%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU206+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 : n005.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 08:58:29 AM UTC 2026
% Result : Theorem 192.54s 192.87s
% Output : Proof 192.95s
% 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_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d13_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('theBenchmark.p',d13_relat_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
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(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(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc4_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(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_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(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_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_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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t144_relat_1,axiom,
! [A,B] :
( relation(B)
=> subset(relation_image(B,A),relation_rng(B)) ),
file('theBenchmark.p',t144_relat_1) ).
fof(t146_relat_1,conjecture,
! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
file('theBenchmark.p',t146_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(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] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_2_2,plain,
! [U_2] :
( relation(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( relation(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_3_2,plain,
! [U_4,U_3] : unordered_pair(U_4,U_3) = unordered_pair(U_3,U_4),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
unordered_pair(U_4,U_3) = unordered_pair(U_3,U_4),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_4_2,plain,
! [U_6,U_5] :
( ( U_6 = U_5
| ~ subset(U_5,U_6)
| ~ subset(U_6,U_5) )
& ( ( subset(U_5,U_6)
& subset(U_6,U_5) )
| U_6 != U_5 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_10,U_8] :
( U_10 = U_8
| ~ subset(U_8,U_10)
| ~ subset(U_10,U_8) )
& ! [U_9,U_7] :
( ( subset(U_7,U_9)
& subset(U_9,U_7) )
| U_9 != U_7 ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( subset(U_9,U_7)
| U_9 != U_7 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( subset(U_7,U_9)
| U_9 != U_7 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( U_10 = U_8
| ~ subset(U_8,U_10)
| ~ subset(U_10,U_8) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ! [B,C] :
( ( C = relation_image(A,B)
| ? [D] :
( ( ~ in(D,C)
& ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) ) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d13_relat_1]) ).
fof(f_5_2,plain,
! [U_19] :
( ! [U_18,U_17] :
( ( U_17 = relation_image(U_19,U_18)
| ? [U_16] :
( ( ~ in(U_16,U_17)
& ? [U_15] :
( in(U_15,U_18)
& in(ordered_pair(U_15,U_16),U_19) ) )
| ( ! [U_14] :
( ~ in(U_14,U_18)
| ~ in(ordered_pair(U_14,U_16),U_19) )
& in(U_16,U_17) ) ) )
& ( ! [U_13] :
( ( in(U_13,U_17)
| ! [U_12] :
( ~ in(U_12,U_18)
| ~ in(ordered_pair(U_12,U_13),U_19) ) )
& ( ? [U_11] :
( in(U_11,U_18)
& in(ordered_pair(U_11,U_13),U_19) )
| ~ in(U_13,U_17) ) )
| U_17 != relation_image(U_19,U_18) ) )
| ~ relation(U_19) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_19] :
( ( ! [U_27,U_25] :
( U_25 = relation_image(U_19,U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& ? [U_15] :
( in(U_15,U_27)
& in(ordered_pair(U_15,U_23),U_19) ) )
| ? [U_22] :
( ! [U_14] :
( ~ in(U_14,U_27)
| ~ in(ordered_pair(U_14,U_22),U_19) )
& in(U_22,U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| ! [U_12] :
( ~ in(U_12,U_26)
| ~ in(ordered_pair(U_12,U_21),U_19) ) )
& ! [U_20] :
( ? [U_11] :
( in(U_11,U_26)
& in(ordered_pair(U_11,U_20),U_19) )
| ~ in(U_20,U_24) ) )
| U_24 != relation_image(U_19,U_26) ) )
| ~ relation(U_19) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
! [U_19] :
( ( ! [U_27,U_25] :
( U_25 = relation_image(U_19,U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& ? [U_15] :
( in(U_15,U_27)
& in(ordered_pair(U_15,U_23),U_19) ) )
| ? [U_22] :
( ! [U_14] :
( ~ in(U_14,U_27)
| ~ in(ordered_pair(U_14,U_22),U_19) )
& in(U_22,U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| ! [U_12] :
( ~ in(U_12,U_26)
| ~ in(ordered_pair(U_12,U_21),U_19) ) )
& ! [U_20] :
( ( in(sK1(U_19,U_26,U_24,U_20),U_26)
& in(ordered_pair(sK1(U_19,U_26,U_24,U_20),U_20),U_19) )
| ~ in(U_20,U_24) ) )
| U_24 != relation_image(U_19,U_26) ) )
| ~ relation(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_19,U_26,U_24,U_20))],[f_5_3]) ).
fof(f_5_5,plain,
! [U_19] :
( ( ! [U_27,U_25] :
( U_25 = relation_image(U_19,U_27)
| ? [U_23] :
( ~ in(U_23,U_25)
& ? [U_15] :
( in(U_15,U_27)
& in(ordered_pair(U_15,U_23),U_19) ) )
| ( ! [U_14] :
( ~ in(U_14,U_27)
| ~ in(ordered_pair(U_14,sK2(U_19,U_27,U_25)),U_19) )
& in(sK2(U_19,U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| ! [U_12] :
( ~ in(U_12,U_26)
| ~ in(ordered_pair(U_12,U_21),U_19) ) )
& ! [U_20] :
( ( in(sK1(U_19,U_26,U_24,U_20),U_26)
& in(ordered_pair(sK1(U_19,U_26,U_24,U_20),U_20),U_19) )
| ~ in(U_20,U_24) ) )
| U_24 != relation_image(U_19,U_26) ) )
| ~ relation(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_22,sK2(U_19,U_27,U_25))],[f_5_4]) ).
fof(f_5_6,plain,
! [U_19] :
( ( ! [U_27,U_25] :
( U_25 = relation_image(U_19,U_27)
| ( ~ in(sK3(U_19,U_27,U_25),U_25)
& ? [U_15] :
( in(U_15,U_27)
& in(ordered_pair(U_15,sK3(U_19,U_27,U_25)),U_19) ) )
| ( ! [U_14] :
( ~ in(U_14,U_27)
| ~ in(ordered_pair(U_14,sK2(U_19,U_27,U_25)),U_19) )
& in(sK2(U_19,U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| ! [U_12] :
( ~ in(U_12,U_26)
| ~ in(ordered_pair(U_12,U_21),U_19) ) )
& ! [U_20] :
( ( in(sK1(U_19,U_26,U_24,U_20),U_26)
& in(ordered_pair(sK1(U_19,U_26,U_24,U_20),U_20),U_19) )
| ~ in(U_20,U_24) ) )
| U_24 != relation_image(U_19,U_26) ) )
| ~ relation(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_23,sK3(U_19,U_27,U_25))],[f_5_5]) ).
fof(f_5_7,plain,
! [U_19] :
( ( ! [U_27,U_25] :
( U_25 = relation_image(U_19,U_27)
| ( ~ in(sK3(U_19,U_27,U_25),U_25)
& in(sK4(U_19,U_27,U_25),U_27)
& in(ordered_pair(sK4(U_19,U_27,U_25),sK3(U_19,U_27,U_25)),U_19) )
| ( ! [U_14] :
( ~ in(U_14,U_27)
| ~ in(ordered_pair(U_14,sK2(U_19,U_27,U_25)),U_19) )
& in(sK2(U_19,U_27,U_25),U_25) ) )
& ! [U_26,U_24] :
( ( ! [U_21] :
( in(U_21,U_24)
| ! [U_12] :
( ~ in(U_12,U_26)
| ~ in(ordered_pair(U_12,U_21),U_19) ) )
& ! [U_20] :
( ( in(sK1(U_19,U_26,U_24,U_20),U_26)
& in(ordered_pair(sK1(U_19,U_26,U_24,U_20),U_20),U_19) )
| ~ in(U_20,U_24) ) )
| U_24 != relation_image(U_19,U_26) ) )
| ~ relation(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_15,sK4(U_19,U_27,U_25))],[f_5_6]) ).
cnf(f_5_8,plain,
( in(ordered_pair(sK1(U_19,U_26,U_24,U_20),U_20),U_19)
| ~ in(U_20,U_24)
| U_24 != relation_image(U_19,U_26)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,plain,
( in(sK1(U_19,U_26,U_24,U_20),U_26)
| ~ in(U_20,U_24)
| U_24 != relation_image(U_19,U_26)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_10,plain,
( in(U_21,U_24)
| ~ in(U_12,U_26)
| ~ in(ordered_pair(U_12,U_21),U_19)
| U_24 != relation_image(U_19,U_26)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_11,plain,
( in(ordered_pair(sK4(U_19,U_27,U_25),sK3(U_19,U_27,U_25)),U_19)
| in(sK2(U_19,U_27,U_25),U_25)
| U_25 = relation_image(U_19,U_27)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_12,plain,
( in(sK4(U_19,U_27,U_25),U_27)
| in(sK2(U_19,U_27,U_25),U_25)
| U_25 = relation_image(U_19,U_27)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_13,plain,
( ~ in(sK3(U_19,U_27,U_25),U_25)
| in(sK2(U_19,U_27,U_25),U_25)
| U_25 = relation_image(U_19,U_27)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_14,plain,
( in(ordered_pair(sK4(U_19,U_27,U_25),sK3(U_19,U_27,U_25)),U_19)
| ~ in(U_14,U_27)
| ~ in(ordered_pair(U_14,sK2(U_19,U_27,U_25)),U_19)
| U_25 = relation_image(U_19,U_27)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_15,plain,
( in(sK4(U_19,U_27,U_25),U_27)
| ~ in(U_14,U_27)
| ~ in(ordered_pair(U_14,sK2(U_19,U_27,U_25)),U_19)
| U_25 = relation_image(U_19,U_27)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_16,plain,
( ~ in(sK3(U_19,U_27,U_25),U_25)
| ~ in(U_14,U_27)
| ~ in(ordered_pair(U_14,sK2(U_19,U_27,U_25)),U_19)
| U_25 = relation_image(U_19,U_27)
| ~ relation(U_19) ),
inference(clausify,[status(thm)],[f_5_7]) ).
fof(f_6_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_6_2,plain,
! [U_31,U_30] :
( ( subset(U_31,U_30)
| ? [U_29] :
( ~ in(U_29,U_30)
& in(U_29,U_31) ) )
& ( ! [U_28] :
( in(U_28,U_30)
| ~ in(U_28,U_31) )
| ~ subset(U_31,U_30) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_35,U_33] :
( subset(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_33)
& in(U_29,U_35) ) )
& ! [U_34,U_32] :
( ! [U_28] :
( in(U_28,U_32)
| ~ in(U_28,U_34) )
| ~ subset(U_34,U_32) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_35,U_33] :
( subset(U_35,U_33)
| ( ~ in(sK5(U_35,U_33),U_33)
& in(sK5(U_35,U_33),U_35) ) )
& ! [U_34,U_32] :
( ! [U_28] :
( in(U_28,U_32)
| ~ in(U_28,U_34) )
| ~ subset(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_29,sK5(U_35,U_33))],[f_6_3]) ).
cnf(f_6_5,plain,
( in(U_28,U_32)
| ~ in(U_28,U_34)
| ~ subset(U_34,U_32) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( in(sK5(U_35,U_33),U_35)
| subset(U_35,U_33) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ~ in(sK5(U_35,U_33),U_33)
| subset(U_35,U_33) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] :
( ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(C,D),A) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_1]) ).
fof(f_7_2,plain,
! [U_43] :
( ! [U_42] :
( ( U_42 = relation_dom(U_43)
| ? [U_41] :
( ( ~ in(U_41,U_42)
& ? [U_40] : in(ordered_pair(U_41,U_40),U_43) )
| ( ! [U_39] : ~ in(ordered_pair(U_41,U_39),U_43)
& in(U_41,U_42) ) ) )
& ( ! [U_38] :
( ( in(U_38,U_42)
| ! [U_37] : ~ in(ordered_pair(U_38,U_37),U_43) )
& ( ? [U_36] : in(ordered_pair(U_38,U_36),U_43)
| ~ in(U_38,U_42) ) )
| U_42 != relation_dom(U_43) ) )
| ~ relation(U_43) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_43] :
( ( ! [U_49] :
( U_49 = relation_dom(U_43)
| ? [U_47] :
( ~ in(U_47,U_49)
& ? [U_40] : in(ordered_pair(U_47,U_40),U_43) )
| ? [U_46] :
( ! [U_39] : ~ in(ordered_pair(U_46,U_39),U_43)
& in(U_46,U_49) ) )
& ! [U_48] :
( ( ! [U_45] :
( in(U_45,U_48)
| ! [U_37] : ~ in(ordered_pair(U_45,U_37),U_43) )
& ! [U_44] :
( ? [U_36] : in(ordered_pair(U_44,U_36),U_43)
| ~ in(U_44,U_48) ) )
| U_48 != relation_dom(U_43) ) )
| ~ relation(U_43) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
! [U_43] :
( ( ! [U_49] :
( U_49 = relation_dom(U_43)
| ? [U_47] :
( ~ in(U_47,U_49)
& ? [U_40] : in(ordered_pair(U_47,U_40),U_43) )
| ? [U_46] :
( ! [U_39] : ~ in(ordered_pair(U_46,U_39),U_43)
& in(U_46,U_49) ) )
& ! [U_48] :
( ( ! [U_45] :
( in(U_45,U_48)
| ! [U_37] : ~ in(ordered_pair(U_45,U_37),U_43) )
& ! [U_44] :
( in(ordered_pair(U_44,sK6(U_43,U_48,U_44)),U_43)
| ~ in(U_44,U_48) ) )
| U_48 != relation_dom(U_43) ) )
| ~ relation(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_36,sK6(U_43,U_48,U_44))],[f_7_3]) ).
fof(f_7_5,plain,
! [U_43] :
( ( ! [U_49] :
( U_49 = relation_dom(U_43)
| ? [U_47] :
( ~ in(U_47,U_49)
& ? [U_40] : in(ordered_pair(U_47,U_40),U_43) )
| ( ! [U_39] : ~ in(ordered_pair(sK7(U_43,U_49),U_39),U_43)
& in(sK7(U_43,U_49),U_49) ) )
& ! [U_48] :
( ( ! [U_45] :
( in(U_45,U_48)
| ! [U_37] : ~ in(ordered_pair(U_45,U_37),U_43) )
& ! [U_44] :
( in(ordered_pair(U_44,sK6(U_43,U_48,U_44)),U_43)
| ~ in(U_44,U_48) ) )
| U_48 != relation_dom(U_43) ) )
| ~ relation(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_46,sK7(U_43,U_49))],[f_7_4]) ).
fof(f_7_6,plain,
! [U_43] :
( ( ! [U_49] :
( U_49 = relation_dom(U_43)
| ( ~ in(sK8(U_43,U_49),U_49)
& ? [U_40] : in(ordered_pair(sK8(U_43,U_49),U_40),U_43) )
| ( ! [U_39] : ~ in(ordered_pair(sK7(U_43,U_49),U_39),U_43)
& in(sK7(U_43,U_49),U_49) ) )
& ! [U_48] :
( ( ! [U_45] :
( in(U_45,U_48)
| ! [U_37] : ~ in(ordered_pair(U_45,U_37),U_43) )
& ! [U_44] :
( in(ordered_pair(U_44,sK6(U_43,U_48,U_44)),U_43)
| ~ in(U_44,U_48) ) )
| U_48 != relation_dom(U_43) ) )
| ~ relation(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_47,sK8(U_43,U_49))],[f_7_5]) ).
fof(f_7_7,plain,
! [U_43] :
( ( ! [U_49] :
( U_49 = relation_dom(U_43)
| ( ~ in(sK8(U_43,U_49),U_49)
& in(ordered_pair(sK8(U_43,U_49),sK9(U_43,U_49)),U_43) )
| ( ! [U_39] : ~ in(ordered_pair(sK7(U_43,U_49),U_39),U_43)
& in(sK7(U_43,U_49),U_49) ) )
& ! [U_48] :
( ( ! [U_45] :
( in(U_45,U_48)
| ! [U_37] : ~ in(ordered_pair(U_45,U_37),U_43) )
& ! [U_44] :
( in(ordered_pair(U_44,sK6(U_43,U_48,U_44)),U_43)
| ~ in(U_44,U_48) ) )
| U_48 != relation_dom(U_43) ) )
| ~ relation(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_40,sK9(U_43,U_49))],[f_7_6]) ).
cnf(f_7_8,plain,
( in(ordered_pair(U_44,sK6(U_43,U_48,U_44)),U_43)
| ~ in(U_44,U_48)
| U_48 != relation_dom(U_43)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_9,plain,
( in(U_45,U_48)
| ~ in(ordered_pair(U_45,U_37),U_43)
| U_48 != relation_dom(U_43)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_10,plain,
( in(ordered_pair(sK8(U_43,U_49),sK9(U_43,U_49)),U_43)
| in(sK7(U_43,U_49),U_49)
| U_49 = relation_dom(U_43)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_11,plain,
( ~ in(sK8(U_43,U_49),U_49)
| in(sK7(U_43,U_49),U_49)
| U_49 = relation_dom(U_43)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_12,plain,
( in(ordered_pair(sK8(U_43,U_49),sK9(U_43,U_49)),U_43)
| ~ in(ordered_pair(sK7(U_43,U_49),U_39),U_43)
| U_49 = relation_dom(U_43)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_7_7]) ).
cnf(f_7_13,plain,
( ~ in(sK8(U_43,U_49),U_49)
| ~ in(ordered_pair(sK7(U_43,U_49),U_39),U_43)
| U_49 = relation_dom(U_43)
| ~ relation(U_43) ),
inference(clausify,[status(thm)],[f_7_7]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(D,C),A) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_relat_1]) ).
fof(f_8_2,plain,
! [U_57] :
( ! [U_56] :
( ( U_56 = relation_rng(U_57)
| ? [U_55] :
( ( ~ in(U_55,U_56)
& ? [U_54] : in(ordered_pair(U_54,U_55),U_57) )
| ( ! [U_53] : ~ in(ordered_pair(U_53,U_55),U_57)
& in(U_55,U_56) ) ) )
& ( ! [U_52] :
( ( in(U_52,U_56)
| ! [U_51] : ~ in(ordered_pair(U_51,U_52),U_57) )
& ( ? [U_50] : in(ordered_pair(U_50,U_52),U_57)
| ~ in(U_52,U_56) ) )
| U_56 != relation_rng(U_57) ) )
| ~ relation(U_57) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_57] :
( ( ! [U_63] :
( U_63 = relation_rng(U_57)
| ? [U_61] :
( ~ in(U_61,U_63)
& ? [U_54] : in(ordered_pair(U_54,U_61),U_57) )
| ? [U_60] :
( ! [U_53] : ~ in(ordered_pair(U_53,U_60),U_57)
& in(U_60,U_63) ) )
& ! [U_62] :
( ( ! [U_59] :
( in(U_59,U_62)
| ! [U_51] : ~ in(ordered_pair(U_51,U_59),U_57) )
& ! [U_58] :
( ? [U_50] : in(ordered_pair(U_50,U_58),U_57)
| ~ in(U_58,U_62) ) )
| U_62 != relation_rng(U_57) ) )
| ~ relation(U_57) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
! [U_57] :
( ( ! [U_63] :
( U_63 = relation_rng(U_57)
| ? [U_61] :
( ~ in(U_61,U_63)
& ? [U_54] : in(ordered_pair(U_54,U_61),U_57) )
| ? [U_60] :
( ! [U_53] : ~ in(ordered_pair(U_53,U_60),U_57)
& in(U_60,U_63) ) )
& ! [U_62] :
( ( ! [U_59] :
( in(U_59,U_62)
| ! [U_51] : ~ in(ordered_pair(U_51,U_59),U_57) )
& ! [U_58] :
( in(ordered_pair(sK10(U_57,U_62,U_58),U_58),U_57)
| ~ in(U_58,U_62) ) )
| U_62 != relation_rng(U_57) ) )
| ~ relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_50,sK10(U_57,U_62,U_58))],[f_8_3]) ).
fof(f_8_5,plain,
! [U_57] :
( ( ! [U_63] :
( U_63 = relation_rng(U_57)
| ? [U_61] :
( ~ in(U_61,U_63)
& ? [U_54] : in(ordered_pair(U_54,U_61),U_57) )
| ( ! [U_53] : ~ in(ordered_pair(U_53,sK11(U_57,U_63)),U_57)
& in(sK11(U_57,U_63),U_63) ) )
& ! [U_62] :
( ( ! [U_59] :
( in(U_59,U_62)
| ! [U_51] : ~ in(ordered_pair(U_51,U_59),U_57) )
& ! [U_58] :
( in(ordered_pair(sK10(U_57,U_62,U_58),U_58),U_57)
| ~ in(U_58,U_62) ) )
| U_62 != relation_rng(U_57) ) )
| ~ relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_60,sK11(U_57,U_63))],[f_8_4]) ).
fof(f_8_6,plain,
! [U_57] :
( ( ! [U_63] :
( U_63 = relation_rng(U_57)
| ( ~ in(sK12(U_57,U_63),U_63)
& ? [U_54] : in(ordered_pair(U_54,sK12(U_57,U_63)),U_57) )
| ( ! [U_53] : ~ in(ordered_pair(U_53,sK11(U_57,U_63)),U_57)
& in(sK11(U_57,U_63),U_63) ) )
& ! [U_62] :
( ( ! [U_59] :
( in(U_59,U_62)
| ! [U_51] : ~ in(ordered_pair(U_51,U_59),U_57) )
& ! [U_58] :
( in(ordered_pair(sK10(U_57,U_62,U_58),U_58),U_57)
| ~ in(U_58,U_62) ) )
| U_62 != relation_rng(U_57) ) )
| ~ relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_61,sK12(U_57,U_63))],[f_8_5]) ).
fof(f_8_7,plain,
! [U_57] :
( ( ! [U_63] :
( U_63 = relation_rng(U_57)
| ( ~ in(sK12(U_57,U_63),U_63)
& in(ordered_pair(sK13(U_57,U_63),sK12(U_57,U_63)),U_57) )
| ( ! [U_53] : ~ in(ordered_pair(U_53,sK11(U_57,U_63)),U_57)
& in(sK11(U_57,U_63),U_63) ) )
& ! [U_62] :
( ( ! [U_59] :
( in(U_59,U_62)
| ! [U_51] : ~ in(ordered_pair(U_51,U_59),U_57) )
& ! [U_58] :
( in(ordered_pair(sK10(U_57,U_62,U_58),U_58),U_57)
| ~ in(U_58,U_62) ) )
| U_62 != relation_rng(U_57) ) )
| ~ relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_54,sK13(U_57,U_63))],[f_8_6]) ).
cnf(f_8_8,plain,
( in(ordered_pair(sK10(U_57,U_62,U_58),U_58),U_57)
| ~ in(U_58,U_62)
| U_62 != relation_rng(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_9,plain,
( in(U_59,U_62)
| ~ in(ordered_pair(U_51,U_59),U_57)
| U_62 != relation_rng(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_10,plain,
( in(ordered_pair(sK13(U_57,U_63),sK12(U_57,U_63)),U_57)
| in(sK11(U_57,U_63),U_63)
| U_63 = relation_rng(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_11,plain,
( ~ in(sK12(U_57,U_63),U_63)
| in(sK11(U_57,U_63),U_63)
| U_63 = relation_rng(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_12,plain,
( in(ordered_pair(sK13(U_57,U_63),sK12(U_57,U_63)),U_57)
| ~ in(ordered_pair(U_53,sK11(U_57,U_63)),U_57)
| U_63 = relation_rng(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_8_7]) ).
cnf(f_8_13,plain,
( ~ in(sK12(U_57,U_63),U_63)
| ~ in(ordered_pair(U_53,sK11(U_57,U_63)),U_57)
| U_63 = relation_rng(U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_8_7]) ).
fof(f_9_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_9_2,plain,
! [U_65,U_64] : ordered_pair(U_65,U_64) = unordered_pair(unordered_pair(U_65,U_64),singleton(U_65)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
ordered_pair(U_65,U_64) = unordered_pair(unordered_pair(U_65,U_64),singleton(U_65)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_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_k2_relat_1]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k9_relat_1]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_18_2,plain,
$true,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_19_2,plain,
! [U_67] :
? [U_66] : element(U_66,U_67),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_67] : element(sK14(U_67),U_67),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_66,sK14(U_67))],[f_19_2]) ).
cnf(f_19_4,plain,
element(sK14(U_67),U_67),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_20_2,plain,
! [U_68] : ~ empty(powerset(U_68)),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
~ empty(powerset(U_68)),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_21_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_22_2,plain,
! [U_70,U_69] : ~ empty(ordered_pair(U_70,U_69)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
~ empty(ordered_pair(U_70,U_69)),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_23_2,plain,
! [U_71] : ~ empty(singleton(U_71)),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
~ empty(singleton(U_71)),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_24_2,plain,
! [U_73,U_72] : ~ empty(unordered_pair(U_73,U_72)),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
~ empty(unordered_pair(U_73,U_72)),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_25_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_26_2,plain,
! [U_74] :
( ~ empty(relation_dom(U_74))
| ~ relation(U_74)
| empty(U_74) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ~ empty(relation_dom(U_74))
| ~ relation(U_74)
| empty(U_74) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_27_2,plain,
! [U_75] :
( ~ empty(relation_rng(U_75))
| ~ relation(U_75)
| empty(U_75) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( ~ empty(relation_rng(U_75))
| ~ relation(U_75)
| empty(U_75) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_28_2,plain,
! [U_76] :
( ( relation(relation_dom(U_76))
& empty(relation_dom(U_76)) )
| ~ empty(U_76) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( empty(relation_dom(U_76))
| ~ empty(U_76) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( relation(relation_dom(U_76))
| ~ empty(U_76) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_29_2,plain,
! [U_77] :
( ( relation(relation_rng(U_77))
& empty(relation_rng(U_77)) )
| ~ empty(U_77) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( empty(relation_rng(U_77))
| ~ empty(U_77) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( relation(relation_rng(U_77))
| ~ empty(U_77) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_30_2,plain,
? [U_78] :
( relation(U_78)
& empty(U_78) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( relation(sK15)
& empty(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_78,sK15)],[f_30_2]) ).
cnf(f_30_4,plain,
empty(sK15),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_31_2,plain,
! [U_80] :
( ? [U_79] :
( ~ empty(U_79)
& element(U_79,powerset(U_80)) )
| empty(U_80) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_80] :
( ( ~ empty(sK16(U_80))
& element(sK16(U_80),powerset(U_80)) )
| empty(U_80) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_79,sK16(U_80))],[f_31_2]) ).
cnf(f_31_4,plain,
( element(sK16(U_80),powerset(U_80))
| empty(U_80) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( ~ empty(sK16(U_80))
| empty(U_80) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_32_2,plain,
? [U_81] : empty(U_81),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
empty(sK17),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_81,sK17)],[f_32_2]) ).
cnf(f_32_4,plain,
empty(sK17),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_33_2,plain,
? [U_82] :
( relation(U_82)
& ~ empty(U_82) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( relation(sK18)
& ~ empty(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_82,sK18)],[f_33_2]) ).
cnf(f_33_4,plain,
~ empty(sK18),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
relation(sK18),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_34_2,plain,
! [U_84] :
? [U_83] :
( empty(U_83)
& element(U_83,powerset(U_84)) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_84] :
( empty(sK19(U_84))
& element(sK19(U_84),powerset(U_84)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_83,sK19(U_84))],[f_34_2]) ).
cnf(f_34_4,plain,
element(sK19(U_84),powerset(U_84)),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
empty(sK19(U_84)),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_35_2,plain,
? [U_85] : ~ empty(U_85),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
~ empty(sK20),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_85,sK20)],[f_35_2]) ).
cnf(f_35_4,plain,
~ empty(sK20),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_36_2,plain,
! [U_87,U_86] : subset(U_87,U_87),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_87] : subset(U_87,U_87),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
subset(U_87,U_87),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B] :
( subset(relation_image(B,A),relation_rng(B))
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t144_relat_1]) ).
fof(f_37_2,plain,
! [U_89,U_88] :
( subset(relation_image(U_88,U_89),relation_rng(U_88))
| ~ relation(U_88) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( subset(relation_image(U_88,U_89),relation_rng(U_88))
| ~ relation(U_88) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> relation_image(A,relation_dom(A)) = relation_rng(A) ),
inference(negate,[status(cth)],[t146_relat_1]) ).
fof(f_38_2,negated_conjecture,
? [A] :
( relation_image(A,relation_dom(A)) != relation_rng(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_38_1]) ).
fof(f_38_3,negated_conjecture,
? [U_90] :
( relation_image(U_90,relation_dom(U_90)) != relation_rng(U_90)
& relation(U_90) ),
inference(variable_rename,[status(thm)],[f_38_2]) ).
fof(f_38_4,negated_conjecture,
( relation_image(sK21,relation_dom(sK21)) != relation_rng(sK21)
& relation(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_90,sK21)],[f_38_3]) ).
cnf(f_38_5,negated_conjecture,
relation(sK21),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,negated_conjecture,
relation_image(sK21,relation_dom(sK21)) != relation_rng(sK21),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_39_2,plain,
! [U_92,U_91] :
( element(U_92,U_91)
| ~ in(U_92,U_91) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( element(U_92,U_91)
| ~ in(U_92,U_91) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_40_2,plain,
! [U_94,U_93] :
( in(U_94,U_93)
| empty(U_93)
| ~ element(U_94,U_93) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( in(U_94,U_93)
| empty(U_93)
| ~ element(U_94,U_93) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
! [U_96,U_95] :
( ( element(U_96,powerset(U_95))
| ~ subset(U_96,U_95) )
& ( subset(U_96,U_95)
| ~ element(U_96,powerset(U_95)) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( ! [U_100,U_98] :
( element(U_100,powerset(U_98))
| ~ subset(U_100,U_98) )
& ! [U_99,U_97] :
( subset(U_99,U_97)
| ~ element(U_99,powerset(U_97)) ) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( subset(U_99,U_97)
| ~ element(U_99,powerset(U_97)) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( element(U_100,powerset(U_98))
| ~ subset(U_100,U_98) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_42_2,plain,
! [U_103,U_102,U_101] :
( element(U_103,U_101)
| ~ element(U_102,powerset(U_101))
| ~ in(U_103,U_102) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( element(U_103,U_101)
| ~ element(U_102,powerset(U_101))
| ~ in(U_103,U_102) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_43_2,plain,
! [U_106,U_105,U_104] :
( ~ empty(U_104)
| ~ element(U_105,powerset(U_104))
| ~ in(U_106,U_105) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_106,U_105] :
( ! [U_104] :
( ~ empty(U_104)
| ~ element(U_105,powerset(U_104)) )
| ~ in(U_106,U_105) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( ~ empty(U_104)
| ~ element(U_105,powerset(U_104))
| ~ in(U_106,U_105) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_44_2,plain,
! [U_107] :
( U_107 = empty_set
| ~ empty(U_107) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( U_107 = empty_set
| ~ empty(U_107) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_45_2,plain,
! [U_109,U_108] :
( ~ empty(U_108)
| ~ in(U_109,U_108) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( ~ empty(U_108)
| ~ in(U_109,U_108) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_46_2,plain,
! [U_111,U_110] :
( ~ empty(U_110)
| U_111 = U_110
| ~ empty(U_111) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_111] :
( ! [U_110] :
( ~ empty(U_110)
| U_111 = U_110 )
| ~ empty(U_111) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( ~ empty(U_110)
| U_111 = U_110
| ~ empty(U_111) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_2]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_2]) ).
cnf(f_17_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_2]) ).
cnf(f_18_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( 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_6,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,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_13,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_14,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_15,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(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,
( 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_17,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_18,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( sK19(Eq_x_0) = sK19(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,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_28,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,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_31,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU206+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
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 23:31:33 UTC 2026
% 0.09/0.38 % CPUTime :
% 192.54/192.87 % SZS status Theorem for theBenchmark
% 192.54/192.87 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------