%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU246+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 : n015.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 08:58:41 AM UTC 2026
% Result : Theorem 263.93s 264.40s
% Output : Proof 264.67s
% 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_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d11_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('theBenchmark.p',d11_relat_1) ).
fof(d12_relat_1,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('theBenchmark.p',d12_relat_1) ).
fof(d2_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d2_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(d6_wellord1,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('theBenchmark.p',d6_wellord1) ).
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_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('theBenchmark.p',dt_k2_wellord1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(dt_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_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(fc4_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
fof(fc5_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('theBenchmark.p',fc5_funct_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(t106_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t16_wellord1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t17_wellord1,conjecture,
! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
file('theBenchmark.p',t17_wellord1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
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] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( one_to_one(U_3)
& function(U_3)
& relation(U_3) )
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( function(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_5,plain,
( one_to_one(U_3)
| ~ function(U_3)
| ~ empty(U_3)
| ~ relation(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_4_2,plain,
! [U_5,U_4] : unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_5_2,plain,
! [U_7,U_6] : set_intersection2(U_7,U_6) = set_intersection2(U_6,U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_intersection2(U_7,U_6) = set_intersection2(U_6,U_7),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = relation_dom_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),A)
& in(D,B) )
| ( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),A)
| ~ in(D,B) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d11_relat_1]) ).
fof(f_6_2,plain,
! [U_14] :
( ! [U_13,U_12] :
( ( ( U_12 = relation_dom_restriction(U_14,U_13)
| ? [U_11,U_10] :
( ( ~ in(ordered_pair(U_11,U_10),U_12)
& in(ordered_pair(U_11,U_10),U_14)
& in(U_11,U_13) )
| ( ( ~ in(ordered_pair(U_11,U_10),U_14)
| ~ in(U_11,U_13) )
& in(ordered_pair(U_11,U_10),U_12) ) ) )
& ( ! [U_9,U_8] :
( ( in(ordered_pair(U_9,U_8),U_12)
| ~ in(ordered_pair(U_9,U_8),U_14)
| ~ in(U_9,U_13) )
& ( ( in(ordered_pair(U_9,U_8),U_14)
& in(U_9,U_13) )
| ~ in(ordered_pair(U_9,U_8),U_12) ) )
| U_12 != relation_dom_restriction(U_14,U_13) ) )
| ~ relation(U_12) )
| ~ relation(U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_14] :
( ! [U_13,U_12] :
( ( ( U_12 = relation_dom_restriction(U_14,U_13)
| ? [U_22,U_20] :
( ~ in(ordered_pair(U_22,U_20),U_12)
& in(ordered_pair(U_22,U_20),U_14)
& in(U_22,U_13) )
| ? [U_21,U_19] :
( ( ~ in(ordered_pair(U_21,U_19),U_14)
| ~ in(U_21,U_13) )
& in(ordered_pair(U_21,U_19),U_12) ) )
& ( ( ! [U_18,U_16] :
( in(ordered_pair(U_18,U_16),U_12)
| ~ in(ordered_pair(U_18,U_16),U_14)
| ~ in(U_18,U_13) )
& ! [U_17,U_15] :
( ( in(ordered_pair(U_17,U_15),U_14)
& in(U_17,U_13) )
| ~ in(ordered_pair(U_17,U_15),U_12) ) )
| U_12 != relation_dom_restriction(U_14,U_13) ) )
| ~ relation(U_12) )
| ~ relation(U_14) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_14] :
( ! [U_13,U_12] :
( ( ( U_12 = relation_dom_restriction(U_14,U_13)
| ? [U_22,U_20] :
( ~ in(ordered_pair(U_22,U_20),U_12)
& in(ordered_pair(U_22,U_20),U_14)
& in(U_22,U_13) )
| ? [U_19] :
( ( ~ in(ordered_pair(sK1(U_14,U_13,U_12),U_19),U_14)
| ~ in(sK1(U_14,U_13,U_12),U_13) )
& in(ordered_pair(sK1(U_14,U_13,U_12),U_19),U_12) ) )
& ( ( ! [U_18,U_16] :
( in(ordered_pair(U_18,U_16),U_12)
| ~ in(ordered_pair(U_18,U_16),U_14)
| ~ in(U_18,U_13) )
& ! [U_17,U_15] :
( ( in(ordered_pair(U_17,U_15),U_14)
& in(U_17,U_13) )
| ~ in(ordered_pair(U_17,U_15),U_12) ) )
| U_12 != relation_dom_restriction(U_14,U_13) ) )
| ~ relation(U_12) )
| ~ relation(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_21,sK1(U_14,U_13,U_12))],[f_6_3]) ).
fof(f_6_5,plain,
! [U_14] :
( ! [U_13,U_12] :
( ( ( U_12 = relation_dom_restriction(U_14,U_13)
| ? [U_22,U_20] :
( ~ in(ordered_pair(U_22,U_20),U_12)
& in(ordered_pair(U_22,U_20),U_14)
& in(U_22,U_13) )
| ( ( ~ in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_14)
| ~ in(sK1(U_14,U_13,U_12),U_13) )
& in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_12) ) )
& ( ( ! [U_18,U_16] :
( in(ordered_pair(U_18,U_16),U_12)
| ~ in(ordered_pair(U_18,U_16),U_14)
| ~ in(U_18,U_13) )
& ! [U_17,U_15] :
( ( in(ordered_pair(U_17,U_15),U_14)
& in(U_17,U_13) )
| ~ in(ordered_pair(U_17,U_15),U_12) ) )
| U_12 != relation_dom_restriction(U_14,U_13) ) )
| ~ relation(U_12) )
| ~ relation(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_19,sK2(U_14,U_13,U_12))],[f_6_4]) ).
fof(f_6_6,plain,
! [U_14] :
( ! [U_13,U_12] :
( ( ( U_12 = relation_dom_restriction(U_14,U_13)
| ? [U_20] :
( ~ in(ordered_pair(sK3(U_14,U_13,U_12),U_20),U_12)
& in(ordered_pair(sK3(U_14,U_13,U_12),U_20),U_14)
& in(sK3(U_14,U_13,U_12),U_13) )
| ( ( ~ in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_14)
| ~ in(sK1(U_14,U_13,U_12),U_13) )
& in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_12) ) )
& ( ( ! [U_18,U_16] :
( in(ordered_pair(U_18,U_16),U_12)
| ~ in(ordered_pair(U_18,U_16),U_14)
| ~ in(U_18,U_13) )
& ! [U_17,U_15] :
( ( in(ordered_pair(U_17,U_15),U_14)
& in(U_17,U_13) )
| ~ in(ordered_pair(U_17,U_15),U_12) ) )
| U_12 != relation_dom_restriction(U_14,U_13) ) )
| ~ relation(U_12) )
| ~ relation(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3(U_14,U_13,U_12))],[f_6_5]) ).
fof(f_6_7,plain,
! [U_14] :
( ! [U_13,U_12] :
( ( ( U_12 = relation_dom_restriction(U_14,U_13)
| ( ~ in(ordered_pair(sK3(U_14,U_13,U_12),sK4(U_14,U_13,U_12)),U_12)
& in(ordered_pair(sK3(U_14,U_13,U_12),sK4(U_14,U_13,U_12)),U_14)
& in(sK3(U_14,U_13,U_12),U_13) )
| ( ( ~ in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_14)
| ~ in(sK1(U_14,U_13,U_12),U_13) )
& in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_12) ) )
& ( ( ! [U_18,U_16] :
( in(ordered_pair(U_18,U_16),U_12)
| ~ in(ordered_pair(U_18,U_16),U_14)
| ~ in(U_18,U_13) )
& ! [U_17,U_15] :
( ( in(ordered_pair(U_17,U_15),U_14)
& in(U_17,U_13) )
| ~ in(ordered_pair(U_17,U_15),U_12) ) )
| U_12 != relation_dom_restriction(U_14,U_13) ) )
| ~ relation(U_12) )
| ~ relation(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4(U_14,U_13,U_12))],[f_6_6]) ).
cnf(f_6_8,plain,
( in(U_17,U_13)
| ~ in(ordered_pair(U_17,U_15),U_12)
| U_12 != relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_9,plain,
( in(ordered_pair(U_17,U_15),U_14)
| ~ in(ordered_pair(U_17,U_15),U_12)
| U_12 != relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_10,plain,
( in(ordered_pair(U_18,U_16),U_12)
| ~ in(ordered_pair(U_18,U_16),U_14)
| ~ in(U_18,U_13)
| U_12 != relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_11,plain,
( in(sK3(U_14,U_13,U_12),U_13)
| in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_12)
| U_12 = relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_12,plain,
( in(ordered_pair(sK3(U_14,U_13,U_12),sK4(U_14,U_13,U_12)),U_14)
| in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_12)
| U_12 = relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_13,plain,
( ~ in(ordered_pair(sK3(U_14,U_13,U_12),sK4(U_14,U_13,U_12)),U_12)
| in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_12)
| U_12 = relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_14,plain,
( in(sK3(U_14,U_13,U_12),U_13)
| ~ in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_14)
| ~ in(sK1(U_14,U_13,U_12),U_13)
| U_12 = relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_15,plain,
( in(ordered_pair(sK3(U_14,U_13,U_12),sK4(U_14,U_13,U_12)),U_14)
| ~ in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_14)
| ~ in(sK1(U_14,U_13,U_12),U_13)
| U_12 = relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_16,plain,
( ~ in(ordered_pair(sK3(U_14,U_13,U_12),sK4(U_14,U_13,U_12)),U_12)
| ~ in(ordered_pair(sK1(U_14,U_13,U_12),sK2(U_14,U_13,U_12)),U_14)
| ~ in(sK1(U_14,U_13,U_12),U_13)
| U_12 = relation_dom_restriction(U_14,U_13)
| ~ relation(U_12)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_6_7]) ).
fof(f_7_1,plain,
! [A,B] :
( ! [C] :
( ( ( C = relation_rng_restriction(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
& in(ordered_pair(D,E),B)
& in(E,A) )
| ( ( ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& in(ordered_pair(D,E),C) ) ) )
& ( ! [D,E] :
( ( in(ordered_pair(D,E),C)
| ~ in(ordered_pair(D,E),B)
| ~ in(E,A) )
& ( ( in(ordered_pair(D,E),B)
& in(E,A) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_rng_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d12_relat_1]) ).
fof(f_7_2,plain,
! [U_29,U_28] :
( ! [U_27] :
( ( ( U_27 = relation_rng_restriction(U_29,U_28)
| ? [U_26,U_25] :
( ( ~ in(ordered_pair(U_26,U_25),U_27)
& in(ordered_pair(U_26,U_25),U_28)
& in(U_25,U_29) )
| ( ( ~ in(ordered_pair(U_26,U_25),U_28)
| ~ in(U_25,U_29) )
& in(ordered_pair(U_26,U_25),U_27) ) ) )
& ( ! [U_24,U_23] :
( ( in(ordered_pair(U_24,U_23),U_27)
| ~ in(ordered_pair(U_24,U_23),U_28)
| ~ in(U_23,U_29) )
& ( ( in(ordered_pair(U_24,U_23),U_28)
& in(U_23,U_29) )
| ~ in(ordered_pair(U_24,U_23),U_27) ) )
| U_27 != relation_rng_restriction(U_29,U_28) ) )
| ~ relation(U_27) )
| ~ relation(U_28) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_29,U_28] :
( ! [U_27] :
( ( ( U_27 = relation_rng_restriction(U_29,U_28)
| ? [U_37,U_35] :
( ~ in(ordered_pair(U_37,U_35),U_27)
& in(ordered_pair(U_37,U_35),U_28)
& in(U_35,U_29) )
| ? [U_36,U_34] :
( ( ~ in(ordered_pair(U_36,U_34),U_28)
| ~ in(U_34,U_29) )
& in(ordered_pair(U_36,U_34),U_27) ) )
& ( ( ! [U_33,U_31] :
( in(ordered_pair(U_33,U_31),U_27)
| ~ in(ordered_pair(U_33,U_31),U_28)
| ~ in(U_31,U_29) )
& ! [U_32,U_30] :
( ( in(ordered_pair(U_32,U_30),U_28)
& in(U_30,U_29) )
| ~ in(ordered_pair(U_32,U_30),U_27) ) )
| U_27 != relation_rng_restriction(U_29,U_28) ) )
| ~ relation(U_27) )
| ~ relation(U_28) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_29,U_28] :
( ! [U_27] :
( ( ( U_27 = relation_rng_restriction(U_29,U_28)
| ? [U_37,U_35] :
( ~ in(ordered_pair(U_37,U_35),U_27)
& in(ordered_pair(U_37,U_35),U_28)
& in(U_35,U_29) )
| ? [U_34] :
( ( ~ in(ordered_pair(sK5(U_29,U_28,U_27),U_34),U_28)
| ~ in(U_34,U_29) )
& in(ordered_pair(sK5(U_29,U_28,U_27),U_34),U_27) ) )
& ( ( ! [U_33,U_31] :
( in(ordered_pair(U_33,U_31),U_27)
| ~ in(ordered_pair(U_33,U_31),U_28)
| ~ in(U_31,U_29) )
& ! [U_32,U_30] :
( ( in(ordered_pair(U_32,U_30),U_28)
& in(U_30,U_29) )
| ~ in(ordered_pair(U_32,U_30),U_27) ) )
| U_27 != relation_rng_restriction(U_29,U_28) ) )
| ~ relation(U_27) )
| ~ relation(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_36,sK5(U_29,U_28,U_27))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_29,U_28] :
( ! [U_27] :
( ( ( U_27 = relation_rng_restriction(U_29,U_28)
| ? [U_37,U_35] :
( ~ in(ordered_pair(U_37,U_35),U_27)
& in(ordered_pair(U_37,U_35),U_28)
& in(U_35,U_29) )
| ( ( ~ in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_28)
| ~ in(sK6(U_29,U_28,U_27),U_29) )
& in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_27) ) )
& ( ( ! [U_33,U_31] :
( in(ordered_pair(U_33,U_31),U_27)
| ~ in(ordered_pair(U_33,U_31),U_28)
| ~ in(U_31,U_29) )
& ! [U_32,U_30] :
( ( in(ordered_pair(U_32,U_30),U_28)
& in(U_30,U_29) )
| ~ in(ordered_pair(U_32,U_30),U_27) ) )
| U_27 != relation_rng_restriction(U_29,U_28) ) )
| ~ relation(U_27) )
| ~ relation(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_34,sK6(U_29,U_28,U_27))],[f_7_4]) ).
fof(f_7_6,plain,
! [U_29,U_28] :
( ! [U_27] :
( ( ( U_27 = relation_rng_restriction(U_29,U_28)
| ? [U_35] :
( ~ in(ordered_pair(sK7(U_29,U_28,U_27),U_35),U_27)
& in(ordered_pair(sK7(U_29,U_28,U_27),U_35),U_28)
& in(U_35,U_29) )
| ( ( ~ in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_28)
| ~ in(sK6(U_29,U_28,U_27),U_29) )
& in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_27) ) )
& ( ( ! [U_33,U_31] :
( in(ordered_pair(U_33,U_31),U_27)
| ~ in(ordered_pair(U_33,U_31),U_28)
| ~ in(U_31,U_29) )
& ! [U_32,U_30] :
( ( in(ordered_pair(U_32,U_30),U_28)
& in(U_30,U_29) )
| ~ in(ordered_pair(U_32,U_30),U_27) ) )
| U_27 != relation_rng_restriction(U_29,U_28) ) )
| ~ relation(U_27) )
| ~ relation(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_37,sK7(U_29,U_28,U_27))],[f_7_5]) ).
fof(f_7_7,plain,
! [U_29,U_28] :
( ! [U_27] :
( ( ( U_27 = relation_rng_restriction(U_29,U_28)
| ( ~ in(ordered_pair(sK7(U_29,U_28,U_27),sK8(U_29,U_28,U_27)),U_27)
& in(ordered_pair(sK7(U_29,U_28,U_27),sK8(U_29,U_28,U_27)),U_28)
& in(sK8(U_29,U_28,U_27),U_29) )
| ( ( ~ in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_28)
| ~ in(sK6(U_29,U_28,U_27),U_29) )
& in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_27) ) )
& ( ( ! [U_33,U_31] :
( in(ordered_pair(U_33,U_31),U_27)
| ~ in(ordered_pair(U_33,U_31),U_28)
| ~ in(U_31,U_29) )
& ! [U_32,U_30] :
( ( in(ordered_pair(U_32,U_30),U_28)
& in(U_30,U_29) )
| ~ in(ordered_pair(U_32,U_30),U_27) ) )
| U_27 != relation_rng_restriction(U_29,U_28) ) )
| ~ relation(U_27) )
| ~ relation(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_35,sK8(U_29,U_28,U_27))],[f_7_6]) ).
cnf(f_7_8,plain,
( in(U_30,U_29)
| ~ in(ordered_pair(U_32,U_30),U_27)
| U_27 != relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_9,plain,
( in(ordered_pair(U_32,U_30),U_28)
| ~ in(ordered_pair(U_32,U_30),U_27)
| U_27 != relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_10,plain,
( in(ordered_pair(U_33,U_31),U_27)
| ~ in(ordered_pair(U_33,U_31),U_28)
| ~ in(U_31,U_29)
| U_27 != relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_11,plain,
( in(sK8(U_29,U_28,U_27),U_29)
| in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_27)
| U_27 = relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_12,plain,
( in(ordered_pair(sK7(U_29,U_28,U_27),sK8(U_29,U_28,U_27)),U_28)
| in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_27)
| U_27 = relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_13,plain,
( ~ in(ordered_pair(sK7(U_29,U_28,U_27),sK8(U_29,U_28,U_27)),U_27)
| in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_27)
| U_27 = relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_14,plain,
( in(sK8(U_29,U_28,U_27),U_29)
| ~ in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_28)
| ~ in(sK6(U_29,U_28,U_27),U_29)
| U_27 = relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_15,plain,
( in(ordered_pair(sK7(U_29,U_28,U_27),sK8(U_29,U_28,U_27)),U_28)
| ~ in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_28)
| ~ in(sK6(U_29,U_28,U_27),U_29)
| U_27 = relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_16,plain,
( ~ in(ordered_pair(sK7(U_29,U_28,U_27),sK8(U_29,U_28,U_27)),U_27)
| ~ in(ordered_pair(sK5(U_29,U_28,U_27),sK6(U_29,U_28,U_27)),U_28)
| ~ in(sK6(U_29,U_28,U_27),U_29)
| U_27 = relation_rng_restriction(U_29,U_28)
| ~ relation(U_27)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_7_7]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( ( ( A = B
| ? [C,D] :
( ( ~ in(ordered_pair(C,D),A)
& in(ordered_pair(C,D),B) )
| ( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) ) ) )
& ( ! [C,D] :
( ( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d2_relat_1]) ).
fof(f_8_2,plain,
! [U_43] :
( ! [U_42] :
( ( ( U_43 = U_42
| ? [U_41,U_40] :
( ( ~ in(ordered_pair(U_41,U_40),U_43)
& in(ordered_pair(U_41,U_40),U_42) )
| ( ~ in(ordered_pair(U_41,U_40),U_42)
& in(ordered_pair(U_41,U_40),U_43) ) ) )
& ( ! [U_39,U_38] :
( ( in(ordered_pair(U_39,U_38),U_43)
| ~ in(ordered_pair(U_39,U_38),U_42) )
& ( in(ordered_pair(U_39,U_38),U_42)
| ~ in(ordered_pair(U_39,U_38),U_43) ) )
| U_43 != U_42 ) )
| ~ relation(U_42) )
| ~ relation(U_43) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_43] :
( ! [U_42] :
( ( ( U_43 = U_42
| ? [U_51,U_49] :
( ~ in(ordered_pair(U_51,U_49),U_43)
& in(ordered_pair(U_51,U_49),U_42) )
| ? [U_50,U_48] :
( ~ in(ordered_pair(U_50,U_48),U_42)
& in(ordered_pair(U_50,U_48),U_43) ) )
& ( ( ! [U_47,U_45] :
( in(ordered_pair(U_47,U_45),U_43)
| ~ in(ordered_pair(U_47,U_45),U_42) )
& ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_42)
| ~ in(ordered_pair(U_46,U_44),U_43) ) )
| U_43 != U_42 ) )
| ~ relation(U_42) )
| ~ relation(U_43) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
! [U_43] :
( ! [U_42] :
( ( ( U_43 = U_42
| ? [U_51,U_49] :
( ~ in(ordered_pair(U_51,U_49),U_43)
& in(ordered_pair(U_51,U_49),U_42) )
| ? [U_48] :
( ~ in(ordered_pair(sK9(U_43,U_42),U_48),U_42)
& in(ordered_pair(sK9(U_43,U_42),U_48),U_43) ) )
& ( ( ! [U_47,U_45] :
( in(ordered_pair(U_47,U_45),U_43)
| ~ in(ordered_pair(U_47,U_45),U_42) )
& ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_42)
| ~ in(ordered_pair(U_46,U_44),U_43) ) )
| U_43 != U_42 ) )
| ~ relation(U_42) )
| ~ relation(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_50,sK9(U_43,U_42))],[f_8_3]) ).
fof(f_8_5,plain,
! [U_43] :
( ! [U_42] :
( ( ( U_43 = U_42
| ? [U_51,U_49] :
( ~ in(ordered_pair(U_51,U_49),U_43)
& in(ordered_pair(U_51,U_49),U_42) )
| ( ~ in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_42)
& in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_43) ) )
& ( ( ! [U_47,U_45] :
( in(ordered_pair(U_47,U_45),U_43)
| ~ in(ordered_pair(U_47,U_45),U_42) )
& ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_42)
| ~ in(ordered_pair(U_46,U_44),U_43) ) )
| U_43 != U_42 ) )
| ~ relation(U_42) )
| ~ relation(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_48,sK10(U_43,U_42))],[f_8_4]) ).
fof(f_8_6,plain,
! [U_43] :
( ! [U_42] :
( ( ( U_43 = U_42
| ? [U_49] :
( ~ in(ordered_pair(sK11(U_43,U_42),U_49),U_43)
& in(ordered_pair(sK11(U_43,U_42),U_49),U_42) )
| ( ~ in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_42)
& in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_43) ) )
& ( ( ! [U_47,U_45] :
( in(ordered_pair(U_47,U_45),U_43)
| ~ in(ordered_pair(U_47,U_45),U_42) )
& ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_42)
| ~ in(ordered_pair(U_46,U_44),U_43) ) )
| U_43 != U_42 ) )
| ~ relation(U_42) )
| ~ relation(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_51,sK11(U_43,U_42))],[f_8_5]) ).
fof(f_8_7,plain,
! [U_43] :
( ! [U_42] :
( ( ( U_43 = U_42
| ( ~ in(ordered_pair(sK11(U_43,U_42),sK12(U_43,U_42)),U_43)
& in(ordered_pair(sK11(U_43,U_42),sK12(U_43,U_42)),U_42) )
| ( ~ in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_42)
& in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_43) ) )
& ( ( ! [U_47,U_45] :
( in(ordered_pair(U_47,U_45),U_43)
| ~ in(ordered_pair(U_47,U_45),U_42) )
& ! [U_46,U_44] :
( in(ordered_pair(U_46,U_44),U_42)
| ~ in(ordered_pair(U_46,U_44),U_43) ) )
| U_43 != U_42 ) )
| ~ relation(U_42) )
| ~ relation(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_49,sK12(U_43,U_42))],[f_8_6]) ).
cnf(f_8_8,plain,
( in(ordered_pair(U_46,U_44),U_42)
| ~ in(ordered_pair(U_46,U_44),U_43)
| U_43 != U_42
| ~ relation(U_42)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_9,plain,
( in(ordered_pair(U_47,U_45),U_43)
| ~ in(ordered_pair(U_47,U_45),U_42)
| U_43 != U_42
| ~ relation(U_42)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_10,plain,
( in(ordered_pair(sK11(U_43,U_42),sK12(U_43,U_42)),U_42)
| in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_43)
| U_43 = U_42
| ~ relation(U_42)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_11,plain,
( ~ in(ordered_pair(sK11(U_43,U_42),sK12(U_43,U_42)),U_43)
| in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_43)
| U_43 = U_42
| ~ relation(U_42)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_12,plain,
( in(ordered_pair(sK11(U_43,U_42),sK12(U_43,U_42)),U_42)
| ~ in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_42)
| U_43 = U_42
| ~ relation(U_42)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_13,plain,
( ~ in(ordered_pair(sK11(U_43,U_42),sK12(U_43,U_42)),U_43)
| ~ in(ordered_pair(sK9(U_43,U_42),sK10(U_43,U_42)),U_42)
| U_43 = U_42
| ~ relation(U_42)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_8_7]) ).
fof(f_9_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_9_2,plain,
! [U_53,U_52] : ordered_pair(U_53,U_52) = unordered_pair(unordered_pair(U_53,U_52),singleton(U_53)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
ordered_pair(U_53,U_52) = unordered_pair(unordered_pair(U_53,U_52),singleton(U_53)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_wellord1]) ).
fof(f_10_2,plain,
! [U_55] :
( ! [U_54] : relation_restriction(U_55,U_54) = set_intersection2(U_55,cartesian_product2(U_54,U_54))
| ~ relation(U_55) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( relation_restriction(U_55,U_54) = set_intersection2(U_55,cartesian_product2(U_54,U_54))
| ~ relation(U_55) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
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_k1_xboole_0]) ).
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_k2_tarski]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_14_2,plain,
! [U_57,U_56] :
( relation(relation_restriction(U_57,U_56))
| ~ relation(U_57) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_57] :
( ! [U_56] : relation(relation_restriction(U_57,U_56))
| ~ relation(U_57) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( relation(relation_restriction(U_57,U_56))
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_18_2,plain,
! [U_59,U_58] :
( relation(relation_dom_restriction(U_59,U_58))
| ~ relation(U_59) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_59] :
( ! [U_58] : relation(relation_dom_restriction(U_59,U_58))
| ~ relation(U_59) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( relation(relation_dom_restriction(U_59,U_58))
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[dt_k8_relat_1]) ).
fof(f_19_2,plain,
! [U_61,U_60] :
( relation(relation_rng_restriction(U_61,U_60))
| ~ relation(U_60) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( relation(relation_rng_restriction(U_61,U_60))
| ~ relation(U_60) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_21_2,plain,
! [U_63] :
? [U_62] : element(U_62,U_63),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_63] : element(sK13(U_63),U_63),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_62,sK13(U_63))],[f_21_2]) ).
cnf(f_21_4,plain,
element(sK13(U_63),U_63),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_22_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_23_2,plain,
! [U_65,U_64] : ~ empty(ordered_pair(U_65,U_64)),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
~ empty(ordered_pair(U_65,U_64)),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc4_funct_1]) ).
fof(f_24_2,plain,
! [U_67,U_66] :
( ( function(relation_dom_restriction(U_67,U_66))
& relation(relation_dom_restriction(U_67,U_66)) )
| ~ function(U_67)
| ~ relation(U_67) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_67] :
( ( ! [U_69] : function(relation_dom_restriction(U_67,U_69))
& ! [U_68] : relation(relation_dom_restriction(U_67,U_68)) )
| ~ function(U_67)
| ~ relation(U_67) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( relation(relation_dom_restriction(U_67,U_68))
| ~ function(U_67)
| ~ relation(U_67) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( function(relation_dom_restriction(U_67,U_69))
| ~ function(U_67)
| ~ relation(U_67) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[fc5_funct_1]) ).
fof(f_25_2,plain,
! [U_71,U_70] :
( ( function(relation_rng_restriction(U_71,U_70))
& relation(relation_rng_restriction(U_71,U_70)) )
| ~ function(U_70)
| ~ relation(U_70) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( relation(relation_rng_restriction(U_71,U_70))
| ~ function(U_70)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( function(relation_rng_restriction(U_71,U_70))
| ~ function(U_70)
| ~ relation(U_70) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_26_2,plain,
! [U_73,U_72] : set_intersection2(U_73,U_73) = U_73,
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_73] : set_intersection2(U_73,U_73) = U_73,
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
set_intersection2(U_73,U_73) = U_73,
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_27_2,plain,
? [U_74] :
( function(U_74)
& relation(U_74) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_74,sK14)],[f_27_2]) ).
cnf(f_27_4,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
function(sK14),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_28_2,plain,
? [U_75] : empty(U_75),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
empty(sK15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_75,sK15)],[f_28_2]) ).
cnf(f_28_4,plain,
empty(sK15),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_29_2,plain,
? [U_76] :
( function(U_76)
& empty(U_76)
& relation(U_76) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( function(sK16)
& empty(sK16)
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_76,sK16)],[f_29_2]) ).
cnf(f_29_4,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
empty(sK16),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
function(sK16),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_30_2,plain,
? [U_77] : ~ empty(U_77),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
~ empty(sK17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_77,sK17)],[f_30_2]) ).
cnf(f_30_4,plain,
~ empty(sK17),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_31_2,plain,
? [U_78] :
( one_to_one(U_78)
& function(U_78)
& relation(U_78) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( one_to_one(sK18)
& function(sK18)
& relation(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_78,sK18)],[f_31_2]) ).
cnf(f_31_4,plain,
relation(sK18),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
function(sK18),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_6,plain,
one_to_one(sK18),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[t106_zfmisc_1]) ).
fof(f_32_2,plain,
! [U_82,U_81,U_80,U_79] :
( ( in(ordered_pair(U_82,U_81),cartesian_product2(U_80,U_79))
| ~ in(U_81,U_79)
| ~ in(U_82,U_80) )
& ( ( in(U_81,U_79)
& in(U_82,U_80) )
| ~ in(ordered_pair(U_82,U_81),cartesian_product2(U_80,U_79)) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_90,U_88,U_86,U_84] :
( in(ordered_pair(U_90,U_88),cartesian_product2(U_86,U_84))
| ~ in(U_88,U_84)
| ~ in(U_90,U_86) )
& ! [U_89,U_87,U_85,U_83] :
( ( in(U_87,U_83)
& in(U_89,U_85) )
| ~ in(ordered_pair(U_89,U_87),cartesian_product2(U_85,U_83)) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( in(U_89,U_85)
| ~ in(ordered_pair(U_89,U_87),cartesian_product2(U_85,U_83)) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( in(U_87,U_83)
| ~ in(ordered_pair(U_89,U_87),cartesian_product2(U_85,U_83)) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_6,plain,
( in(ordered_pair(U_90,U_88),cartesian_product2(U_86,U_84))
| ~ in(U_88,U_84)
| ~ in(U_90,U_86) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A,B,C] :
( ( ( in(A,relation_restriction(C,B))
| ~ in(A,cartesian_product2(B,B))
| ~ in(A,C) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t16_wellord1]) ).
fof(f_33_2,plain,
! [U_93,U_92,U_91] :
( ( ( in(U_93,relation_restriction(U_91,U_92))
| ~ in(U_93,cartesian_product2(U_92,U_92))
| ~ in(U_93,U_91) )
& ( ( in(U_93,cartesian_product2(U_92,U_92))
& in(U_93,U_91) )
| ~ in(U_93,relation_restriction(U_91,U_92)) ) )
| ~ relation(U_91) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( in(U_93,U_91)
| ~ in(U_93,relation_restriction(U_91,U_92))
| ~ relation(U_91) ),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( in(U_93,cartesian_product2(U_92,U_92))
| ~ in(U_93,relation_restriction(U_91,U_92))
| ~ relation(U_91) ),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_5,plain,
( in(U_93,relation_restriction(U_91,U_92))
| ~ in(U_93,cartesian_product2(U_92,U_92))
| ~ in(U_93,U_91)
| ~ relation(U_91) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> relation_restriction(B,A) = relation_dom_restriction(relation_rng_restriction(A,B),A) ),
inference(negate,[status(cth)],[t17_wellord1]) ).
fof(f_34_2,negated_conjecture,
? [A,B] :
( relation_restriction(B,A) != relation_dom_restriction(relation_rng_restriction(A,B),A)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_34_1]) ).
fof(f_34_3,negated_conjecture,
? [U_95,U_94] :
( relation_restriction(U_94,U_95) != relation_dom_restriction(relation_rng_restriction(U_95,U_94),U_95)
& relation(U_94) ),
inference(variable_rename,[status(thm)],[f_34_2]) ).
fof(f_34_4,negated_conjecture,
? [U_94] :
( relation_restriction(U_94,sK19) != relation_dom_restriction(relation_rng_restriction(sK19,U_94),sK19)
& relation(U_94) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_95,sK19)],[f_34_3]) ).
fof(f_34_5,negated_conjecture,
( relation_restriction(sK20,sK19) != relation_dom_restriction(relation_rng_restriction(sK19,sK20),sK19)
& relation(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_94,sK20)],[f_34_4]) ).
cnf(f_34_6,negated_conjecture,
relation(sK20),
inference(clausify,[status(thm)],[f_34_5]) ).
cnf(f_34_7,negated_conjecture,
relation_restriction(sK20,sK19) != relation_dom_restriction(relation_rng_restriction(sK19,sK20),sK19),
inference(clausify,[status(thm)],[f_34_5]) ).
fof(f_35_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_35_2,plain,
! [U_97,U_96] :
( element(U_97,U_96)
| ~ in(U_97,U_96) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( element(U_97,U_96)
| ~ in(U_97,U_96) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_36_2,plain,
! [U_98] : set_intersection2(U_98,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
set_intersection2(U_98,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_37_2,plain,
! [U_100,U_99] :
( in(U_100,U_99)
| empty(U_99)
| ~ element(U_100,U_99) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( in(U_100,U_99)
| empty(U_99)
| ~ element(U_100,U_99) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_38_2,plain,
! [U_101] :
( U_101 = empty_set
| ~ empty(U_101) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( U_101 = empty_set
| ~ empty(U_101) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_39_2,plain,
! [U_103,U_102] :
( ~ empty(U_102)
| ~ in(U_103,U_102) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( ~ empty(U_102)
| ~ in(U_103,U_102) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_40_2,plain,
! [U_105,U_104] :
( ~ empty(U_104)
| U_105 = U_104
| ~ empty(U_105) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_105] :
( ! [U_104] :
( ~ empty(U_104)
| U_105 = U_104 )
| ~ empty(U_105) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( ~ empty(U_104)
| U_105 = U_104
| ~ empty(U_105) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_3_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_3]) ).
cnf(f_3_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_4]) ).
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(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_2]) ).
cnf(f_17_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_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,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( relation_dom_restriction(Eq_x_0,Eq_x_1) = relation_dom_restriction(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,
( 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_8,axiom,
( relation_rng_restriction(Eq_x_0,Eq_x_1) = relation_rng_restriction(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| 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,
( relation_restriction(Eq_x_0,Eq_x_1) = relation_restriction(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,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(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,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(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_13,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(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_14,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(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,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(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_16,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_17,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(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_18,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(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,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(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_20,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(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,
( 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_22,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_23,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_24,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| 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,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,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 : SEU246+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
% 0.10/0.59 % Computer : n015.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8046.5625MB
% 0.10/0.59 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Sat Sep 19 23:42:51 UTC 2026
% 0.10/0.59 % CPUTime :
% 263.93/264.40 % SZS status Theorem for theBenchmark
% 263.93/264.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------