%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU212+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 : 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 08:58:31 AM UTC 2026
% Result : Theorem 0.44s 0.73s
% Output : Proof 0.44s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
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_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k1_funct_1,axiom,
$true,
file('theBenchmark.p',dt_k1_funct_1) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
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(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(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(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_3)
| ~ empty(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_4_2,plain,
! [U_5,U_4] : unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
unordered_pair(U_5,U_4) = unordered_pair(U_4,U_5),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ! [B,C] :
( ( ( ( C = apply(A,B)
| C != empty_set )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_funct_1]) ).
fof(f_5_2,plain,
! [U_8] :
( ! [U_7,U_6] :
( ( ( ( U_6 = apply(U_8,U_7)
| U_6 != empty_set )
& ( U_6 = empty_set
| U_6 != apply(U_8,U_7) ) )
| in(U_7,relation_dom(U_8)) )
& ( ( ( U_6 = apply(U_8,U_7)
| ~ in(ordered_pair(U_7,U_6),U_8) )
& ( in(ordered_pair(U_7,U_6),U_8)
| U_6 != apply(U_8,U_7) ) )
| ~ in(U_7,relation_dom(U_8)) ) )
| ~ function(U_8)
| ~ relation(U_8) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_8] :
( ( ! [U_16] :
( ( ! [U_14] :
( U_14 = apply(U_8,U_16)
| U_14 != empty_set )
& ! [U_13] :
( U_13 = empty_set
| U_13 != apply(U_8,U_16) ) )
| in(U_16,relation_dom(U_8)) )
& ! [U_15] :
( ( ! [U_12] :
( U_12 = apply(U_8,U_15)
| ~ in(ordered_pair(U_15,U_12),U_8) )
& ! [U_11] :
( in(ordered_pair(U_15,U_11),U_8)
| U_11 != apply(U_8,U_15) ) )
| ~ in(U_15,relation_dom(U_8)) ) )
| ~ function(U_8)
| ~ relation(U_8) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( in(ordered_pair(U_15,U_11),U_8)
| U_11 != apply(U_8,U_15)
| ~ in(U_15,relation_dom(U_8))
| ~ function(U_8)
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( U_12 = apply(U_8,U_15)
| ~ in(ordered_pair(U_15,U_12),U_8)
| ~ in(U_15,relation_dom(U_8))
| ~ function(U_8)
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( U_13 = empty_set
| U_13 != apply(U_8,U_16)
| in(U_16,relation_dom(U_8))
| ~ function(U_8)
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( U_14 = apply(U_8,U_16)
| U_14 != empty_set
| in(U_16,relation_dom(U_8))
| ~ function(U_8)
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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_6_2,plain,
! [U_24] :
( ! [U_23] :
( ( U_23 = relation_dom(U_24)
| ? [U_22] :
( ( ~ in(U_22,U_23)
& ? [U_21] : in(ordered_pair(U_22,U_21),U_24) )
| ( ! [U_20] : ~ in(ordered_pair(U_22,U_20),U_24)
& in(U_22,U_23) ) ) )
& ( ! [U_19] :
( ( in(U_19,U_23)
| ! [U_18] : ~ in(ordered_pair(U_19,U_18),U_24) )
& ( ? [U_17] : in(ordered_pair(U_19,U_17),U_24)
| ~ in(U_19,U_23) ) )
| U_23 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ? [U_28] :
( ~ in(U_28,U_30)
& ? [U_21] : in(ordered_pair(U_28,U_21),U_24) )
| ? [U_27] :
( ! [U_20] : ~ in(ordered_pair(U_27,U_20),U_24)
& in(U_27,U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( ? [U_17] : in(ordered_pair(U_25,U_17),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ? [U_28] :
( ~ in(U_28,U_30)
& ? [U_21] : in(ordered_pair(U_28,U_21),U_24) )
| ? [U_27] :
( ! [U_20] : ~ in(ordered_pair(U_27,U_20),U_24)
& in(U_27,U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_17,sK1(U_24,U_29,U_25))],[f_6_3]) ).
fof(f_6_5,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ? [U_28] :
( ~ in(U_28,U_30)
& ? [U_21] : in(ordered_pair(U_28,U_21),U_24) )
| ( ! [U_20] : ~ in(ordered_pair(sK2(U_24,U_30),U_20),U_24)
& in(sK2(U_24,U_30),U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_27,sK2(U_24,U_30))],[f_6_4]) ).
fof(f_6_6,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ( ~ in(sK3(U_24,U_30),U_30)
& ? [U_21] : in(ordered_pair(sK3(U_24,U_30),U_21),U_24) )
| ( ! [U_20] : ~ in(ordered_pair(sK2(U_24,U_30),U_20),U_24)
& in(sK2(U_24,U_30),U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_28,sK3(U_24,U_30))],[f_6_5]) ).
fof(f_6_7,plain,
! [U_24] :
( ( ! [U_30] :
( U_30 = relation_dom(U_24)
| ( ~ in(sK3(U_24,U_30),U_30)
& in(ordered_pair(sK3(U_24,U_30),sK4(U_24,U_30)),U_24) )
| ( ! [U_20] : ~ in(ordered_pair(sK2(U_24,U_30),U_20),U_24)
& in(sK2(U_24,U_30),U_30) ) )
& ! [U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ! [U_18] : ~ in(ordered_pair(U_26,U_18),U_24) )
& ! [U_25] :
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29) ) )
| U_29 != relation_dom(U_24) ) )
| ~ relation(U_24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4(U_24,U_30))],[f_6_6]) ).
cnf(f_6_8,plain,
( in(ordered_pair(U_25,sK1(U_24,U_29,U_25)),U_24)
| ~ in(U_25,U_29)
| U_29 != relation_dom(U_24)
| ~ relation(U_24) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_9,plain,
( in(U_26,U_29)
| ~ in(ordered_pair(U_26,U_18),U_24)
| U_29 != relation_dom(U_24)
| ~ relation(U_24) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_10,plain,
( in(ordered_pair(sK3(U_24,U_30),sK4(U_24,U_30)),U_24)
| in(sK2(U_24,U_30),U_30)
| U_30 = relation_dom(U_24)
| ~ relation(U_24) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_11,plain,
( ~ in(sK3(U_24,U_30),U_30)
| in(sK2(U_24,U_30),U_30)
| U_30 = relation_dom(U_24)
| ~ relation(U_24) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_12,plain,
( in(ordered_pair(sK3(U_24,U_30),sK4(U_24,U_30)),U_24)
| ~ in(ordered_pair(sK2(U_24,U_30),U_20),U_24)
| U_30 = relation_dom(U_24)
| ~ relation(U_24) ),
inference(clausify,[status(thm)],[f_6_7]) ).
cnf(f_6_13,plain,
( ~ in(sK3(U_24,U_30),U_30)
| ~ in(ordered_pair(sK2(U_24,U_30),U_20),U_24)
| U_30 = relation_dom(U_24)
| ~ relation(U_24) ),
inference(clausify,[status(thm)],[f_6_7]) ).
fof(f_7_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_7_2,plain,
! [U_32,U_31] : ordered_pair(U_32,U_31) = unordered_pair(unordered_pair(U_32,U_31),singleton(U_32)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
ordered_pair(U_32,U_31) = unordered_pair(unordered_pair(U_32,U_31),singleton(U_32)),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_funct_1]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_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_k4_tarski]) ).
cnf(f_13_2,plain,
$true,
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_14_2,plain,
$true,
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_15_2,plain,
! [U_34] :
? [U_33] : element(U_33,U_34),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_34] : element(sK5(U_34),U_34),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_33,sK5(U_34))],[f_15_2]) ).
cnf(f_15_4,plain,
element(sK5(U_34),U_34),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_16_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_17_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_18_2,plain,
! [U_36,U_35] : ~ empty(ordered_pair(U_36,U_35)),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
~ empty(ordered_pair(U_36,U_35)),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_19_2,plain,
! [U_37] : ~ empty(singleton(U_37)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
~ empty(singleton(U_37)),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_20_2,plain,
! [U_39,U_38] : ~ empty(unordered_pair(U_39,U_38)),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
~ empty(unordered_pair(U_39,U_38)),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_21_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_22_2,plain,
! [U_40] :
( ~ empty(relation_dom(U_40))
| ~ relation(U_40)
| empty(U_40) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( ~ empty(relation_dom(U_40))
| ~ relation(U_40)
| empty(U_40) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_23_2,plain,
! [U_41] :
( ( relation(relation_dom(U_41))
& empty(relation_dom(U_41)) )
| ~ empty(U_41) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( empty(relation_dom(U_41))
| ~ empty(U_41) ),
inference(clausify,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( relation(relation_dom(U_41))
| ~ empty(U_41) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_24_2,plain,
? [U_42] :
( function(U_42)
& relation(U_42) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
function(sK6),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_25_2,plain,
? [U_43] :
( relation(U_43)
& empty(U_43) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation(sK7)
& empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_43,sK7)],[f_25_2]) ).
cnf(f_25_4,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_26_2,plain,
? [U_44] : empty(U_44),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_44,sK8)],[f_26_2]) ).
cnf(f_26_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_27_2,plain,
? [U_45] :
( relation(U_45)
& ~ empty(U_45) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_45,sK9)],[f_27_2]) ).
cnf(f_27_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_28_2,plain,
? [U_46] : ~ empty(U_46),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
~ empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_46,sK10)],[f_28_2]) ).
cnf(f_28_4,plain,
~ empty(sK10),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_29_2,plain,
? [U_47] :
( relation_empty_yielding(U_47)
& relation(U_47) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( relation_empty_yielding(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_47,sK11)],[f_29_2]) ).
cnf(f_29_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
relation_empty_yielding(sK11),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_30_2,plain,
! [U_49,U_48] :
( element(U_49,U_48)
| ~ in(U_49,U_48) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( element(U_49,U_48)
| ~ in(U_49,U_48) ),
inference(clausify,[status(thm)],[f_30_2]) ).
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_51,U_50] :
( in(U_51,U_50)
| empty(U_50)
| ~ element(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( in(U_51,U_50)
| empty(U_50)
| ~ element(U_51,U_50) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_32_2,plain,
! [U_52] :
( U_52 = empty_set
| ~ empty(U_52) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( U_52 = empty_set
| ~ empty(U_52) ),
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_54,U_53] :
( ~ empty(U_53)
| ~ in(U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( ~ empty(U_53)
| ~ in(U_54,U_53) ),
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_56,U_55] :
( ~ empty(U_55)
| U_56 = U_55
| ~ empty(U_56) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_56] :
( ! [U_55] :
( ~ empty(U_55)
| U_56 = U_55 )
| ~ empty(U_56) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ empty(U_55)
| U_56 = U_55
| ~ empty(U_56) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
inference(negate,[status(cth)],[t8_funct_1]) ).
fof(f_35_2,negated_conjecture,
? [A,B,C] :
( ( ( ~ in(ordered_pair(A,B),C)
& B = apply(C,A)
& in(A,relation_dom(C)) )
| ( ( B != apply(C,A)
| ~ in(A,relation_dom(C)) )
& in(ordered_pair(A,B),C) ) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
? [U_59,U_58,U_57] :
( ( ( ~ in(ordered_pair(U_59,U_58),U_57)
& U_58 = apply(U_57,U_59)
& in(U_59,relation_dom(U_57)) )
| ( ( U_58 != apply(U_57,U_59)
| ~ in(U_59,relation_dom(U_57)) )
& in(ordered_pair(U_59,U_58),U_57) ) )
& function(U_57)
& relation(U_57) ),
inference(variable_rename,[status(thm)],[f_35_2]) ).
fof(f_35_4,negated_conjecture,
? [U_58,U_57] :
( ( ( ~ in(ordered_pair(sK12,U_58),U_57)
& U_58 = apply(U_57,sK12)
& in(sK12,relation_dom(U_57)) )
| ( ( U_58 != apply(U_57,sK12)
| ~ in(sK12,relation_dom(U_57)) )
& in(ordered_pair(sK12,U_58),U_57) ) )
& function(U_57)
& relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_59,sK12)],[f_35_3]) ).
fof(f_35_5,negated_conjecture,
? [U_57] :
( ( ( ~ in(ordered_pair(sK12,sK13),U_57)
& sK13 = apply(U_57,sK12)
& in(sK12,relation_dom(U_57)) )
| ( ( sK13 != apply(U_57,sK12)
| ~ in(sK12,relation_dom(U_57)) )
& in(ordered_pair(sK12,sK13),U_57) ) )
& function(U_57)
& relation(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_58,sK13)],[f_35_4]) ).
fof(f_35_6,negated_conjecture,
( ( ( ~ in(ordered_pair(sK12,sK13),sK14)
& sK13 = apply(sK14,sK12)
& in(sK12,relation_dom(sK14)) )
| ( ( sK13 != apply(sK14,sK12)
| ~ in(sK12,relation_dom(sK14)) )
& in(ordered_pair(sK12,sK13),sK14) ) )
& function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_57,sK14)],[f_35_5]) ).
fof(f_35_7,negated_conjecture,
( ( ~ in(ordered_pair(sK12,sK13),sK14)
| ~ sP1 )
& ( sK13 = apply(sK14,sK12)
| ~ sP1 )
& ( in(sK12,relation_dom(sK14))
| ~ sP1 )
& ( sK13 != apply(sK14,sK12)
| ~ in(sK12,relation_dom(sK14))
| ~ sP0 )
& ( in(ordered_pair(sK12,sK13),sK14)
| ~ sP0 )
& ( sP1
| sP0 )
& function(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_35_6]) ).
cnf(f_35_8,negated_conjecture,
relation(sK14),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_9,negated_conjecture,
function(sK14),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_11,negated_conjecture,
( in(ordered_pair(sK12,sK13),sK14)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_12,negated_conjecture,
( sK13 != apply(sK14,sK12)
| ~ in(sK12,relation_dom(sK14))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_13,negated_conjecture,
( in(sK12,relation_dom(sK14))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_14,negated_conjecture,
( sK13 = apply(sK14,sK12)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_15,negated_conjecture,
( ~ in(ordered_pair(sK12,sK13),sK14)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_2]) ).
cnf(f_13_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_13_2]) ).
cnf(f_14_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( 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,
( apply(Eq_x_0,Eq_x_1) = apply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( 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_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) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU212+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sat Sep 19 23:31:41 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.44/0.73 % SZS status Theorem for theBenchmark
% 0.44/0.73 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------