%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU266+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 08:58:47 AM UTC 2026
% Result : Theorem 228.68s 244.46s
% Output : Proof 229.77s
% 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_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
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_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
fof(dt_k5_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> element(relation_rng_as_subset(A,B,C),powerset(B)) ),
file('theBenchmark.p',dt_k5_relset_1) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : relation_of2(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
file('theBenchmark.p',existence_m2_relset_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(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(redefinition_k5_relset_1,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_rng_as_subset(A,B,C) = relation_rng(C) ),
file('theBenchmark.p',redefinition_k5_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t20_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t23_relset_1,conjecture,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ! [D] :
~ ( ! [E] : ~ in(ordered_pair(E,D),C)
& in(D,B) )
<=> relation_rng_as_subset(A,B,C) = B ) ),
file('theBenchmark.p',t23_relset_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
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,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(fof_nnf,[status(thm)],[cc1_relset_1]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] :
( relation(U_2)
| ~ element(U_2,powerset(cartesian_product2(U_4,U_3))) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( relation(U_2)
| ~ element(U_2,powerset(cartesian_product2(U_4,U_3))) ),
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_6,U_5] : unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
unordered_pair(U_6,U_5) = unordered_pair(U_5,U_6),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_14] :
( ! [U_13] :
( ( U_13 = relation_rng(U_14)
| ? [U_12] :
( ( ~ in(U_12,U_13)
& ? [U_11] : in(ordered_pair(U_11,U_12),U_14) )
| ( ! [U_10] : ~ in(ordered_pair(U_10,U_12),U_14)
& in(U_12,U_13) ) ) )
& ( ! [U_9] :
( ( in(U_9,U_13)
| ! [U_8] : ~ in(ordered_pair(U_8,U_9),U_14) )
& ( ? [U_7] : in(ordered_pair(U_7,U_9),U_14)
| ~ in(U_9,U_13) ) )
| U_13 != relation_rng(U_14) ) )
| ~ relation(U_14) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_14] :
( ( ! [U_20] :
( U_20 = relation_rng(U_14)
| ? [U_18] :
( ~ in(U_18,U_20)
& ? [U_11] : in(ordered_pair(U_11,U_18),U_14) )
| ? [U_17] :
( ! [U_10] : ~ in(ordered_pair(U_10,U_17),U_14)
& in(U_17,U_20) ) )
& ! [U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] : ~ in(ordered_pair(U_8,U_16),U_14) )
& ! [U_15] :
( ? [U_7] : in(ordered_pair(U_7,U_15),U_14)
| ~ in(U_15,U_19) ) )
| U_19 != relation_rng(U_14) ) )
| ~ relation(U_14) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
! [U_14] :
( ( ! [U_20] :
( U_20 = relation_rng(U_14)
| ? [U_18] :
( ~ in(U_18,U_20)
& ? [U_11] : in(ordered_pair(U_11,U_18),U_14) )
| ? [U_17] :
( ! [U_10] : ~ in(ordered_pair(U_10,U_17),U_14)
& in(U_17,U_20) ) )
& ! [U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] : ~ in(ordered_pair(U_8,U_16),U_14) )
& ! [U_15] :
( in(ordered_pair(sK1(U_14,U_19,U_15),U_15),U_14)
| ~ in(U_15,U_19) ) )
| U_19 != relation_rng(U_14) ) )
| ~ relation(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_7,sK1(U_14,U_19,U_15))],[f_4_3]) ).
fof(f_4_5,plain,
! [U_14] :
( ( ! [U_20] :
( U_20 = relation_rng(U_14)
| ? [U_18] :
( ~ in(U_18,U_20)
& ? [U_11] : in(ordered_pair(U_11,U_18),U_14) )
| ( ! [U_10] : ~ in(ordered_pair(U_10,sK2(U_14,U_20)),U_14)
& in(sK2(U_14,U_20),U_20) ) )
& ! [U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] : ~ in(ordered_pair(U_8,U_16),U_14) )
& ! [U_15] :
( in(ordered_pair(sK1(U_14,U_19,U_15),U_15),U_14)
| ~ in(U_15,U_19) ) )
| U_19 != relation_rng(U_14) ) )
| ~ relation(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_17,sK2(U_14,U_20))],[f_4_4]) ).
fof(f_4_6,plain,
! [U_14] :
( ( ! [U_20] :
( U_20 = relation_rng(U_14)
| ( ~ in(sK3(U_14,U_20),U_20)
& ? [U_11] : in(ordered_pair(U_11,sK3(U_14,U_20)),U_14) )
| ( ! [U_10] : ~ in(ordered_pair(U_10,sK2(U_14,U_20)),U_14)
& in(sK2(U_14,U_20),U_20) ) )
& ! [U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] : ~ in(ordered_pair(U_8,U_16),U_14) )
& ! [U_15] :
( in(ordered_pair(sK1(U_14,U_19,U_15),U_15),U_14)
| ~ in(U_15,U_19) ) )
| U_19 != relation_rng(U_14) ) )
| ~ relation(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_18,sK3(U_14,U_20))],[f_4_5]) ).
fof(f_4_7,plain,
! [U_14] :
( ( ! [U_20] :
( U_20 = relation_rng(U_14)
| ( ~ in(sK3(U_14,U_20),U_20)
& in(ordered_pair(sK4(U_14,U_20),sK3(U_14,U_20)),U_14) )
| ( ! [U_10] : ~ in(ordered_pair(U_10,sK2(U_14,U_20)),U_14)
& in(sK2(U_14,U_20),U_20) ) )
& ! [U_19] :
( ( ! [U_16] :
( in(U_16,U_19)
| ! [U_8] : ~ in(ordered_pair(U_8,U_16),U_14) )
& ! [U_15] :
( in(ordered_pair(sK1(U_14,U_19,U_15),U_15),U_14)
| ~ in(U_15,U_19) ) )
| U_19 != relation_rng(U_14) ) )
| ~ relation(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_11,sK4(U_14,U_20))],[f_4_6]) ).
cnf(f_4_8,plain,
( in(ordered_pair(sK1(U_14,U_19,U_15),U_15),U_14)
| ~ in(U_15,U_19)
| U_19 != relation_rng(U_14)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_9,plain,
( in(U_16,U_19)
| ~ in(ordered_pair(U_8,U_16),U_14)
| U_19 != relation_rng(U_14)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_10,plain,
( in(ordered_pair(sK4(U_14,U_20),sK3(U_14,U_20)),U_14)
| in(sK2(U_14,U_20),U_20)
| U_20 = relation_rng(U_14)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_11,plain,
( ~ in(sK3(U_14,U_20),U_20)
| in(sK2(U_14,U_20),U_20)
| U_20 = relation_rng(U_14)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_12,plain,
( in(ordered_pair(sK4(U_14,U_20),sK3(U_14,U_20)),U_14)
| ~ in(ordered_pair(U_10,sK2(U_14,U_20)),U_14)
| U_20 = relation_rng(U_14)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_13,plain,
( ~ in(sK3(U_14,U_20),U_20)
| ~ in(ordered_pair(U_10,sK2(U_14,U_20)),U_14)
| U_20 = relation_rng(U_14)
| ~ relation(U_14) ),
inference(clausify,[status(thm)],[f_4_7]) ).
fof(f_5_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_5_2,plain,
! [U_22,U_21] : ordered_pair(U_22,U_21) = unordered_pair(unordered_pair(U_22,U_21),singleton(U_22)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
ordered_pair(U_22,U_21) = unordered_pair(unordered_pair(U_22,U_21),singleton(U_22)),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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_zfmisc_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_k2_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_k2_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_k2_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_k4_tarski]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A,B,C] :
( element(relation_rng_as_subset(A,B,C),powerset(B))
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_k5_relset_1]) ).
fof(f_14_2,plain,
! [U_25,U_24,U_23] :
( element(relation_rng_as_subset(U_25,U_24,U_23),powerset(U_24))
| ~ relation_of2(U_23,U_25,U_24) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( element(relation_rng_as_subset(U_25,U_24,U_23),powerset(U_24))
| ~ relation_of2(U_23,U_25,U_24) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
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_m1_subset_1]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_17_2,plain,
! [U_28,U_27,U_26] :
( element(U_26,powerset(cartesian_product2(U_28,U_27)))
| ~ relation_of2_as_subset(U_26,U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( element(U_26,powerset(cartesian_product2(U_28,U_27)))
| ~ relation_of2_as_subset(U_26,U_28,U_27) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_18_2,plain,
! [U_31,U_30] :
? [U_29] : relation_of2(U_29,U_31,U_30),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_31,U_30] : relation_of2(sK5(U_31,U_30),U_31,U_30),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_29,sK5(U_31,U_30))],[f_18_2]) ).
cnf(f_18_4,plain,
relation_of2(sK5(U_31,U_30),U_31,U_30),
inference(clausify,[status(thm)],[f_18_3]) ).
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_33] :
? [U_32] : element(U_32,U_33),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_33] : element(sK6(U_33),U_33),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_32,sK6(U_33))],[f_19_2]) ).
cnf(f_19_4,plain,
element(sK6(U_33),U_33),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_20_2,plain,
! [U_36,U_35] :
? [U_34] : relation_of2_as_subset(U_34,U_36,U_35),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_36,U_35] : relation_of2_as_subset(sK7(U_36,U_35),U_36,U_35),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_34,sK7(U_36,U_35))],[f_20_2]) ).
cnf(f_20_4,plain,
relation_of2_as_subset(sK7(U_36,U_35),U_36,U_35),
inference(clausify,[status(thm)],[f_20_3]) ).
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_38,U_37] : ~ empty(ordered_pair(U_38,U_37)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
~ empty(ordered_pair(U_38,U_37)),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_23_2,plain,
? [U_39] : empty(U_39),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_39,sK8)],[f_23_2]) ).
cnf(f_23_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_24_2,plain,
? [U_40] : ~ empty(U_40),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_40,sK9)],[f_24_2]) ).
cnf(f_24_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A,B,C] :
( relation_rng_as_subset(A,B,C) = relation_rng(C)
| ~ relation_of2(C,A,B) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_relset_1]) ).
fof(f_25_2,plain,
! [U_43,U_42,U_41] :
( relation_rng_as_subset(U_43,U_42,U_41) = relation_rng(U_41)
| ~ relation_of2(U_41,U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( relation_rng_as_subset(U_43,U_42,U_41) = relation_rng(U_41)
| ~ relation_of2(U_41,U_43,U_42) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_26_2,plain,
! [U_46,U_45,U_44] :
( ( relation_of2_as_subset(U_44,U_46,U_45)
| ~ relation_of2(U_44,U_46,U_45) )
& ( relation_of2(U_44,U_46,U_45)
| ~ relation_of2_as_subset(U_44,U_46,U_45) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_52,U_50,U_48] :
( relation_of2_as_subset(U_48,U_52,U_50)
| ~ relation_of2(U_48,U_52,U_50) )
& ! [U_51,U_49,U_47] :
( relation_of2(U_47,U_51,U_49)
| ~ relation_of2_as_subset(U_47,U_51,U_49) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( relation_of2(U_47,U_51,U_49)
| ~ relation_of2_as_subset(U_47,U_51,U_49) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( relation_of2_as_subset(U_48,U_52,U_50)
| ~ relation_of2(U_48,U_52,U_50) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_27_2,plain,
! [U_54,U_53] : subset(U_54,U_54),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_54] : subset(U_54,U_54),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
subset(U_54,U_54),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_28_2,plain,
! [U_56,U_55] :
( element(U_56,U_55)
| ~ in(U_56,U_55) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( element(U_56,U_55)
| ~ in(U_56,U_55) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B,C] :
( ( in(B,relation_rng(C))
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t20_relat_1]) ).
fof(f_29_2,plain,
! [U_59,U_58,U_57] :
( ( in(U_58,relation_rng(U_57))
& in(U_59,relation_dom(U_57)) )
| ~ in(ordered_pair(U_59,U_58),U_57)
| ~ relation(U_57) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( in(U_59,relation_dom(U_57))
| ~ in(ordered_pair(U_59,U_58),U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( in(U_58,relation_rng(U_57))
| ~ in(ordered_pair(U_59,U_58),U_57)
| ~ relation(U_57) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,negated_conjecture,
~ ! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ! [D] :
~ ( ! [E] : ~ in(ordered_pair(E,D),C)
& in(D,B) )
<=> relation_rng_as_subset(A,B,C) = B ) ),
inference(negate,[status(cth)],[t23_relset_1]) ).
fof(f_30_2,negated_conjecture,
? [A,B,C] :
( ( ( ? [D] :
( ! [E] : ~ in(ordered_pair(E,D),C)
& in(D,B) )
& relation_rng_as_subset(A,B,C) = B )
| ( relation_rng_as_subset(A,B,C) != B
& ! [D] :
( ? [E] : in(ordered_pair(E,D),C)
| ~ in(D,B) ) ) )
& relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[f_30_1]) ).
fof(f_30_3,negated_conjecture,
? [U_66,U_65,U_64] :
( ( ( ? [U_63] :
( ! [U_62] : ~ in(ordered_pair(U_62,U_63),U_64)
& in(U_63,U_65) )
& relation_rng_as_subset(U_66,U_65,U_64) = U_65 )
| ( relation_rng_as_subset(U_66,U_65,U_64) != U_65
& ! [U_61] :
( ? [U_60] : in(ordered_pair(U_60,U_61),U_64)
| ~ in(U_61,U_65) ) ) )
& relation_of2_as_subset(U_64,U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_30_2]) ).
fof(f_30_4,negated_conjecture,
? [U_65,U_64] :
( ( ( ? [U_63] :
( ! [U_62] : ~ in(ordered_pair(U_62,U_63),U_64)
& in(U_63,U_65) )
& relation_rng_as_subset(sK10,U_65,U_64) = U_65 )
| ( relation_rng_as_subset(sK10,U_65,U_64) != U_65
& ! [U_61] :
( ? [U_60] : in(ordered_pair(U_60,U_61),U_64)
| ~ in(U_61,U_65) ) ) )
& relation_of2_as_subset(U_64,sK10,U_65) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_66,sK10)],[f_30_3]) ).
fof(f_30_5,negated_conjecture,
? [U_64] :
( ( ( ? [U_63] :
( ! [U_62] : ~ in(ordered_pair(U_62,U_63),U_64)
& in(U_63,sK11) )
& relation_rng_as_subset(sK10,sK11,U_64) = sK11 )
| ( relation_rng_as_subset(sK10,sK11,U_64) != sK11
& ! [U_61] :
( ? [U_60] : in(ordered_pair(U_60,U_61),U_64)
| ~ in(U_61,sK11) ) ) )
& relation_of2_as_subset(U_64,sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_65,sK11)],[f_30_4]) ).
fof(f_30_6,negated_conjecture,
( ( ( ? [U_63] :
( ! [U_62] : ~ in(ordered_pair(U_62,U_63),sK12)
& in(U_63,sK11) )
& relation_rng_as_subset(sK10,sK11,sK12) = sK11 )
| ( relation_rng_as_subset(sK10,sK11,sK12) != sK11
& ! [U_61] :
( ? [U_60] : in(ordered_pair(U_60,U_61),sK12)
| ~ in(U_61,sK11) ) ) )
& relation_of2_as_subset(sK12,sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_64,sK12)],[f_30_5]) ).
fof(f_30_7,negated_conjecture,
( ( ( ? [U_63] :
( ! [U_62] : ~ in(ordered_pair(U_62,U_63),sK12)
& in(U_63,sK11) )
& relation_rng_as_subset(sK10,sK11,sK12) = sK11 )
| ( relation_rng_as_subset(sK10,sK11,sK12) != sK11
& ! [U_61] :
( in(ordered_pair(sK13(U_61),U_61),sK12)
| ~ in(U_61,sK11) ) ) )
& relation_of2_as_subset(sK12,sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_60,sK13(U_61))],[f_30_6]) ).
fof(f_30_8,negated_conjecture,
( ( ( ! [U_62] : ~ in(ordered_pair(U_62,sK14),sK12)
& in(sK14,sK11)
& relation_rng_as_subset(sK10,sK11,sK12) = sK11 )
| ( relation_rng_as_subset(sK10,sK11,sK12) != sK11
& ! [U_61] :
( in(ordered_pair(sK13(U_61),U_61),sK12)
| ~ in(U_61,sK11) ) ) )
& relation_of2_as_subset(sK12,sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_63,sK14)],[f_30_7]) ).
cnf(f_30_9,negated_conjecture,
relation_of2_as_subset(sK12,sK10,sK11),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_10,negated_conjecture,
( relation_rng_as_subset(sK10,sK11,sK12) = sK11
| in(ordered_pair(sK13(U_61),U_61),sK12)
| ~ in(U_61,sK11) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_11,negated_conjecture,
( in(sK14,sK11)
| in(ordered_pair(sK13(U_61),U_61),sK12)
| ~ in(U_61,sK11) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_12,negated_conjecture,
( ~ in(ordered_pair(U_62,sK14),sK12)
| in(ordered_pair(sK13(U_61),U_61),sK12)
| ~ in(U_61,sK11) ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_13,negated_conjecture,
( relation_rng_as_subset(sK10,sK11,sK12) = sK11
| relation_rng_as_subset(sK10,sK11,sK12) != sK11 ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_14,negated_conjecture,
( in(sK14,sK11)
| relation_rng_as_subset(sK10,sK11,sK12) != sK11 ),
inference(clausify,[status(thm)],[f_30_8]) ).
cnf(f_30_15,negated_conjecture,
( ~ in(ordered_pair(U_62,sK14),sK12)
| relation_rng_as_subset(sK10,sK11,sK12) != sK11 ),
inference(clausify,[status(thm)],[f_30_8]) ).
fof(f_31_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_31_2,plain,
! [U_68,U_67] :
( in(U_68,U_67)
| empty(U_67)
| ~ element(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( in(U_68,U_67)
| empty(U_67)
| ~ element(U_68,U_67) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_32_2,plain,
! [U_71,U_70] :
( U_71 = U_70
| ? [U_69] :
( ( ~ in(U_69,U_71)
& in(U_69,U_70) )
| ( ~ in(U_69,U_70)
& in(U_69,U_71) ) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_71,U_70] :
( U_71 = U_70
| ? [U_73] :
( ~ in(U_73,U_71)
& in(U_73,U_70) )
| ? [U_72] :
( ~ in(U_72,U_70)
& in(U_72,U_71) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_71,U_70] :
( U_71 = U_70
| ? [U_73] :
( ~ in(U_73,U_71)
& in(U_73,U_70) )
| ( ~ in(sK15(U_71,U_70),U_70)
& in(sK15(U_71,U_70),U_71) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_72,sK15(U_71,U_70))],[f_32_3]) ).
fof(f_32_5,plain,
! [U_71,U_70] :
( U_71 = U_70
| ( ~ in(sK16(U_71,U_70),U_71)
& in(sK16(U_71,U_70),U_70) )
| ( ~ in(sK15(U_71,U_70),U_70)
& in(sK15(U_71,U_70),U_71) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_73,sK16(U_71,U_70))],[f_32_4]) ).
cnf(f_32_6,plain,
( in(sK16(U_71,U_70),U_70)
| in(sK15(U_71,U_70),U_71)
| U_71 = U_70 ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_7,plain,
( ~ in(sK16(U_71,U_70),U_71)
| in(sK15(U_71,U_70),U_71)
| U_71 = U_70 ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_8,plain,
( in(sK16(U_71,U_70),U_70)
| ~ in(sK15(U_71,U_70),U_70)
| U_71 = U_70 ),
inference(clausify,[status(thm)],[f_32_5]) ).
cnf(f_32_9,plain,
( ~ in(sK16(U_71,U_70),U_71)
| ~ in(sK15(U_71,U_70),U_70)
| U_71 = U_70 ),
inference(clausify,[status(thm)],[f_32_5]) ).
fof(f_33_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_33_2,plain,
! [U_75,U_74] :
( ( element(U_75,powerset(U_74))
| ~ subset(U_75,U_74) )
& ( subset(U_75,U_74)
| ~ element(U_75,powerset(U_74)) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_79,U_77] :
( element(U_79,powerset(U_77))
| ~ subset(U_79,U_77) )
& ! [U_78,U_76] :
( subset(U_78,U_76)
| ~ element(U_78,powerset(U_76)) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( subset(U_78,U_76)
| ~ element(U_78,powerset(U_76)) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( element(U_79,powerset(U_77))
| ~ subset(U_79,U_77) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_34_2,plain,
! [U_82,U_81,U_80] :
( element(U_82,U_80)
| ~ element(U_81,powerset(U_80))
| ~ in(U_82,U_81) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( element(U_82,U_80)
| ~ element(U_81,powerset(U_80))
| ~ in(U_82,U_81) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_35_2,plain,
! [U_85,U_84,U_83] :
( ~ empty(U_83)
| ~ element(U_84,powerset(U_83))
| ~ in(U_85,U_84) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_85,U_84] :
( ! [U_83] :
( ~ empty(U_83)
| ~ element(U_84,powerset(U_83)) )
| ~ in(U_85,U_84) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( ~ empty(U_83)
| ~ element(U_84,powerset(U_83))
| ~ in(U_85,U_84) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_36_2,plain,
! [U_86] :
( U_86 = empty_set
| ~ empty(U_86) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( U_86 = empty_set
| ~ empty(U_86) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_37_2,plain,
! [U_88,U_87] :
( ~ empty(U_87)
| ~ in(U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( ~ empty(U_87)
| ~ in(U_88,U_87) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_38_2,plain,
! [U_90,U_89] :
( ~ empty(U_89)
| U_90 = U_89
| ~ empty(U_90) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_90] :
( ! [U_89] :
( ~ empty(U_89)
| U_90 = U_89 )
| ~ empty(U_90) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ empty(U_89)
| U_90 = U_89
| ~ empty(U_90) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_2]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
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_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_30_13_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_30_13]) ).
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,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( relation_rng_as_subset(Eq_x_0,Eq_x_1,Eq_x_2) = relation_rng_as_subset(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,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(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,
( 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_17,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,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_19,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK15(Eq_x_0,Eq_x_1) = sK15(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(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,
( 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_23,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_24,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( relation_of2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( relation_of2_as_subset(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2_as_subset(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU266+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/15.80 % Computer : n004.cluster.edu
% 0.11/15.80 % Model : x86_64 x86_64
% 0.11/15.80 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.80 % Memory : 8046.5625MB
% 0.11/15.80 % OS : Linux 6.8.0-71-generic
% 0.11/15.80 % CPULimit : 300
% 0.11/15.80 % WCLimit : 300
% 0.11/15.81 % DateTime : Sat Sep 19 23:43:53 UTC 2026
% 0.11/15.81 % CPUTime :
% 228.68/244.46 % SZS status Theorem for theBenchmark
% 228.68/244.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------