%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP027+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 : Sun Sep 27 09:52:29 AM UTC 2026
% Result : Theorem 7.42s 2.92s
% Output : Refutation 7.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 73
% Syntax : Number of formulae : 148 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 610 ( 21 equ; 0 cnn)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 1685 ( 45 ~; 2 |; 281 &;1178 @)
% ( 1 <=>; 178 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 2 con; 0-3 aty)
% Number of variables : 277 ( 0 ^; 247 !; 30 ?; 277 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v2_pre_topc_decl,type,
v2_pre_topc: $i > $o ).
thf(l1_pre_topc_decl,type,
l1_pre_topc: $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(v1_tsp_2_decl,type,
v1_tsp_2: $i > $i > $o ).
thf(k1_tops_1_decl,type,
k1_tops_1: $i > $i > $i ).
thf(k3_tex_4_decl,type,
k3_tex_4: $i > $i > $i ).
thf(k5_subset_1_decl,type,
k5_subset_1: $i > $i > $i > $i ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v4_membered_decl,type,
v4_membered: $i > $o ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(v5_membered_decl,type,
v5_membered: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(v2_tops_1_decl,type,
v2_tops_1: $i > $i > $o ).
thf(v3_pre_topc_decl,type,
v3_pre_topc: $i > $i > $o ).
thf(v1_xcmplx_0_decl,type,
v1_xcmplx_0: $i > $o ).
thf(v4_ordinal2_decl,type,
v4_ordinal2: $i > $o ).
thf(v1_xreal_0_decl,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_decl,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_decl,type,
v1_rat_1: $i > $o ).
thf(v4_pre_topc_decl,type,
v4_pre_topc: $i > $i > $o ).
thf(v3_tops_1_decl,type,
v3_tops_1: $i > $i > $o ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc28_membered) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc19_membered) ).
thf(393,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(67,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(386,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v3_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc32_membered) ).
thf(101,plain,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v3_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_tops_1) ).
thf(347,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(333,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(74,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(408,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_membered) ).
thf(276,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(22,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(185,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( B @ v1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_tops_1) ).
thf(301,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v3_pre_topc ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( B @ v1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_membered) ).
thf(389,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
thf(372,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ( A @ ( B @ ( A @ k1_tops_1 ) @ v3_pre_topc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v3_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc31_membered) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v3_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(51,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v2_tops_1 ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_tops_1) ).
thf(325,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( A @ ( B @ v2_tops_1 ) )
& ( A @ ( B @ v4_pre_topc ) ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_subset_1) ).
thf(289,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( C @ ( B @ k3_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( C
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k3_tex_4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tsp_2) ).
thf(316,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( A @ ( C @ v3_pre_topc ) )
=> ( C
= ( C @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k3_tex_4 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v5_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v4_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v3_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc36_membered) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v5_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v4_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v3_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).
thf(89,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(206,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc20_membered) ).
thf(292,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(65,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(380,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
thf(85,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(61,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_tops_1) ).
thf(366,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(58,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_tops_1) ).
thf(349,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_tops_1 ) )
& ( A @ ( B @ v2_tops_1 ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(229,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_tops_1) ).
thf(329,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(43,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(285,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(18,axiom,
( ( k1_xboole_0 @ v5_membered )
& ( k1_xboole_0 @ v4_membered )
& ( k1_xboole_0 @ v3_membered )
& ( k1_xboole_0 @ v2_membered )
& ( k1_xboole_0 @ v1_membered )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
thf(169,plain,
( ( k1_xboole_0 @ v5_membered )
& ( k1_xboole_0 @ v4_membered )
& ( k1_xboole_0 @ v3_membered )
& ( k1_xboole_0 @ v2_membered )
& ( k1_xboole_0 @ v1_membered )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc29_membered) ).
thf(124,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(339,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc27_membered) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v5_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v4_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v3_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc35_membered) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v5_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v4_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v3_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
thf(256,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v4_ordinal2 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc14_membered) ).
thf(244,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v4_ordinal2 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_tops_1) ).
thf(266,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(166,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(180,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k3_tex_4 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tex_4) ).
thf(281,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k3_tex_4 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).
thf(204,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(66,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(382,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_subset_1) ).
thf(313,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( C @ ( B @ ( A @ k5_subset_1 ) ) )
= ( B @ ( C @ ( A @ k5_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc15_membered) ).
thf(144,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(159,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc30_membered) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(73,axiom,
? [A: $i] : ( A @ l1_pre_topc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(406,plain,
? [A: $i] : ( A @ l1_pre_topc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] :
( ( A @ ( B @ v2_tops_1 ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_tops_1) ).
thf(219,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ? [B: $i] :
( ( A @ ( B @ v2_tops_1 ) )
& ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered )
& ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_subset_1) ).
thf(362,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( A @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k5_subset_1 ) ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(39,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc7_pre_topc) ).
thf(271,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( A @ ( B @ v4_pre_topc ) )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v4_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v3_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc34_membered) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( A @ ( B @ k3_xboole_0 ) @ v4_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v3_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v2_membered )
& ( A @ ( B @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc12_membered) ).
thf(251,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_membered) ).
thf(130,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xcmplx_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_membered) ).
thf(399,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( B @ v1_xcmplx_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_tops_1) ).
thf(299,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v3_tops_1 ) )
=> ( A @ ( B @ v2_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(162,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k5_subset_1) ).
thf(374,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) )
=> ( ( B @ ( B @ ( A @ k5_subset_1 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v4_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v3_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc33_membered) ).
thf(209,plain,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( B @ ( A @ k3_xboole_0 ) @ v4_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v3_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v2_membered )
& ( B @ ( A @ k3_xboole_0 ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(177,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(182,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_tops_1) ).
thf(231,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ? [B: $i] :
( ( A @ ( B @ v3_pre_topc ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(319,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(401,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k3_tex_4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tsp_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k3_tex_4 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(75,plain,
~ ! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( A @ ( B @ v1_tsp_2 ) )
=> ! [C: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( ( C @ ( A @ k1_tops_1 ) )
= ( C @ ( A @ k1_tops_1 ) @ ( B @ ( A @ u1_struct_0 @ k5_subset_1 ) ) @ ( A @ k3_tex_4 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(378,plain,
! [A: $i] :
( ( A @ l1_pre_topc )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v2_tops_1 ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k1_tops_1 ) @ v2_tops_1 ) )
& ( B @ ( A @ k1_tops_1 ) @ v5_membered )
& ( B @ ( A @ k1_tops_1 ) @ v4_membered )
& ( B @ ( A @ k1_tops_1 ) @ v3_membered )
& ( B @ ( A @ k1_tops_1 ) @ v2_membered )
& ( B @ ( A @ k1_tops_1 ) @ v1_membered )
& ( B @ ( A @ k1_tops_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_tops_1) ).
thf(235,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ ( B @ v2_tops_1 ) )
& ( A @ l1_pre_topc ) )
=> ( ( A @ ( B @ ( A @ k1_tops_1 ) @ v2_tops_1 ) )
& ( B @ ( A @ k1_tops_1 ) @ v5_membered )
& ( B @ ( A @ k1_tops_1 ) @ v4_membered )
& ( B @ ( A @ k1_tops_1 ) @ v3_membered )
& ( B @ ( A @ k1_tops_1 ) @ v2_membered )
& ( B @ ( A @ k1_tops_1 ) @ v1_membered )
& ( B @ ( A @ k1_tops_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(14,axiom,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_membered) ).
thf(151,plain,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(37,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(262,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc13_membered) ).
thf(341,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
thf(283,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( A @ l1_pre_topc ) )
=> ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k1_tops_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(337,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(60,axiom,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_tops_1) ).
thf(364,plain,
! [A: $i] :
( ( ( A @ l1_pre_topc )
& ( A @ v2_pre_topc ) )
=> ! [B: $i] :
( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_xboole_0 )
=> ( A @ ( B @ v3_tops_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(418,plain,
$false,
inference(e,[status(thm)],[121,393,386,101,347,333,408,276,185,301,389,372,196,325,289,316,132,89,206,292,380,85,366,260,349,229,329,285,403,169,124,339,193,109,256,244,266,166,180,281,204,382,313,144,159,187,406,219,362,271,91,251,130,399,299,162,374,209,177,182,231,87,319,401,75,378,235,151,262,341,283,337,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP027+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n018.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 20:35:52 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.87 % [INFO] Parsing done (156ms).
% 0.94/0.87 % [INFO] Running in sequential loop mode.
% 1.80/1.12 % [INFO] eprover registered as external prover.
% 2.04/1.13 % [INFO] Scanning for conjecture ...
% 2.19/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 78 axioms. Running axiom selection ...
% 2.40/1.38 % [INFO] Axiom selection finished. Selected 72 axioms (removed 6 axioms).
% 2.75/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 3.02/1.51 % [INFO] Type checking passed.
% 3.02/1.51 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.42/2.92 % External prover 'e' found a proof!
% 7.42/2.92 % [INFO] Killing All external provers ...
% 7.42/2.92 % Time passed: 2422ms (effective reasoning time: 2041ms)
% 7.42/2.92 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.42/2.92 % Axioms used in derivation (72): cc1_tops_1, cc12_membered, rc1_tops_1, cc6_tops_1, cc18_membered, cc15_membered, rc7_pre_topc, existence_l1_struct_0, antisymmetry_r2_hidden, idempotence_k3_xboole_0, redefinition_k5_subset_1, cc10_membered, rc3_tops_1, t1_subset, fc34_membered, dt_k1_tops_1, fc31_membered, rc1_membered, t2_boole, t6_tsp_2, fc6_tops_1, cc5_tops_1, cc3_tops_1, idempotence_k5_subset_1, commutativity_k3_xboole_0, fc28_membered, rc6_pre_topc, fc32_membered, fc30_membered, dt_l1_pre_topc, t6_boole, rc2_subset_1, rc5_tops_1, fc33_membered, t5_subset, cc19_membered, commutativity_k5_subset_1, fc10_tops_1, fc6_membered, rc4_tops_1, cc11_membered, t4_subset, cc20_membered, t7_boole, rc3_struct_0, fc1_subset_1, fc29_membered, rc1_subset_1, cc4_membered, dt_k3_tex_4, t3_subset, cc13_membered, existence_m1_subset_1, cc2_tops_1, dt_k5_subset_1, fc1_struct_0, existence_l1_pre_topc, fc35_membered, reflexivity_r1_tarski, fc36_membered, cc17_membered, rc2_tops_1, t8_boole, t2_subset, cc1_membered, rc5_struct_0, cc4_tops_1, cc2_membered, cc3_membered, cc14_membered, cc16_membered, fc27_membered
% 7.42/2.92 % No. of inferences in proof: 148
% 7.42/2.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2422 ms resp. 2041 ms w/o parsing
% 7.80/3.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.80/3.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------