%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM387+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n007.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 08:52:09 AM UTC 2026
% Result : Theorem 0.63s 0.90s
% Output : Proof 0.63s
% 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(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
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_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
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_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
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_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(rc5_funct_1,axiom,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
file('theBenchmark.p',rc5_funct_1) ).
fof(t10_ordinal1,axiom,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t14_ordinal1,conjecture,
! [A] : A != succ(A),
file('theBenchmark.p',t14_ordinal1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
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(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] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_4_2,plain,
! [U_4] :
( ( one_to_one(U_4)
& function(U_4)
& relation(U_4) )
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( function(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( one_to_one(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_5_2,plain,
! [U_6,U_5] : set_union2(U_6,U_5) = set_union2(U_5,U_6),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_union2(U_6,U_5) = set_union2(U_5,U_6),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_6_2,plain,
! [U_7] : succ(U_7) = set_union2(U_7,singleton(U_7)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
succ(U_7) = set_union2(U_7,singleton(U_7)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_7_2,plain,
! [U_9] :
? [U_8] : element(U_8,U_9),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_9] : element(sK1(U_9),U_9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_9))],[f_7_2]) ).
cnf(f_7_4,plain,
element(sK1(U_9),U_9),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_8_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
cnf(f_8_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_9_2,plain,
! [U_10] : ~ empty(succ(U_10)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
~ empty(succ(U_10)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_10_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_11_2,plain,
! [U_12,U_11] :
( relation(set_union2(U_12,U_11))
| ~ relation(U_11)
| ~ relation(U_12) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( relation(set_union2(U_12,U_11))
| ~ relation(U_11)
| ~ relation(U_12) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_12_2,plain,
! [U_14,U_13] :
( ~ empty(set_union2(U_14,U_13))
| empty(U_14) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_14] :
( ! [U_13] : ~ empty(set_union2(U_14,U_13))
| empty(U_14) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( ~ empty(set_union2(U_14,U_13))
| empty(U_14) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_13_2,plain,
! [U_16,U_15] :
( ~ empty(set_union2(U_15,U_16))
| empty(U_16) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_16] :
( ! [U_15] : ~ empty(set_union2(U_15,U_16))
| empty(U_16) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( ~ empty(set_union2(U_15,U_16))
| empty(U_16) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_14_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_15_2,plain,
! [U_18,U_17] : set_union2(U_18,U_18) = U_18,
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_18] : set_union2(U_18,U_18) = U_18,
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
set_union2(U_18,U_18) = U_18,
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_16_2,plain,
? [U_19] :
( function(U_19)
& relation(U_19) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_19,sK2)],[f_16_2]) ).
cnf(f_16_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_17_2,plain,
? [U_20] :
( relation(U_20)
& empty(U_20) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( relation(sK3)
& empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3)],[f_17_2]) ).
cnf(f_17_4,plain,
empty(sK3),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_18_2,plain,
? [U_21] : empty(U_21),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4)],[f_18_2]) ).
cnf(f_18_4,plain,
empty(sK4),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_19_2,plain,
? [U_22] :
( function(U_22)
& empty(U_22)
& relation(U_22) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( function(sK5)
& empty(sK5)
& relation(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_22,sK5)],[f_19_2]) ).
cnf(f_19_4,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
function(sK5),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_20_2,plain,
? [U_23] :
( relation(U_23)
& ~ empty(U_23) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( relation(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_23,sK6)],[f_20_2]) ).
cnf(f_20_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_21_2,plain,
? [U_24] : ~ empty(U_24),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_24,sK7)],[f_21_2]) ).
cnf(f_21_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_22_2,plain,
? [U_25] :
( one_to_one(U_25)
& function(U_25)
& relation(U_25) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( one_to_one(sK8)
& function(sK8)
& relation(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_25,sK8)],[f_22_2]) ).
cnf(f_22_4,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
function(sK8),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
one_to_one(sK8),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_23_2,plain,
? [U_26] :
( relation_empty_yielding(U_26)
& relation(U_26) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( relation_empty_yielding(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_26,sK9)],[f_23_2]) ).
cnf(f_23_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
relation_empty_yielding(sK9),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_24_2,plain,
? [U_27] :
( function(U_27)
& relation_empty_yielding(U_27)
& relation(U_27) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( function(sK10)
& relation_empty_yielding(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_27,sK10)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
relation_empty_yielding(sK10),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
function(sK10),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_25_2,plain,
? [U_28] :
( function(U_28)
& relation_non_empty(U_28)
& relation(U_28) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( function(sK11)
& relation_non_empty(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_28,sK11)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation_non_empty(sK11),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
function(sK11),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_26_2,plain,
! [U_29] : in(U_29,succ(U_29)),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
in(U_29,succ(U_29)),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,negated_conjecture,
~ ! [A] : A != succ(A),
inference(negate,[status(cth)],[t14_ordinal1]) ).
fof(f_27_2,negated_conjecture,
? [A] : A = succ(A),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
? [U_30] : U_30 = succ(U_30),
inference(variable_rename,[status(thm)],[f_27_2]) ).
fof(f_27_4,negated_conjecture,
sK12 = succ(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_30,sK12)],[f_27_3]) ).
fof(f_27_5,negated_conjecture,
sK12 = succ(sK12),
inference(definitional_conversion,[status(esa)],[f_27_4]) ).
cnf(f_27_6,negated_conjecture,
sK12 = succ(sK12),
inference(clausify,[status(thm)],[f_27_5]) ).
fof(f_28_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_28_2,plain,
! [U_31] : set_union2(U_31,empty_set) = U_31,
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
set_union2(U_31,empty_set) = U_31,
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_29_2,plain,
! [U_33,U_32] :
( element(U_33,U_32)
| ~ in(U_33,U_32) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( element(U_33,U_32)
| ~ in(U_33,U_32) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_30_2,plain,
! [U_35,U_34] :
( in(U_35,U_34)
| empty(U_34)
| ~ element(U_35,U_34) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( in(U_35,U_34)
| empty(U_34)
| ~ element(U_35,U_34) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_31_2,plain,
! [U_36] :
( U_36 = empty_set
| ~ empty(U_36) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( U_36 = empty_set
| ~ empty(U_36) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_32_2,plain,
! [U_38,U_37] :
( ~ empty(U_37)
| ~ in(U_38,U_37) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( ~ empty(U_37)
| ~ in(U_38,U_37) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_33_2,plain,
! [U_40,U_39] :
( ~ empty(U_39)
| U_40 = U_39
| ~ empty(U_40) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_40] :
( ! [U_39] :
( ~ empty(U_39)
| U_40 = U_39 )
| ~ empty(U_40) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( ~ empty(U_39)
| U_40 = U_39
| ~ empty(U_40) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
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,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(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,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,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_14,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_15,axiom,
( relation_non_empty(Eq_y_0)
| ~ relation_non_empty(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
% 0.00/0.03 % Problem : NUM387+1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.37 % Computer : n007.cluster.edu
% 0.07/0.37 % Model : x86_64 x86_64
% 0.07/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.37 % Memory : 8046.5625MB
% 0.07/0.37 % OS : Linux 6.8.0-71-generic
% 0.07/0.37 % CPULimit : 300
% 0.07/0.37 % WCLimit : 300
% 0.07/0.37 % DateTime : Sat Sep 19 18:18:51 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.63/0.90 % SZS status Theorem for theBenchmark
% 0.63/0.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------