%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:34 AM UTC 2026
% Result : Theorem 222.26s 222.68s
% Output : Proof 224.33s
% 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_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
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_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
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(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,conjecture,
! [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(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]) ).
fof(f_1_3,plain,
! [U_0,U_1] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
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]) ).
fof(f_2_3,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
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]) ).
fof(f_3_3,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( relation(U_3)
| ~ empty(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
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]) ).
fof(f_4_3,plain,
( ! [U_4] :
( one_to_one(U_4)
| ~ sP0(U_4) )
& ! [U_4] :
( function(U_4)
| ~ sP0(U_4) )
& ! [U_4] :
( relation(U_4)
| ~ sP0(U_4) )
& ! [U_4] :
( sP0(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP0(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( relation(U_4)
| ~ sP0(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( function(U_4)
| ~ sP0(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( one_to_one(U_4)
| ~ sP0(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
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_6,U_5] : set_intersection2(U_6,U_5) = set_intersection2(U_5,U_6),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_6,U_5] : set_intersection2(U_6,U_5) = set_intersection2(U_5,U_6),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
set_intersection2(U_6,U_5) = set_intersection2(U_5,U_6),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_6_2,plain,
! [U_11,U_10,U_9] :
( ( U_9 = set_intersection2(U_11,U_10)
| ? [U_8] :
( ( ~ in(U_8,U_9)
& in(U_8,U_10)
& in(U_8,U_11) )
| ( ( ~ in(U_8,U_10)
| ~ in(U_8,U_11) )
& in(U_8,U_9) ) ) )
& ( ! [U_7] :
( ( in(U_7,U_9)
| ~ in(U_7,U_10)
| ~ in(U_7,U_11) )
& ( ( in(U_7,U_10)
& in(U_7,U_11) )
| ~ in(U_7,U_9) ) )
| U_9 != set_intersection2(U_11,U_10) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_21,U_19,U_17] :
( U_17 = set_intersection2(U_21,U_19)
| ? [U_15] :
( ~ in(U_15,U_17)
& in(U_15,U_19)
& in(U_15,U_21) )
| ? [U_14] :
( ( ~ in(U_14,U_19)
| ~ in(U_14,U_21) )
& in(U_14,U_17) ) )
& ! [U_20,U_18,U_16] :
( ( ! [U_13] :
( in(U_13,U_16)
| ~ in(U_13,U_18)
| ~ in(U_13,U_20) )
& ! [U_12] :
( ( in(U_12,U_18)
& in(U_12,U_20) )
| ~ in(U_12,U_16) ) )
| U_16 != set_intersection2(U_20,U_18) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_21,U_19,U_17] :
( U_17 = set_intersection2(U_21,U_19)
| ? [U_15] :
( ~ in(U_15,U_17)
& in(U_15,U_19)
& in(U_15,U_21) )
| ( ( ~ in(sK1(U_21,U_19,U_17),U_19)
| ~ in(sK1(U_21,U_19,U_17),U_21) )
& in(sK1(U_21,U_19,U_17),U_17) ) )
& ! [U_20,U_18,U_16] :
( ( ! [U_13] :
( in(U_13,U_16)
| ~ in(U_13,U_18)
| ~ in(U_13,U_20) )
& ! [U_12] :
( ( in(U_12,U_18)
& in(U_12,U_20) )
| ~ in(U_12,U_16) ) )
| U_16 != set_intersection2(U_20,U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_14,sK1(U_21,U_19,U_17))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_21,U_19,U_17] :
( U_17 = set_intersection2(U_21,U_19)
| ( ~ in(sK2(U_21,U_19,U_17),U_17)
& in(sK2(U_21,U_19,U_17),U_19)
& in(sK2(U_21,U_19,U_17),U_21) )
| ( ( ~ in(sK1(U_21,U_19,U_17),U_19)
| ~ in(sK1(U_21,U_19,U_17),U_21) )
& in(sK1(U_21,U_19,U_17),U_17) ) )
& ! [U_20,U_18,U_16] :
( ( ! [U_13] :
( in(U_13,U_16)
| ~ in(U_13,U_18)
| ~ in(U_13,U_20) )
& ! [U_12] :
( ( in(U_12,U_18)
& in(U_12,U_20) )
| ~ in(U_12,U_16) ) )
| U_16 != set_intersection2(U_20,U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_21,U_19,U_17))],[f_6_4]) ).
fof(f_6_6,plain,
( ! [U_19,U_17,U_21] :
( ~ in(sK2(U_21,U_19,U_17),U_17)
| ~ sP4(U_19,U_17,U_21) )
& ! [U_19,U_17,U_21] :
( in(sK2(U_21,U_19,U_17),U_19)
| ~ sP4(U_19,U_17,U_21) )
& ! [U_19,U_17,U_21] :
( in(sK2(U_21,U_19,U_17),U_21)
| ~ sP4(U_19,U_17,U_21) )
& ! [U_19,U_17,U_21] :
( ~ in(sK1(U_21,U_19,U_17),U_19)
| ~ in(sK1(U_21,U_19,U_17),U_21)
| ~ sP3(U_19,U_17,U_21) )
& ! [U_19,U_17,U_21] :
( in(sK1(U_21,U_19,U_17),U_17)
| ~ sP3(U_19,U_17,U_21) )
& ! [U_18,U_12,U_20] :
( in(U_12,U_18)
| ~ sP1(U_18,U_12,U_20) )
& ! [U_18,U_12,U_20] :
( in(U_12,U_20)
| ~ sP1(U_18,U_12,U_20) )
& ! [U_18,U_12,U_13,U_16,U_20] :
( in(U_13,U_16)
| ~ in(U_13,U_18)
| ~ in(U_13,U_20)
| ~ sP2(U_18,U_12,U_13,U_16,U_20) )
& ! [U_18,U_12,U_13,U_16,U_20] :
( sP1(U_18,U_12,U_20)
| ~ in(U_12,U_16)
| ~ sP2(U_18,U_12,U_13,U_16,U_20) )
& ! [U_19,U_17,U_21] :
( U_17 = set_intersection2(U_21,U_19)
| sP4(U_19,U_17,U_21)
| sP3(U_19,U_17,U_21) )
& ! [U_18,U_12,U_13,U_16,U_20] :
( sP2(U_18,U_12,U_13,U_16,U_20)
| U_16 != set_intersection2(U_20,U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3,sP4])],[f_6_5]) ).
cnf(f_6_7,plain,
( sP2(U_18,U_12,U_13,U_16,U_20)
| U_16 != set_intersection2(U_20,U_18) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_8,plain,
( U_17 = set_intersection2(U_21,U_19)
| sP4(U_19,U_17,U_21)
| sP3(U_19,U_17,U_21) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_9,plain,
( sP1(U_18,U_12,U_20)
| ~ in(U_12,U_16)
| ~ sP2(U_18,U_12,U_13,U_16,U_20) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_10,plain,
( in(U_13,U_16)
| ~ in(U_13,U_18)
| ~ in(U_13,U_20)
| ~ sP2(U_18,U_12,U_13,U_16,U_20) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_11,plain,
( in(U_12,U_20)
| ~ sP1(U_18,U_12,U_20) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_12,plain,
( in(U_12,U_18)
| ~ sP1(U_18,U_12,U_20) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_13,plain,
( in(sK1(U_21,U_19,U_17),U_17)
| ~ sP3(U_19,U_17,U_21) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_14,plain,
( ~ in(sK1(U_21,U_19,U_17),U_19)
| ~ in(sK1(U_21,U_19,U_17),U_21)
| ~ sP3(U_19,U_17,U_21) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_15,plain,
( in(sK2(U_21,U_19,U_17),U_21)
| ~ sP4(U_19,U_17,U_21) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_16,plain,
( in(sK2(U_21,U_19,U_17),U_19)
| ~ sP4(U_19,U_17,U_21) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_17,plain,
( ~ in(sK2(U_21,U_19,U_17),U_17)
| ~ sP4(U_19,U_17,U_21) ),
inference(clausify,[status(thm)],[f_6_6]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
fof(f_7_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,plain,
$true,
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_8_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
$true,
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_9_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
$true,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_10_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
$true,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k7_relat_1]) ).
fof(f_11_2,plain,
! [U_23,U_22] :
( relation(relation_dom_restriction(U_23,U_22))
| ~ relation(U_23) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_23] :
( ! [U_22] : relation(relation_dom_restriction(U_23,U_22))
| ~ relation(U_23) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
! [U_22,U_23] :
( relation(relation_dom_restriction(U_23,U_22))
| ~ relation(U_23) ),
inference(definitional_conversion,[status(esa)],[f_11_3]) ).
cnf(f_11_5,plain,
( relation(relation_dom_restriction(U_23,U_22))
| ~ relation(U_23) ),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_12_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
$true,
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_13_2,plain,
! [U_25] :
? [U_24] : element(U_24,U_25),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_25] : element(sK3(U_25),U_25),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3(U_25))],[f_13_2]) ).
fof(f_13_4,plain,
! [U_25] : element(sK3(U_25),U_25),
inference(definitional_conversion,[status(esa)],[f_13_3]) ).
cnf(f_13_5,plain,
element(sK3(U_25),U_25),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_14_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_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_15_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_15_1]) ).
fof(f_15_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_15_2]) ).
fof(f_15_4,plain,
( ! [U_27,U_28,U_29] :
( relation_empty_yielding(relation_dom_restriction(U_27,U_29))
| ~ sP5(U_27,U_28,U_29) )
& ! [U_27,U_28,U_29] :
( relation(relation_dom_restriction(U_27,U_28))
| ~ sP5(U_27,U_28,U_29) )
& ! [U_27,U_28,U_29] :
( sP5(U_27,U_28,U_29)
| ~ relation_empty_yielding(U_27)
| ~ relation(U_27) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_15_3]) ).
cnf(f_15_5,plain,
( sP5(U_27,U_28,U_29)
| ~ relation_empty_yielding(U_27)
| ~ relation(U_27) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( relation(relation_dom_restriction(U_27,U_28))
| ~ sP5(U_27,U_28,U_29) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( relation_empty_yielding(relation_dom_restriction(U_27,U_29))
| ~ sP5(U_27,U_28,U_29) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [A,B] :
( relation(set_intersection2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_relat_1]) ).
fof(f_16_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_16_1]) ).
fof(f_16_3,plain,
! [U_30,U_31] :
( relation(set_intersection2(U_31,U_30))
| ~ relation(U_30)
| ~ relation(U_31) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( relation(set_intersection2(U_31,U_30))
| ~ relation(U_30)
| ~ relation(U_31) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_17_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_33,U_32] :
( ( function(relation_dom_restriction(U_33,U_32))
& relation(relation_dom_restriction(U_33,U_32)) )
| ~ function(U_33)
| ~ relation(U_33) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_33] :
( ( ! [U_35] : function(relation_dom_restriction(U_33,U_35))
& ! [U_34] : relation(relation_dom_restriction(U_33,U_34)) )
| ~ function(U_33)
| ~ relation(U_33) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_34,U_35,U_33] :
( function(relation_dom_restriction(U_33,U_35))
| ~ sP6(U_34,U_35,U_33) )
& ! [U_34,U_35,U_33] :
( relation(relation_dom_restriction(U_33,U_34))
| ~ sP6(U_34,U_35,U_33) )
& ! [U_34,U_35,U_33] :
( sP6(U_34,U_35,U_33)
| ~ function(U_33)
| ~ relation(U_33) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_18_3]) ).
cnf(f_18_5,plain,
( sP6(U_34,U_35,U_33)
| ~ function(U_33)
| ~ relation(U_33) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( relation(relation_dom_restriction(U_33,U_34))
| ~ sP6(U_34,U_35,U_33) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_7,plain,
( function(relation_dom_restriction(U_33,U_35))
| ~ sP6(U_34,U_35,U_33) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_19_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_20_2,plain,
! [U_36] :
( ~ empty(relation_dom(U_36))
| ~ relation(U_36)
| empty(U_36) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_36] :
( ~ empty(relation_dom(U_36))
| ~ relation(U_36)
| empty(U_36) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( ~ empty(relation_dom(U_36))
| ~ relation(U_36)
| empty(U_36) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_21_2,plain,
! [U_37] :
( ( relation(relation_dom(U_37))
& empty(relation_dom(U_37)) )
| ~ empty(U_37) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_37] :
( relation(relation_dom(U_37))
| ~ sP7(U_37) )
& ! [U_37] :
( empty(relation_dom(U_37))
| ~ sP7(U_37) )
& ! [U_37] :
( sP7(U_37)
| ~ empty(U_37) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_21_2]) ).
cnf(f_21_4,plain,
( sP7(U_37)
| ~ empty(U_37) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( empty(relation_dom(U_37))
| ~ sP7(U_37) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
( relation(relation_dom(U_37))
| ~ sP7(U_37) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_22_2,plain,
! [U_39,U_38] : set_intersection2(U_39,U_39) = U_39,
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_39] : set_intersection2(U_39,U_39) = U_39,
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
! [U_39] : set_intersection2(U_39,U_39) = U_39,
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
set_intersection2(U_39,U_39) = U_39,
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
inference(negate,[status(cth)],[l82_funct_1]) ).
fof(f_23_2,negated_conjecture,
? [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)],[f_23_1]) ).
fof(f_23_3,negated_conjecture,
? [U_42,U_41,U_40] :
( ( ( ~ in(U_41,relation_dom(relation_dom_restriction(U_40,U_42)))
& in(U_41,U_42)
& in(U_41,relation_dom(U_40)) )
| ( ( ~ in(U_41,U_42)
| ~ in(U_41,relation_dom(U_40)) )
& in(U_41,relation_dom(relation_dom_restriction(U_40,U_42))) ) )
& function(U_40)
& relation(U_40) ),
inference(variable_rename,[status(thm)],[f_23_2]) ).
fof(f_23_4,negated_conjecture,
? [U_41,U_40] :
( ( ( ~ in(U_41,relation_dom(relation_dom_restriction(U_40,sK4)))
& in(U_41,sK4)
& in(U_41,relation_dom(U_40)) )
| ( ( ~ in(U_41,sK4)
| ~ in(U_41,relation_dom(U_40)) )
& in(U_41,relation_dom(relation_dom_restriction(U_40,sK4))) ) )
& function(U_40)
& relation(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_42,sK4)],[f_23_3]) ).
fof(f_23_5,negated_conjecture,
? [U_40] :
( ( ( ~ in(sK5,relation_dom(relation_dom_restriction(U_40,sK4)))
& in(sK5,sK4)
& in(sK5,relation_dom(U_40)) )
| ( ( ~ in(sK5,sK4)
| ~ in(sK5,relation_dom(U_40)) )
& in(sK5,relation_dom(relation_dom_restriction(U_40,sK4))) ) )
& function(U_40)
& relation(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_41,sK5)],[f_23_4]) ).
fof(f_23_6,negated_conjecture,
( ( ( ~ in(sK5,relation_dom(relation_dom_restriction(sK6,sK4)))
& in(sK5,sK4)
& in(sK5,relation_dom(sK6)) )
| ( ( ~ in(sK5,sK4)
| ~ in(sK5,relation_dom(sK6)) )
& in(sK5,relation_dom(relation_dom_restriction(sK6,sK4))) ) )
& function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_40,sK6)],[f_23_5]) ).
fof(f_23_7,negated_conjecture,
( ( ~ in(sK5,relation_dom(relation_dom_restriction(sK6,sK4)))
| ~ sP9 )
& ( in(sK5,sK4)
| ~ sP9 )
& ( in(sK5,relation_dom(sK6))
| ~ sP9 )
& ( ~ in(sK5,sK4)
| ~ in(sK5,relation_dom(sK6))
| ~ sP8 )
& ( in(sK5,relation_dom(relation_dom_restriction(sK6,sK4)))
| ~ sP8 )
& ( sP9
| sP8 )
& function(sK6)
& relation(sK6) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9])],[f_23_6]) ).
cnf(f_23_8,negated_conjecture,
relation(sK6),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_9,negated_conjecture,
function(sK6),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_10,negated_conjecture,
( sP9
| sP8 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_11,negated_conjecture,
( in(sK5,relation_dom(relation_dom_restriction(sK6,sK4)))
| ~ sP8 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_12,negated_conjecture,
( ~ in(sK5,sK4)
| ~ in(sK5,relation_dom(sK6))
| ~ sP8 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_13,negated_conjecture,
( in(sK5,relation_dom(sK6))
| ~ sP9 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_14,negated_conjecture,
( in(sK5,sK4)
| ~ sP9 ),
inference(clausify,[status(thm)],[f_23_7]) ).
cnf(f_23_15,negated_conjecture,
( ~ in(sK5,relation_dom(relation_dom_restriction(sK6,sK4)))
| ~ sP9 ),
inference(clausify,[status(thm)],[f_23_7]) ).
fof(f_24_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_24_2,plain,
? [U_43] :
( function(U_43)
& relation(U_43) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( function(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_43,sK7)],[f_24_2]) ).
fof(f_24_4,plain,
( function(sK7)
& relation(sK7) ),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
function(sK7),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_25_2,plain,
? [U_44] :
( relation(U_44)
& empty(U_44) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_44,sK8)],[f_25_2]) ).
fof(f_25_4,plain,
( relation(sK8)
& empty(sK8) ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_26_2,plain,
? [U_45] : empty(U_45),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_45,sK9)],[f_26_2]) ).
fof(f_26_4,plain,
empty(sK9),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_27_2,plain,
? [U_46] :
( function(U_46)
& empty(U_46)
& relation(U_46) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_46,sK10)],[f_27_2]) ).
fof(f_27_4,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_7,plain,
function(sK10),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_28_2,plain,
? [U_47] :
( relation(U_47)
& ~ empty(U_47) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( relation(sK11)
& ~ empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_47,sK11)],[f_28_2]) ).
fof(f_28_4,plain,
( relation(sK11)
& ~ empty(sK11) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_29_2,plain,
? [U_48] : ~ empty(U_48),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
~ empty(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_48,sK12)],[f_29_2]) ).
fof(f_29_4,plain,
~ empty(sK12),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_30_2,plain,
? [U_49] :
( one_to_one(U_49)
& function(U_49)
& relation(U_49) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( one_to_one(sK13)
& function(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_49,sK13)],[f_30_2]) ).
fof(f_30_4,plain,
( one_to_one(sK13)
& function(sK13)
& relation(sK13) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
function(sK13),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_7,plain,
one_to_one(sK13),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_31_2,plain,
? [U_50] :
( relation_empty_yielding(U_50)
& relation(U_50) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( relation_empty_yielding(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_50,sK14)],[f_31_2]) ).
fof(f_31_4,plain,
( relation_empty_yielding(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
relation_empty_yielding(sK14),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_32_2,plain,
! [U_52,U_51] :
( element(U_52,U_51)
| ~ in(U_52,U_51) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_51,U_52] :
( element(U_52,U_51)
| ~ in(U_52,U_51) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( element(U_52,U_51)
| ~ in(U_52,U_51) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_33_2,plain,
! [U_53] : set_intersection2(U_53,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_53] : set_intersection2(U_53,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
set_intersection2(U_53,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_34_2,plain,
! [U_55,U_54] :
( in(U_55,U_54)
| empty(U_54)
| ~ element(U_55,U_54) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_55,U_54] :
( in(U_55,U_54)
| empty(U_54)
| ~ element(U_55,U_54) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( in(U_55,U_54)
| empty(U_54)
| ~ element(U_55,U_54) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_60,U_59] :
( ! [U_58] :
( ( ( U_59 = relation_dom_restriction(U_58,U_60)
| ? [U_57] :
( apply(U_59,U_57) != apply(U_58,U_57)
& in(U_57,relation_dom(U_59)) )
| relation_dom(U_59) != set_intersection2(relation_dom(U_58),U_60) )
& ( ( ! [U_56] :
( apply(U_59,U_56) = apply(U_58,U_56)
| ~ in(U_56,relation_dom(U_59)) )
& relation_dom(U_59) = set_intersection2(relation_dom(U_58),U_60) )
| U_59 != relation_dom_restriction(U_58,U_60) ) )
| ~ function(U_58)
| ~ relation(U_58) )
| ~ function(U_59)
| ~ relation(U_59) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_60,U_59] :
( ! [U_58] :
( ( ( U_59 = relation_dom_restriction(U_58,U_60)
| ( apply(U_59,sK15(U_60,U_59,U_58)) != apply(U_58,sK15(U_60,U_59,U_58))
& in(sK15(U_60,U_59,U_58),relation_dom(U_59)) )
| relation_dom(U_59) != set_intersection2(relation_dom(U_58),U_60) )
& ( ( ! [U_56] :
( apply(U_59,U_56) = apply(U_58,U_56)
| ~ in(U_56,relation_dom(U_59)) )
& relation_dom(U_59) = set_intersection2(relation_dom(U_58),U_60) )
| U_59 != relation_dom_restriction(U_58,U_60) ) )
| ~ function(U_58)
| ~ relation(U_58) )
| ~ function(U_59)
| ~ relation(U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_57,sK15(U_60,U_59,U_58))],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_58,U_59,U_60] :
( apply(U_59,sK15(U_60,U_59,U_58)) != apply(U_58,sK15(U_60,U_59,U_58))
| ~ sP11(U_58,U_59,U_60) )
& ! [U_58,U_59,U_60] :
( in(sK15(U_60,U_59,U_58),relation_dom(U_59))
| ~ sP11(U_58,U_59,U_60) )
& ! [U_56,U_58,U_59,U_60] :
( apply(U_59,U_56) = apply(U_58,U_56)
| ~ in(U_56,relation_dom(U_59))
| ~ sP10(U_56,U_58,U_59,U_60) )
& ! [U_56,U_58,U_59,U_60] :
( relation_dom(U_59) = set_intersection2(relation_dom(U_58),U_60)
| ~ sP10(U_56,U_58,U_59,U_60) )
& ! [U_56,U_58,U_59,U_60] :
( U_59 = relation_dom_restriction(U_58,U_60)
| sP11(U_58,U_59,U_60)
| relation_dom(U_59) != set_intersection2(relation_dom(U_58),U_60)
| ~ sP12(U_56,U_58,U_59,U_60) )
& ! [U_56,U_58,U_59,U_60] :
( sP10(U_56,U_58,U_59,U_60)
| U_59 != relation_dom_restriction(U_58,U_60)
| ~ sP12(U_56,U_58,U_59,U_60) )
& ! [U_56,U_58,U_59,U_60] :
( sP12(U_56,U_58,U_59,U_60)
| ~ function(U_58)
| ~ relation(U_58)
| ~ function(U_59)
| ~ relation(U_59) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11,sP12])],[f_35_3]) ).
cnf(f_35_5,plain,
( sP12(U_56,U_58,U_59,U_60)
| ~ function(U_58)
| ~ relation(U_58)
| ~ function(U_59)
| ~ relation(U_59) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
( sP10(U_56,U_58,U_59,U_60)
| U_59 != relation_dom_restriction(U_58,U_60)
| ~ sP12(U_56,U_58,U_59,U_60) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
( U_59 = relation_dom_restriction(U_58,U_60)
| sP11(U_58,U_59,U_60)
| relation_dom(U_59) != set_intersection2(relation_dom(U_58),U_60)
| ~ sP12(U_56,U_58,U_59,U_60) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,plain,
( relation_dom(U_59) = set_intersection2(relation_dom(U_58),U_60)
| ~ sP10(U_56,U_58,U_59,U_60) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_9,plain,
( apply(U_59,U_56) = apply(U_58,U_56)
| ~ in(U_56,relation_dom(U_59))
| ~ sP10(U_56,U_58,U_59,U_60) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_10,plain,
( in(sK15(U_60,U_59,U_58),relation_dom(U_59))
| ~ sP11(U_58,U_59,U_60) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_11,plain,
( apply(U_59,sK15(U_60,U_59,U_58)) != apply(U_58,sK15(U_60,U_59,U_58))
| ~ sP11(U_58,U_59,U_60) ),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_36_2,plain,
! [U_61] :
( U_61 = empty_set
| ~ empty(U_61) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_61] :
( U_61 = empty_set
| ~ empty(U_61) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( U_61 = empty_set
| ~ empty(U_61) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_37_2,plain,
! [U_63,U_62] :
( ~ empty(U_62)
| ~ in(U_63,U_62) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_62,U_63] :
( ~ empty(U_62)
| ~ in(U_63,U_62) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( ~ empty(U_62)
| ~ in(U_63,U_62) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_38_2,plain,
! [U_65,U_64] :
( ~ empty(U_64)
| U_65 = U_64
| ~ empty(U_65) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_65] :
( ! [U_64] :
( ~ empty(U_64)
| U_65 = U_64 )
| ~ empty(U_65) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
fof(f_38_4,plain,
! [U_64,U_65] :
( ~ empty(U_64)
| U_65 = U_64
| ~ empty(U_65) ),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
( ~ empty(U_64)
| U_65 = U_64
| ~ empty(U_65) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_3]) ).
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,
( 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_5,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_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,
( 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_9,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_10,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(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_12,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_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,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_17,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_18,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| 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
% 0.00/0.02 % Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:29:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 222.26/222.68 % SZS status Theorem for theBenchmark
% 222.26/222.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------