%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU308+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 : n015.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 08:58:57 AM UTC 2026
% Result : Theorem 78.24s 78.59s
% Output : Proof 78.40s
% 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(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(cc1_membered,axiom,
! [A] :
( v5_membered(A)
=> v4_membered(A) ),
file('theBenchmark.p',cc1_membered) ).
fof(cc2_membered,axiom,
! [A] :
( v4_membered(A)
=> v3_membered(A) ),
file('theBenchmark.p',cc2_membered) ).
fof(cc3_membered,axiom,
! [A] :
( v3_membered(A)
=> v2_membered(A) ),
file('theBenchmark.p',cc3_membered) ).
fof(cc4_membered,axiom,
! [A] :
( v2_membered(A)
=> v1_membered(A) ),
file('theBenchmark.p',cc4_membered) ).
fof(rc1_membered,axiom,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_membered) ).
fof(cc10_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( element(B,A)
=> v1_xcmplx_0(B) ) ),
file('theBenchmark.p',cc10_membered) ).
fof(cc11_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc11_membered) ).
fof(cc12_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc12_membered) ).
fof(cc13_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc13_membered) ).
fof(cc14_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& natural(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc14_membered) ).
fof(fc6_membered,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc6_membered) ).
fof(cc16_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> v1_membered(B) ) ),
file('theBenchmark.p',cc16_membered) ).
fof(cc17_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc17_membered) ).
fof(cc18_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc18_membered) ).
fof(cc19_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc19_membered) ).
fof(cc20_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc20_membered) ).
fof(fc37_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(set_difference(A,B)) ),
file('theBenchmark.p',fc37_membered) ).
fof(fc38_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc38_membered) ).
fof(fc39_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc39_membered) ).
fof(fc40_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc40_membered) ).
fof(fc41_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v5_membered(set_difference(A,B))
& v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc41_membered) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
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(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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(cc15_membered,axiom,
! [A] :
( empty(A)
=> ( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A) ) ),
file('theBenchmark.p',cc15_membered) ).
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(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(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(redefinition_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_difference(A,B,C) = set_difference(B,C) ),
file('theBenchmark.p',redefinition_k6_subset_1) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k2_pre_topc) ).
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_k6_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_difference(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k6_subset_1) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(d3_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',d3_pre_topc) ).
fof(t17_pre_topc,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
file('theBenchmark.p',t17_pre_topc) ).
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(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,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_2_2,plain,
$true,
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
! [A] :
( v4_membered(A)
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc1_membered]) ).
fof(f_3_2,plain,
! [U_2] :
( v4_membered(U_2)
| ~ v5_membered(U_2) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v4_membered(U_2)
| ~ v5_membered(U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( v3_membered(A)
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc2_membered]) ).
fof(f_4_2,plain,
! [U_3] :
( v3_membered(U_3)
| ~ v4_membered(U_3) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v3_membered(U_3)
| ~ v4_membered(U_3) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( v2_membered(A)
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc3_membered]) ).
fof(f_5_2,plain,
! [U_4] :
( v2_membered(U_4)
| ~ v3_membered(U_4) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v2_membered(U_4)
| ~ v3_membered(U_4) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( v1_membered(A)
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc4_membered]) ).
fof(f_6_2,plain,
! [U_5] :
( v1_membered(U_5)
| ~ v2_membered(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( v1_membered(U_5)
| ~ v2_membered(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_membered]) ).
fof(f_7_2,plain,
? [U_6] :
( v5_membered(U_6)
& v4_membered(U_6)
& v3_membered(U_6)
& v2_membered(U_6)
& v1_membered(U_6)
& ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( v5_membered(sK1)
& v4_membered(sK1)
& v3_membered(sK1)
& v2_membered(sK1)
& v1_membered(sK1)
& ~ empty(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1)],[f_7_2]) ).
cnf(f_7_4,plain,
~ empty(sK1),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
v1_membered(sK1),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
v2_membered(sK1),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
v3_membered(sK1),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_8,plain,
v4_membered(sK1),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_9,plain,
v5_membered(sK1),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( v1_xcmplx_0(B)
| ~ element(B,A) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc10_membered]) ).
fof(f_8_2,plain,
! [U_8] :
( ! [U_7] :
( v1_xcmplx_0(U_7)
| ~ element(U_7,U_8) )
| ~ v1_membered(U_8) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( v1_xcmplx_0(U_7)
| ~ element(U_7,U_8)
| ~ v1_membered(U_8) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ! [B] :
( ( v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc11_membered]) ).
fof(f_9_2,plain,
! [U_10] :
( ! [U_9] :
( ( v1_xreal_0(U_9)
& v1_xcmplx_0(U_9) )
| ~ element(U_9,U_10) )
| ~ v2_membered(U_10) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( v1_xcmplx_0(U_9)
| ~ element(U_9,U_10)
| ~ v2_membered(U_10) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( v1_xreal_0(U_9)
| ~ element(U_9,U_10)
| ~ v2_membered(U_10) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc12_membered]) ).
fof(f_10_2,plain,
! [U_12] :
( ! [U_11] :
( ( v1_rat_1(U_11)
& v1_xreal_0(U_11)
& v1_xcmplx_0(U_11) )
| ~ element(U_11,U_12) )
| ~ v3_membered(U_12) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( v1_xcmplx_0(U_11)
| ~ element(U_11,U_12)
| ~ v3_membered(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( v1_xreal_0(U_11)
| ~ element(U_11,U_12)
| ~ v3_membered(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_5,plain,
( v1_rat_1(U_11)
| ~ element(U_11,U_12)
| ~ v3_membered(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc13_membered]) ).
fof(f_11_2,plain,
! [U_14] :
( ! [U_13] :
( ( v1_rat_1(U_13)
& v1_int_1(U_13)
& v1_xreal_0(U_13)
& v1_xcmplx_0(U_13) )
| ~ element(U_13,U_14) )
| ~ v4_membered(U_14) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_xcmplx_0(U_13)
| ~ element(U_13,U_14)
| ~ v4_membered(U_14) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( v1_xreal_0(U_13)
| ~ element(U_13,U_14)
| ~ v4_membered(U_14) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( v1_int_1(U_13)
| ~ element(U_13,U_14)
| ~ v4_membered(U_14) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_6,plain,
( v1_rat_1(U_13)
| ~ element(U_13,U_14)
| ~ v4_membered(U_14) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& natural(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc14_membered]) ).
fof(f_12_2,plain,
! [U_16] :
( ! [U_15] :
( ( v1_rat_1(U_15)
& v1_int_1(U_15)
& v1_xreal_0(U_15)
& natural(U_15)
& v1_xcmplx_0(U_15) )
| ~ element(U_15,U_16) )
| ~ v5_membered(U_16) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v1_xcmplx_0(U_15)
| ~ element(U_15,U_16)
| ~ v5_membered(U_16) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( natural(U_15)
| ~ element(U_15,U_16)
| ~ v5_membered(U_16) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
( v1_xreal_0(U_15)
| ~ element(U_15,U_16)
| ~ v5_membered(U_16) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_6,plain,
( v1_int_1(U_15)
| ~ element(U_15,U_16)
| ~ v5_membered(U_16) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_7,plain,
( v1_rat_1(U_15)
| ~ element(U_15,U_16)
| ~ v5_membered(U_16) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc6_membered]) ).
cnf(f_13_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
v1_membered(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
cnf(f_13_4,plain,
v2_membered(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
cnf(f_13_5,plain,
v3_membered(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
cnf(f_13_6,plain,
v4_membered(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
cnf(f_13_7,plain,
v5_membered(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A] :
( ! [B] :
( v1_membered(B)
| ~ element(B,powerset(A)) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc16_membered]) ).
fof(f_14_2,plain,
! [U_18] :
( ! [U_17] :
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18)) )
| ~ v1_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v1_membered(U_18) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ! [B] :
( ( v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc17_membered]) ).
fof(f_15_2,plain,
! [U_20] :
( ! [U_19] :
( ( v2_membered(U_19)
& v1_membered(U_19) )
| ~ element(U_19,powerset(U_20)) )
| ~ v2_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( v1_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v2_membered(U_20) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( v2_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v2_membered(U_20) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( ! [B] :
( ( v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc18_membered]) ).
fof(f_16_2,plain,
! [U_22] :
( ! [U_21] :
( ( v3_membered(U_21)
& v2_membered(U_21)
& v1_membered(U_21) )
| ~ element(U_21,powerset(U_22)) )
| ~ v3_membered(U_22) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( v1_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v3_membered(U_22) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( v2_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v3_membered(U_22) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_5,plain,
( v3_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v3_membered(U_22) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] :
( ! [B] :
( ( v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc19_membered]) ).
fof(f_17_2,plain,
! [U_24] :
( ! [U_23] :
( ( v4_membered(U_23)
& v3_membered(U_23)
& v2_membered(U_23)
& v1_membered(U_23) )
| ~ element(U_23,powerset(U_24)) )
| ~ v4_membered(U_24) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( v1_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v4_membered(U_24) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( v2_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v4_membered(U_24) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_5,plain,
( v3_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v4_membered(U_24) ),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_6,plain,
( v4_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v4_membered(U_24) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( ! [B] :
( ( v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc20_membered]) ).
fof(f_18_2,plain,
! [U_26] :
( ! [U_25] :
( ( v5_membered(U_25)
& v4_membered(U_25)
& v3_membered(U_25)
& v2_membered(U_25)
& v1_membered(U_25) )
| ~ element(U_25,powerset(U_26)) )
| ~ v5_membered(U_26) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( v1_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v5_membered(U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( v2_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v5_membered(U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_5,plain,
( v3_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v5_membered(U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_6,plain,
( v4_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v5_membered(U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_7,plain,
( v5_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v5_membered(U_26) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A,B] :
( v1_membered(set_difference(A,B))
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[fc37_membered]) ).
fof(f_19_2,plain,
! [U_28,U_27] :
( v1_membered(set_difference(U_28,U_27))
| ~ v1_membered(U_28) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_28] :
( ! [U_27] : v1_membered(set_difference(U_28,U_27))
| ~ v1_membered(U_28) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( v1_membered(set_difference(U_28,U_27))
| ~ v1_membered(U_28) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A,B] :
( ( v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[fc38_membered]) ).
fof(f_20_2,plain,
! [U_30,U_29] :
( ( v2_membered(set_difference(U_30,U_29))
& v1_membered(set_difference(U_30,U_29)) )
| ~ v2_membered(U_30) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_30] :
( ( ! [U_32] : v2_membered(set_difference(U_30,U_32))
& ! [U_31] : v1_membered(set_difference(U_30,U_31)) )
| ~ v2_membered(U_30) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( v1_membered(set_difference(U_30,U_31))
| ~ v2_membered(U_30) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( v2_membered(set_difference(U_30,U_32))
| ~ v2_membered(U_30) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] :
( ( v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[fc39_membered]) ).
fof(f_21_2,plain,
! [U_34,U_33] :
( ( v3_membered(set_difference(U_34,U_33))
& v2_membered(set_difference(U_34,U_33))
& v1_membered(set_difference(U_34,U_33)) )
| ~ v3_membered(U_34) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_34] :
( ( ! [U_37] : v3_membered(set_difference(U_34,U_37))
& ! [U_36] : v2_membered(set_difference(U_34,U_36))
& ! [U_35] : v1_membered(set_difference(U_34,U_35)) )
| ~ v3_membered(U_34) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( v1_membered(set_difference(U_34,U_35))
| ~ v3_membered(U_34) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( v2_membered(set_difference(U_34,U_36))
| ~ v3_membered(U_34) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
( v3_membered(set_difference(U_34,U_37))
| ~ v3_membered(U_34) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] :
( ( v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[fc40_membered]) ).
fof(f_22_2,plain,
! [U_39,U_38] :
( ( v4_membered(set_difference(U_39,U_38))
& v3_membered(set_difference(U_39,U_38))
& v2_membered(set_difference(U_39,U_38))
& v1_membered(set_difference(U_39,U_38)) )
| ~ v4_membered(U_39) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_39] :
( ( ! [U_43] : v4_membered(set_difference(U_39,U_43))
& ! [U_42] : v3_membered(set_difference(U_39,U_42))
& ! [U_41] : v2_membered(set_difference(U_39,U_41))
& ! [U_40] : v1_membered(set_difference(U_39,U_40)) )
| ~ v4_membered(U_39) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( v1_membered(set_difference(U_39,U_40))
| ~ v4_membered(U_39) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( v2_membered(set_difference(U_39,U_41))
| ~ v4_membered(U_39) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
( v3_membered(set_difference(U_39,U_42))
| ~ v4_membered(U_39) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_7,plain,
( v4_membered(set_difference(U_39,U_43))
| ~ v4_membered(U_39) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A,B] :
( ( v5_membered(set_difference(A,B))
& v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[fc41_membered]) ).
fof(f_23_2,plain,
! [U_45,U_44] :
( ( v5_membered(set_difference(U_45,U_44))
& v4_membered(set_difference(U_45,U_44))
& v3_membered(set_difference(U_45,U_44))
& v2_membered(set_difference(U_45,U_44))
& v1_membered(set_difference(U_45,U_44)) )
| ~ v5_membered(U_45) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_45] :
( ( ! [U_50] : v5_membered(set_difference(U_45,U_50))
& ! [U_49] : v4_membered(set_difference(U_45,U_49))
& ! [U_48] : v3_membered(set_difference(U_45,U_48))
& ! [U_47] : v2_membered(set_difference(U_45,U_47))
& ! [U_46] : v1_membered(set_difference(U_45,U_46)) )
| ~ v5_membered(U_45) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( v1_membered(set_difference(U_45,U_46))
| ~ v5_membered(U_45) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( v2_membered(set_difference(U_45,U_47))
| ~ v5_membered(U_45) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_6,plain,
( v3_membered(set_difference(U_45,U_48))
| ~ v5_membered(U_45) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_7,plain,
( v4_membered(set_difference(U_45,U_49))
| ~ v5_membered(U_45) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_8,plain,
( v5_membered(set_difference(U_45,U_50))
| ~ v5_membered(U_45) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_24_2,plain,
! [U_52,U_51] :
( element(U_52,U_51)
| ~ in(U_52,U_51) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( element(U_52,U_51)
| ~ in(U_52,U_51) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_25_2,plain,
! [U_53] : set_difference(U_53,empty_set) = U_53,
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
set_difference(U_53,empty_set) = U_53,
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_26_2,plain,
! [U_54] : set_difference(empty_set,U_54) = empty_set,
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
set_difference(empty_set,U_54) = empty_set,
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_27_2,plain,
! [U_57,U_56,U_55] :
( element(U_57,U_55)
| ~ element(U_56,powerset(U_55))
| ~ in(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( element(U_57,U_55)
| ~ element(U_56,powerset(U_55))
| ~ in(U_57,U_56) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_28_2,plain,
! [U_60,U_59,U_58] :
( ~ empty(U_58)
| ~ element(U_59,powerset(U_58))
| ~ in(U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_60,U_59] :
( ! [U_58] :
( ~ empty(U_58)
| ~ element(U_59,powerset(U_58)) )
| ~ in(U_60,U_59) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( ~ empty(U_58)
| ~ element(U_59,powerset(U_58))
| ~ in(U_60,U_59) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_29_2,plain,
! [U_62,U_61] : subset(U_62,U_62),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_62] : subset(U_62,U_62),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
subset(U_62,U_62),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_30_2,plain,
! [U_64] :
( ? [U_63] :
( ~ empty(U_63)
& element(U_63,powerset(U_64)) )
| empty(U_64) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_64] :
( ( ~ empty(sK2(U_64))
& element(sK2(U_64),powerset(U_64)) )
| empty(U_64) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_63,sK2(U_64))],[f_30_2]) ).
cnf(f_30_4,plain,
( element(sK2(U_64),powerset(U_64))
| empty(U_64) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ empty(sK2(U_64))
| empty(U_64) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_31_2,plain,
! [U_66] :
? [U_65] :
( empty(U_65)
& element(U_65,powerset(U_66)) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_66] :
( empty(sK3(U_66))
& element(sK3(U_66),powerset(U_66)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_65,sK3(U_66))],[f_31_2]) ).
cnf(f_31_4,plain,
element(sK3(U_66),powerset(U_66)),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
empty(sK3(U_66)),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] :
( ( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc15_membered]) ).
fof(f_32_2,plain,
! [U_67] :
( ( v5_membered(U_67)
& v4_membered(U_67)
& v3_membered(U_67)
& v2_membered(U_67)
& v1_membered(U_67) )
| ~ empty(U_67) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( v1_membered(U_67)
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( v2_membered(U_67)
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_32_2]) ).
cnf(f_32_5,plain,
( v3_membered(U_67)
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_32_2]) ).
cnf(f_32_6,plain,
( v4_membered(U_67)
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_32_2]) ).
cnf(f_32_7,plain,
( v5_membered(U_67)
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_33_2,plain,
! [U_69,U_68] :
( in(U_69,U_68)
| empty(U_68)
| ~ element(U_69,U_68) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( in(U_69,U_68)
| empty(U_68)
| ~ element(U_69,U_68) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_34_2,plain,
! [U_70] :
( U_70 = empty_set
| ~ empty(U_70) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( U_70 = empty_set
| ~ empty(U_70) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_35_2,plain,
! [U_72,U_71] :
( ~ empty(U_71)
| ~ in(U_72,U_71) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( ~ empty(U_71)
| ~ in(U_72,U_71) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_74,U_73] :
( ~ empty(U_73)
| U_74 = U_73
| ~ empty(U_74) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_74] :
( ! [U_73] :
( ~ empty(U_73)
| U_74 = U_73 )
| ~ empty(U_74) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_73)
| U_74 = U_73
| ~ empty(U_74) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_76,U_75] :
( subset_complement(U_76,subset_complement(U_76,U_75)) = U_75
| ~ element(U_75,powerset(U_76)) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( subset_complement(U_76,subset_complement(U_76,U_75)) = U_75
| ~ element(U_75,powerset(U_76)) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_38_2,plain,
? [U_77] : one_sorted_str(U_77),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
one_sorted_str(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_77,sK4)],[f_38_2]) ).
cnf(f_38_4,plain,
one_sorted_str(sK4),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_39_2,plain,
! [U_79] :
? [U_78] : element(U_78,U_79),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_79] : element(sK5(U_79),U_79),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_78,sK5(U_79))],[f_39_2]) ).
cnf(f_39_4,plain,
element(sK5(U_79),U_79),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B,C] :
( subset_difference(A,B,C) = set_difference(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1]) ).
fof(f_40_2,plain,
! [U_82,U_81,U_80] :
( subset_difference(U_82,U_81,U_80) = set_difference(U_81,U_80)
| ~ element(U_80,powerset(U_82))
| ~ element(U_81,powerset(U_82)) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( subset_difference(U_82,U_81,U_80) = set_difference(U_81,U_80)
| ~ element(U_80,powerset(U_82))
| ~ element(U_81,powerset(U_82)) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_41_2,plain,
$true,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_pre_topc]) ).
fof(f_42_2,plain,
! [U_83] :
( element(cast_as_carrier_subset(U_83),powerset(the_carrier(U_83)))
| ~ one_sorted_str(U_83) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( element(cast_as_carrier_subset(U_83),powerset(the_carrier(U_83)))
| ~ one_sorted_str(U_83) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_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_43_2,plain,
! [U_85,U_84] :
( element(subset_complement(U_85,U_84),powerset(U_85))
| ~ element(U_84,powerset(U_85)) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( element(subset_complement(U_85,U_84),powerset(U_85))
| ~ element(U_84,powerset(U_85)) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_44_2,plain,
$true,
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
! [A,B,C] :
( element(subset_difference(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k6_subset_1]) ).
fof(f_45_2,plain,
! [U_88,U_87,U_86] :
( element(subset_difference(U_88,U_87,U_86),powerset(U_88))
| ~ element(U_86,powerset(U_88))
| ~ element(U_87,powerset(U_88)) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( element(subset_difference(U_88,U_87,U_86),powerset(U_88))
| ~ element(U_86,powerset(U_88))
| ~ element(U_87,powerset(U_88)) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_46_2,plain,
$true,
inference(clausify,[status(thm)],[f_46_1]) ).
fof(f_47_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_47_2,plain,
$true,
inference(clausify,[status(thm)],[f_47_1]) ).
fof(f_48_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_48_2,plain,
$true,
inference(clausify,[status(thm)],[f_48_1]) ).
fof(f_49_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_49_2,plain,
! [U_89] : ~ empty(powerset(U_89)),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
~ empty(powerset(U_89)),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_91,U_90] :
( ( element(U_91,powerset(U_90))
| ~ subset(U_91,U_90) )
& ( subset(U_91,U_90)
| ~ element(U_91,powerset(U_90)) ) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( ! [U_95,U_93] :
( element(U_95,powerset(U_93))
| ~ subset(U_95,U_93) )
& ! [U_94,U_92] :
( subset(U_94,U_92)
| ~ element(U_94,powerset(U_92)) ) ),
inference(miniscope,[status(thm)],[f_50_2]) ).
cnf(f_50_4,plain,
( subset(U_94,U_92)
| ~ element(U_94,powerset(U_92)) ),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_5,plain,
( element(U_95,powerset(U_93))
| ~ subset(U_95,U_93) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[d3_pre_topc]) ).
fof(f_51_2,plain,
! [U_96] :
( cast_as_carrier_subset(U_96) = the_carrier(U_96)
| ~ one_sorted_str(U_96) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( cast_as_carrier_subset(U_96) = the_carrier(U_96)
| ~ one_sorted_str(U_96) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ) ),
inference(negate,[status(cth)],[t17_pre_topc]) ).
fof(f_52_2,negated_conjecture,
? [A] :
( ? [B] :
( subset_complement(the_carrier(A),B) != subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[f_52_1]) ).
fof(f_52_3,negated_conjecture,
? [U_98] :
( ? [U_97] :
( subset_complement(the_carrier(U_98),U_97) != subset_difference(the_carrier(U_98),cast_as_carrier_subset(U_98),U_97)
& element(U_97,powerset(the_carrier(U_98))) )
& one_sorted_str(U_98) ),
inference(variable_rename,[status(thm)],[f_52_2]) ).
fof(f_52_4,negated_conjecture,
( ? [U_97] :
( subset_complement(the_carrier(sK6),U_97) != subset_difference(the_carrier(sK6),cast_as_carrier_subset(sK6),U_97)
& element(U_97,powerset(the_carrier(sK6))) )
& one_sorted_str(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_98,sK6)],[f_52_3]) ).
fof(f_52_5,negated_conjecture,
( subset_complement(the_carrier(sK6),sK7) != subset_difference(the_carrier(sK6),cast_as_carrier_subset(sK6),sK7)
& element(sK7,powerset(the_carrier(sK6)))
& one_sorted_str(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_97,sK7)],[f_52_4]) ).
cnf(f_52_6,negated_conjecture,
one_sorted_str(sK6),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_7,negated_conjecture,
element(sK7,powerset(the_carrier(sK6))),
inference(clausify,[status(thm)],[f_52_5]) ).
cnf(f_52_8,negated_conjecture,
subset_complement(the_carrier(sK6),sK7) != subset_difference(the_carrier(sK6),cast_as_carrier_subset(sK6),sK7),
inference(clausify,[status(thm)],[f_52_5]) ).
fof(f_53_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_53_2,plain,
! [U_100,U_99] :
( subset_complement(U_100,U_99) = set_difference(U_100,U_99)
| ~ element(U_99,powerset(U_100)) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( subset_complement(U_100,U_99) = set_difference(U_100,U_99)
| ~ element(U_99,powerset(U_100)) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_2_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_2]) ).
cnf(f_41_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_41_2]) ).
cnf(f_44_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_44_2]) ).
cnf(f_46_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_46_2]) ).
cnf(f_47_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_47_2]) ).
cnf(f_48_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_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,
( 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,
( 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,
( subset_difference(Eq_x_0,Eq_x_1,Eq_x_2) = subset_difference(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,
( cast_as_carrier_subset(Eq_x_0) = cast_as_carrier_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| 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,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,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_21,axiom,
( v1_xcmplx_0(Eq_y_0)
| ~ v1_xcmplx_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( v1_xreal_0(Eq_y_0)
| ~ v1_xreal_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( v1_rat_1(Eq_y_0)
| ~ v1_rat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( v1_int_1(Eq_y_0)
| ~ v1_int_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,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_27,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(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 : SEU308+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
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 23:55:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 78.24/78.59 % SZS status Theorem for theBenchmark
% 78.24/78.59 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------