%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 08:58:20 AM UTC 2026
% Result : Theorem 0.57s 0.87s
% Output : Proof 0.57s
% 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(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
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(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k3_subset_1) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_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(involutiveness_k3_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,subset_complement(A,B)) = B ),
file('theBenchmark.p',involutiveness_k3_subset_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_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(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t4_boole,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('theBenchmark.p',t4_boole) ).
fof(t50_subset_1,conjecture,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ( ( ( element(B,A)
| ~ empty(B) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( element(B,A)
| ~ in(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(fof_nnf,[status(thm)],[d2_subset_1]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ( ( ( element(U_2,U_3)
| ~ empty(U_2) )
& ( empty(U_2)
| ~ element(U_2,U_3) ) )
| ~ empty(U_3) )
& ( ( ( element(U_2,U_3)
| ~ in(U_2,U_3) )
& ( in(U_2,U_3)
| ~ element(U_2,U_3) ) )
| empty(U_3) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_11] :
( ( ! [U_9] :
( element(U_9,U_11)
| ~ empty(U_9) )
& ! [U_8] :
( empty(U_8)
| ~ element(U_8,U_11) ) )
| ~ empty(U_11) )
& ! [U_10] :
( ( ! [U_7] :
( element(U_7,U_10)
| ~ in(U_7,U_10) )
& ! [U_6] :
( in(U_6,U_10)
| ~ element(U_6,U_10) ) )
| empty(U_10) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( in(U_6,U_10)
| ~ element(U_6,U_10)
| empty(U_10) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( element(U_7,U_10)
| ~ in(U_7,U_10)
| empty(U_10) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( empty(U_8)
| ~ element(U_8,U_11)
| ~ empty(U_11) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_7,plain,
( element(U_9,U_11)
| ~ empty(U_9)
| ~ empty(U_11) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_16,U_15,U_14] :
( ( U_14 = set_difference(U_16,U_15)
| ? [U_13] :
( ( ~ in(U_13,U_14)
& ~ in(U_13,U_15)
& in(U_13,U_16) )
| ( ( in(U_13,U_15)
| ~ in(U_13,U_16) )
& in(U_13,U_14) ) ) )
& ( ! [U_12] :
( ( in(U_12,U_14)
| in(U_12,U_15)
| ~ in(U_12,U_16) )
& ( ( ~ in(U_12,U_15)
& in(U_12,U_16) )
| ~ in(U_12,U_14) ) )
| U_14 != set_difference(U_16,U_15) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_26,U_24,U_22] :
( U_22 = set_difference(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ~ in(U_20,U_24)
& in(U_20,U_26) )
| ? [U_19] :
( ( in(U_19,U_24)
| ~ in(U_19,U_26) )
& in(U_19,U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| in(U_18,U_23)
| ~ in(U_18,U_25) )
& ! [U_17] :
( ( ~ in(U_17,U_23)
& in(U_17,U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != set_difference(U_25,U_23) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_26,U_24,U_22] :
( U_22 = set_difference(U_26,U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& ~ in(U_20,U_24)
& in(U_20,U_26) )
| ( ( in(sK1(U_26,U_24,U_22),U_24)
| ~ in(sK1(U_26,U_24,U_22),U_26) )
& in(sK1(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| in(U_18,U_23)
| ~ in(U_18,U_25) )
& ! [U_17] :
( ( ~ in(U_17,U_23)
& in(U_17,U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != set_difference(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_19,sK1(U_26,U_24,U_22))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_26,U_24,U_22] :
( U_22 = set_difference(U_26,U_24)
| ( ~ in(sK2(U_26,U_24,U_22),U_22)
& ~ in(sK2(U_26,U_24,U_22),U_24)
& in(sK2(U_26,U_24,U_22),U_26) )
| ( ( in(sK1(U_26,U_24,U_22),U_24)
| ~ in(sK1(U_26,U_24,U_22),U_26) )
& in(sK1(U_26,U_24,U_22),U_22) ) )
& ! [U_25,U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| in(U_18,U_23)
| ~ in(U_18,U_25) )
& ! [U_17] :
( ( ~ in(U_17,U_23)
& in(U_17,U_25) )
| ~ in(U_17,U_21) ) )
| U_21 != set_difference(U_25,U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_20,sK2(U_26,U_24,U_22))],[f_3_4]) ).
cnf(f_3_6,plain,
( in(U_17,U_25)
| ~ in(U_17,U_21)
| U_21 != set_difference(U_25,U_23) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( ~ in(U_17,U_23)
| ~ in(U_17,U_21)
| U_21 != set_difference(U_25,U_23) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( in(U_18,U_21)
| in(U_18,U_23)
| ~ in(U_18,U_25)
| U_21 != set_difference(U_25,U_23) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( in(sK2(U_26,U_24,U_22),U_26)
| in(sK1(U_26,U_24,U_22),U_22)
| U_22 = set_difference(U_26,U_24) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( ~ in(sK2(U_26,U_24,U_22),U_24)
| in(sK1(U_26,U_24,U_22),U_22)
| U_22 = set_difference(U_26,U_24) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ in(sK2(U_26,U_24,U_22),U_22)
| in(sK1(U_26,U_24,U_22),U_22)
| U_22 = set_difference(U_26,U_24) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_12,plain,
( in(sK2(U_26,U_24,U_22),U_26)
| in(sK1(U_26,U_24,U_22),U_24)
| ~ in(sK1(U_26,U_24,U_22),U_26)
| U_22 = set_difference(U_26,U_24) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_13,plain,
( ~ in(sK2(U_26,U_24,U_22),U_24)
| in(sK1(U_26,U_24,U_22),U_24)
| ~ in(sK1(U_26,U_24,U_22),U_26)
| U_22 = set_difference(U_26,U_24) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_14,plain,
( ~ in(sK2(U_26,U_24,U_22),U_22)
| in(sK1(U_26,U_24,U_22),U_24)
| ~ in(sK1(U_26,U_24,U_22),U_26)
| U_22 = set_difference(U_26,U_24) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [A,B] :
( subset_complement(A,B) = set_difference(A,B)
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[d5_subset_1]) ).
fof(f_4_2,plain,
! [U_28,U_27] :
( subset_complement(U_28,U_27) = set_difference(U_28,U_27)
| ~ element(U_27,powerset(U_28)) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( subset_complement(U_28,U_27) = set_difference(U_28,U_27)
| ~ element(U_27,powerset(U_28)) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k3_subset_1]) ).
fof(f_7_2,plain,
! [U_30,U_29] :
( element(subset_complement(U_30,U_29),powerset(U_30))
| ~ element(U_29,powerset(U_30)) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( element(subset_complement(U_30,U_29),powerset(U_30))
| ~ element(U_29,powerset(U_30)) ),
inference(clausify,[status(thm)],[f_7_2]) ).
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,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_10_2,plain,
! [U_32] :
? [U_31] : element(U_31,U_32),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_32] : element(sK3(U_32),U_32),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_31,sK3(U_32))],[f_10_2]) ).
cnf(f_10_4,plain,
element(sK3(U_32),U_32),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_11_2,plain,
! [U_33] : ~ empty(powerset(U_33)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
~ empty(powerset(U_33)),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_12_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
! [A,B] :
( subset_complement(A,subset_complement(A,B)) = B
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1]) ).
fof(f_13_2,plain,
! [U_35,U_34] :
( subset_complement(U_35,subset_complement(U_35,U_34)) = U_34
| ~ element(U_34,powerset(U_35)) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( subset_complement(U_35,subset_complement(U_35,U_34)) = U_34
| ~ element(U_34,powerset(U_35)) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_14_2,plain,
! [U_37] :
( ? [U_36] :
( ~ empty(U_36)
& element(U_36,powerset(U_37)) )
| empty(U_37) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_37] :
( ( ~ empty(sK4(U_37))
& element(sK4(U_37),powerset(U_37)) )
| empty(U_37) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_36,sK4(U_37))],[f_14_2]) ).
cnf(f_14_4,plain,
( element(sK4(U_37),powerset(U_37))
| empty(U_37) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( ~ empty(sK4(U_37))
| empty(U_37) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_15_2,plain,
? [U_38] : empty(U_38),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_38,sK5)],[f_15_2]) ).
cnf(f_15_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_16_2,plain,
! [U_40] :
? [U_39] :
( empty(U_39)
& element(U_39,powerset(U_40)) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_40] :
( empty(sK6(U_40))
& element(sK6(U_40),powerset(U_40)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_39,sK6(U_40))],[f_16_2]) ).
cnf(f_16_4,plain,
element(sK6(U_40),powerset(U_40)),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
empty(sK6(U_40)),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_17_2,plain,
? [U_41] : ~ empty(U_41),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_41,sK7)],[f_17_2]) ).
cnf(f_17_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
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_42] : set_difference(U_42,empty_set) = U_42,
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
set_difference(U_42,empty_set) = U_42,
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_19_2,plain,
! [U_43] : set_difference(empty_set,U_43) = empty_set,
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
set_difference(empty_set,U_43) = empty_set,
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,negated_conjecture,
~ ! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
inference(negate,[status(cth)],[t50_subset_1]) ).
fof(f_20_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(C,subset_complement(A,B))
& ~ in(C,B)
& element(C,A) )
& element(B,powerset(A)) )
& A != empty_set ),
inference(fof_nnf,[status(thm)],[f_20_1]) ).
fof(f_20_3,negated_conjecture,
? [U_46] :
( ? [U_45] :
( ? [U_44] :
( ~ in(U_44,subset_complement(U_46,U_45))
& ~ in(U_44,U_45)
& element(U_44,U_46) )
& element(U_45,powerset(U_46)) )
& U_46 != empty_set ),
inference(variable_rename,[status(thm)],[f_20_2]) ).
fof(f_20_4,negated_conjecture,
( ? [U_45] :
( ? [U_44] :
( ~ in(U_44,subset_complement(sK8,U_45))
& ~ in(U_44,U_45)
& element(U_44,sK8) )
& element(U_45,powerset(sK8)) )
& sK8 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_46,sK8)],[f_20_3]) ).
fof(f_20_5,negated_conjecture,
( ? [U_44] :
( ~ in(U_44,subset_complement(sK8,sK9))
& ~ in(U_44,sK9)
& element(U_44,sK8) )
& element(sK9,powerset(sK8))
& sK8 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_45,sK9)],[f_20_4]) ).
fof(f_20_6,negated_conjecture,
( ~ in(sK10,subset_complement(sK8,sK9))
& ~ in(sK10,sK9)
& element(sK10,sK8)
& element(sK9,powerset(sK8))
& sK8 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_44,sK10)],[f_20_5]) ).
fof(f_20_7,negated_conjecture,
( ~ in(sK10,subset_complement(sK8,sK9))
& ~ in(sK10,sK9)
& element(sK10,sK8)
& element(sK9,powerset(sK8))
& sK8 != empty_set ),
inference(definitional_conversion,[status(esa)],[f_20_6]) ).
cnf(f_20_8,negated_conjecture,
sK8 != empty_set,
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_9,negated_conjecture,
element(sK9,powerset(sK8)),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_10,negated_conjecture,
element(sK10,sK8),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_11,negated_conjecture,
~ in(sK10,sK9),
inference(clausify,[status(thm)],[f_20_7]) ).
cnf(f_20_12,negated_conjecture,
~ in(sK10,subset_complement(sK8,sK9)),
inference(clausify,[status(thm)],[f_20_7]) ).
fof(f_21_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_21_2,plain,
! [U_47] :
( U_47 = empty_set
| ~ empty(U_47) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( U_47 = empty_set
| ~ empty(U_47) ),
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_49,U_48] :
( ~ empty(U_48)
| ~ in(U_49,U_48) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( ~ empty(U_48)
| ~ in(U_49,U_48) ),
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_51,U_50] :
( ~ empty(U_50)
| U_51 = U_50
| ~ empty(U_51) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_51] :
( ! [U_50] :
( ~ empty(U_50)
| U_51 = U_50 )
| ~ empty(U_51) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( ~ empty(U_50)
| U_51 = U_50
| ~ empty(U_51) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
cnf(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_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_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( subset_complement(Eq_x_0,Eq_x_1) = subset_complement(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,
( 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_8,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_9,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n007.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Sat Sep 19 23:23:04 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.57/0.87 % SZS status Theorem for theBenchmark
% 0.57/0.87 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------