%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU137+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 : n020.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 08:58:09 AM UTC 2026
% Result : Theorem 1.25s 6.57s
% Output : Proof 1.34s
% 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(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
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(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t45_xboole_1,conjecture,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('theBenchmark.p',t45_xboole_1) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_3_2,plain,
! [U_8,U_7,U_6] :
( ( U_6 = set_union2(U_8,U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& ( in(U_5,U_7)
| in(U_5,U_8) ) )
| ( ~ in(U_5,U_7)
& ~ in(U_5,U_8)
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| ( ~ in(U_4,U_7)
& ~ in(U_4,U_8) ) )
& ( in(U_4,U_7)
| in(U_4,U_8)
| ~ in(U_4,U_6) ) )
| U_6 != set_union2(U_8,U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( in(U_12,U_16)
| in(U_12,U_18) ) )
| ? [U_11] :
( ~ in(U_11,U_16)
& ~ in(U_11,U_18)
& in(U_11,U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( in(U_12,U_16)
| in(U_12,U_18) ) )
| ( ~ in(sK1(U_18,U_16,U_14),U_16)
& ~ in(sK1(U_18,U_16,U_14),U_18)
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_18,U_16,U_14))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_union2(U_18,U_16)
| ( ~ in(sK2(U_18,U_16,U_14),U_14)
& ( in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18) ) )
| ( ~ in(sK1(U_18,U_16,U_14),U_16)
& ~ in(sK1(U_18,U_16,U_14),U_18)
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( ~ in(U_10,U_15)
& ~ in(U_10,U_17) ) )
& ! [U_9] :
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13) ) )
| U_13 != set_union2(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_12,sK2(U_18,U_16,U_14))],[f_3_4]) ).
cnf(f_3_6,plain,
( in(U_9,U_15)
| in(U_9,U_17)
| ~ in(U_9,U_13)
| U_13 != set_union2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( ~ in(U_10,U_17)
| in(U_10,U_13)
| U_13 != set_union2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( ~ in(U_10,U_15)
| in(U_10,U_13)
| U_13 != set_union2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18)
| in(sK1(U_18,U_16,U_14),U_14)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( ~ in(sK2(U_18,U_16,U_14),U_14)
| in(sK1(U_18,U_16,U_14),U_14)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ in(sK1(U_18,U_16,U_14),U_18)
| in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_12,plain,
( ~ in(sK1(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_16)
| in(sK2(U_18,U_16,U_14),U_18)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_13,plain,
( ~ in(sK1(U_18,U_16,U_14),U_18)
| ~ in(sK2(U_18,U_16,U_14),U_14)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_14,plain,
( ~ in(sK1(U_18,U_16,U_14),U_16)
| ~ in(sK2(U_18,U_16,U_14),U_14)
| U_14 = set_union2(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_4_2,plain,
! [U_22,U_21] :
( ( subset(U_22,U_21)
| ? [U_20] :
( ~ in(U_20,U_21)
& in(U_20,U_22) ) )
& ( ! [U_19] :
( in(U_19,U_21)
| ~ in(U_19,U_22) )
| ~ subset(U_22,U_21) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_26,U_24] :
( subset(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_24)
& in(U_20,U_26) ) )
& ! [U_25,U_23] :
( ! [U_19] :
( in(U_19,U_23)
| ~ in(U_19,U_25) )
| ~ subset(U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_26,U_24] :
( subset(U_26,U_24)
| ( ~ in(sK3(U_26,U_24),U_24)
& in(sK3(U_26,U_24),U_26) ) )
& ! [U_25,U_23] :
( ! [U_19] :
( in(U_19,U_23)
| ~ in(U_19,U_25) )
| ~ subset(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3(U_26,U_24))],[f_4_3]) ).
cnf(f_4_5,plain,
( in(U_19,U_23)
| ~ in(U_19,U_25)
| ~ subset(U_25,U_23) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( in(sK3(U_26,U_24),U_26)
| subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( ~ in(sK3(U_26,U_24),U_24)
| subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [A,B,C] :
( ( C = set_difference(A,B)
| ? [D] :
( ( ~ in(D,C)
& ~ in(D,B)
& in(D,A) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| in(D,B)
| ~ in(D,A) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_5_2,plain,
! [U_31,U_30,U_29] :
( ( U_29 = set_difference(U_31,U_30)
| ? [U_28] :
( ( ~ in(U_28,U_29)
& ~ in(U_28,U_30)
& in(U_28,U_31) )
| ( ( in(U_28,U_30)
| ~ in(U_28,U_31) )
& in(U_28,U_29) ) ) )
& ( ! [U_27] :
( ( in(U_27,U_29)
| in(U_27,U_30)
| ~ in(U_27,U_31) )
& ( ( ~ in(U_27,U_30)
& in(U_27,U_31) )
| ~ in(U_27,U_29) ) )
| U_29 != set_difference(U_31,U_30) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_41,U_39,U_37] :
( U_37 = set_difference(U_41,U_39)
| ? [U_35] :
( ~ in(U_35,U_37)
& ~ in(U_35,U_39)
& in(U_35,U_41) )
| ? [U_34] :
( ( in(U_34,U_39)
| ~ in(U_34,U_41) )
& in(U_34,U_37) ) )
& ! [U_40,U_38,U_36] :
( ( ! [U_33] :
( in(U_33,U_36)
| in(U_33,U_38)
| ~ in(U_33,U_40) )
& ! [U_32] :
( ( ~ in(U_32,U_38)
& in(U_32,U_40) )
| ~ in(U_32,U_36) ) )
| U_36 != set_difference(U_40,U_38) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_41,U_39,U_37] :
( U_37 = set_difference(U_41,U_39)
| ? [U_35] :
( ~ in(U_35,U_37)
& ~ in(U_35,U_39)
& in(U_35,U_41) )
| ( ( in(sK4(U_41,U_39,U_37),U_39)
| ~ in(sK4(U_41,U_39,U_37),U_41) )
& in(sK4(U_41,U_39,U_37),U_37) ) )
& ! [U_40,U_38,U_36] :
( ( ! [U_33] :
( in(U_33,U_36)
| in(U_33,U_38)
| ~ in(U_33,U_40) )
& ! [U_32] :
( ( ~ in(U_32,U_38)
& in(U_32,U_40) )
| ~ in(U_32,U_36) ) )
| U_36 != set_difference(U_40,U_38) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_34,sK4(U_41,U_39,U_37))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_41,U_39,U_37] :
( U_37 = set_difference(U_41,U_39)
| ( ~ in(sK5(U_41,U_39,U_37),U_37)
& ~ in(sK5(U_41,U_39,U_37),U_39)
& in(sK5(U_41,U_39,U_37),U_41) )
| ( ( in(sK4(U_41,U_39,U_37),U_39)
| ~ in(sK4(U_41,U_39,U_37),U_41) )
& in(sK4(U_41,U_39,U_37),U_37) ) )
& ! [U_40,U_38,U_36] :
( ( ! [U_33] :
( in(U_33,U_36)
| in(U_33,U_38)
| ~ in(U_33,U_40) )
& ! [U_32] :
( ( ~ in(U_32,U_38)
& in(U_32,U_40) )
| ~ in(U_32,U_36) ) )
| U_36 != set_difference(U_40,U_38) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_35,sK5(U_41,U_39,U_37))],[f_5_4]) ).
cnf(f_5_6,plain,
( in(U_32,U_40)
| ~ in(U_32,U_36)
| U_36 != set_difference(U_40,U_38) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( ~ in(U_32,U_38)
| ~ in(U_32,U_36)
| U_36 != set_difference(U_40,U_38) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( in(U_33,U_36)
| in(U_33,U_38)
| ~ in(U_33,U_40)
| U_36 != set_difference(U_40,U_38) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( in(sK5(U_41,U_39,U_37),U_41)
| in(sK4(U_41,U_39,U_37),U_37)
| U_37 = set_difference(U_41,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_10,plain,
( ~ in(sK5(U_41,U_39,U_37),U_39)
| in(sK4(U_41,U_39,U_37),U_37)
| U_37 = set_difference(U_41,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_11,plain,
( ~ in(sK5(U_41,U_39,U_37),U_37)
| in(sK4(U_41,U_39,U_37),U_37)
| U_37 = set_difference(U_41,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_12,plain,
( in(sK5(U_41,U_39,U_37),U_41)
| in(sK4(U_41,U_39,U_37),U_39)
| ~ in(sK4(U_41,U_39,U_37),U_41)
| U_37 = set_difference(U_41,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_13,plain,
( ~ in(sK5(U_41,U_39,U_37),U_39)
| in(sK4(U_41,U_39,U_37),U_39)
| ~ in(sK4(U_41,U_39,U_37),U_41)
| U_37 = set_difference(U_41,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_14,plain,
( ~ in(sK5(U_41,U_39,U_37),U_37)
| in(sK4(U_41,U_39,U_37),U_39)
| ~ in(sK4(U_41,U_39,U_37),U_41)
| U_37 = set_difference(U_41,U_39) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
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_k4_xboole_0]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_9_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_10_2,plain,
! [U_43,U_42] :
( ~ empty(set_union2(U_43,U_42))
| empty(U_43) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_43] :
( ! [U_42] : ~ empty(set_union2(U_43,U_42))
| empty(U_43) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( ~ empty(set_union2(U_43,U_42))
| empty(U_43) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_11_2,plain,
! [U_45,U_44] :
( ~ empty(set_union2(U_44,U_45))
| empty(U_45) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_45] :
( ! [U_44] : ~ empty(set_union2(U_44,U_45))
| empty(U_45) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( ~ empty(set_union2(U_44,U_45))
| empty(U_45) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_12_2,plain,
! [U_47,U_46] : set_union2(U_47,U_47) = U_47,
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_47] : set_union2(U_47,U_47) = U_47,
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
set_union2(U_47,U_47) = U_47,
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_13_2,plain,
? [U_48] : empty(U_48),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_48,sK6)],[f_13_2]) ).
cnf(f_13_4,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_14_2,plain,
? [U_49] : ~ empty(U_49),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_49,sK7)],[f_14_2]) ).
cnf(f_14_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_15_2,plain,
! [U_51,U_50] : subset(U_51,U_51),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_51] : subset(U_51,U_51),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
subset(U_51,U_51),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_16_2,plain,
! [U_52] : set_union2(U_52,empty_set) = U_52,
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
set_union2(U_52,empty_set) = U_52,
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_17_2,plain,
! [U_55,U_54] :
( U_55 = U_54
| ? [U_53] :
( ( ~ in(U_53,U_55)
& in(U_53,U_54) )
| ( ~ in(U_53,U_54)
& in(U_53,U_55) ) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_55,U_54] :
( U_55 = U_54
| ? [U_57] :
( ~ in(U_57,U_55)
& in(U_57,U_54) )
| ? [U_56] :
( ~ in(U_56,U_54)
& in(U_56,U_55) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_55,U_54] :
( U_55 = U_54
| ? [U_57] :
( ~ in(U_57,U_55)
& in(U_57,U_54) )
| ( ~ in(sK8(U_55,U_54),U_54)
& in(sK8(U_55,U_54),U_55) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_56,sK8(U_55,U_54))],[f_17_3]) ).
fof(f_17_5,plain,
! [U_55,U_54] :
( U_55 = U_54
| ( ~ in(sK9(U_55,U_54),U_55)
& in(sK9(U_55,U_54),U_54) )
| ( ~ in(sK8(U_55,U_54),U_54)
& in(sK8(U_55,U_54),U_55) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_57,sK9(U_55,U_54))],[f_17_4]) ).
cnf(f_17_6,plain,
( in(sK9(U_55,U_54),U_54)
| in(sK8(U_55,U_54),U_55)
| U_55 = U_54 ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_7,plain,
( ~ in(sK9(U_55,U_54),U_55)
| in(sK8(U_55,U_54),U_55)
| U_55 = U_54 ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_8,plain,
( in(sK9(U_55,U_54),U_54)
| ~ in(sK8(U_55,U_54),U_54)
| U_55 = U_54 ),
inference(clausify,[status(thm)],[f_17_5]) ).
cnf(f_17_9,plain,
( ~ in(sK9(U_55,U_54),U_55)
| ~ in(sK8(U_55,U_54),U_54)
| U_55 = U_54 ),
inference(clausify,[status(thm)],[f_17_5]) ).
fof(f_18_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_18_2,plain,
! [U_58] : set_difference(U_58,empty_set) = U_58,
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
set_difference(U_58,empty_set) = U_58,
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
inference(negate,[status(cth)],[t45_xboole_1]) ).
fof(f_19_2,negated_conjecture,
? [A,B] :
( B != set_union2(A,set_difference(B,A))
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_19_1]) ).
fof(f_19_3,negated_conjecture,
? [U_60,U_59] :
( U_59 != set_union2(U_60,set_difference(U_59,U_60))
& subset(U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_19_2]) ).
fof(f_19_4,negated_conjecture,
? [U_59] :
( U_59 != set_union2(sK10,set_difference(U_59,sK10))
& subset(sK10,U_59) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_60,sK10)],[f_19_3]) ).
fof(f_19_5,negated_conjecture,
( sK11 != set_union2(sK10,set_difference(sK11,sK10))
& subset(sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_59,sK11)],[f_19_4]) ).
fof(f_19_6,negated_conjecture,
( sK11 != set_union2(sK10,set_difference(sK11,sK10))
& subset(sK10,sK11) ),
inference(definitional_conversion,[status(esa)],[f_19_5]) ).
cnf(f_19_7,negated_conjecture,
subset(sK10,sK11),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_8,negated_conjecture,
sK11 != set_union2(sK10,set_difference(sK11,sK10)),
inference(clausify,[status(thm)],[f_19_6]) ).
fof(f_20_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_20_2,plain,
! [U_61] : set_difference(empty_set,U_61) = empty_set,
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
set_difference(empty_set,U_61) = empty_set,
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_21_2,plain,
! [U_62] :
( U_62 = empty_set
| ~ empty(U_62) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( U_62 = empty_set
| ~ empty(U_62) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_22_2,plain,
! [U_64,U_63] :
( ~ empty(U_63)
| ~ in(U_64,U_63) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( ~ empty(U_63)
| ~ in(U_64,U_63) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_23_2,plain,
! [U_66,U_65] :
( ~ empty(U_65)
| U_66 = U_65
| ~ empty(U_66) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_66] :
( ! [U_65] :
( ~ empty(U_65)
| U_66 = U_65 )
| ~ empty(U_66) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( ~ empty(U_65)
| U_66 = U_65
| ~ empty(U_66) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_2]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(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,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(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_8,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_9,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(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,
( 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_11,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_12,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(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,
( 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_14,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(equality_15,axiom,
( empty(Eq_y_0)
| ~ 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 : SEU137+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.10/5.37 % Computer : n020.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 19 23:22:08 UTC 2026
% 0.10/5.37 % CPUTime :
% 1.25/6.57 % SZS status Theorem for theBenchmark
% 1.25/6.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------