%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU306+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:58:55 AM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : Proof 0.09s
% 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(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
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(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
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(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
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_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
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(t12_pre_topc,conjecture,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',t12_pre_topc) ).
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] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_19_2,plain,
! [U_28,U_27] :
( element(U_28,U_27)
| ~ in(U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( element(U_28,U_27)
| ~ in(U_28,U_27) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_20_2,plain,
! [U_31,U_30,U_29] :
( element(U_31,U_29)
| ~ element(U_30,powerset(U_29))
| ~ in(U_31,U_30) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( element(U_31,U_29)
| ~ element(U_30,powerset(U_29))
| ~ in(U_31,U_30) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_21_2,plain,
! [U_34,U_33,U_32] :
( ~ empty(U_32)
| ~ element(U_33,powerset(U_32))
| ~ in(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_34,U_33] :
( ! [U_32] :
( ~ empty(U_32)
| ~ element(U_33,powerset(U_32)) )
| ~ in(U_34,U_33) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( ~ empty(U_32)
| ~ element(U_33,powerset(U_32))
| ~ in(U_34,U_33) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_22_2,plain,
! [U_36,U_35] : subset(U_36,U_36),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_36] : subset(U_36,U_36),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
subset(U_36,U_36),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_23_2,plain,
! [U_38] :
( ? [U_37] :
( ~ empty(U_37)
& element(U_37,powerset(U_38)) )
| empty(U_38) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_38] :
( ( ~ empty(sK2(U_38))
& element(sK2(U_38),powerset(U_38)) )
| empty(U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_37,sK2(U_38))],[f_23_2]) ).
cnf(f_23_4,plain,
( element(sK2(U_38),powerset(U_38))
| empty(U_38) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( ~ empty(sK2(U_38))
| empty(U_38) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_24_2,plain,
! [U_40] :
? [U_39] :
( empty(U_39)
& element(U_39,powerset(U_40)) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_40] :
( empty(sK3(U_40))
& element(sK3(U_40),powerset(U_40)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_39,sK3(U_40))],[f_24_2]) ).
cnf(f_24_4,plain,
element(sK3(U_40),powerset(U_40)),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
empty(sK3(U_40)),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_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_25_2,plain,
! [U_41] :
( ( v5_membered(U_41)
& v4_membered(U_41)
& v3_membered(U_41)
& v2_membered(U_41)
& v1_membered(U_41) )
| ~ empty(U_41) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( v1_membered(U_41)
| ~ empty(U_41) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( v2_membered(U_41)
| ~ empty(U_41) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_5,plain,
( v3_membered(U_41)
| ~ empty(U_41) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_6,plain,
( v4_membered(U_41)
| ~ empty(U_41) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_7,plain,
( v5_membered(U_41)
| ~ empty(U_41) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_26_2,plain,
! [U_43,U_42] :
( in(U_43,U_42)
| empty(U_42)
| ~ element(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( in(U_43,U_42)
| empty(U_42)
| ~ element(U_43,U_42) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_27_2,plain,
! [U_44] :
( U_44 = empty_set
| ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( U_44 = empty_set
| ~ empty(U_44) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_28_2,plain,
! [U_46,U_45] :
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_29_2,plain,
! [U_48,U_47] :
( ~ empty(U_47)
| U_48 = U_47
| ~ empty(U_48) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_48] :
( ! [U_47] :
( ~ empty(U_47)
| U_48 = U_47 )
| ~ empty(U_48) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( ~ empty(U_47)
| U_48 = U_47
| ~ empty(U_48) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_30_2,plain,
! [U_50] :
? [U_49] : element(U_49,U_50),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_50] : element(sK4(U_50),U_50),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_49,sK4(U_50))],[f_30_2]) ).
cnf(f_30_4,plain,
element(sK4(U_50),U_50),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_31_2,plain,
$true,
inference(clausify,[status(thm)],[f_31_1]) ).
fof(f_32_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_32_2,plain,
$true,
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_33_2,plain,
! [U_51] : ~ empty(powerset(U_51)),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
~ empty(powerset(U_51)),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
! [U_53,U_52] :
( ( element(U_53,powerset(U_52))
| ~ subset(U_53,U_52) )
& ( subset(U_53,U_52)
| ~ element(U_53,powerset(U_52)) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_57,U_55] :
( element(U_57,powerset(U_55))
| ~ subset(U_57,U_55) )
& ! [U_56,U_54] :
( subset(U_56,U_54)
| ~ element(U_56,powerset(U_54)) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( subset(U_56,U_54)
| ~ element(U_56,powerset(U_54)) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( element(U_57,powerset(U_55))
| ~ subset(U_57,U_55) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_35_2,plain,
? [U_58] : one_sorted_str(U_58),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
one_sorted_str(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_58,sK5)],[f_35_2]) ).
cnf(f_35_4,plain,
one_sorted_str(sK5),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_59] :
( element(cast_as_carrier_subset(U_59),powerset(the_carrier(U_59)))
| ~ one_sorted_str(U_59) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( element(cast_as_carrier_subset(U_59),powerset(the_carrier(U_59)))
| ~ one_sorted_str(U_59) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_37_2,plain,
$true,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_38_2,plain,
$true,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_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_39_2,plain,
! [U_60] :
( cast_as_carrier_subset(U_60) = the_carrier(U_60)
| ~ one_sorted_str(U_60) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( cast_as_carrier_subset(U_60) = the_carrier(U_60)
| ~ one_sorted_str(U_60) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
inference(negate,[status(cth)],[t12_pre_topc]) ).
fof(f_40_2,negated_conjecture,
? [A] :
( cast_as_carrier_subset(A) != the_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[f_40_1]) ).
fof(f_40_3,negated_conjecture,
? [U_61] :
( cast_as_carrier_subset(U_61) != the_carrier(U_61)
& one_sorted_str(U_61) ),
inference(variable_rename,[status(thm)],[f_40_2]) ).
fof(f_40_4,negated_conjecture,
( cast_as_carrier_subset(sK6) != the_carrier(sK6)
& one_sorted_str(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_61,sK6)],[f_40_3]) ).
fof(f_40_5,negated_conjecture,
( cast_as_carrier_subset(sK6) != the_carrier(sK6)
& one_sorted_str(sK6) ),
inference(definitional_conversion,[status(esa)],[f_40_4]) ).
cnf(f_40_6,negated_conjecture,
one_sorted_str(sK6),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_40_7,negated_conjecture,
cast_as_carrier_subset(sK6) != the_carrier(sK6),
inference(clausify,[status(thm)],[f_40_5]) ).
cnf(f_2_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_2]) ).
cnf(f_31_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_31_2]) ).
cnf(f_32_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_32_2]) ).
cnf(f_37_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_37_2]) ).
cnf(f_38_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_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_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_6,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,axiom,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,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_18,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_19,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_20,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_21,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_22,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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_24,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 : SEU306+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 19 23:54:33 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------