(sK3(U_10,U_9),U_16),U_9)
& sK3(U_10,U_9) = U_16
& in(sK3(U_10,U_9),U_10) )
| ( ( sK1(U_10,U_9) != sK2(U_10,U_9)
| ~ in(sK1(U_10,U_9),U_10) )
& in(ordered_pair(sK1(U_10,U_9),sK2(U_10,U_9)),U_9) ) )
& ( ( ! [U_14,U_12] :
( in(ordered_pair(U_14,U_12),U_9)
| U_14 != U_12
| ~ in(U_14,U_10) )
& ! [U_13,U_11] :
( ( U_13 = U_11
& in(U_13,U_10) )
| ~ in(ordered_pair(U_13,U_11),U_9) ) )
| U_9 != identity_relation(U_10) ) )
| ~ relation(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_18,sK3(U_10,U_9))],[f_4_5]) ).
fof(f_4_7,plain,
! [U_10,U_9] :
( ( ( U_9 = identity_relation(U_10)
| ( ~ in(ordered_pair(sK3(U_10,U_9),sK4(U_10,U_9)),U_9)
& sK3(U_10,U_9) = sK4(U_10,U_9)
& in(sK3(U_10,U_9),U_10) )
| ( ( sK1(U_10,U_9) != sK2(U_10,U_9)
| ~ in(sK1(U_10,U_9),U_10) )
& in(ordered_pair(sK1(U_10,U_9),sK2(U_10,U_9)),U_9) ) )
& ( ( ! [U_14,U_12] :
( in(ordered_pair(U_14,U_12),U_9)
| U_14 != U_12
| ~ in(U_14,U_10) )
& ! [U_13,U_11] :
( ( U_13 = U_11
& in(U_13,U_10) )
| ~ in(ordered_pair(U_13,U_11),U_9) ) )
| U_9 != identity_relation(U_10) ) )
| ~ relation(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_16,sK4(U_10,U_9))],[f_4_6]) ).
cnf(f_4_8,plain,
( in(U_13,U_10)
| ~ in(ordered_pair(U_13,U_11),U_9)
| U_9 != identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_9,plain,
( U_13 = U_11
| ~ in(ordered_pair(U_13,U_11),U_9)
| U_9 != identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_10,plain,
( in(ordered_pair(U_14,U_12),U_9)
| U_14 != U_12
| ~ in(U_14,U_10)
| U_9 != identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_11,plain,
( in(sK3(U_10,U_9),U_10)
| in(ordered_pair(sK1(U_10,U_9),sK2(U_10,U_9)),U_9)
| U_9 = identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_12,plain,
( sK3(U_10,U_9) = sK4(U_10,U_9)
| in(ordered_pair(sK1(U_10,U_9),sK2(U_10,U_9)),U_9)
| U_9 = identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_13,plain,
( ~ in(ordered_pair(sK3(U_10,U_9),sK4(U_10,U_9)),U_9)
| in(ordered_pair(sK1(U_10,U_9),sK2(U_10,U_9)),U_9)
| U_9 = identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_14,plain,
( in(sK3(U_10,U_9),U_10)
| sK1(U_10,U_9) != sK2(U_10,U_9)
| ~ in(sK1(U_10,U_9),U_10)
| U_9 = identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_15,plain,
( sK3(U_10,U_9) = sK4(U_10,U_9)
| sK1(U_10,U_9) != sK2(U_10,U_9)
| ~ in(sK1(U_10,U_9),U_10)
| U_9 = identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_16,plain,
( ~ in(ordered_pair(sK3(U_10,U_9),sK4(U_10,U_9)),U_9)
| sK1(U_10,U_9) != sK2(U_10,U_9)
| ~ in(sK1(U_10,U_9),U_10)
| U_9 = identity_relation(U_10)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_4_7]) ).
fof(f_5_1,plain,
! [A] :
( ! [B] :
( ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(C,D),A) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_1]) ).
fof(f_5_2,plain,
! [U_26] :
( ! [U_25] :
( ( U_25 = relation_dom(U_26)
| ? [U_24] :
( ( ~ in(U_24,U_25)
& ? [U_23] : in(ordered_pair(U_24,U_23),U_26) )
| ( ! [U_22] : ~ in(ordered_pair(U_24,U_22),U_26)
& in(U_24,U_25) ) ) )
& ( ! [U_21] :
( ( in(U_21,U_25)
| ! [U_20] : ~ in(ordered_pair(U_21,U_20),U_26) )
& ( ? [U_19] : in(ordered_pair(U_21,U_19),U_26)
| ~ in(U_21,U_25) ) )
| U_25 != relation_dom(U_26) ) )
| ~ relation(U_26) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_dom(U_26)
| ? [U_30] :
( ~ in(U_30,U_32)
& ? [U_23] : in(ordered_pair(U_30,U_23),U_26) )
| ? [U_29] :
( ! [U_22] : ~ in(ordered_pair(U_29,U_22),U_26)
& in(U_29,U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_28,U_20),U_26) )
& ! [U_27] :
( ? [U_19] : in(ordered_pair(U_27,U_19),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_dom(U_26) ) )
| ~ relation(U_26) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_dom(U_26)
| ? [U_30] :
( ~ in(U_30,U_32)
& ? [U_23] : in(ordered_pair(U_30,U_23),U_26) )
| ? [U_29] :
( ! [U_22] : ~ in(ordered_pair(U_29,U_22),U_26)
& in(U_29,U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_28,U_20),U_26) )
& ! [U_27] :
( in(ordered_pair(U_27,sK5(U_26,U_31,U_27)),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_dom(U_26) ) )
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_19,sK5(U_26,U_31,U_27))],[f_5_3]) ).
fof(f_5_5,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_dom(U_26)
| ? [U_30] :
( ~ in(U_30,U_32)
& ? [U_23] : in(ordered_pair(U_30,U_23),U_26) )
| ( ! [U_22] : ~ in(ordered_pair(sK6(U_26,U_32),U_22),U_26)
& in(sK6(U_26,U_32),U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_28,U_20),U_26) )
& ! [U_27] :
( in(ordered_pair(U_27,sK5(U_26,U_31,U_27)),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_dom(U_26) ) )
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_29,sK6(U_26,U_32))],[f_5_4]) ).
fof(f_5_6,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_dom(U_26)
| ( ~ in(sK7(U_26,U_32),U_32)
& ? [U_23] : in(ordered_pair(sK7(U_26,U_32),U_23),U_26) )
| ( ! [U_22] : ~ in(ordered_pair(sK6(U_26,U_32),U_22),U_26)
& in(sK6(U_26,U_32),U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_28,U_20),U_26) )
& ! [U_27] :
( in(ordered_pair(U_27,sK5(U_26,U_31,U_27)),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_dom(U_26) ) )
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_30,sK7(U_26,U_32))],[f_5_5]) ).
fof(f_5_7,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_dom(U_26)
| ( ~ in(sK7(U_26,U_32),U_32)
& in(ordered_pair(sK7(U_26,U_32),sK8(U_26,U_32)),U_26) )
| ( ! [U_22] : ~ in(ordered_pair(sK6(U_26,U_32),U_22),U_26)
& in(sK6(U_26,U_32),U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_28,U_20),U_26) )
& ! [U_27] :
( in(ordered_pair(U_27,sK5(U_26,U_31,U_27)),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_dom(U_26) ) )
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_23,sK8(U_26,U_32))],[f_5_6]) ).
cnf(f_5_8,plain,
( in(ordered_pair(U_27,sK5(U_26,U_31,U_27)),U_26)
| ~ in(U_27,U_31)
| U_31 != relation_dom(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,plain,
( in(U_28,U_31)
| ~ in(ordered_pair(U_28,U_20),U_26)
| U_31 != relation_dom(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_10,plain,
( in(ordered_pair(sK7(U_26,U_32),sK8(U_26,U_32)),U_26)
| in(sK6(U_26,U_32),U_32)
| U_32 = relation_dom(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_11,plain,
( ~ in(sK7(U_26,U_32),U_32)
| in(sK6(U_26,U_32),U_32)
| U_32 = relation_dom(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_12,plain,
( in(ordered_pair(sK7(U_26,U_32),sK8(U_26,U_32)),U_26)
| ~ in(ordered_pair(sK6(U_26,U_32),U_22),U_26)
| U_32 = relation_dom(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_13,plain,
( ~ in(sK7(U_26,U_32),U_32)
| ~ in(ordered_pair(sK6(U_26,U_32),U_22),U_26)
| U_32 = relation_dom(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
fof(f_6_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(D,C),A) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_relat_1]) ).
fof(f_6_2,plain,
! [U_40] :
( ! [U_39] :
( ( U_39 = relation_rng(U_40)
| ? [U_38] :
( ( ~ in(U_38,U_39)
& ? [U_37] : in(ordered_pair(U_37,U_38),U_40) )
| ( ! [U_36] : ~ in(ordered_pair(U_36,U_38),U_40)
& in(U_38,U_39) ) ) )
& ( ! [U_35] :
( ( in(U_35,U_39)
| ! [U_34] : ~ in(ordered_pair(U_34,U_35),U_40) )
& ( ? [U_33] : in(ordered_pair(U_33,U_35),U_40)
| ~ in(U_35,U_39) ) )
| U_39 != relation_rng(U_40) ) )
| ~ relation(U_40) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_40] :
( ( ! [U_46] :
( U_46 = relation_rng(U_40)
| ? [U_44] :
( ~ in(U_44,U_46)
& ? [U_37] : in(ordered_pair(U_37,U_44),U_40) )
| ? [U_43] :
( ! [U_36] : ~ in(ordered_pair(U_36,U_43),U_40)
& in(U_43,U_46) ) )
& ! [U_45] :
( ( ! [U_42] :
( in(U_42,U_45)
| ! [U_34] : ~ in(ordered_pair(U_34,U_42),U_40) )
& ! [U_41] :
( ? [U_33] : in(ordered_pair(U_33,U_41),U_40)
| ~ in(U_41,U_45) ) )
| U_45 != relation_rng(U_40) ) )
| ~ relation(U_40) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_40] :
( ( ! [U_46] :
( U_46 = relation_rng(U_40)
| ? [U_44] :
( ~ in(U_44,U_46)
& ? [U_37] : in(ordered_pair(U_37,U_44),U_40) )
| ? [U_43] :
( ! [U_36] : ~ in(ordered_pair(U_36,U_43),U_40)
& in(U_43,U_46) ) )
& ! [U_45] :
( ( ! [U_42] :
( in(U_42,U_45)
| ! [U_34] : ~ in(ordered_pair(U_34,U_42),U_40) )
& ! [U_41] :
( in(ordered_pair(sK9(U_40,U_45,U_41),U_41),U_40)
| ~ in(U_41,U_45) ) )
| U_45 != relation_rng(U_40) ) )
| ~ relation(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_33,sK9(U_40,U_45,U_41))],[f_6_3]) ).
fof(f_6_5,plain,
! [U_40] :
( ( ! [U_46] :
( U_46 = relation_rng(U_40)
| ? [U_44] :
( ~ in(U_44,U_46)
& ? [U_37] : in(ordered_pair(U_37,U_44),U_40) )
| ( ! [U_36] : ~ in(ordered_pair(U_36,sK10(U_40,U_46)),U_40)
& in(sK10(U_40,U_46),U_46) ) )
& ! [U_45] :
( ( ! [U_42] :
( in(U_42,U_45)
| ! [U_34] : ~ in(ordered_pair(U_34,U_42),U_40) )
& ! [U_41] :
( in(ordered_pair(sK9(U_40,U_45,U_41),U_41),U_40)
| ~ in(U_41,U_45) ) )
| U_45 != relation_rng(U_40) ) )
| ~ relation(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_43,sK10(U_40,U_46))],[f_6_4]) ).
fof(f_6_6,plain,
! [U_40] :
( ( ! [U_46] :
( U_46 = relation_rng(U_40)
| ( ~ in(sK11(U_40,U_46),U_46)
& ? [U_37] : in(ordered_pair(U_37,sK11(U_40,U_46)),U_40) )
| ( ! [U_36] : ~ in(ordered_pair(U_36,sK10(U_40,U_46)),U_40)
& in(sK10(U_40,U_46),U_46) ) )
& ! [U_45] :
( ( ! [U_42] :
( in(U_42,U_45)
| ! [U_34] : ~ in(ordered_pair(U_34,U_42),U_40) )
& ! [U_41] :
( in(ordered_pair(sK9(U_40,U_45,U_41),U_41),U_40)
| ~ in(U_41,U_45) ) )
| U_45 != relation_rng(U_40) ) )
| ~ relation(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_44,sK11(U_40,U_46))],[f_6_5]) ).
fof(f_6_7,plain,
! [U_40] :
( ( ! [U_46] :
( U_46 = relation_rng(U_40)
| ( ~ in(sK11(U_40,U_46),U_46)
& in(ordered_pair(sK12(U_40,U_46),sK11(U_40,U_46)),U_40) )
| ( ! [U_36] : ~ in(ordered_pair(U_36,sK10(U_40,U_46)),U_40)
& in(sK10(U_40,U_46),U_46) ) )
& ! [U_45] :
( ( ! [U_42] :
( in(U_42,U_45)
| ! [U_34] : ~ in(ordered_pair(U_34,U_42),U_40) )
& ! [U_41] :
( in(ordered_pair(sK9(U_40,U_45,U_41),U_41),U_40)
| ~ in(U_41,U_45) ) )
| U_45 != relation_rng(U_40) ) )
| ~ relation(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_37,sK12(U_40,U_46))],[f_6_6]) ).
cnf(f_6_8,plain,
( in(ordered_pair(sK9(U_40,U_45,U_41),U_41),U_40)
| ~ in(U_41,U_45)
| U_45 != relation_rng(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_9,plain,
( in(U_42,U_45)
| ~ in(ordered_pair(U_34,U_42),U_40)
| U_45 != relation_rng(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_10,plain,
( in(ordered_pair(sK12(U_40,U_46),sK11(U_40,U_46)),U_40)
| in(sK10(U_40,U_46),U_46)
| U_46 = relation_rng(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_11,plain,
( ~ in(sK11(U_40,U_46),U_46)
| in(sK10(U_40,U_46),U_46)
| U_46 = relation_rng(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_12,plain,
( in(ordered_pair(sK12(U_40,U_46),sK11(U_40,U_46)),U_40)
| ~ in(ordered_pair(U_36,sK10(U_40,U_46)),U_40)
| U_46 = relation_rng(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_13,plain,
( ~ in(sK11(U_40,U_46),U_46)
| ~ in(ordered_pair(U_36,sK10(U_40,U_46)),U_40)
| U_46 = relation_rng(U_40)
| ~ relation(U_40) ),
inference(clausify,[status(thm)],[f_6_7]) ).
fof(f_7_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_7_2,plain,
! [U_48,U_47] : ordered_pair(U_48,U_47) = unordered_pair(unordered_pair(U_48,U_47),singleton(U_48)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
ordered_pair(U_48,U_47) = unordered_pair(unordered_pair(U_48,U_47),singleton(U_48)),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A] : relation(identity_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k6_relat_1]) ).
fof(f_14_2,plain,
! [U_49] : relation(identity_relation(U_49)),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
relation(identity_relation(U_49)),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_16_2,plain,
! [U_51] :
? [U_50] : element(U_50,U_51),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_51] : element(sK13(U_51),U_51),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_50,sK13(U_51))],[f_16_2]) ).
cnf(f_16_4,plain,
element(sK13(U_51),U_51),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_17_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_18_2,plain,
! [U_53,U_52] : ~ empty(ordered_pair(U_53,U_52)),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
~ empty(ordered_pair(U_53,U_52)),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_19_2,plain,
! [U_54] : ~ empty(singleton(U_54)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
~ empty(singleton(U_54)),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_20_2,plain,
! [U_56,U_55] : ~ empty(unordered_pair(U_56,U_55)),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
~ empty(unordered_pair(U_56,U_55)),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_21_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_22_2,plain,
! [U_57] :
( ~ empty(relation_dom(U_57))
| ~ relation(U_57)
| empty(U_57) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( ~ empty(relation_dom(U_57))
| ~ relation(U_57)
| empty(U_57) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_23_2,plain,
! [U_58] :
( ~ empty(relation_rng(U_58))
| ~ relation(U_58)
| empty(U_58) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( ~ empty(relation_rng(U_58))
| ~ relation(U_58)
| empty(U_58) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_24_2,plain,
! [U_59] :
( ( relation(relation_dom(U_59))
& empty(relation_dom(U_59)) )
| ~ empty(U_59) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( empty(relation_dom(U_59))
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( relation(relation_dom(U_59))
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_25_2,plain,
! [U_60] :
( ( relation(relation_rng(U_60))
& empty(relation_rng(U_60)) )
| ~ empty(U_60) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( empty(relation_rng(U_60))
| ~ empty(U_60) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( relation(relation_rng(U_60))
| ~ empty(U_60) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_26_2,plain,
? [U_61] :
( relation(U_61)
& empty(U_61) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( relation(sK14)
& empty(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_61,sK14)],[f_26_2]) ).
cnf(f_26_4,plain,
empty(sK14),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_27_2,plain,
? [U_62] : empty(U_62),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
empty(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_62,sK15)],[f_27_2]) ).
cnf(f_27_4,plain,
empty(sK15),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_28_2,plain,
? [U_63] :
( relation(U_63)
& ~ empty(U_63) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( relation(sK16)
& ~ empty(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_63,sK16)],[f_28_2]) ).
cnf(f_28_4,plain,
~ empty(sK16),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_29_2,plain,
? [U_64] : ~ empty(U_64),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
~ empty(sK17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_64,sK17)],[f_29_2]) ).
cnf(f_29_4,plain,
~ empty(sK17),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_30_2,plain,
! [U_66,U_65] :
( element(U_66,U_65)
| ~ in(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( element(U_66,U_65)
| ~ in(U_66,U_65) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_31_2,plain,
! [U_68,U_67] :
( in(U_68,U_67)
| empty(U_67)
| ~ element(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( in(U_68,U_67)
| empty(U_67)
| ~ element(U_68,U_67) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_32_2,plain,
! [U_71,U_70] :
( U_71 = U_70
| ? [U_69] :
( ( ~ in(U_69,U_71)
& in(U_69,U_70) )
| ( ~ in(U_69,U_70)
& in(U_69,U_71) ) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_71,U_70] :
( U_71 = U_70
| ? [U_73] :
( ~ in(U_73,U_71)
& in(U_73,U_70) )
| ? [U_72] :
( ~ in(U_72,U_70)
& in(U_72,U_71) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_71,U_70] :
( U_71 = U_70
| ? [U_73] :
( ~ in(U_73,U_71)
& in(U_73,U_70) )
| ( ~ in(sK18(U_71,U_70),U_70)
& in(sK18(U_71,U_70),U_71) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_72,sK18(U_71,U_70))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_71,U_70] :
( U_71 = U_70
| ( ~ in(sK19(U_71,U_70),U_71)
& in(sK19(U_71,U_70),U_70) )
| ( ~ in(sK18(U_71,U_70),U_70)
& in(sK18(U_71,U_70),U_71) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_73,sK19(U_71,U_70))],[f_32_4]) ).
cnf(f_32_6,plain,
( in(sK19(U_71,U_70),U_70)
| in(sK18(U_71,U_70),U_71)
| U_71 = U_70 ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_7,plain,
( ~ in(sK19(U_71,U_70),U_71)
| in(sK18(U_71,U_70),U_71)
| U_71 = U_70 ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_8,plain,
( in(sK19(U_71,U_70),U_70)
| ~ in(sK18(U_71,U_70),U_70)
| U_71 = U_70 ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_9,plain,
( ~ in(sK19(U_71,U_70),U_71)
| ~ in(sK18(U_71,U_70),U_70)
| U_71 = U_70 ),
inference(clausify,[status(thm)],[f_32_5]) ).
fof(f_33_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_33_2,plain,
! [U_74] :
( U_74 = empty_set
| ~ empty(U_74) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( U_74 = empty_set
| ~ empty(U_74) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,negated_conjecture,
~ ! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
inference(negate,[status(cth)],[t71_relat_1]) ).
fof(f_34_2,negated_conjecture,
? [A] :
( relation_rng(identity_relation(A)) != A
| relation_dom(identity_relation(A)) != A ),
inference(fof_nnf,[status(thm)],[f_34_1]) ).
fof(f_34_3,negated_conjecture,
? [U_75] :
( relation_rng(identity_relation(U_75)) != U_75
| relation_dom(identity_relation(U_75)) != U_75 ),
inference(variable_rename,[status(thm)],[f_34_2]) ).
fof(f_34_4,negated_conjecture,
( ? [U_77] : relation_rng(identity_relation(U_77)) != U_77
| ? [U_76] : relation_dom(identity_relation(U_76)) != U_76 ),
inference(miniscope,[status(thm)],[f_34_3]) ).
fof(f_34_5,negated_conjecture,
( ? [U_77] : relation_rng(identity_relation(U_77)) != U_77
| relation_dom(identity_relation(sK20)) != sK20 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_76,sK20)],[f_34_4]) ).
fof(f_34_6,negated_conjecture,
( relation_rng(identity_relation(sK21)) != sK21
| relation_dom(identity_relation(sK20)) != sK20 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_77,sK21)],[f_34_5]) ).
cnf(f_34_7,negated_conjecture,
( relation_rng(identity_relation(sK21)) != sK21
| relation_dom(identity_relation(sK20)) != sK20 ),
inference(clausify,[status(thm)],[f_34_6]) ).
fof(f_35_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_35_2,plain,
! [U_79,U_78] :
( ~ empty(U_78)
| ~ in(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ empty(U_78)
| ~ in(U_79,U_78) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_81,U_80] :
( ~ empty(U_80)
| U_81 = U_80
| ~ empty(U_81) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_81] :
( ! [U_80] :
( ~ empty(U_80)
| U_81 = U_80 )
| ~ empty(U_81) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_80)
| U_81 = U_80
| ~ empty(U_81) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
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,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_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(Eq_x_0) = identity_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( singleton(Eq_x_0) = singleton(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,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(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,
( 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_14,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(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,
( 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_18,axiom,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU190+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sat Sep 19 23:32:59 UTC 2026
% 0.09/5.38 % CPUTime :
% 257.87/263.18 % SZS status Theorem for theBenchmark
% 257.87/263.18 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------