%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU226+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 : n012.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 194.45s 194.79s
% Output : Proof 196.26s
% 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(d12_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d12_funct_1) ).
fof(d13_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(apply(A,D),B)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d13_funct_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(dt_k10_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k10_relat_1) ).
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_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k9_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k9_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(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_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_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_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_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_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t145_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> subset(relation_image(B,relation_inverse_image(B,A)),A) ),
file('theBenchmark.p',t145_funct_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(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( 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,C] :
( ( C = relation_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) ) )
| ( ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( D != apply(A,E)
| ~ in(E,B)
| ~ in(E,relation_dom(A)) ) )
& ( ? [E] :
( D = apply(A,E)
& in(E,B)
& in(E,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d12_funct_1]) ).
fof(f_5_2,plain,
! [U_13] :
( ! [U_12,U_11] :
( ( U_11 = relation_image(U_13,U_12)
| ? [U_10] :
( ( ~ in(U_10,U_11)
& ? [U_9] :
( U_10 = apply(U_13,U_9)
& in(U_9,U_12)
& in(U_9,relation_dom(U_13)) ) )
| ( ! [U_8] :
( U_10 != apply(U_13,U_8)
| ~ in(U_8,U_12)
| ~ in(U_8,relation_dom(U_13)) )
& in(U_10,U_11) ) ) )
& ( ! [U_7] :
( ( in(U_7,U_11)
| ! [U_6] :
( U_7 != apply(U_13,U_6)
| ~ in(U_6,U_12)
| ~ in(U_6,relation_dom(U_13)) ) )
& ( ? [U_5] :
( U_7 = apply(U_13,U_5)
& in(U_5,U_12)
& in(U_5,relation_dom(U_13)) )
| ~ in(U_7,U_11) ) )
| U_11 != relation_image(U_13,U_12) ) )
| ~ function(U_13)
| ~ relation(U_13) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_image(U_13,U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& ? [U_9] :
( U_17 = apply(U_13,U_9)
& in(U_9,U_21)
& in(U_9,relation_dom(U_13)) ) )
| ? [U_16] :
( ! [U_8] :
( U_16 != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13)) )
& in(U_16,U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( U_15 != apply(U_13,U_6)
| ~ in(U_6,U_20)
| ~ in(U_6,relation_dom(U_13)) ) )
& ! [U_14] :
( ? [U_5] :
( U_14 = apply(U_13,U_5)
& in(U_5,U_20)
& in(U_5,relation_dom(U_13)) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_image(U_13,U_20) ) )
| ~ function(U_13)
| ~ relation(U_13) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_image(U_13,U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& ? [U_9] :
( U_17 = apply(U_13,U_9)
& in(U_9,U_21)
& in(U_9,relation_dom(U_13)) ) )
| ? [U_16] :
( ! [U_8] :
( U_16 != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13)) )
& in(U_16,U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( U_15 != apply(U_13,U_6)
| ~ in(U_6,U_20)
| ~ in(U_6,relation_dom(U_13)) ) )
& ! [U_14] :
( ( U_14 = apply(U_13,sK1(U_13,U_20,U_18,U_14))
& in(sK1(U_13,U_20,U_18,U_14),U_20)
& in(sK1(U_13,U_20,U_18,U_14),relation_dom(U_13)) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_image(U_13,U_20) ) )
| ~ function(U_13)
| ~ relation(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_13,U_20,U_18,U_14))],[f_5_3]) ).
fof(f_5_5,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_image(U_13,U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& ? [U_9] :
( U_17 = apply(U_13,U_9)
& in(U_9,U_21)
& in(U_9,relation_dom(U_13)) ) )
| ( ! [U_8] :
( sK2(U_13,U_21,U_19) != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13)) )
& in(sK2(U_13,U_21,U_19),U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( U_15 != apply(U_13,U_6)
| ~ in(U_6,U_20)
| ~ in(U_6,relation_dom(U_13)) ) )
& ! [U_14] :
( ( U_14 = apply(U_13,sK1(U_13,U_20,U_18,U_14))
& in(sK1(U_13,U_20,U_18,U_14),U_20)
& in(sK1(U_13,U_20,U_18,U_14),relation_dom(U_13)) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_image(U_13,U_20) ) )
| ~ function(U_13)
| ~ relation(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_13,U_21,U_19))],[f_5_4]) ).
fof(f_5_6,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_image(U_13,U_21)
| ( ~ in(sK3(U_13,U_21,U_19),U_19)
& ? [U_9] :
( sK3(U_13,U_21,U_19) = apply(U_13,U_9)
& in(U_9,U_21)
& in(U_9,relation_dom(U_13)) ) )
| ( ! [U_8] :
( sK2(U_13,U_21,U_19) != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13)) )
& in(sK2(U_13,U_21,U_19),U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( U_15 != apply(U_13,U_6)
| ~ in(U_6,U_20)
| ~ in(U_6,relation_dom(U_13)) ) )
& ! [U_14] :
( ( U_14 = apply(U_13,sK1(U_13,U_20,U_18,U_14))
& in(sK1(U_13,U_20,U_18,U_14),U_20)
& in(sK1(U_13,U_20,U_18,U_14),relation_dom(U_13)) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_image(U_13,U_20) ) )
| ~ function(U_13)
| ~ relation(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3(U_13,U_21,U_19))],[f_5_5]) ).
fof(f_5_7,plain,
! [U_13] :
( ( ! [U_21,U_19] :
( U_19 = relation_image(U_13,U_21)
| ( ~ in(sK3(U_13,U_21,U_19),U_19)
& sK3(U_13,U_21,U_19) = apply(U_13,sK4(U_13,U_21,U_19))
& in(sK4(U_13,U_21,U_19),U_21)
& in(sK4(U_13,U_21,U_19),relation_dom(U_13)) )
| ( ! [U_8] :
( sK2(U_13,U_21,U_19) != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13)) )
& in(sK2(U_13,U_21,U_19),U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| ! [U_6] :
( U_15 != apply(U_13,U_6)
| ~ in(U_6,U_20)
| ~ in(U_6,relation_dom(U_13)) ) )
& ! [U_14] :
( ( U_14 = apply(U_13,sK1(U_13,U_20,U_18,U_14))
& in(sK1(U_13,U_20,U_18,U_14),U_20)
& in(sK1(U_13,U_20,U_18,U_14),relation_dom(U_13)) )
| ~ in(U_14,U_18) ) )
| U_18 != relation_image(U_13,U_20) ) )
| ~ function(U_13)
| ~ relation(U_13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_9,sK4(U_13,U_21,U_19))],[f_5_6]) ).
cnf(f_5_8,plain,
( in(sK1(U_13,U_20,U_18,U_14),relation_dom(U_13))
| ~ in(U_14,U_18)
| U_18 != relation_image(U_13,U_20)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,plain,
( in(sK1(U_13,U_20,U_18,U_14),U_20)
| ~ in(U_14,U_18)
| U_18 != relation_image(U_13,U_20)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_10,plain,
( U_14 = apply(U_13,sK1(U_13,U_20,U_18,U_14))
| ~ in(U_14,U_18)
| U_18 != relation_image(U_13,U_20)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_11,plain,
( in(U_15,U_18)
| U_15 != apply(U_13,U_6)
| ~ in(U_6,U_20)
| ~ in(U_6,relation_dom(U_13))
| U_18 != relation_image(U_13,U_20)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_12,plain,
( in(sK4(U_13,U_21,U_19),relation_dom(U_13))
| in(sK2(U_13,U_21,U_19),U_19)
| U_19 = relation_image(U_13,U_21)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_13,plain,
( in(sK4(U_13,U_21,U_19),U_21)
| in(sK2(U_13,U_21,U_19),U_19)
| U_19 = relation_image(U_13,U_21)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_14,plain,
( sK3(U_13,U_21,U_19) = apply(U_13,sK4(U_13,U_21,U_19))
| in(sK2(U_13,U_21,U_19),U_19)
| U_19 = relation_image(U_13,U_21)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_15,plain,
( ~ in(sK3(U_13,U_21,U_19),U_19)
| in(sK2(U_13,U_21,U_19),U_19)
| U_19 = relation_image(U_13,U_21)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_16,plain,
( in(sK4(U_13,U_21,U_19),relation_dom(U_13))
| sK2(U_13,U_21,U_19) != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13))
| U_19 = relation_image(U_13,U_21)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_17,plain,
( in(sK4(U_13,U_21,U_19),U_21)
| sK2(U_13,U_21,U_19) != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13))
| U_19 = relation_image(U_13,U_21)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_18,plain,
( sK3(U_13,U_21,U_19) = apply(U_13,sK4(U_13,U_21,U_19))
| sK2(U_13,U_21,U_19) != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13))
| U_19 = relation_image(U_13,U_21)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_19,plain,
( ~ in(sK3(U_13,U_21,U_19),U_19)
| sK2(U_13,U_21,U_19) != apply(U_13,U_8)
| ~ in(U_8,U_21)
| ~ in(U_8,relation_dom(U_13))
| U_19 = relation_image(U_13,U_21)
| ~ function(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_5_7]) ).
fof(f_6_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ( ( ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(apply(A,D),B)
| ~ in(D,relation_dom(A)) )
& ( ( in(apply(A,D),B)
& in(D,relation_dom(A)) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_funct_1]) ).
fof(f_6_2,plain,
! [U_26] :
( ! [U_25,U_24] :
( ( U_24 = relation_inverse_image(U_26,U_25)
| ? [U_23] :
( ( ~ in(U_23,U_24)
& in(apply(U_26,U_23),U_25)
& in(U_23,relation_dom(U_26)) )
| ( ( ~ in(apply(U_26,U_23),U_25)
| ~ in(U_23,relation_dom(U_26)) )
& in(U_23,U_24) ) ) )
& ( ! [U_22] :
( ( in(U_22,U_24)
| ~ in(apply(U_26,U_22),U_25)
| ~ in(U_22,relation_dom(U_26)) )
& ( ( in(apply(U_26,U_22),U_25)
& in(U_22,relation_dom(U_26)) )
| ~ in(U_22,U_24) ) )
| U_24 != relation_inverse_image(U_26,U_25) ) )
| ~ function(U_26)
| ~ relation(U_26) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_26] :
( ( ! [U_34,U_32] :
( U_32 = relation_inverse_image(U_26,U_34)
| ? [U_30] :
( ~ in(U_30,U_32)
& in(apply(U_26,U_30),U_34)
& in(U_30,relation_dom(U_26)) )
| ? [U_29] :
( ( ~ in(apply(U_26,U_29),U_34)
| ~ in(U_29,relation_dom(U_26)) )
& in(U_29,U_32) ) )
& ! [U_33,U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ~ in(apply(U_26,U_28),U_33)
| ~ in(U_28,relation_dom(U_26)) )
& ! [U_27] :
( ( in(apply(U_26,U_27),U_33)
& in(U_27,relation_dom(U_26)) )
| ~ in(U_27,U_31) ) )
| U_31 != relation_inverse_image(U_26,U_33) ) )
| ~ function(U_26)
| ~ relation(U_26) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_26] :
( ( ! [U_34,U_32] :
( U_32 = relation_inverse_image(U_26,U_34)
| ? [U_30] :
( ~ in(U_30,U_32)
& in(apply(U_26,U_30),U_34)
& in(U_30,relation_dom(U_26)) )
| ( ( ~ in(apply(U_26,sK5(U_26,U_34,U_32)),U_34)
| ~ in(sK5(U_26,U_34,U_32),relation_dom(U_26)) )
& in(sK5(U_26,U_34,U_32),U_32) ) )
& ! [U_33,U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ~ in(apply(U_26,U_28),U_33)
| ~ in(U_28,relation_dom(U_26)) )
& ! [U_27] :
( ( in(apply(U_26,U_27),U_33)
& in(U_27,relation_dom(U_26)) )
| ~ in(U_27,U_31) ) )
| U_31 != relation_inverse_image(U_26,U_33) ) )
| ~ function(U_26)
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_29,sK5(U_26,U_34,U_32))],[f_6_3]) ).
fof(f_6_5,plain,
! [U_26] :
( ( ! [U_34,U_32] :
( U_32 = relation_inverse_image(U_26,U_34)
| ( ~ in(sK6(U_26,U_34,U_32),U_32)
& in(apply(U_26,sK6(U_26,U_34,U_32)),U_34)
& in(sK6(U_26,U_34,U_32),relation_dom(U_26)) )
| ( ( ~ in(apply(U_26,sK5(U_26,U_34,U_32)),U_34)
| ~ in(sK5(U_26,U_34,U_32),relation_dom(U_26)) )
& in(sK5(U_26,U_34,U_32),U_32) ) )
& ! [U_33,U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ~ in(apply(U_26,U_28),U_33)
| ~ in(U_28,relation_dom(U_26)) )
& ! [U_27] :
( ( in(apply(U_26,U_27),U_33)
& in(U_27,relation_dom(U_26)) )
| ~ in(U_27,U_31) ) )
| U_31 != relation_inverse_image(U_26,U_33) ) )
| ~ function(U_26)
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_30,sK6(U_26,U_34,U_32))],[f_6_4]) ).
cnf(f_6_6,plain,
( in(U_27,relation_dom(U_26))
| ~ in(U_27,U_31)
| U_31 != relation_inverse_image(U_26,U_33)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( in(apply(U_26,U_27),U_33)
| ~ in(U_27,U_31)
| U_31 != relation_inverse_image(U_26,U_33)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_8,plain,
( in(U_28,U_31)
| ~ in(apply(U_26,U_28),U_33)
| ~ in(U_28,relation_dom(U_26))
| U_31 != relation_inverse_image(U_26,U_33)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_9,plain,
( in(sK6(U_26,U_34,U_32),relation_dom(U_26))
| in(sK5(U_26,U_34,U_32),U_32)
| U_32 = relation_inverse_image(U_26,U_34)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_10,plain,
( in(apply(U_26,sK6(U_26,U_34,U_32)),U_34)
| in(sK5(U_26,U_34,U_32),U_32)
| U_32 = relation_inverse_image(U_26,U_34)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_11,plain,
( ~ in(sK6(U_26,U_34,U_32),U_32)
| in(sK5(U_26,U_34,U_32),U_32)
| U_32 = relation_inverse_image(U_26,U_34)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_12,plain,
( in(sK6(U_26,U_34,U_32),relation_dom(U_26))
| ~ in(apply(U_26,sK5(U_26,U_34,U_32)),U_34)
| ~ in(sK5(U_26,U_34,U_32),relation_dom(U_26))
| U_32 = relation_inverse_image(U_26,U_34)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_13,plain,
( in(apply(U_26,sK6(U_26,U_34,U_32)),U_34)
| ~ in(apply(U_26,sK5(U_26,U_34,U_32)),U_34)
| ~ in(sK5(U_26,U_34,U_32),relation_dom(U_26))
| U_32 = relation_inverse_image(U_26,U_34)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_14,plain,
( ~ in(sK6(U_26,U_34,U_32),U_32)
| ~ in(apply(U_26,sK5(U_26,U_34,U_32)),U_34)
| ~ in(sK5(U_26,U_34,U_32),relation_dom(U_26))
| U_32 = relation_inverse_image(U_26,U_34)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_7_2,plain,
! [U_38,U_37] :
( ( subset(U_38,U_37)
| ? [U_36] :
( ~ in(U_36,U_37)
& in(U_36,U_38) ) )
& ( ! [U_35] :
( in(U_35,U_37)
| ~ in(U_35,U_38) )
| ~ subset(U_38,U_37) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_42,U_40] :
( subset(U_42,U_40)
| ? [U_36] :
( ~ in(U_36,U_40)
& in(U_36,U_42) ) )
& ! [U_41,U_39] :
( ! [U_35] :
( in(U_35,U_39)
| ~ in(U_35,U_41) )
| ~ subset(U_41,U_39) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_42,U_40] :
( subset(U_42,U_40)
| ( ~ in(sK7(U_42,U_40),U_40)
& in(sK7(U_42,U_40),U_42) ) )
& ! [U_41,U_39] :
( ! [U_35] :
( in(U_35,U_39)
| ~ in(U_35,U_41) )
| ~ subset(U_41,U_39) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_36,sK7(U_42,U_40))],[f_7_3]) ).
cnf(f_7_5,plain,
( in(U_35,U_39)
| ~ in(U_35,U_41)
| ~ subset(U_41,U_39) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( in(sK7(U_42,U_40),U_42)
| subset(U_42,U_40) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_7,plain,
( ~ in(sK7(U_42,U_40),U_40)
| subset(U_42,U_40) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k10_relat_1]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_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_xboole_0]) ).
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_zfmisc_1]) ).
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_k9_relat_1]) ).
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_m1_subset_1]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_15_2,plain,
! [U_44] :
? [U_43] : element(U_43,U_44),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_44] : element(sK8(U_44),U_44),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8(U_44))],[f_15_2]) ).
cnf(f_15_4,plain,
element(sK8(U_44),U_44),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_16_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_17_2,plain,
! [U_45] : ~ empty(powerset(U_45)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
~ empty(powerset(U_45)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_18_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_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]) ).
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_46] :
( ~ empty(relation_dom(U_46))
| ~ relation(U_46)
| empty(U_46) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ~ empty(relation_dom(U_46))
| ~ relation(U_46)
| empty(U_46) ),
inference(clausify,[status(thm)],[f_20_2]) ).
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_47] :
( ( relation(relation_dom(U_47))
& empty(relation_dom(U_47)) )
| ~ empty(U_47) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( empty(relation_dom(U_47))
| ~ empty(U_47) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( relation(relation_dom(U_47))
| ~ empty(U_47) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_22_2,plain,
? [U_48] :
( function(U_48)
& relation(U_48) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( function(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_48,sK9)],[f_22_2]) ).
cnf(f_22_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
function(sK9),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_23_2,plain,
? [U_49] :
( relation(U_49)
& empty(U_49) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( relation(sK10)
& empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_49,sK10)],[f_23_2]) ).
cnf(f_23_4,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_24_2,plain,
! [U_51] :
( ? [U_50] :
( ~ empty(U_50)
& element(U_50,powerset(U_51)) )
| empty(U_51) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_51] :
( ( ~ empty(sK11(U_51))
& element(sK11(U_51),powerset(U_51)) )
| empty(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_50,sK11(U_51))],[f_24_2]) ).
cnf(f_24_4,plain,
( element(sK11(U_51),powerset(U_51))
| empty(U_51) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( ~ empty(sK11(U_51))
| empty(U_51) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_25_2,plain,
? [U_52] : empty(U_52),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
empty(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_52,sK12)],[f_25_2]) ).
cnf(f_25_4,plain,
empty(sK12),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_26_2,plain,
? [U_53] :
( function(U_53)
& empty(U_53)
& relation(U_53) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( function(sK13)
& empty(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_53,sK13)],[f_26_2]) ).
cnf(f_26_4,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
empty(sK13),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
function(sK13),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_27_2,plain,
? [U_54] :
( relation(U_54)
& ~ empty(U_54) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( relation(sK14)
& ~ empty(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_54,sK14)],[f_27_2]) ).
cnf(f_27_4,plain,
~ empty(sK14),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_28_2,plain,
! [U_56] :
? [U_55] :
( empty(U_55)
& element(U_55,powerset(U_56)) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_56] :
( empty(sK15(U_56))
& element(sK15(U_56),powerset(U_56)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_55,sK15(U_56))],[f_28_2]) ).
cnf(f_28_4,plain,
element(sK15(U_56),powerset(U_56)),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
empty(sK15(U_56)),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_29_2,plain,
? [U_57] : ~ empty(U_57),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
~ empty(sK16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_57,sK16)],[f_29_2]) ).
cnf(f_29_4,plain,
~ empty(sK16),
inference(clausify,[status(thm)],[f_29_3]) ).
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_58] :
( one_to_one(U_58)
& function(U_58)
& relation(U_58) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( one_to_one(sK17)
& function(sK17)
& relation(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_58,sK17)],[f_30_2]) ).
cnf(f_30_4,plain,
relation(sK17),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
function(sK17),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
one_to_one(sK17),
inference(clausify,[status(thm)],[f_30_3]) ).
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_59] :
( relation_empty_yielding(U_59)
& relation(U_59) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( relation_empty_yielding(sK18)
& relation(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_59,sK18)],[f_31_2]) ).
cnf(f_31_4,plain,
relation(sK18),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
relation_empty_yielding(sK18),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_32_2,plain,
! [U_61,U_60] : subset(U_61,U_61),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_61] : subset(U_61,U_61),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
subset(U_61,U_61),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> subset(relation_image(B,relation_inverse_image(B,A)),A) ),
inference(negate,[status(cth)],[t145_funct_1]) ).
fof(f_33_2,negated_conjecture,
? [A,B] :
( ~ subset(relation_image(B,relation_inverse_image(B,A)),A)
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
? [U_63,U_62] :
( ~ subset(relation_image(U_62,relation_inverse_image(U_62,U_63)),U_63)
& function(U_62)
& relation(U_62) ),
inference(variable_rename,[status(thm)],[f_33_2]) ).
fof(f_33_4,negated_conjecture,
? [U_62] :
( ~ subset(relation_image(U_62,relation_inverse_image(U_62,sK19)),sK19)
& function(U_62)
& relation(U_62) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_63,sK19)],[f_33_3]) ).
fof(f_33_5,negated_conjecture,
( ~ subset(relation_image(sK20,relation_inverse_image(sK20,sK19)),sK19)
& function(sK20)
& relation(sK20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_62,sK20)],[f_33_4]) ).
cnf(f_33_6,negated_conjecture,
relation(sK20),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,negated_conjecture,
function(sK20),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_8,negated_conjecture,
~ subset(relation_image(sK20,relation_inverse_image(sK20,sK19)),sK19),
inference(clausify,[status(thm)],[f_33_5]) ).
fof(f_34_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_34_2,plain,
! [U_65,U_64] :
( element(U_65,U_64)
| ~ in(U_65,U_64) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( element(U_65,U_64)
| ~ in(U_65,U_64) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_35_2,plain,
! [U_67,U_66] :
( in(U_67,U_66)
| empty(U_66)
| ~ element(U_67,U_66) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( in(U_67,U_66)
| empty(U_66)
| ~ element(U_67,U_66) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_36_2,plain,
! [U_69,U_68] :
( ( element(U_69,powerset(U_68))
| ~ subset(U_69,U_68) )
& ( subset(U_69,U_68)
| ~ element(U_69,powerset(U_68)) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_73,U_71] :
( element(U_73,powerset(U_71))
| ~ subset(U_73,U_71) )
& ! [U_72,U_70] :
( subset(U_72,U_70)
| ~ element(U_72,powerset(U_70)) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( subset(U_72,U_70)
| ~ element(U_72,powerset(U_70)) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( element(U_73,powerset(U_71))
| ~ subset(U_73,U_71) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_37_2,plain,
! [U_76,U_75,U_74] :
( element(U_76,U_74)
| ~ element(U_75,powerset(U_74))
| ~ in(U_76,U_75) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( element(U_76,U_74)
| ~ element(U_75,powerset(U_74))
| ~ in(U_76,U_75) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_38_2,plain,
! [U_79,U_78,U_77] :
( ~ empty(U_77)
| ~ element(U_78,powerset(U_77))
| ~ in(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_79,U_78] :
( ! [U_77] :
( ~ empty(U_77)
| ~ element(U_78,powerset(U_77)) )
| ~ in(U_79,U_78) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ empty(U_77)
| ~ element(U_78,powerset(U_77))
| ~ in(U_79,U_78) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_39_2,plain,
! [U_80] :
( U_80 = empty_set
| ~ empty(U_80) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( U_80 = empty_set
| ~ empty(U_80) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_40_2,plain,
! [U_82,U_81] :
( ~ empty(U_81)
| ~ in(U_82,U_81) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( ~ empty(U_81)
| ~ in(U_82,U_81) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_41_2,plain,
! [U_84,U_83] :
( ~ empty(U_83)
| U_84 = U_83
| ~ empty(U_84) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_84] :
( ! [U_83] :
( ~ empty(U_83)
| U_84 = U_83 )
| ~ empty(U_84) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( ~ empty(U_83)
| U_84 = U_83
| ~ empty(U_84) ),
inference(clausify,[status(thm)],[f_41_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_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_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,
( relation_image(Eq_x_0,Eq_x_1) = relation_image(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(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,axiom,
( relation_inverse_image(Eq_x_0,Eq_x_1) = relation_inverse_image(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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_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_functions]) ).
cnf(equality_10,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_11,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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_24,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,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
% 0.00/0.01 % Problem : SEU226+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 19 23:34:22 UTC 2026
% 0.03/0.29 % CPUTime :
% 194.45/194.79 % SZS status Theorem for theBenchmark
% 194.45/194.79 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------