%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU188+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 08:58:24 AM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : Proof 0.08s
% 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(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_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_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_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_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(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(t56_relat_1,axiom,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('theBenchmark.p',t56_relat_1) ).
fof(t64_relat_1,conjecture,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('theBenchmark.p',t64_relat_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
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] :
( ( 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_4_2,plain,
! [U_12] :
( ! [U_11] :
( ( U_11 = relation_dom(U_12)
| ? [U_10] :
( ( ~ in(U_10,U_11)
& ? [U_9] : in(ordered_pair(U_10,U_9),U_12) )
| ( ! [U_8] : ~ in(ordered_pair(U_10,U_8),U_12)
& in(U_10,U_11) ) ) )
& ( ! [U_7] :
( ( in(U_7,U_11)
| ! [U_6] : ~ in(ordered_pair(U_7,U_6),U_12) )
& ( ? [U_5] : in(ordered_pair(U_7,U_5),U_12)
| ~ in(U_7,U_11) ) )
| U_11 != relation_dom(U_12) ) )
| ~ relation(U_12) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_dom(U_12)
| ? [U_16] :
( ~ in(U_16,U_18)
& ? [U_9] : in(ordered_pair(U_16,U_9),U_12) )
| ? [U_15] :
( ! [U_8] : ~ in(ordered_pair(U_15,U_8),U_12)
& in(U_15,U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] : ~ in(ordered_pair(U_14,U_6),U_12) )
& ! [U_13] :
( ? [U_5] : in(ordered_pair(U_13,U_5),U_12)
| ~ in(U_13,U_17) ) )
| U_17 != relation_dom(U_12) ) )
| ~ relation(U_12) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_dom(U_12)
| ? [U_16] :
( ~ in(U_16,U_18)
& ? [U_9] : in(ordered_pair(U_16,U_9),U_12) )
| ? [U_15] :
( ! [U_8] : ~ in(ordered_pair(U_15,U_8),U_12)
& in(U_15,U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] : ~ in(ordered_pair(U_14,U_6),U_12) )
& ! [U_13] :
( in(ordered_pair(U_13,sK1(U_12,U_17,U_13)),U_12)
| ~ in(U_13,U_17) ) )
| U_17 != relation_dom(U_12) ) )
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_12,U_17,U_13))],[f_4_3]) ).
fof(f_4_5,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_dom(U_12)
| ? [U_16] :
( ~ in(U_16,U_18)
& ? [U_9] : in(ordered_pair(U_16,U_9),U_12) )
| ( ! [U_8] : ~ in(ordered_pair(sK2(U_12,U_18),U_8),U_12)
& in(sK2(U_12,U_18),U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] : ~ in(ordered_pair(U_14,U_6),U_12) )
& ! [U_13] :
( in(ordered_pair(U_13,sK1(U_12,U_17,U_13)),U_12)
| ~ in(U_13,U_17) ) )
| U_17 != relation_dom(U_12) ) )
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_12,U_18))],[f_4_4]) ).
fof(f_4_6,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_dom(U_12)
| ( ~ in(sK3(U_12,U_18),U_18)
& ? [U_9] : in(ordered_pair(sK3(U_12,U_18),U_9),U_12) )
| ( ! [U_8] : ~ in(ordered_pair(sK2(U_12,U_18),U_8),U_12)
& in(sK2(U_12,U_18),U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] : ~ in(ordered_pair(U_14,U_6),U_12) )
& ! [U_13] :
( in(ordered_pair(U_13,sK1(U_12,U_17,U_13)),U_12)
| ~ in(U_13,U_17) ) )
| U_17 != relation_dom(U_12) ) )
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_16,sK3(U_12,U_18))],[f_4_5]) ).
fof(f_4_7,plain,
! [U_12] :
( ( ! [U_18] :
( U_18 = relation_dom(U_12)
| ( ~ in(sK3(U_12,U_18),U_18)
& in(ordered_pair(sK3(U_12,U_18),sK4(U_12,U_18)),U_12) )
| ( ! [U_8] : ~ in(ordered_pair(sK2(U_12,U_18),U_8),U_12)
& in(sK2(U_12,U_18),U_18) ) )
& ! [U_17] :
( ( ! [U_14] :
( in(U_14,U_17)
| ! [U_6] : ~ in(ordered_pair(U_14,U_6),U_12) )
& ! [U_13] :
( in(ordered_pair(U_13,sK1(U_12,U_17,U_13)),U_12)
| ~ in(U_13,U_17) ) )
| U_17 != relation_dom(U_12) ) )
| ~ relation(U_12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_9,sK4(U_12,U_18))],[f_4_6]) ).
cnf(f_4_8,plain,
( in(ordered_pair(U_13,sK1(U_12,U_17,U_13)),U_12)
| ~ in(U_13,U_17)
| U_17 != relation_dom(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_9,plain,
( in(U_14,U_17)
| ~ in(ordered_pair(U_14,U_6),U_12)
| U_17 != relation_dom(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_10,plain,
( in(ordered_pair(sK3(U_12,U_18),sK4(U_12,U_18)),U_12)
| in(sK2(U_12,U_18),U_18)
| U_18 = relation_dom(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_11,plain,
( ~ in(sK3(U_12,U_18),U_18)
| in(sK2(U_12,U_18),U_18)
| U_18 = relation_dom(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_12,plain,
( in(ordered_pair(sK3(U_12,U_18),sK4(U_12,U_18)),U_12)
| ~ in(ordered_pair(sK2(U_12,U_18),U_8),U_12)
| U_18 = relation_dom(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_13,plain,
( ~ in(sK3(U_12,U_18),U_18)
| ~ in(ordered_pair(sK2(U_12,U_18),U_8),U_12)
| U_18 = relation_dom(U_12)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_4_7]) ).
fof(f_5_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_5_2,plain,
! [U_26] :
( ! [U_25] :
( ( U_25 = relation_rng(U_26)
| ? [U_24] :
( ( ~ in(U_24,U_25)
& ? [U_23] : in(ordered_pair(U_23,U_24),U_26) )
| ( ! [U_22] : ~ in(ordered_pair(U_22,U_24),U_26)
& in(U_24,U_25) ) ) )
& ( ! [U_21] :
( ( in(U_21,U_25)
| ! [U_20] : ~ in(ordered_pair(U_20,U_21),U_26) )
& ( ? [U_19] : in(ordered_pair(U_19,U_21),U_26)
| ~ in(U_21,U_25) ) )
| U_25 != relation_rng(U_26) ) )
| ~ relation(U_26) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_rng(U_26)
| ? [U_30] :
( ~ in(U_30,U_32)
& ? [U_23] : in(ordered_pair(U_23,U_30),U_26) )
| ? [U_29] :
( ! [U_22] : ~ in(ordered_pair(U_22,U_29),U_26)
& in(U_29,U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_20,U_28),U_26) )
& ! [U_27] :
( ? [U_19] : in(ordered_pair(U_19,U_27),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_rng(U_26) ) )
| ~ relation(U_26) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_rng(U_26)
| ? [U_30] :
( ~ in(U_30,U_32)
& ? [U_23] : in(ordered_pair(U_23,U_30),U_26) )
| ? [U_29] :
( ! [U_22] : ~ in(ordered_pair(U_22,U_29),U_26)
& in(U_29,U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_20,U_28),U_26) )
& ! [U_27] :
( in(ordered_pair(sK5(U_26,U_31,U_27),U_27),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_rng(U_26) ) )
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_19,sK5(U_26,U_31,U_27))],[f_5_3]) ).
fof(f_5_5,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_rng(U_26)
| ? [U_30] :
( ~ in(U_30,U_32)
& ? [U_23] : in(ordered_pair(U_23,U_30),U_26) )
| ( ! [U_22] : ~ in(ordered_pair(U_22,sK6(U_26,U_32)),U_26)
& in(sK6(U_26,U_32),U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_20,U_28),U_26) )
& ! [U_27] :
( in(ordered_pair(sK5(U_26,U_31,U_27),U_27),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_rng(U_26) ) )
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_29,sK6(U_26,U_32))],[f_5_4]) ).
fof(f_5_6,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_rng(U_26)
| ( ~ in(sK7(U_26,U_32),U_32)
& ? [U_23] : in(ordered_pair(U_23,sK7(U_26,U_32)),U_26) )
| ( ! [U_22] : ~ in(ordered_pair(U_22,sK6(U_26,U_32)),U_26)
& in(sK6(U_26,U_32),U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_20,U_28),U_26) )
& ! [U_27] :
( in(ordered_pair(sK5(U_26,U_31,U_27),U_27),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_rng(U_26) ) )
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_30,sK7(U_26,U_32))],[f_5_5]) ).
fof(f_5_7,plain,
! [U_26] :
( ( ! [U_32] :
( U_32 = relation_rng(U_26)
| ( ~ in(sK7(U_26,U_32),U_32)
& in(ordered_pair(sK8(U_26,U_32),sK7(U_26,U_32)),U_26) )
| ( ! [U_22] : ~ in(ordered_pair(U_22,sK6(U_26,U_32)),U_26)
& in(sK6(U_26,U_32),U_32) ) )
& ! [U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ! [U_20] : ~ in(ordered_pair(U_20,U_28),U_26) )
& ! [U_27] :
( in(ordered_pair(sK5(U_26,U_31,U_27),U_27),U_26)
| ~ in(U_27,U_31) ) )
| U_31 != relation_rng(U_26) ) )
| ~ relation(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_23,sK8(U_26,U_32))],[f_5_6]) ).
cnf(f_5_8,plain,
( in(ordered_pair(sK5(U_26,U_31,U_27),U_27),U_26)
| ~ in(U_27,U_31)
| U_31 != relation_rng(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,plain,
( in(U_28,U_31)
| ~ in(ordered_pair(U_20,U_28),U_26)
| U_31 != relation_rng(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_10,plain,
( in(ordered_pair(sK8(U_26,U_32),sK7(U_26,U_32)),U_26)
| in(sK6(U_26,U_32),U_32)
| U_32 = relation_rng(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_11,plain,
( ~ in(sK7(U_26,U_32),U_32)
| in(sK6(U_26,U_32),U_32)
| U_32 = relation_rng(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_12,plain,
( in(ordered_pair(sK8(U_26,U_32),sK7(U_26,U_32)),U_26)
| ~ in(ordered_pair(U_22,sK6(U_26,U_32)),U_26)
| U_32 = relation_rng(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_13,plain,
( ~ in(sK7(U_26,U_32),U_32)
| ~ in(ordered_pair(U_22,sK6(U_26,U_32)),U_26)
| U_32 = relation_rng(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_5_7]) ).
fof(f_6_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_6_2,plain,
! [U_34,U_33] : ordered_pair(U_34,U_33) = unordered_pair(unordered_pair(U_34,U_33),singleton(U_34)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
ordered_pair(U_34,U_33) = unordered_pair(unordered_pair(U_34,U_33),singleton(U_34)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
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_tarski]) ).
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_xboole_0]) ).
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_k4_tarski]) ).
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_m1_subset_1]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_14_2,plain,
! [U_36] :
? [U_35] : element(U_35,U_36),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_36] : element(sK9(U_36),U_36),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_35,sK9(U_36))],[f_14_2]) ).
cnf(f_14_4,plain,
element(sK9(U_36),U_36),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_15_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_16_2,plain,
! [U_38,U_37] : ~ empty(ordered_pair(U_38,U_37)),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
~ empty(ordered_pair(U_38,U_37)),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_17_2,plain,
! [U_39] : ~ empty(singleton(U_39)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
~ empty(singleton(U_39)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_18_2,plain,
! [U_41,U_40] : ~ empty(unordered_pair(U_41,U_40)),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
~ empty(unordered_pair(U_41,U_40)),
inference(clausify,[status(thm)],[f_18_2]) ).
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_42] :
( ~ empty(relation_dom(U_42))
| ~ relation(U_42)
| empty(U_42) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ~ empty(relation_dom(U_42))
| ~ relation(U_42)
| empty(U_42) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_21_2,plain,
! [U_43] :
( ~ empty(relation_rng(U_43))
| ~ relation(U_43)
| empty(U_43) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( ~ empty(relation_rng(U_43))
| ~ relation(U_43)
| empty(U_43) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_22_2,plain,
! [U_44] :
( ( relation(relation_dom(U_44))
& empty(relation_dom(U_44)) )
| ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( empty(relation_dom(U_44))
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( relation(relation_dom(U_44))
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_23_2,plain,
! [U_45] :
( ( relation(relation_rng(U_45))
& empty(relation_rng(U_45)) )
| ~ empty(U_45) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( empty(relation_rng(U_45))
| ~ empty(U_45) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( relation(relation_rng(U_45))
| ~ empty(U_45) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_24_2,plain,
? [U_46] :
( relation(U_46)
& empty(U_46) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( relation(sK10)
& empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_46,sK10)],[f_24_2]) ).
cnf(f_24_4,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
relation(sK10),
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_47] : empty(U_47),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_47,sK11)],[f_25_2]) ).
cnf(f_25_4,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_26_2,plain,
? [U_48] :
( relation(U_48)
& ~ empty(U_48) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_48,sK12)],[f_26_2]) ).
cnf(f_26_4,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_27_2,plain,
? [U_49] : ~ empty(U_49),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_49,sK13)],[f_27_2]) ).
cnf(f_27_4,plain,
~ empty(sK13),
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_51,U_50] :
( element(U_51,U_50)
| ~ in(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( element(U_51,U_50)
| ~ in(U_51,U_50) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_29_2,plain,
! [U_53,U_52] :
( in(U_53,U_52)
| empty(U_52)
| ~ element(U_53,U_52) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( in(U_53,U_52)
| empty(U_52)
| ~ element(U_53,U_52) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A] :
( A = empty_set
| ? [B,C] : in(ordered_pair(B,C),A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[t56_relat_1]) ).
fof(f_30_2,plain,
! [U_56] :
( U_56 = empty_set
| ? [U_55,U_54] : in(ordered_pair(U_55,U_54),U_56)
| ~ relation(U_56) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_56] :
( U_56 = empty_set
| ? [U_54] : in(ordered_pair(sK14(U_56),U_54),U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_55,sK14(U_56))],[f_30_2]) ).
fof(f_30_4,plain,
! [U_56] :
( U_56 = empty_set
| in(ordered_pair(sK14(U_56),sK15(U_56)),U_56)
| ~ relation(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_54,sK15(U_56))],[f_30_3]) ).
cnf(f_30_5,plain,
( U_56 = empty_set
| in(ordered_pair(sK14(U_56),sK15(U_56)),U_56)
| ~ relation(U_56) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
inference(negate,[status(cth)],[t64_relat_1]) ).
fof(f_31_2,negated_conjecture,
? [A] :
( A != empty_set
& ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
& relation(A) ),
inference(fof_nnf,[status(thm)],[f_31_1]) ).
fof(f_31_3,negated_conjecture,
? [U_57] :
( U_57 != empty_set
& ( relation_rng(U_57) = empty_set
| relation_dom(U_57) = empty_set )
& relation(U_57) ),
inference(variable_rename,[status(thm)],[f_31_2]) ).
fof(f_31_4,negated_conjecture,
( sK16 != empty_set
& ( relation_rng(sK16) = empty_set
| relation_dom(sK16) = empty_set )
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_57,sK16)],[f_31_3]) ).
fof(f_31_5,negated_conjecture,
( sK16 != empty_set
& ( relation_rng(sK16) = empty_set
| relation_dom(sK16) = empty_set )
& relation(sK16) ),
inference(definitional_conversion,[status(esa)],[f_31_4]) ).
cnf(f_31_6,negated_conjecture,
relation(sK16),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_7,negated_conjecture,
( relation_rng(sK16) = empty_set
| relation_dom(sK16) = empty_set ),
inference(clausify,[status(thm)],[f_31_5]) ).
cnf(f_31_8,negated_conjecture,
sK16 != empty_set,
inference(clausify,[status(thm)],[f_31_5]) ).
fof(f_32_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_32_2,plain,
! [U_58] :
( U_58 = empty_set
| ~ empty(U_58) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( U_58 = empty_set
| ~ empty(U_58) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_33_2,plain,
! [U_60,U_59] :
( ~ empty(U_59)
| ~ in(U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( ~ empty(U_59)
| ~ in(U_60,U_59) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_34_2,plain,
! [U_62,U_61] :
( ~ empty(U_61)
| U_62 = U_61
| ~ empty(U_62) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_62] :
( ! [U_61] :
( ~ empty(U_61)
| U_62 = U_61 )
| ~ empty(U_62) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ empty(U_61)
| U_62 = U_61
| ~ empty(U_62) ),
inference(clausify,[status(thm)],[f_34_3]) ).
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(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_dom(Eq_x_0) = relation_dom(Eq_y_0)
| 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_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( singleton(Eq_x_0) = singleton(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) = 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_10,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_11,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_12,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_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) = sK6(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,
( 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,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_17,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK14(Eq_x_0) = sK14(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,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_21,axiom,
( empty(Eq_y_0)
| ~ empty(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,
( 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
% 0.00/0.01 % Problem : SEU188+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
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 19 23:28:23 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.08/0.36 % SZS status Theorem for theBenchmark
% 0.08/0.36 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------