%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU215+3 : TPTP v9.3.1. Released v3.2.0.
% 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 : n009.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 2.90s 3.14s
% Output : Proof 2.97s
% 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(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc10_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) ) ),
file('theBenchmark.p',fc10_relat_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_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
fof(fc2_subset_1,axiom,
! [A] : ~ empty(singleton(A)),
file('theBenchmark.p',fc2_subset_1) ).
fof(fc3_subset_1,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('theBenchmark.p',fc3_subset_1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('theBenchmark.p',fc5_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_relat_1) ).
fof(fc9_relat_1,axiom,
! [A,B] :
( ( relation(B)
& empty(A) )
=> ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc9_relat_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t21_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('theBenchmark.p',t21_funct_1) ).
fof(t22_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('theBenchmark.p',t22_funct_1) ).
fof(t23_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_3)
| ~ empty(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,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] : 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_18,U_17] : ordered_pair(U_18,U_17) = unordered_pair(unordered_pair(U_18,U_17),singleton(U_18)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
ordered_pair(U_18,U_17) = unordered_pair(unordered_pair(U_18,U_17),singleton(U_18)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k5_relat_1]) ).
fof(f_7_2,plain,
! [U_20,U_19] :
( relation(relation_composition(U_20,U_19))
| ~ relation(U_19)
| ~ relation(U_20) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( relation(relation_composition(U_20,U_19))
| ~ relation(U_19)
| ~ relation(U_20) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_8_2,plain,
! [U_22] :
? [U_21] : element(U_21,U_22),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_22] : element(sK1(U_22),U_22),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_21,sK1(U_22))],[f_8_2]) ).
cnf(f_8_4,plain,
element(sK1(U_22),U_22),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] :
( ( relation(relation_composition(B,A))
& empty(relation_composition(B,A)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc10_relat_1]) ).
fof(f_9_2,plain,
! [U_24,U_23] :
( ( relation(relation_composition(U_23,U_24))
& empty(relation_composition(U_23,U_24)) )
| ~ relation(U_23)
| ~ empty(U_24) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( empty(relation_composition(U_23,U_24))
| ~ relation(U_23)
| ~ empty(U_24) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( relation(relation_composition(U_23,U_24))
| ~ relation(U_23)
| ~ empty(U_24) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_10_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
cnf(f_10_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc1_funct_1]) ).
fof(f_11_2,plain,
! [U_26,U_25] :
( ( function(relation_composition(U_26,U_25))
& relation(relation_composition(U_26,U_25)) )
| ~ function(U_25)
| ~ relation(U_25)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(relation_composition(U_26,U_25))
| ~ function(U_25)
| ~ relation(U_25)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( function(relation_composition(U_26,U_25))
| ~ function(U_25)
| ~ relation(U_25)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_12_2,plain,
! [U_27] : ~ empty(powerset(U_27)),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
~ empty(powerset(U_27)),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_13_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_14_2,plain,
! [U_29,U_28] : ~ empty(ordered_pair(U_29,U_28)),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
~ empty(ordered_pair(U_29,U_28)),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] : ~ empty(singleton(A)),
inference(fof_nnf,[status(thm)],[fc2_subset_1]) ).
fof(f_15_2,plain,
! [U_30] : ~ empty(singleton(U_30)),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
~ empty(singleton(U_30)),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc3_subset_1]) ).
fof(f_16_2,plain,
! [U_32,U_31] : ~ empty(unordered_pair(U_32,U_31)),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
~ empty(unordered_pair(U_32,U_31)),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_17_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc5_relat_1]) ).
fof(f_18_2,plain,
! [U_33] :
( ~ empty(relation_dom(U_33))
| ~ relation(U_33)
| empty(U_33) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( ~ empty(relation_dom(U_33))
| ~ relation(U_33)
| empty(U_33) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_19_2,plain,
! [U_34] :
( ( relation(relation_dom(U_34))
& empty(relation_dom(U_34)) )
| ~ empty(U_34) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( empty(relation_dom(U_34))
| ~ empty(U_34) ),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( relation(relation_dom(U_34))
| ~ empty(U_34) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] :
( ( relation(relation_composition(A,B))
& empty(relation_composition(A,B)) )
| ~ relation(B)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc9_relat_1]) ).
fof(f_20_2,plain,
! [U_36,U_35] :
( ( relation(relation_composition(U_36,U_35))
& empty(relation_composition(U_36,U_35)) )
| ~ relation(U_35)
| ~ empty(U_36) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( empty(relation_composition(U_36,U_35))
| ~ relation(U_35)
| ~ empty(U_36) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( relation(relation_composition(U_36,U_35))
| ~ relation(U_35)
| ~ empty(U_36) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_21_2,plain,
? [U_37] :
( function(U_37)
& relation(U_37) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_37,sK2)],[f_21_2]) ).
cnf(f_21_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_22_2,plain,
? [U_38] :
( relation(U_38)
& empty(U_38) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_38,sK3)],[f_22_2]) ).
cnf(f_22_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_23_2,plain,
! [U_40] :
( ? [U_39] :
( ~ empty(U_39)
& element(U_39,powerset(U_40)) )
| empty(U_40) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_40] :
( ( ~ empty(sK4(U_40))
& element(sK4(U_40),powerset(U_40)) )
| empty(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_39,sK4(U_40))],[f_23_2]) ).
cnf(f_23_4,plain,
( element(sK4(U_40),powerset(U_40))
| empty(U_40) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( ~ empty(sK4(U_40))
| empty(U_40) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_24_2,plain,
? [U_41] : empty(U_41),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_41,sK5)],[f_24_2]) ).
cnf(f_24_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_25_2,plain,
? [U_42] :
( relation(U_42)
& ~ empty(U_42) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_25_2]) ).
cnf(f_25_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_26_2,plain,
! [U_44] :
? [U_43] :
( empty(U_43)
& element(U_43,powerset(U_44)) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_44] :
( empty(sK7(U_44))
& element(sK7(U_44),powerset(U_44)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_43,sK7(U_44))],[f_26_2]) ).
cnf(f_26_4,plain,
element(sK7(U_44),powerset(U_44)),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
empty(sK7(U_44)),
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_45] : ~ empty(U_45),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_45,sK8)],[f_27_2]) ).
cnf(f_27_4,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_28_2,plain,
? [U_46] :
( relation_empty_yielding(U_46)
& relation(U_46) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( relation_empty_yielding(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_46,sK9)],[f_28_2]) ).
cnf(f_28_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
relation_empty_yielding(sK9),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_29_2,plain,
! [U_48,U_47] : subset(U_48,U_48),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_48] : subset(U_48,U_48),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
subset(U_48,U_48),
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_50,U_49] :
( element(U_50,U_49)
| ~ in(U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( element(U_50,U_49)
| ~ in(U_50,U_49) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,B] :
( ! [C] :
( ( ( in(A,relation_dom(relation_composition(C,B)))
| ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C)) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t21_funct_1]) ).
fof(f_31_2,plain,
! [U_53,U_52] :
( ! [U_51] :
( ( ( in(U_53,relation_dom(relation_composition(U_51,U_52)))
| ~ in(apply(U_51,U_53),relation_dom(U_52))
| ~ in(U_53,relation_dom(U_51)) )
& ( ( in(apply(U_51,U_53),relation_dom(U_52))
& in(U_53,relation_dom(U_51)) )
| ~ in(U_53,relation_dom(relation_composition(U_51,U_52))) ) )
| ~ function(U_51)
| ~ relation(U_51) )
| ~ function(U_52)
| ~ relation(U_52) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( in(U_53,relation_dom(U_51))
| ~ in(U_53,relation_dom(relation_composition(U_51,U_52)))
| ~ function(U_51)
| ~ relation(U_51)
| ~ function(U_52)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( in(apply(U_51,U_53),relation_dom(U_52))
| ~ in(U_53,relation_dom(relation_composition(U_51,U_52)))
| ~ function(U_51)
| ~ relation(U_51)
| ~ function(U_52)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_5,plain,
( in(U_53,relation_dom(relation_composition(U_51,U_52)))
| ~ in(apply(U_51,U_53),relation_dom(U_52))
| ~ in(U_53,relation_dom(U_51))
| ~ function(U_51)
| ~ relation(U_51)
| ~ function(U_52)
| ~ relation(U_52) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B)))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_funct_1]) ).
fof(f_32_2,plain,
! [U_56,U_55] :
( ! [U_54] :
( apply(relation_composition(U_54,U_55),U_56) = apply(U_55,apply(U_54,U_56))
| ~ in(U_56,relation_dom(relation_composition(U_54,U_55)))
| ~ function(U_54)
| ~ relation(U_54) )
| ~ function(U_55)
| ~ relation(U_55) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( apply(relation_composition(U_54,U_55),U_56) = apply(U_55,apply(U_54,U_56))
| ~ in(U_56,relation_dom(relation_composition(U_54,U_55)))
| ~ function(U_54)
| ~ relation(U_54)
| ~ function(U_55)
| ~ relation(U_55) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
inference(negate,[status(cth)],[t23_funct_1]) ).
fof(f_33_2,negated_conjecture,
? [A,B] :
( ? [C] :
( apply(relation_composition(B,C),A) != apply(C,apply(B,A))
& in(A,relation_dom(B))
& function(C)
& relation(C) )
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
? [U_59,U_58] :
( ? [U_57] :
( apply(relation_composition(U_58,U_57),U_59) != apply(U_57,apply(U_58,U_59))
& in(U_59,relation_dom(U_58))
& function(U_57)
& relation(U_57) )
& function(U_58)
& relation(U_58) ),
inference(variable_rename,[status(thm)],[f_33_2]) ).
fof(f_33_4,negated_conjecture,
? [U_58] :
( ? [U_57] :
( apply(relation_composition(U_58,U_57),sK10) != apply(U_57,apply(U_58,sK10))
& in(sK10,relation_dom(U_58))
& function(U_57)
& relation(U_57) )
& function(U_58)
& relation(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_59,sK10)],[f_33_3]) ).
fof(f_33_5,negated_conjecture,
( ? [U_57] :
( apply(relation_composition(sK11,U_57),sK10) != apply(U_57,apply(sK11,sK10))
& in(sK10,relation_dom(sK11))
& function(U_57)
& relation(U_57) )
& function(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_58,sK11)],[f_33_4]) ).
fof(f_33_6,negated_conjecture,
( apply(relation_composition(sK11,sK12),sK10) != apply(sK12,apply(sK11,sK10))
& in(sK10,relation_dom(sK11))
& function(sK12)
& relation(sK12)
& function(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_57,sK12)],[f_33_5]) ).
fof(f_33_7,negated_conjecture,
( apply(relation_composition(sK11,sK12),sK10) != apply(sK12,apply(sK11,sK10))
& in(sK10,relation_dom(sK11))
& function(sK12)
& relation(sK12)
& function(sK11)
& relation(sK11) ),
inference(definitional_conversion,[status(esa)],[f_33_6]) ).
cnf(f_33_8,negated_conjecture,
relation(sK11),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_9,negated_conjecture,
function(sK11),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_10,negated_conjecture,
relation(sK12),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_11,negated_conjecture,
function(sK12),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_12,negated_conjecture,
in(sK10,relation_dom(sK11)),
inference(clausify,[status(thm)],[f_33_7]) ).
cnf(f_33_13,negated_conjecture,
apply(relation_composition(sK11,sK12),sK10) != apply(sK12,apply(sK11,sK10)),
inference(clausify,[status(thm)],[f_33_7]) ).
fof(f_34_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_34_2,plain,
! [U_61,U_60] :
( in(U_61,U_60)
| empty(U_60)
| ~ element(U_61,U_60) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( in(U_61,U_60)
| empty(U_60)
| ~ element(U_61,U_60) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_63,U_62] :
( ( element(U_63,powerset(U_62))
| ~ subset(U_63,U_62) )
& ( subset(U_63,U_62)
| ~ element(U_63,powerset(U_62)) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_67,U_65] :
( element(U_67,powerset(U_65))
| ~ subset(U_67,U_65) )
& ! [U_66,U_64] :
( subset(U_66,U_64)
| ~ element(U_66,powerset(U_64)) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( subset(U_66,U_64)
| ~ element(U_66,powerset(U_64)) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( element(U_67,powerset(U_65))
| ~ subset(U_67,U_65) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_36_2,plain,
! [U_70,U_69,U_68] :
( element(U_70,U_68)
| ~ element(U_69,powerset(U_68))
| ~ in(U_70,U_69) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( element(U_70,U_68)
| ~ element(U_69,powerset(U_68))
| ~ in(U_70,U_69) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_37_2,plain,
! [U_73,U_72,U_71] :
( ~ empty(U_71)
| ~ element(U_72,powerset(U_71))
| ~ in(U_73,U_72) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_73,U_72] :
( ! [U_71] :
( ~ empty(U_71)
| ~ element(U_72,powerset(U_71)) )
| ~ in(U_73,U_72) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( ~ empty(U_71)
| ~ element(U_72,powerset(U_71))
| ~ in(U_73,U_72) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_38_2,plain,
! [U_74] :
( U_74 = empty_set
| ~ empty(U_74) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( U_74 = empty_set
| ~ empty(U_74) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_39_2,plain,
! [U_76,U_75] :
( ~ empty(U_75)
| ~ in(U_76,U_75) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( ~ empty(U_75)
| ~ in(U_76,U_75) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_40_2,plain,
! [U_78,U_77] :
( ~ empty(U_77)
| U_78 = U_77
| ~ empty(U_78) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_78] :
( ! [U_77] :
( ~ empty(U_77)
| U_78 = U_77 )
| ~ empty(U_78) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
( ~ empty(U_77)
| U_78 = U_77
| ~ empty(U_78) ),
inference(clausify,[status(thm)],[f_40_3]) ).
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,
( relation_composition(Eq_x_0,Eq_x_1) = relation_composition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK7(Eq_x_0) = sK7(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(equality_20,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
% 0.00/0.03 % Problem : SEU215+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 19 23:32:26 UTC 2026
% 0.14/0.36 % CPUTime :
% 2.90/3.14 % SZS status Theorem for theBenchmark
% 2.90/3.14 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------