%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU225+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 : n019.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 08:58:35 AM UTC 2026
% Result : Theorem 13.23s 29.16s
% Output : Proof 13.85s
% 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(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_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(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_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_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
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_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
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_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(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc13_relat_1,axiom,
! [A,B] :
( ( relation_empty_yielding(A)
& relation(A) )
=> ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc13_relat_1) ).
fof(fc1_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_intersection2(A,B)) ),
file('theBenchmark.p',fc1_relat_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_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(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(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(l82_funct_1,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',l82_funct_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_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_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
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(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
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(t68_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t72_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t72_funct_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] :
( 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] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_3)
| ~ empty(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_4] :
( ( one_to_one(U_4)
& function(U_4)
& relation(U_4) )
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( function(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( one_to_one(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_5_2,plain,
! [U_6,U_5] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_6_2,plain,
! [U_8,U_7] : set_intersection2(U_8,U_7) = set_intersection2(U_7,U_8),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
set_intersection2(U_8,U_7) = set_intersection2(U_7,U_8),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ! [B,C] :
( ( ( ( C = apply(A,B)
| C != empty_set )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_funct_1]) ).
fof(f_7_2,plain,
! [U_11] :
( ! [U_10,U_9] :
( ( ( ( U_9 = apply(U_11,U_10)
| U_9 != empty_set )
& ( U_9 = empty_set
| U_9 != apply(U_11,U_10) ) )
| in(U_10,relation_dom(U_11)) )
& ( ( ( U_9 = apply(U_11,U_10)
| ~ in(ordered_pair(U_10,U_9),U_11) )
& ( in(ordered_pair(U_10,U_9),U_11)
| U_9 != apply(U_11,U_10) ) )
| ~ in(U_10,relation_dom(U_11)) ) )
| ~ function(U_11)
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_11] :
( ( ! [U_19] :
( ( ! [U_17] :
( U_17 = apply(U_11,U_19)
| U_17 != empty_set )
& ! [U_16] :
( U_16 = empty_set
| U_16 != apply(U_11,U_19) ) )
| in(U_19,relation_dom(U_11)) )
& ! [U_18] :
( ( ! [U_15] :
( U_15 = apply(U_11,U_18)
| ~ in(ordered_pair(U_18,U_15),U_11) )
& ! [U_14] :
( in(ordered_pair(U_18,U_14),U_11)
| U_14 != apply(U_11,U_18) ) )
| ~ in(U_18,relation_dom(U_11)) ) )
| ~ function(U_11)
| ~ relation(U_11) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( in(ordered_pair(U_18,U_14),U_11)
| U_14 != apply(U_11,U_18)
| ~ in(U_18,relation_dom(U_11))
| ~ function(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( U_15 = apply(U_11,U_18)
| ~ in(ordered_pair(U_18,U_15),U_11)
| ~ in(U_18,relation_dom(U_11))
| ~ function(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( U_16 = empty_set
| U_16 != apply(U_11,U_19)
| in(U_19,relation_dom(U_11))
| ~ function(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( U_17 = apply(U_11,U_19)
| U_17 != empty_set
| in(U_19,relation_dom(U_11))
| ~ function(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_2,plain,
! [U_21,U_20] : ordered_pair(U_21,U_20) = unordered_pair(unordered_pair(U_21,U_20),singleton(U_21)),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
ordered_pair(U_21,U_20) = unordered_pair(unordered_pair(U_21,U_20),singleton(U_21)),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
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_relat_1]) ).
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_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,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_16_2,plain,
! [U_23,U_22] :
( relation(relation_dom_restriction(U_23,U_22))
| ~ relation(U_23) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_23] :
( ! [U_22] : relation(relation_dom_restriction(U_23,U_22))
| ~ relation(U_23) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( relation(relation_dom_restriction(U_23,U_22))
| ~ relation(U_23) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_18_2,plain,
! [U_25] :
? [U_24] : element(U_24,U_25),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_25] : element(sK1(U_25),U_25),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_24,sK1(U_25))],[f_18_2]) ).
cnf(f_18_4,plain,
element(sK1(U_25),U_25),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_19_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
! [A,B] :
( ( relation_empty_yielding(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ relation_empty_yielding(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc13_relat_1]) ).
fof(f_20_2,plain,
! [U_27,U_26] :
( ( relation_empty_yielding(relation_dom_restriction(U_27,U_26))
& relation(relation_dom_restriction(U_27,U_26)) )
| ~ relation_empty_yielding(U_27)
| ~ relation(U_27) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_27] :
( ( ! [U_29] : relation_empty_yielding(relation_dom_restriction(U_27,U_29))
& ! [U_28] : relation(relation_dom_restriction(U_27,U_28)) )
| ~ relation_empty_yielding(U_27)
| ~ relation(U_27) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( relation(relation_dom_restriction(U_27,U_28))
| ~ relation_empty_yielding(U_27)
| ~ relation(U_27) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( relation_empty_yielding(relation_dom_restriction(U_27,U_29))
| ~ relation_empty_yielding(U_27)
| ~ relation(U_27) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_21_2,plain,
! [U_31,U_30] :
( relation(set_intersection2(U_31,U_30))
| ~ relation(U_30)
| ~ relation(U_31) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( relation(set_intersection2(U_31,U_30))
| ~ relation(U_30)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
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_33,U_32] : ~ empty(ordered_pair(U_33,U_32)),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
~ empty(ordered_pair(U_33,U_32)),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_24_2,plain,
! [U_34] : ~ empty(singleton(U_34)),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
~ empty(singleton(U_34)),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_25_2,plain,
! [U_36,U_35] : ~ empty(unordered_pair(U_36,U_35)),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
~ empty(unordered_pair(U_36,U_35)),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_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_26_2,plain,
! [U_38,U_37] :
( ( function(relation_dom_restriction(U_38,U_37))
& relation(relation_dom_restriction(U_38,U_37)) )
| ~ function(U_38)
| ~ relation(U_38) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_38] :
( ( ! [U_40] : function(relation_dom_restriction(U_38,U_40))
& ! [U_39] : relation(relation_dom_restriction(U_38,U_39)) )
| ~ function(U_38)
| ~ relation(U_38) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( relation(relation_dom_restriction(U_38,U_39))
| ~ function(U_38)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( function(relation_dom_restriction(U_38,U_40))
| ~ function(U_38)
| ~ relation(U_38) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_27_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_28_2,plain,
! [U_41] :
( ~ empty(relation_dom(U_41))
| ~ relation(U_41)
| empty(U_41) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( ~ empty(relation_dom(U_41))
| ~ relation(U_41)
| empty(U_41) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_29_2,plain,
! [U_42] :
( ( relation(relation_dom(U_42))
& empty(relation_dom(U_42)) )
| ~ empty(U_42) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( empty(relation_dom(U_42))
| ~ empty(U_42) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( relation(relation_dom(U_42))
| ~ empty(U_42) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_30_2,plain,
! [U_44,U_43] : set_intersection2(U_44,U_44) = U_44,
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_44] : set_intersection2(U_44,U_44) = U_44,
inference(miniscope,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
set_intersection2(U_44,U_44) = U_44,
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B,C] :
( ( ( in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ in(B,A)
| ~ in(B,relation_dom(C)) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[l82_funct_1]) ).
fof(f_31_2,plain,
! [U_47,U_46,U_45] :
( ( ( in(U_46,relation_dom(relation_dom_restriction(U_45,U_47)))
| ~ in(U_46,U_47)
| ~ in(U_46,relation_dom(U_45)) )
& ( ( in(U_46,U_47)
& in(U_46,relation_dom(U_45)) )
| ~ in(U_46,relation_dom(relation_dom_restriction(U_45,U_47))) ) )
| ~ function(U_45)
| ~ relation(U_45) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( in(U_46,relation_dom(U_45))
| ~ in(U_46,relation_dom(relation_dom_restriction(U_45,U_47)))
| ~ function(U_45)
| ~ relation(U_45) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( in(U_46,U_47)
| ~ in(U_46,relation_dom(relation_dom_restriction(U_45,U_47)))
| ~ function(U_45)
| ~ relation(U_45) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_5,plain,
( in(U_46,relation_dom(relation_dom_restriction(U_45,U_47)))
| ~ in(U_46,U_47)
| ~ in(U_46,relation_dom(U_45))
| ~ function(U_45)
| ~ relation(U_45) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_32_2,plain,
? [U_48] :
( function(U_48)
& relation(U_48) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_48,sK2)],[f_32_2]) ).
cnf(f_32_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_33_2,plain,
? [U_49] :
( relation(U_49)
& empty(U_49) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_49,sK3)],[f_33_2]) ).
cnf(f_33_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_34_2,plain,
? [U_50] : empty(U_50),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_50,sK4)],[f_34_2]) ).
cnf(f_34_4,plain,
empty(sK4),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_35_2,plain,
? [U_51] :
( function(U_51)
& empty(U_51)
& relation(U_51) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( function(sK5)
& empty(sK5)
& relation(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_51,sK5)],[f_35_2]) ).
cnf(f_35_4,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
function(sK5),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_36_2,plain,
? [U_52] :
( relation(U_52)
& ~ empty(U_52) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_52,sK6)],[f_36_2]) ).
cnf(f_36_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_37_2,plain,
? [U_53] : ~ empty(U_53),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_53,sK7)],[f_37_2]) ).
cnf(f_37_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_38_2,plain,
? [U_54] :
( one_to_one(U_54)
& function(U_54)
& relation(U_54) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( one_to_one(sK8)
& function(sK8)
& relation(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_54,sK8)],[f_38_2]) ).
cnf(f_38_4,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
function(sK8),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
one_to_one(sK8),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_39_2,plain,
? [U_55] :
( relation_empty_yielding(U_55)
& relation(U_55) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( relation_empty_yielding(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_55,sK9)],[f_39_2]) ).
cnf(f_39_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
relation_empty_yielding(sK9),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_40_2,plain,
! [U_57,U_56] :
( element(U_57,U_56)
| ~ in(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( element(U_57,U_56)
| ~ in(U_57,U_56) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_41_2,plain,
! [U_58] : set_intersection2(U_58,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
set_intersection2(U_58,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_42_2,plain,
! [U_60,U_59] :
( in(U_60,U_59)
| empty(U_59)
| ~ element(U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( in(U_60,U_59)
| empty(U_59)
| ~ element(U_60,U_59) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B] :
( ! [C] :
( ( ( B = relation_dom_restriction(C,A)
| ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t68_funct_1]) ).
fof(f_43_2,plain,
! [U_65,U_64] :
( ! [U_63] :
( ( ( U_64 = relation_dom_restriction(U_63,U_65)
| ? [U_62] :
( apply(U_64,U_62) != apply(U_63,U_62)
& in(U_62,relation_dom(U_64)) )
| relation_dom(U_64) != set_intersection2(relation_dom(U_63),U_65) )
& ( ( ! [U_61] :
( apply(U_64,U_61) = apply(U_63,U_61)
| ~ in(U_61,relation_dom(U_64)) )
& relation_dom(U_64) = set_intersection2(relation_dom(U_63),U_65) )
| U_64 != relation_dom_restriction(U_63,U_65) ) )
| ~ function(U_63)
| ~ relation(U_63) )
| ~ function(U_64)
| ~ relation(U_64) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_65,U_64] :
( ! [U_63] :
( ( ( U_64 = relation_dom_restriction(U_63,U_65)
| ( apply(U_64,sK10(U_65,U_64,U_63)) != apply(U_63,sK10(U_65,U_64,U_63))
& in(sK10(U_65,U_64,U_63),relation_dom(U_64)) )
| relation_dom(U_64) != set_intersection2(relation_dom(U_63),U_65) )
& ( ( ! [U_61] :
( apply(U_64,U_61) = apply(U_63,U_61)
| ~ in(U_61,relation_dom(U_64)) )
& relation_dom(U_64) = set_intersection2(relation_dom(U_63),U_65) )
| U_64 != relation_dom_restriction(U_63,U_65) ) )
| ~ function(U_63)
| ~ relation(U_63) )
| ~ function(U_64)
| ~ relation(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_62,sK10(U_65,U_64,U_63))],[f_43_2]) ).
cnf(f_43_4,plain,
( relation_dom(U_64) = set_intersection2(relation_dom(U_63),U_65)
| U_64 != relation_dom_restriction(U_63,U_65)
| ~ function(U_63)
| ~ relation(U_63)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
( apply(U_64,U_61) = apply(U_63,U_61)
| ~ in(U_61,relation_dom(U_64))
| U_64 != relation_dom_restriction(U_63,U_65)
| ~ function(U_63)
| ~ relation(U_63)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_6,plain,
( in(sK10(U_65,U_64,U_63),relation_dom(U_64))
| relation_dom(U_64) != set_intersection2(relation_dom(U_63),U_65)
| U_64 = relation_dom_restriction(U_63,U_65)
| ~ function(U_63)
| ~ relation(U_63)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_7,plain,
( apply(U_64,sK10(U_65,U_64,U_63)) != apply(U_63,sK10(U_65,U_64,U_63))
| relation_dom(U_64) != set_intersection2(relation_dom(U_63),U_65)
| U_64 = relation_dom_restriction(U_63,U_65)
| ~ function(U_63)
| ~ relation(U_63)
| ~ function(U_64)
| ~ relation(U_64) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_44_2,plain,
! [U_66] :
( U_66 = empty_set
| ~ empty(U_66) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( U_66 = empty_set
| ~ empty(U_66) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negate,[status(cth)],[t72_funct_1]) ).
fof(f_45_2,negated_conjecture,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,A)
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_45_1]) ).
fof(f_45_3,negated_conjecture,
? [U_69,U_68,U_67] :
( apply(relation_dom_restriction(U_67,U_69),U_68) != apply(U_67,U_68)
& in(U_68,U_69)
& function(U_67)
& relation(U_67) ),
inference(variable_rename,[status(thm)],[f_45_2]) ).
fof(f_45_4,negated_conjecture,
? [U_68,U_67] :
( apply(relation_dom_restriction(U_67,sK11),U_68) != apply(U_67,U_68)
& in(U_68,sK11)
& function(U_67)
& relation(U_67) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_69,sK11)],[f_45_3]) ).
fof(f_45_5,negated_conjecture,
? [U_67] :
( apply(relation_dom_restriction(U_67,sK11),sK12) != apply(U_67,sK12)
& in(sK12,sK11)
& function(U_67)
& relation(U_67) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_68,sK12)],[f_45_4]) ).
fof(f_45_6,negated_conjecture,
( apply(relation_dom_restriction(sK13,sK11),sK12) != apply(sK13,sK12)
& in(sK12,sK11)
& function(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_67,sK13)],[f_45_5]) ).
fof(f_45_7,negated_conjecture,
( apply(relation_dom_restriction(sK13,sK11),sK12) != apply(sK13,sK12)
& in(sK12,sK11)
& function(sK13)
& relation(sK13) ),
inference(definitional_conversion,[status(esa)],[f_45_6]) ).
cnf(f_45_8,negated_conjecture,
relation(sK13),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_9,negated_conjecture,
function(sK13),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_10,negated_conjecture,
in(sK12,sK11),
inference(clausify,[status(thm)],[f_45_7]) ).
cnf(f_45_11,negated_conjecture,
apply(relation_dom_restriction(sK13,sK11),sK12) != apply(sK13,sK12),
inference(clausify,[status(thm)],[f_45_7]) ).
fof(f_46_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_46_2,plain,
! [U_71,U_70] :
( ~ empty(U_70)
| ~ in(U_71,U_70) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( ~ empty(U_70)
| ~ in(U_71,U_70) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_47_2,plain,
! [U_73,U_72] :
( ~ empty(U_72)
| U_73 = U_72
| ~ empty(U_73) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_73] :
( ! [U_72] :
( ~ empty(U_72)
| U_73 = U_72 )
| ~ empty(U_73) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
( ~ empty(U_72)
| U_73 = U_72
| ~ empty(U_73) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
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_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_2]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_17_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_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(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( apply(Eq_x_0,Eq_x_1) = apply(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,
( 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_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_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_11,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(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,
( 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_14,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,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_18,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(equality_19,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(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
% 0.00/0.03 % Problem : SEU225+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
% 0.10/16.02 % Computer : n019.cluster.edu
% 0.10/16.02 % Model : x86_64 x86_64
% 0.10/16.02 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/16.02 % Memory : 8046.5625MB
% 0.10/16.02 % OS : Linux 6.8.0-71-generic
% 0.10/16.02 % CPULimit : 300
% 0.10/16.02 % WCLimit : 300
% 0.10/16.02 % DateTime : Sat Sep 19 23:35:22 UTC 2026
% 0.10/16.02 % CPUTime :
% 13.23/29.16 % SZS status Theorem for theBenchmark
% 13.23/29.16 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------