%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU327+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 : n006.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 08:59:00 AM UTC 2026
% Result : Theorem 276.16s 276.41s
% Output : Proof 277.90s
% 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(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(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(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(cc1_membered,axiom,
! [A] :
( v5_membered(A)
=> v4_membered(A) ),
file('theBenchmark.p',cc1_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(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(d4_subset_1,axiom,
! [A] : cast_to_subset(A) = A,
file('theBenchmark.p',d4_subset_1) ).
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_setfam_1,axiom,
$true,
file('theBenchmark.p',dt_k1_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_k2_subset_1,axiom,
! [A] : element(cast_to_subset(A),powerset(A)),
file('theBenchmark.p',dt_k2_subset_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_k3_tarski,axiom,
$true,
file('theBenchmark.p',dt_k3_tarski) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(dt_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(meet_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k6_setfam_1) ).
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_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(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(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(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_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(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(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(redefinition_k6_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> meet_of_subsets(A,B) = set_meet(B) ),
file('theBenchmark.p',redefinition_k6_setfam_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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t11_tops_2,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B)) ) ),
file('theBenchmark.p',t11_tops_2) ).
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_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t47_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B)) ) ),
file('theBenchmark.p',t47_setfam_1) ).
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(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] :
( v1_xcmplx_0(B)
| ~ element(B,A) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc10_membered]) ).
fof(f_2_2,plain,
! [U_3] :
( ! [U_2] :
( v1_xcmplx_0(U_2)
| ~ element(U_2,U_3) )
| ~ v1_membered(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( v1_xcmplx_0(U_2)
| ~ element(U_2,U_3)
| ~ v1_membered(U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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_3_2,plain,
! [U_5] :
( ! [U_4] :
( ( v1_xreal_0(U_4)
& v1_xcmplx_0(U_4) )
| ~ element(U_4,U_5) )
| ~ v2_membered(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v1_xcmplx_0(U_4)
| ~ element(U_4,U_5)
| ~ v2_membered(U_5) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( v1_xreal_0(U_4)
| ~ element(U_4,U_5)
| ~ v2_membered(U_5) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_7] :
( ! [U_6] :
( ( v1_rat_1(U_6)
& v1_xreal_0(U_6)
& v1_xcmplx_0(U_6) )
| ~ element(U_6,U_7) )
| ~ v3_membered(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v1_xcmplx_0(U_6)
| ~ element(U_6,U_7)
| ~ v3_membered(U_7) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( v1_xreal_0(U_6)
| ~ element(U_6,U_7)
| ~ v3_membered(U_7) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( v1_rat_1(U_6)
| ~ element(U_6,U_7)
| ~ v3_membered(U_7) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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_5_2,plain,
! [U_9] :
( ! [U_8] :
( ( v1_rat_1(U_8)
& v1_int_1(U_8)
& v1_xreal_0(U_8)
& v1_xcmplx_0(U_8) )
| ~ element(U_8,U_9) )
| ~ v4_membered(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_xcmplx_0(U_8)
| ~ element(U_8,U_9)
| ~ v4_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( v1_xreal_0(U_8)
| ~ element(U_8,U_9)
| ~ v4_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( v1_int_1(U_8)
| ~ element(U_8,U_9)
| ~ v4_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_6,plain,
( v1_rat_1(U_8)
| ~ element(U_8,U_9)
| ~ v4_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_11] :
( ! [U_10] :
( ( v1_rat_1(U_10)
& v1_int_1(U_10)
& v1_xreal_0(U_10)
& natural(U_10)
& v1_xcmplx_0(U_10) )
| ~ element(U_10,U_11) )
| ~ v5_membered(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( v1_xcmplx_0(U_10)
| ~ element(U_10,U_11)
| ~ v5_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( natural(U_10)
| ~ element(U_10,U_11)
| ~ v5_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( v1_xreal_0(U_10)
| ~ element(U_10,U_11)
| ~ v5_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_6,plain,
( v1_int_1(U_10)
| ~ element(U_10,U_11)
| ~ v5_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_7,plain,
( v1_rat_1(U_10)
| ~ element(U_10,U_11)
| ~ v5_membered(U_11) ),
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)],[cc15_membered]) ).
fof(f_7_2,plain,
! [U_12] :
( ( v5_membered(U_12)
& v4_membered(U_12)
& v3_membered(U_12)
& v2_membered(U_12)
& v1_membered(U_12) )
| ~ empty(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( v1_membered(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( v2_membered(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( v3_membered(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_6,plain,
( v4_membered(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_7,plain,
( v5_membered(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( v1_membered(B)
| ~ element(B,powerset(A)) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc16_membered]) ).
fof(f_8_2,plain,
! [U_14] :
( ! [U_13] :
( v1_membered(U_13)
| ~ element(U_13,powerset(U_14)) )
| ~ v1_membered(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( v1_membered(U_13)
| ~ element(U_13,powerset(U_14))
| ~ v1_membered(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_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_9_2,plain,
! [U_16] :
( ! [U_15] :
( ( v2_membered(U_15)
& v1_membered(U_15) )
| ~ element(U_15,powerset(U_16)) )
| ~ v2_membered(U_16) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( v1_membered(U_15)
| ~ element(U_15,powerset(U_16))
| ~ v2_membered(U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( v2_membered(U_15)
| ~ element(U_15,powerset(U_16))
| ~ v2_membered(U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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_10_2,plain,
! [U_18] :
( ! [U_17] :
( ( v3_membered(U_17)
& v2_membered(U_17)
& v1_membered(U_17) )
| ~ element(U_17,powerset(U_18)) )
| ~ v3_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v3_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( v2_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v3_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_5,plain,
( v3_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v3_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_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_11_2,plain,
! [U_20] :
( ! [U_19] :
( ( v4_membered(U_19)
& v3_membered(U_19)
& v2_membered(U_19)
& v1_membered(U_19) )
| ~ element(U_19,powerset(U_20)) )
| ~ v4_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v4_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( v2_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v4_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( v3_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v4_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_6,plain,
( v4_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v4_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( v4_membered(A)
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc1_membered]) ).
fof(f_12_2,plain,
! [U_21] :
( v4_membered(U_21)
| ~ v5_membered(U_21) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v4_membered(U_21)
| ~ v5_membered(U_21) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_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_13_2,plain,
! [U_23] :
( ! [U_22] :
( ( v5_membered(U_22)
& v4_membered(U_22)
& v3_membered(U_22)
& v2_membered(U_22)
& v1_membered(U_22) )
| ~ element(U_22,powerset(U_23)) )
| ~ v5_membered(U_23) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( v1_membered(U_22)
| ~ element(U_22,powerset(U_23))
| ~ v5_membered(U_23) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( v2_membered(U_22)
| ~ element(U_22,powerset(U_23))
| ~ v5_membered(U_23) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_5,plain,
( v3_membered(U_22)
| ~ element(U_22,powerset(U_23))
| ~ v5_membered(U_23) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_6,plain,
( v4_membered(U_22)
| ~ element(U_22,powerset(U_23))
| ~ v5_membered(U_23) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_7,plain,
( v5_membered(U_22)
| ~ element(U_22,powerset(U_23))
| ~ v5_membered(U_23) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( v3_membered(A)
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc2_membered]) ).
fof(f_14_2,plain,
! [U_24] :
( v3_membered(U_24)
| ~ v4_membered(U_24) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( v3_membered(U_24)
| ~ v4_membered(U_24) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( v2_membered(A)
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc3_membered]) ).
fof(f_15_2,plain,
! [U_25] :
( v2_membered(U_25)
| ~ v3_membered(U_25) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( v2_membered(U_25)
| ~ v3_membered(U_25) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( v1_membered(A)
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc4_membered]) ).
fof(f_16_2,plain,
! [U_26] :
( v1_membered(U_26)
| ~ v2_membered(U_26) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( v1_membered(U_26)
| ~ v2_membered(U_26) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] : cast_to_subset(A) = A,
inference(fof_nnf,[status(thm)],[d4_subset_1]) ).
fof(f_17_2,plain,
! [U_27] : cast_to_subset(U_27) = U_27,
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
cast_to_subset(U_27) = U_27,
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_29,U_28] :
( subset_complement(U_29,U_28) = set_difference(U_29,U_28)
| ~ element(U_28,powerset(U_29)) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( subset_complement(U_29,U_28) = set_difference(U_29,U_28)
| ~ element(U_28,powerset(U_29)) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_setfam_1]) ).
cnf(f_19_2,plain,
$true,
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_21_2,plain,
$true,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [A] : element(cast_to_subset(A),powerset(A)),
inference(fof_nnf,[status(thm)],[dt_k2_subset_1]) ).
fof(f_22_2,plain,
! [U_30] : element(cast_to_subset(U_30),powerset(U_30)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
element(cast_to_subset(U_30),powerset(U_30)),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_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_23_2,plain,
! [U_32,U_31] :
( element(subset_complement(U_32,U_31),powerset(U_32))
| ~ element(U_31,powerset(U_32)) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( element(subset_complement(U_32,U_31),powerset(U_32))
| ~ element(U_31,powerset(U_32)) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
cnf(f_24_2,plain,
$true,
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
! [A,B] :
( element(union_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k5_setfam_1]) ).
fof(f_26_2,plain,
! [U_34,U_33] :
( element(union_of_subsets(U_34,U_33),powerset(U_34))
| ~ element(U_33,powerset(powerset(U_34))) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( element(union_of_subsets(U_34,U_33),powerset(U_34))
| ~ element(U_33,powerset(powerset(U_34))) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B] :
( element(meet_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k6_setfam_1]) ).
fof(f_27_2,plain,
! [U_36,U_35] :
( element(meet_of_subsets(U_36,U_35),powerset(U_36))
| ~ element(U_35,powerset(powerset(U_36))) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( element(meet_of_subsets(U_36,U_35),powerset(U_36))
| ~ element(U_35,powerset(powerset(U_36))) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_39,U_38,U_37] :
( element(subset_difference(U_39,U_38,U_37),powerset(U_39))
| ~ element(U_37,powerset(U_39))
| ~ element(U_38,powerset(U_39)) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( element(subset_difference(U_39,U_38,U_37),powerset(U_39))
| ~ element(U_37,powerset(U_39))
| ~ element(U_38,powerset(U_39)) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_41,U_40] :
( element(complements_of_subsets(U_41,U_40),powerset(powerset(U_41)))
| ~ element(U_40,powerset(powerset(U_41))) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( element(complements_of_subsets(U_41,U_40),powerset(powerset(U_41)))
| ~ element(U_40,powerset(powerset(U_41))) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_30_2,plain,
$true,
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_31_2,plain,
! [U_43] :
? [U_42] : element(U_42,U_43),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_43] : element(sK1(U_43),U_43),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_42,sK1(U_43))],[f_31_2]) ).
cnf(f_31_4,plain,
element(sK1(U_43),U_43),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_32_2,plain,
! [U_44] : ~ empty(powerset(U_44)),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
~ empty(powerset(U_44)),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( v1_membered(set_difference(A,B))
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[fc37_membered]) ).
fof(f_33_2,plain,
! [U_46,U_45] :
( v1_membered(set_difference(U_46,U_45))
| ~ v1_membered(U_46) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_46] :
( ! [U_45] : v1_membered(set_difference(U_46,U_45))
| ~ v1_membered(U_46) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( v1_membered(set_difference(U_46,U_45))
| ~ v1_membered(U_46) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_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_34_2,plain,
! [U_48,U_47] :
( ( v2_membered(set_difference(U_48,U_47))
& v1_membered(set_difference(U_48,U_47)) )
| ~ v2_membered(U_48) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_48] :
( ( ! [U_50] : v2_membered(set_difference(U_48,U_50))
& ! [U_49] : v1_membered(set_difference(U_48,U_49)) )
| ~ v2_membered(U_48) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( v1_membered(set_difference(U_48,U_49))
| ~ v2_membered(U_48) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( v2_membered(set_difference(U_48,U_50))
| ~ v2_membered(U_48) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_52,U_51] :
( ( v3_membered(set_difference(U_52,U_51))
& v2_membered(set_difference(U_52,U_51))
& v1_membered(set_difference(U_52,U_51)) )
| ~ v3_membered(U_52) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_52] :
( ( ! [U_55] : v3_membered(set_difference(U_52,U_55))
& ! [U_54] : v2_membered(set_difference(U_52,U_54))
& ! [U_53] : v1_membered(set_difference(U_52,U_53)) )
| ~ v3_membered(U_52) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( v1_membered(set_difference(U_52,U_53))
| ~ v3_membered(U_52) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( v2_membered(set_difference(U_52,U_54))
| ~ v3_membered(U_52) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
( v3_membered(set_difference(U_52,U_55))
| ~ v3_membered(U_52) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_57,U_56] :
( ( v4_membered(set_difference(U_57,U_56))
& v3_membered(set_difference(U_57,U_56))
& v2_membered(set_difference(U_57,U_56))
& v1_membered(set_difference(U_57,U_56)) )
| ~ v4_membered(U_57) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_57] :
( ( ! [U_61] : v4_membered(set_difference(U_57,U_61))
& ! [U_60] : v3_membered(set_difference(U_57,U_60))
& ! [U_59] : v2_membered(set_difference(U_57,U_59))
& ! [U_58] : v1_membered(set_difference(U_57,U_58)) )
| ~ v4_membered(U_57) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( v1_membered(set_difference(U_57,U_58))
| ~ v4_membered(U_57) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( v2_membered(set_difference(U_57,U_59))
| ~ v4_membered(U_57) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_6,plain,
( v3_membered(set_difference(U_57,U_60))
| ~ v4_membered(U_57) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_7,plain,
( v4_membered(set_difference(U_57,U_61))
| ~ v4_membered(U_57) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_63,U_62] :
( ( v5_membered(set_difference(U_63,U_62))
& v4_membered(set_difference(U_63,U_62))
& v3_membered(set_difference(U_63,U_62))
& v2_membered(set_difference(U_63,U_62))
& v1_membered(set_difference(U_63,U_62)) )
| ~ v5_membered(U_63) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_63] :
( ( ! [U_68] : v5_membered(set_difference(U_63,U_68))
& ! [U_67] : v4_membered(set_difference(U_63,U_67))
& ! [U_66] : v3_membered(set_difference(U_63,U_66))
& ! [U_65] : v2_membered(set_difference(U_63,U_65))
& ! [U_64] : v1_membered(set_difference(U_63,U_64)) )
| ~ v5_membered(U_63) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( v1_membered(set_difference(U_63,U_64))
| ~ v5_membered(U_63) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( v2_membered(set_difference(U_63,U_65))
| ~ v5_membered(U_63) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( v3_membered(set_difference(U_63,U_66))
| ~ v5_membered(U_63) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_7,plain,
( v4_membered(set_difference(U_63,U_67))
| ~ v5_membered(U_63) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_8,plain,
( v5_membered(set_difference(U_63,U_68))
| ~ v5_membered(U_63) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_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_38_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
v1_membered(empty_set),
inference(clausify,[status(thm)],[f_38_1]) ).
cnf(f_38_4,plain,
v2_membered(empty_set),
inference(clausify,[status(thm)],[f_38_1]) ).
cnf(f_38_5,plain,
v3_membered(empty_set),
inference(clausify,[status(thm)],[f_38_1]) ).
cnf(f_38_6,plain,
v4_membered(empty_set),
inference(clausify,[status(thm)],[f_38_1]) ).
cnf(f_38_7,plain,
v5_membered(empty_set),
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_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_39_2,plain,
! [U_70,U_69] :
( subset_complement(U_70,subset_complement(U_70,U_69)) = U_69
| ~ element(U_69,powerset(U_70)) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( subset_complement(U_70,subset_complement(U_70,U_69)) = U_69
| ~ element(U_69,powerset(U_70)) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_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_40_2,plain,
! [U_72,U_71] :
( complements_of_subsets(U_72,complements_of_subsets(U_72,U_71)) = U_71
| ~ element(U_71,powerset(powerset(U_72))) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( complements_of_subsets(U_72,complements_of_subsets(U_72,U_71)) = U_71
| ~ element(U_71,powerset(powerset(U_72))) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
? [U_73] :
( v5_membered(U_73)
& v4_membered(U_73)
& v3_membered(U_73)
& v2_membered(U_73)
& v1_membered(U_73)
& ~ empty(U_73) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( v5_membered(sK2)
& v4_membered(sK2)
& v3_membered(sK2)
& v2_membered(sK2)
& v1_membered(sK2)
& ~ empty(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_73,sK2)],[f_41_2]) ).
cnf(f_41_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
v1_membered(sK2),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
v2_membered(sK2),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_7,plain,
v3_membered(sK2),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_8,plain,
v4_membered(sK2),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_9,plain,
v5_membered(sK2),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_42_2,plain,
! [U_75] :
( ? [U_74] :
( ~ empty(U_74)
& element(U_74,powerset(U_75)) )
| empty(U_75) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_75] :
( ( ~ empty(sK3(U_75))
& element(sK3(U_75),powerset(U_75)) )
| empty(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_74,sK3(U_75))],[f_42_2]) ).
cnf(f_42_4,plain,
( element(sK3(U_75),powerset(U_75))
| empty(U_75) ),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
( ~ empty(sK3(U_75))
| empty(U_75) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_43_2,plain,
! [U_77] :
? [U_76] :
( empty(U_76)
& element(U_76,powerset(U_77)) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_77] :
( empty(sK4(U_77))
& element(sK4(U_77),powerset(U_77)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_76,sK4(U_77))],[f_43_2]) ).
cnf(f_43_4,plain,
element(sK4(U_77),powerset(U_77)),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
empty(sK4(U_77)),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1]) ).
fof(f_44_2,plain,
! [U_79,U_78] :
( union_of_subsets(U_79,U_78) = union(U_78)
| ~ element(U_78,powerset(powerset(U_79))) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( union_of_subsets(U_79,U_78) = union(U_78)
| ~ element(U_78,powerset(powerset(U_79))) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B] :
( meet_of_subsets(A,B) = set_meet(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k6_setfam_1]) ).
fof(f_45_2,plain,
! [U_81,U_80] :
( meet_of_subsets(U_81,U_80) = set_meet(U_80)
| ~ element(U_80,powerset(powerset(U_81))) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( meet_of_subsets(U_81,U_80) = set_meet(U_80)
| ~ element(U_80,powerset(powerset(U_81))) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_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_46_2,plain,
! [U_84,U_83,U_82] :
( subset_difference(U_84,U_83,U_82) = set_difference(U_83,U_82)
| ~ element(U_82,powerset(U_84))
| ~ element(U_83,powerset(U_84)) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( subset_difference(U_84,U_83,U_82) = set_difference(U_83,U_82)
| ~ element(U_82,powerset(U_84))
| ~ element(U_83,powerset(U_84)) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_47_2,plain,
! [U_86,U_85] : subset(U_86,U_86),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_86] : subset(U_86,U_86),
inference(miniscope,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
subset(U_86,U_86),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( B != empty_set
=> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_complement(A,union_of_subsets(A,B)) ) ),
inference(negate,[status(cth)],[t11_tops_2]) ).
fof(f_48_2,negated_conjecture,
? [A,B] :
( meet_of_subsets(A,complements_of_subsets(A,B)) != subset_complement(A,union_of_subsets(A,B))
& B != empty_set
& element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[f_48_1]) ).
fof(f_48_3,negated_conjecture,
? [U_88,U_87] :
( meet_of_subsets(U_88,complements_of_subsets(U_88,U_87)) != subset_complement(U_88,union_of_subsets(U_88,U_87))
& U_87 != empty_set
& element(U_87,powerset(powerset(U_88))) ),
inference(variable_rename,[status(thm)],[f_48_2]) ).
fof(f_48_4,negated_conjecture,
? [U_87] :
( meet_of_subsets(sK5,complements_of_subsets(sK5,U_87)) != subset_complement(sK5,union_of_subsets(sK5,U_87))
& U_87 != empty_set
& element(U_87,powerset(powerset(sK5))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_88,sK5)],[f_48_3]) ).
fof(f_48_5,negated_conjecture,
( meet_of_subsets(sK5,complements_of_subsets(sK5,sK6)) != subset_complement(sK5,union_of_subsets(sK5,sK6))
& sK6 != empty_set
& element(sK6,powerset(powerset(sK5))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_87,sK6)],[f_48_4]) ).
cnf(f_48_6,negated_conjecture,
element(sK6,powerset(powerset(sK5))),
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_7,negated_conjecture,
sK6 != empty_set,
inference(clausify,[status(thm)],[f_48_5]) ).
cnf(f_48_8,negated_conjecture,
meet_of_subsets(sK5,complements_of_subsets(sK5,sK6)) != subset_complement(sK5,union_of_subsets(sK5,sK6)),
inference(clausify,[status(thm)],[f_48_5]) ).
fof(f_49_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_49_2,plain,
! [U_90,U_89] :
( element(U_90,U_89)
| ~ in(U_90,U_89) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( element(U_90,U_89)
| ~ in(U_90,U_89) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_50_2,plain,
! [U_92,U_91] :
( in(U_92,U_91)
| empty(U_91)
| ~ element(U_92,U_91) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( in(U_92,U_91)
| empty(U_91)
| ~ element(U_92,U_91) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A] : set_difference(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t3_boole]) ).
fof(f_51_2,plain,
! [U_93] : set_difference(U_93,empty_set) = U_93,
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
set_difference(U_93,empty_set) = U_93,
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_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_52_2,plain,
! [U_95,U_94] :
( ( element(U_95,powerset(U_94))
| ~ subset(U_95,U_94) )
& ( subset(U_95,U_94)
| ~ element(U_95,powerset(U_94)) ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_99,U_97] :
( element(U_99,powerset(U_97))
| ~ subset(U_99,U_97) )
& ! [U_98,U_96] :
( subset(U_98,U_96)
| ~ element(U_98,powerset(U_96)) ) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( subset(U_98,U_96)
| ~ element(U_98,powerset(U_96)) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( element(U_99,powerset(U_97))
| ~ subset(U_99,U_97) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A,B] :
( subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B))
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[t47_setfam_1]) ).
fof(f_53_2,plain,
! [U_101,U_100] :
( subset_difference(U_101,cast_to_subset(U_101),union_of_subsets(U_101,U_100)) = meet_of_subsets(U_101,complements_of_subsets(U_101,U_100))
| U_100 = empty_set
| ~ element(U_100,powerset(powerset(U_101))) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( subset_difference(U_101,cast_to_subset(U_101),union_of_subsets(U_101,U_100)) = meet_of_subsets(U_101,complements_of_subsets(U_101,U_100))
| U_100 = empty_set
| ~ element(U_100,powerset(powerset(U_101))) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A] : set_difference(empty_set,A) = empty_set,
inference(fof_nnf,[status(thm)],[t4_boole]) ).
fof(f_54_2,plain,
! [U_102] : set_difference(empty_set,U_102) = empty_set,
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
set_difference(empty_set,U_102) = empty_set,
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_55_2,plain,
! [U_105,U_104,U_103] :
( element(U_105,U_103)
| ~ element(U_104,powerset(U_103))
| ~ in(U_105,U_104) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( element(U_105,U_103)
| ~ element(U_104,powerset(U_103))
| ~ in(U_105,U_104) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_56_2,plain,
! [U_108,U_107,U_106] :
( ~ empty(U_106)
| ~ element(U_107,powerset(U_106))
| ~ in(U_108,U_107) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_108,U_107] :
( ! [U_106] :
( ~ empty(U_106)
| ~ element(U_107,powerset(U_106)) )
| ~ in(U_108,U_107) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
cnf(f_56_4,plain,
( ~ empty(U_106)
| ~ element(U_107,powerset(U_106))
| ~ in(U_108,U_107) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_57_2,plain,
! [U_109] :
( U_109 = empty_set
| ~ empty(U_109) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( U_109 = empty_set
| ~ empty(U_109) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_58_2,plain,
! [U_111,U_110] :
( ~ empty(U_110)
| ~ in(U_111,U_110) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( ~ empty(U_110)
| ~ in(U_111,U_110) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_59_2,plain,
! [U_113,U_112] :
( ~ empty(U_112)
| U_113 = U_112
| ~ empty(U_113) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_113] :
( ! [U_112] :
( ~ empty(U_112)
| U_113 = U_112 )
| ~ empty(U_113) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
cnf(f_59_4,plain,
( ~ empty(U_112)
| U_113 = U_112
| ~ empty(U_113) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_19_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_21_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_2]) ).
cnf(f_24_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_30_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_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,
( cast_to_subset(Eq_x_0) = cast_to_subset(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,
( 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_8,axiom,
( union_of_subsets(Eq_x_0,Eq_x_1) = union_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_9,axiom,
( meet_of_subsets(Eq_x_0,Eq_x_1) = meet_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_10,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_11,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_12,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( set_meet(Eq_x_0) = set_meet(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_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,
( 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_20,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_21,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(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,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,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_25,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,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_27,axiom,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU327+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
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 23:55:12 UTC 2026
% 0.07/0.35 % CPUTime :
% 276.16/276.41 % SZS status Theorem for theBenchmark
% 276.16/276.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------