%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU284+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 : n018.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 08:58:51 AM UTC 2026
% Result : Theorem 216.53s 221.84s
% Output : Proof 218.55s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(s3_funct_1__e16_22__wellord2,conjecture,
! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
file('theBenchmark.p',s3_funct_1__e16_22__wellord2) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
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(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(s2_funct_1__e16_22__wellord2__1,axiom,
! [A] :
( ( ! [B] :
~ ( ! [C] : C != singleton(B)
& in(B,A) )
& ! [B,C,D] :
( ( D = singleton(B)
& C = singleton(B)
& in(B,A) )
=> C = D ) )
=> ? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) )
& relation_dom(B) = A
& function(B)
& relation(B) ) ),
file('theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).
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(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
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(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
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(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(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_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,negated_conjecture,
~ ! [A] :
? [B] :
( ! [C] :
( in(C,A)
=> apply(B,C) = singleton(C) )
& relation_dom(B) = A
& function(B)
& relation(B) ),
inference(negate,[status(cth)],[s3_funct_1__e16_22__wellord2]) ).
fof(f_1_2,negated_conjecture,
? [A] :
! [B] :
( ? [C] :
( apply(B,C) != singleton(C)
& in(C,A) )
| relation_dom(B) != A
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_2] :
! [U_1] :
( ? [U_0] :
( apply(U_1,U_0) != singleton(U_0)
& in(U_0,U_2) )
| relation_dom(U_1) != U_2
| ~ function(U_1)
| ~ relation(U_1) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
! [U_1] :
( ? [U_0] :
( apply(U_1,U_0) != singleton(U_0)
& in(U_0,sK1) )
| relation_dom(U_1) != sK1
| ~ function(U_1)
| ~ relation(U_1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
! [U_1] :
( ( apply(U_1,sK2(U_1)) != singleton(sK2(U_1))
& in(sK2(U_1),sK1) )
| relation_dom(U_1) != sK1
| ~ function(U_1)
| ~ relation(U_1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2(U_1))],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ! [U_1] :
( apply(U_1,sK2(U_1)) != singleton(sK2(U_1))
| ~ sP0(U_1) )
& ! [U_1] :
( in(sK2(U_1),sK1)
| ~ sP0(U_1) )
& ! [U_1] :
( sP0(U_1)
| relation_dom(U_1) != sK1
| ~ function(U_1)
| ~ relation(U_1) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
( sP0(U_1)
| relation_dom(U_1) != sK1
| ~ function(U_1)
| ~ relation(U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
( in(sK2(U_1),sK1)
| ~ sP0(U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
( apply(U_1,sK2(U_1)) != singleton(sK2(U_1))
| ~ sP0(U_1) ),
inference(clausify,[status(thm)],[f_1_6]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_4,U_3] :
( ~ in(U_3,U_4)
| ~ in(U_4,U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_4] :
( ~ in(U_3,U_4)
| ~ in(U_4,U_3) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ in(U_3,U_4)
| ~ in(U_4,U_3) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
fof(f_3_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_3_1]) ).
cnf(f_3_3,plain,
$true,
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
fof(f_4_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_4_1]) ).
cnf(f_4_3,plain,
$true,
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_5_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
$true,
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_6_2,plain,
? [U_5] :
( function(U_5)
& relation(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( function(sK3)
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_5,sK3)],[f_6_2]) ).
fof(f_6_4,plain,
( function(sK3)
& relation(sK3) ),
inference(definitional_conversion,[status(esa)],[f_6_3]) ).
cnf(f_6_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
function(sK3),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [A] :
( ? [B] :
( ! [C] :
( apply(B,C) = singleton(C)
| ~ in(C,A) )
& relation_dom(B) = A
& function(B)
& relation(B) )
| ? [B] :
( ! [C] : C != singleton(B)
& in(B,A) )
| ? [B,C,D] :
( C != D
& D = singleton(B)
& C = singleton(B)
& in(B,A) ) ),
inference(fof_nnf,[status(thm)],[s2_funct_1__e16_22__wellord2__1]) ).
fof(f_7_2,plain,
! [U_13] :
( ? [U_12] :
( ! [U_11] :
( apply(U_12,U_11) = singleton(U_11)
| ~ in(U_11,U_13) )
& relation_dom(U_12) = U_13
& function(U_12)
& relation(U_12) )
| ? [U_10] :
( ! [U_9] : U_9 != singleton(U_10)
& in(U_10,U_13) )
| ? [U_8,U_7,U_6] :
( U_7 != U_6
& U_6 = singleton(U_8)
& U_7 = singleton(U_8)
& in(U_8,U_13) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_13] :
( ? [U_12] :
( ! [U_11] :
( apply(U_12,U_11) = singleton(U_11)
| ~ in(U_11,U_13) )
& relation_dom(U_12) = U_13
& function(U_12)
& relation(U_12) )
| ? [U_10] :
( ! [U_9] : U_9 != singleton(U_10)
& in(U_10,U_13) )
| ? [U_7,U_6] :
( U_7 != U_6
& U_6 = singleton(sK4(U_13))
& U_7 = singleton(sK4(U_13))
& in(sK4(U_13),U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_8,sK4(U_13))],[f_7_2]) ).
fof(f_7_4,plain,
! [U_13] :
( ? [U_12] :
( ! [U_11] :
( apply(U_12,U_11) = singleton(U_11)
| ~ in(U_11,U_13) )
& relation_dom(U_12) = U_13
& function(U_12)
& relation(U_12) )
| ? [U_10] :
( ! [U_9] : U_9 != singleton(U_10)
& in(U_10,U_13) )
| ? [U_6] :
( sK5(U_13) != U_6
& U_6 = singleton(sK4(U_13))
& sK5(U_13) = singleton(sK4(U_13))
& in(sK4(U_13),U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_7,sK5(U_13))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_13] :
( ? [U_12] :
( ! [U_11] :
( apply(U_12,U_11) = singleton(U_11)
| ~ in(U_11,U_13) )
& relation_dom(U_12) = U_13
& function(U_12)
& relation(U_12) )
| ? [U_10] :
( ! [U_9] : U_9 != singleton(U_10)
& in(U_10,U_13) )
| ( sK5(U_13) != sK6(U_13)
& sK6(U_13) = singleton(sK4(U_13))
& sK5(U_13) = singleton(sK4(U_13))
& in(sK4(U_13),U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_6,sK6(U_13))],[f_7_4]) ).
fof(f_7_6,plain,
! [U_13] :
( ? [U_12] :
( ! [U_11] :
( apply(U_12,U_11) = singleton(U_11)
| ~ in(U_11,U_13) )
& relation_dom(U_12) = U_13
& function(U_12)
& relation(U_12) )
| ( ! [U_9] : U_9 != singleton(sK7(U_13))
& in(sK7(U_13),U_13) )
| ( sK5(U_13) != sK6(U_13)
& sK6(U_13) = singleton(sK4(U_13))
& sK5(U_13) = singleton(sK4(U_13))
& in(sK4(U_13),U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_10,sK7(U_13))],[f_7_5]) ).
fof(f_7_7,plain,
! [U_13] :
( ( ! [U_11] :
( apply(sK8(U_13),U_11) = singleton(U_11)
| ~ in(U_11,U_13) )
& relation_dom(sK8(U_13)) = U_13
& function(sK8(U_13))
& relation(sK8(U_13)) )
| ( ! [U_9] : U_9 != singleton(sK7(U_13))
& in(sK7(U_13),U_13) )
| ( sK5(U_13) != sK6(U_13)
& sK6(U_13) = singleton(sK4(U_13))
& sK5(U_13) = singleton(sK4(U_13))
& in(sK4(U_13),U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_12,sK8(U_13))],[f_7_6]) ).
fof(f_7_8,plain,
( ! [U_11,U_13] :
( apply(sK8(U_13),U_11) = singleton(U_11)
| ~ in(U_11,U_13)
| ~ sP3(U_11,U_13) )
& ! [U_11,U_13] :
( relation_dom(sK8(U_13)) = U_13
| ~ sP3(U_11,U_13) )
& ! [U_11,U_13] :
( function(sK8(U_13))
| ~ sP3(U_11,U_13) )
& ! [U_11,U_13] :
( relation(sK8(U_13))
| ~ sP3(U_11,U_13) )
& ! [U_9,U_13] :
( U_9 != singleton(sK7(U_13))
| ~ sP2(U_9,U_13) )
& ! [U_9,U_13] :
( in(sK7(U_13),U_13)
| ~ sP2(U_9,U_13) )
& ! [U_13] :
( sK5(U_13) != sK6(U_13)
| ~ sP1(U_13) )
& ! [U_13] :
( sK6(U_13) = singleton(sK4(U_13))
| ~ sP1(U_13) )
& ! [U_13] :
( sK5(U_13) = singleton(sK4(U_13))
| ~ sP1(U_13) )
& ! [U_13] :
( in(sK4(U_13),U_13)
| ~ sP1(U_13) )
& ! [U_9,U_11,U_13] :
( sP3(U_11,U_13)
| sP2(U_9,U_13)
| sP1(U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3])],[f_7_7]) ).
cnf(f_7_9,plain,
( sP3(U_11,U_13)
| sP2(U_9,U_13)
| sP1(U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,plain,
( in(sK4(U_13),U_13)
| ~ sP1(U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,plain,
( sK5(U_13) = singleton(sK4(U_13))
| ~ sP1(U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_12,plain,
( sK6(U_13) = singleton(sK4(U_13))
| ~ sP1(U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_13,plain,
( sK5(U_13) != sK6(U_13)
| ~ sP1(U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_14,plain,
( in(sK7(U_13),U_13)
| ~ sP2(U_9,U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_15,plain,
( U_9 != singleton(sK7(U_13))
| ~ sP2(U_9,U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_16,plain,
( relation(sK8(U_13))
| ~ sP3(U_11,U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_17,plain,
( function(sK8(U_13))
| ~ sP3(U_11,U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_18,plain,
( relation_dom(sK8(U_13)) = U_13
| ~ sP3(U_11,U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_19,plain,
( apply(sK8(U_13),U_11) = singleton(U_11)
| ~ in(U_11,U_13)
| ~ sP3(U_11,U_13) ),
inference(clausify,[status(thm)],[f_7_8]) ).
fof(f_8_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_8_2,plain,
! [U_14] :
( function(U_14)
| ~ empty(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_14] :
( function(U_14)
| ~ empty(U_14) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( function(U_14)
| ~ empty(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_9_2,plain,
! [U_15] :
( relation(U_15)
| ~ empty(U_15) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_15] :
( relation(U_15)
| ~ empty(U_15) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( relation(U_15)
| ~ empty(U_15) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_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,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_11_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_11_1]) ).
cnf(f_11_3,plain,
$true,
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_12_2,plain,
! [U_17] :
? [U_16] : element(U_16,U_17),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_17] : element(sK9(U_17),U_17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_16,sK9(U_17))],[f_12_2]) ).
fof(f_12_4,plain,
! [U_17] : element(sK9(U_17),U_17),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
element(sK9(U_17),U_17),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_13_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_13_1]) ).
cnf(f_13_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_14_2,plain,
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]) ).
fof(f_15_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_15_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_16_2,plain,
! [U_18] :
( ~ empty(relation_dom(U_18))
| ~ relation(U_18)
| empty(U_18) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_18] :
( ~ empty(relation_dom(U_18))
| ~ relation(U_18)
| empty(U_18) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( ~ empty(relation_dom(U_18))
| ~ relation(U_18)
| empty(U_18) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_17_2,plain,
! [U_19] :
( ( relation(relation_dom(U_19))
& empty(relation_dom(U_19)) )
| ~ empty(U_19) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_19] :
( relation(relation_dom(U_19))
| ~ sP4(U_19) )
& ! [U_19] :
( empty(relation_dom(U_19))
| ~ sP4(U_19) )
& ! [U_19] :
( sP4(U_19)
| ~ empty(U_19) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_17_2]) ).
cnf(f_17_4,plain,
( sP4(U_19)
| ~ empty(U_19) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
( empty(relation_dom(U_19))
| ~ sP4(U_19) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
( relation(relation_dom(U_19))
| ~ sP4(U_19) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_18_2,plain,
? [U_20] :
( relation(U_20)
& empty(U_20) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( relation(sK10)
& empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_20,sK10)],[f_18_2]) ).
fof(f_18_4,plain,
( relation(sK10)
& empty(sK10) ),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_19_2,plain,
? [U_21] : empty(U_21),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_21,sK11)],[f_19_2]) ).
fof(f_19_4,plain,
empty(sK11),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_20_2,plain,
? [U_22] :
( relation(U_22)
& ~ empty(U_22) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_22,sK12)],[f_20_2]) ).
fof(f_20_4,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(definitional_conversion,[status(esa)],[f_20_3]) ).
cnf(f_20_5,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_21_2,plain,
? [U_23] : ~ empty(U_23),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_23,sK13)],[f_21_2]) ).
fof(f_21_4,plain,
~ empty(sK13),
inference(definitional_conversion,[status(esa)],[f_21_3]) ).
cnf(f_21_5,plain,
~ empty(sK13),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_22_2,plain,
? [U_24] :
( relation_empty_yielding(U_24)
& relation(U_24) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( relation_empty_yielding(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_24,sK14)],[f_22_2]) ).
fof(f_22_4,plain,
( relation_empty_yielding(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
relation_empty_yielding(sK14),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_23_2,plain,
! [U_26,U_25] :
( element(U_26,U_25)
| ~ in(U_26,U_25) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_25,U_26] :
( element(U_26,U_25)
| ~ in(U_26,U_25) ),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
( element(U_26,U_25)
| ~ in(U_26,U_25) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_24_2,plain,
! [U_28,U_27] :
( in(U_28,U_27)
| empty(U_27)
| ~ element(U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_28,U_27] :
( in(U_28,U_27)
| empty(U_27)
| ~ element(U_28,U_27) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( in(U_28,U_27)
| empty(U_27)
| ~ element(U_28,U_27) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_25_2,plain,
! [U_29] :
( U_29 = empty_set
| ~ empty(U_29) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_29] :
( U_29 = empty_set
| ~ empty(U_29) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( U_29 = empty_set
| ~ empty(U_29) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_26_2,plain,
! [U_31,U_30] :
( ~ empty(U_30)
| ~ in(U_31,U_30) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_30,U_31] :
( ~ empty(U_30)
| ~ in(U_31,U_30) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ empty(U_30)
| ~ in(U_31,U_30) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_27_2,plain,
! [U_33,U_32] :
( ~ empty(U_32)
| U_33 = U_32
| ~ empty(U_33) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_33] :
( ! [U_32] :
( ~ empty(U_32)
| U_33 = U_32 )
| ~ empty(U_33) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_32,U_33] :
( ~ empty(U_32)
| U_33 = U_32
| ~ empty(U_33) ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
( ~ empty(U_32)
| U_33 = U_32
| ~ empty(U_33) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_3_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_11_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_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,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( relation(Eq_y_0)
| ~ relation(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,
( 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_17,axiom,
( empty(Eq_y_0)
| ~ empty(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(equality_20,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( sP4(Eq_y_0)
| ~ sP4(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 : SEU284+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n018.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 19 23:48:46 UTC 2026
% 0.09/5.38 % CPUTime :
% 216.53/221.84 % SZS status Theorem for theBenchmark
% 216.53/221.84 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------