%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU174+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 : n016.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 08:58:21 AM UTC 2026
% Result : Theorem 93.78s 94.09s
% Output : Proof 94.14s
% 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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d8_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('theBenchmark.p',d8_setfam_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_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('theBenchmark.p',dt_k7_setfam_1) ).
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(involutiveness_k7_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('theBenchmark.p',involutiveness_k7_setfam_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(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(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(t46_setfam_1,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('theBenchmark.p',t46_setfam_1) ).
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,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_2_2,plain,
! [U_5,U_4] :
( ( subset(U_5,U_4)
| ? [U_3] :
( ~ in(U_3,U_4)
& in(U_3,U_5) ) )
& ( ! [U_2] :
( in(U_2,U_4)
| ~ in(U_2,U_5) )
| ~ subset(U_5,U_4) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_9,U_7] :
( subset(U_9,U_7)
| ? [U_3] :
( ~ in(U_3,U_7)
& in(U_3,U_9) ) )
& ! [U_8,U_6] :
( ! [U_2] :
( in(U_2,U_6)
| ~ in(U_2,U_8) )
| ~ subset(U_8,U_6) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_9,U_7] :
( subset(U_9,U_7)
| ( ~ in(sK1(U_9,U_7),U_7)
& in(sK1(U_9,U_7),U_9) ) )
& ! [U_8,U_6] :
( ! [U_2] :
( in(U_2,U_6)
| ~ in(U_2,U_8) )
| ~ subset(U_8,U_6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_9,U_7))],[f_2_3]) ).
cnf(f_2_5,plain,
( in(U_2,U_6)
| ~ in(U_2,U_8)
| ~ subset(U_8,U_6) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( in(sK1(U_9,U_7),U_9)
| subset(U_9,U_7) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( ~ in(sK1(U_9,U_7),U_7)
| subset(U_9,U_7) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [A,B] :
( ! [C] :
( ( ( C = complements_of_subsets(A,B)
| ? [D] :
( ( ( ~ in(D,C)
& in(subset_complement(A,D),B) )
| ( ~ in(subset_complement(A,D),B)
& in(D,C) ) )
& element(D,powerset(A)) ) )
& ( ! [D] :
( ( ( in(D,C)
| ~ in(subset_complement(A,D),B) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[d8_setfam_1]) ).
fof(f_3_2,plain,
! [U_14,U_13] :
( ! [U_12] :
( ( ( U_12 = complements_of_subsets(U_14,U_13)
| ? [U_11] :
( ( ( ~ in(U_11,U_12)
& in(subset_complement(U_14,U_11),U_13) )
| ( ~ in(subset_complement(U_14,U_11),U_13)
& in(U_11,U_12) ) )
& element(U_11,powerset(U_14)) ) )
& ( ! [U_10] :
( ( ( in(U_10,U_12)
| ~ in(subset_complement(U_14,U_10),U_13) )
& ( in(subset_complement(U_14,U_10),U_13)
| ~ in(U_10,U_12) ) )
| ~ element(U_10,powerset(U_14)) )
| U_12 != complements_of_subsets(U_14,U_13) ) )
| ~ element(U_12,powerset(powerset(U_14))) )
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_14,U_13] :
( ! [U_12] :
( ( ( U_12 = complements_of_subsets(U_14,U_13)
| ( ( ( ~ in(sK2(U_14,U_13,U_12),U_12)
& in(subset_complement(U_14,sK2(U_14,U_13,U_12)),U_13) )
| ( ~ in(subset_complement(U_14,sK2(U_14,U_13,U_12)),U_13)
& in(sK2(U_14,U_13,U_12),U_12) ) )
& element(sK2(U_14,U_13,U_12),powerset(U_14)) ) )
& ( ! [U_10] :
( ( ( in(U_10,U_12)
| ~ in(subset_complement(U_14,U_10),U_13) )
& ( in(subset_complement(U_14,U_10),U_13)
| ~ in(U_10,U_12) ) )
| ~ element(U_10,powerset(U_14)) )
| U_12 != complements_of_subsets(U_14,U_13) ) )
| ~ element(U_12,powerset(powerset(U_14))) )
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2(U_14,U_13,U_12))],[f_3_2]) ).
cnf(f_3_4,plain,
( in(subset_complement(U_14,U_10),U_13)
| ~ in(U_10,U_12)
| ~ element(U_10,powerset(U_14))
| U_12 != complements_of_subsets(U_14,U_13)
| ~ element(U_12,powerset(powerset(U_14)))
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( in(U_10,U_12)
| ~ in(subset_complement(U_14,U_10),U_13)
| ~ element(U_10,powerset(U_14))
| U_12 != complements_of_subsets(U_14,U_13)
| ~ element(U_12,powerset(powerset(U_14)))
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( element(sK2(U_14,U_13,U_12),powerset(U_14))
| U_12 = complements_of_subsets(U_14,U_13)
| ~ element(U_12,powerset(powerset(U_14)))
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_7,plain,
( in(subset_complement(U_14,sK2(U_14,U_13,U_12)),U_13)
| in(sK2(U_14,U_13,U_12),U_12)
| U_12 = complements_of_subsets(U_14,U_13)
| ~ element(U_12,powerset(powerset(U_14)))
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_8,plain,
( ~ in(sK2(U_14,U_13,U_12),U_12)
| in(sK2(U_14,U_13,U_12),U_12)
| U_12 = complements_of_subsets(U_14,U_13)
| ~ element(U_12,powerset(powerset(U_14)))
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_9,plain,
( in(subset_complement(U_14,sK2(U_14,U_13,U_12)),U_13)
| ~ in(subset_complement(U_14,sK2(U_14,U_13,U_12)),U_13)
| U_12 = complements_of_subsets(U_14,U_13)
| ~ element(U_12,powerset(powerset(U_14)))
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_10,plain,
( ~ in(sK2(U_14,U_13,U_12),U_12)
| ~ in(subset_complement(U_14,sK2(U_14,U_13,U_12)),U_13)
| U_12 = complements_of_subsets(U_14,U_13)
| ~ element(U_12,powerset(powerset(U_14)))
| ~ element(U_13,powerset(powerset(U_14))) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_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_6_2,plain,
! [U_16,U_15] :
( element(subset_complement(U_16,U_15),powerset(U_16))
| ~ element(U_15,powerset(U_16)) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( element(subset_complement(U_16,U_15),powerset(U_16))
| ~ element(U_15,powerset(U_16)) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k7_setfam_1]) ).
fof(f_7_2,plain,
! [U_18,U_17] :
( element(complements_of_subsets(U_18,U_17),powerset(powerset(U_18)))
| ~ element(U_17,powerset(powerset(U_18))) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( element(complements_of_subsets(U_18,U_17),powerset(powerset(U_18)))
| ~ element(U_17,powerset(powerset(U_18))) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_9_2,plain,
! [U_20] :
? [U_19] : element(U_19,U_20),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_20] : element(sK3(U_20),U_20),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3(U_20))],[f_9_2]) ).
cnf(f_9_4,plain,
element(sK3(U_20),U_20),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_10_2,plain,
! [U_21] : ~ empty(powerset(U_21)),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
~ empty(powerset(U_21)),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_11_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_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_12_2,plain,
! [U_23,U_22] :
( subset_complement(U_23,subset_complement(U_23,U_22)) = U_22
| ~ element(U_22,powerset(U_23)) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( subset_complement(U_23,subset_complement(U_23,U_22)) = U_22
| ~ element(U_22,powerset(U_23)) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B] :
( complements_of_subsets(A,complements_of_subsets(A,B)) = B
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1]) ).
fof(f_13_2,plain,
! [U_25,U_24] :
( complements_of_subsets(U_25,complements_of_subsets(U_25,U_24)) = U_24
| ~ element(U_24,powerset(powerset(U_25))) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( complements_of_subsets(U_25,complements_of_subsets(U_25,U_24)) = U_24
| ~ element(U_24,powerset(powerset(U_25))) ),
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_27] :
( ? [U_26] :
( ~ empty(U_26)
& element(U_26,powerset(U_27)) )
| empty(U_27) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_27] :
( ( ~ empty(sK4(U_27))
& element(sK4(U_27),powerset(U_27)) )
| empty(U_27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4(U_27))],[f_14_2]) ).
cnf(f_14_4,plain,
( element(sK4(U_27),powerset(U_27))
| empty(U_27) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( ~ empty(sK4(U_27))
| empty(U_27) ),
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_28] : empty(U_28),
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_28,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_30] :
? [U_29] :
( empty(U_29)
& element(U_29,powerset(U_30)) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_30] :
( empty(sK6(U_30))
& element(sK6(U_30),powerset(U_30)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_29,sK6(U_30))],[f_16_2]) ).
cnf(f_16_4,plain,
element(sK6(U_30),powerset(U_30)),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
empty(sK6(U_30)),
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_31] : ~ empty(U_31),
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_31,sK7)],[f_17_2]) ).
cnf(f_17_4,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_18_2,plain,
! [U_33,U_32] : subset(U_33,U_33),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_33] : subset(U_33,U_33),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
subset(U_33,U_33),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_19_2,plain,
! [U_35,U_34] :
( element(U_35,U_34)
| ~ in(U_35,U_34) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( element(U_35,U_34)
| ~ in(U_35,U_34) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_20_2,plain,
! [U_37,U_36] :
( in(U_37,U_36)
| empty(U_36)
| ~ element(U_37,U_36) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( in(U_37,U_36)
| empty(U_36)
| ~ element(U_37,U_36) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_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_21_2,plain,
! [U_39,U_38] :
( ( element(U_39,powerset(U_38))
| ~ subset(U_39,U_38) )
& ( subset(U_39,U_38)
| ~ element(U_39,powerset(U_38)) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_43,U_41] :
( element(U_43,powerset(U_41))
| ~ subset(U_43,U_41) )
& ! [U_42,U_40] :
( subset(U_42,U_40)
| ~ element(U_42,powerset(U_40)) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( subset(U_42,U_40)
| ~ element(U_42,powerset(U_40)) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( element(U_43,powerset(U_41))
| ~ subset(U_43,U_41) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
inference(negate,[status(cth)],[t46_setfam_1]) ).
fof(f_22_2,negated_conjecture,
? [A,B] :
( complements_of_subsets(A,B) = empty_set
& B != empty_set
& element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[f_22_1]) ).
fof(f_22_3,negated_conjecture,
? [U_45,U_44] :
( complements_of_subsets(U_45,U_44) = empty_set
& U_44 != empty_set
& element(U_44,powerset(powerset(U_45))) ),
inference(variable_rename,[status(thm)],[f_22_2]) ).
fof(f_22_4,negated_conjecture,
? [U_44] :
( complements_of_subsets(sK8,U_44) = empty_set
& U_44 != empty_set
& element(U_44,powerset(powerset(sK8))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_45,sK8)],[f_22_3]) ).
fof(f_22_5,negated_conjecture,
( complements_of_subsets(sK8,sK9) = empty_set
& sK9 != empty_set
& element(sK9,powerset(powerset(sK8))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_44,sK9)],[f_22_4]) ).
cnf(f_22_6,negated_conjecture,
element(sK9,powerset(powerset(sK8))),
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_7,negated_conjecture,
sK9 != empty_set,
inference(clausify,[status(thm)],[f_22_5]) ).
cnf(f_22_8,negated_conjecture,
complements_of_subsets(sK8,sK9) = empty_set,
inference(clausify,[status(thm)],[f_22_5]) ).
fof(f_23_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_23_2,plain,
! [U_48,U_47,U_46] :
( element(U_48,U_46)
| ~ element(U_47,powerset(U_46))
| ~ in(U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( element(U_48,U_46)
| ~ element(U_47,powerset(U_46))
| ~ in(U_48,U_47) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_24_2,plain,
! [U_51,U_50,U_49] :
( ~ empty(U_49)
| ~ element(U_50,powerset(U_49))
| ~ in(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_51,U_50] :
( ! [U_49] :
( ~ empty(U_49)
| ~ element(U_50,powerset(U_49)) )
| ~ in(U_51,U_50) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
( ~ empty(U_49)
| ~ element(U_50,powerset(U_49))
| ~ in(U_51,U_50) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_25_2,plain,
! [U_52] :
( U_52 = empty_set
| ~ empty(U_52) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( U_52 = empty_set
| ~ empty(U_52) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_26_2,plain,
! [U_54,U_53] :
( ~ empty(U_53)
| ~ in(U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ~ empty(U_53)
| ~ in(U_54,U_53) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_27_2,plain,
! [U_56,U_55] :
( ~ empty(U_55)
| U_56 = U_55
| ~ empty(U_56) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_56] :
( ! [U_55] :
( ~ empty(U_55)
| U_56 = U_55 )
| ~ empty(U_56) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( ~ empty(U_55)
| U_56 = U_55
| ~ empty(U_56) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_3_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_8]) ).
cnf(f_3_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_9]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( complements_of_subsets(Eq_x_0,Eq_x_1) = complements_of_subsets(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,
( 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) = sK1(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,
( 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,
( 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_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(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 : SEU174+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
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:30:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 93.78/94.09 % SZS status Theorem for theBenchmark
% 93.78/94.09 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------