%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU412+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 : n003.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 08:38:44 AM UTC 2026
% Result : Theorem 53.03s 12.60s
% Output : Refutation 53.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 46
% Syntax : Number of formulae : 94 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 266 ( 45 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 955 ( 39 ~; 7 |; 79 &; 744 @)
% ( 8 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 2 con; 0-6 aty)
% Number of variables : 215 ( 0 ^; 201 !; 14 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
thf(l1_orders_2_decl,type,
l1_orders_2: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k4_tarski_decl,type,
k4_tarski: $i > $i > $i ).
thf(u1_orders_2_decl,type,
u1_orders_2: $i > $i ).
thf(k1_latsum_1_decl,type,
k1_latsum_1: $i > $i > $i ).
thf(v13_waybel_0_decl,type,
v13_waybel_0: $i > $i > $o ).
thf(k3_xboole_0_decl,type,
k3_xboole_0: $i > $i > $i ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(g1_orders_2_decl,type,
g1_orders_2: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k7_relset_1_decl,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(v1_orders_2_decl,type,
v1_orders_2: $i > $o ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(101,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(32,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(170,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)],[32]) ).
thf(34,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(174,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)],[34]) ).
thf(27,axiom,
? [A: $i] : ( A @ l1_orders_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(157,plain,
? [A: $i] : ( A @ l1_orders_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(15,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(97,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ l1_orders_2 )
=> ! [D: $i] :
( ( D @ l1_orders_2 )
=> ~ ( ~ ( ( C @ u1_struct_0 @ ( D @ u1_struct_0 @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ u1_struct_0 @ ( B @ r2_hidden ) )
& ( D @ u1_struct_0 @ ( A @ r2_hidden ) ) )
& ~ ( ( C @ u1_struct_0 @ ( B @ r2_hidden ) )
& ( C @ u1_struct_0 @ ( A @ r2_hidden ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k3_xboole_0 ) @ m1_subset_1 ) )
& ( C @ ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k3_xboole_0 ) @ v13_waybel_0 ) )
& ( D @ ( C @ k1_latsum_1 ) @ u1_orders_2 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_latsum_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ l1_orders_2 )
=> ! [D: $i] :
( ( D @ l1_orders_2 )
=> ~ ( ~ ( ( C @ u1_struct_0 @ ( D @ u1_struct_0 @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ u1_struct_0 @ ( B @ r2_hidden ) )
& ( D @ u1_struct_0 @ ( A @ r2_hidden ) ) )
& ~ ( ( C @ u1_struct_0 @ ( B @ r2_hidden ) )
& ( C @ u1_struct_0 @ ( A @ r2_hidden ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k3_xboole_0 ) @ m1_subset_1 ) )
& ( C @ ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k3_xboole_0 ) @ v13_waybel_0 ) )
& ( D @ ( C @ k1_latsum_1 ) @ u1_orders_2 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ l1_orders_2 )
=> ! [D: $i] :
( ( D @ l1_orders_2 )
=> ~ ( ~ ( ( C @ u1_struct_0 @ ( D @ u1_struct_0 @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ u1_struct_0 @ ( B @ r2_hidden ) )
& ( D @ u1_struct_0 @ ( A @ r2_hidden ) ) )
& ~ ( ( C @ u1_struct_0 @ ( B @ r2_hidden ) )
& ( C @ u1_struct_0 @ ( A @ r2_hidden ) ) )
& ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k3_xboole_0 ) @ m1_subset_1 ) )
& ( C @ ( D @ u1_struct_0 @ ( C @ u1_struct_0 @ k3_xboole_0 ) @ v13_waybel_0 ) )
& ( D @ ( C @ k1_latsum_1 ) @ u1_orders_2 @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(177,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(210,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(6,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(68,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,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(93,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_orders_2 )
=> ( A
= ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(228,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( ( A @ v1_orders_2 )
=> ( A
= ( A @ u1_orders_2 @ ( A @ u1_struct_0 @ g1_orders_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(78,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(216,plain,
! [A: $i] :
( ( A @ ( A @ k3_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ( ( B @ ( A @ g1_orders_2 ) @ l1_orders_2 )
& ( B @ ( A @ g1_orders_2 ) @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ( ( B @ ( A @ g1_orders_2 ) @ l1_orders_2 )
& ( B @ ( A @ g1_orders_2 ) @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(84,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( A @ l1_orders_2 ) )
=> ( ( B @ ( A @ k1_latsum_1 ) @ l1_orders_2 )
& ( B @ ( A @ k1_latsum_1 ) @ v1_orders_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
thf(233,plain,
! [A: $i,B: $i] :
( ( ( B @ l1_orders_2 )
& ( A @ l1_orders_2 ) )
=> ( ( B @ ( A @ k1_latsum_1 ) @ l1_orders_2 )
& ( B @ ( A @ k1_latsum_1 ) @ v1_orders_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_orders_2 ) )
= ( D @ ( C @ g1_orders_2 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_orders_2 ) )
= ( D @ ( C @ g1_orders_2 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(109,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( B @ ( A @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(43,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(225,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k3_xboole_0 ) )
= ( A @ ( B @ k3_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(212,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(73,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
<=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(237,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) )
=> ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) ) )
& ( ( D @ ( C @ k2_zfmisc_1 ) @ ( B @ ( A @ k4_tarski ) @ r2_hidden ) )
=> ( ( D @ ( B @ r2_hidden ) )
& ( C @ ( A @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(29,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(161,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k3_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(180,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_orders_2 @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(172,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_orders_2 @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(113,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k2_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k2_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ( B @ ( D @ r2_hidden ) )
| ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(42,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(219,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)],[42]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(81,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(103,plain,
! [A: $i,B: $i] :
( ~ ( A @ v1_xboole_0 )
=> ~ ( A @ ( B @ k2_xboole_0 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(140,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(66,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(155,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(112,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ! [B: $i] :
( ( B @ l1_orders_2 )
=> ! [C: $i] :
( ( ( C @ l1_orders_2 )
& ( C @ v1_orders_2 ) )
=> ( ( C
= ( B @ ( A @ k1_latsum_1 ) ) )
<=> ( ( ( C @ u1_orders_2 )
= ( B @ u1_orders_2 @ ( A @ u1_orders_2 @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_relset_1 ) ) ) ) ) @ ( B @ u1_orders_2 @ ( A @ u1_orders_2 @ k2_xboole_0 ) @ k2_xboole_0 ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_xboole_0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_latsum_1) ).
thf(145,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ! [B: $i] :
( ( B @ l1_orders_2 )
=> ! [C: $i] :
( ( ( C @ l1_orders_2 )
& ( C @ v1_orders_2 ) )
=> ( ( ( ( ( C @ u1_orders_2 )
= ( B @ u1_orders_2 @ ( A @ u1_orders_2 @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_relset_1 ) ) ) ) ) @ ( B @ u1_orders_2 @ ( A @ u1_orders_2 @ k2_xboole_0 ) @ k2_xboole_0 ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_xboole_0 ) ) ) )
=> ( C
= ( B @ ( A @ k1_latsum_1 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_latsum_1 ) ) )
=> ( ( ( C @ u1_orders_2 )
= ( B @ u1_orders_2 @ ( A @ u1_orders_2 @ ( B @ u1_struct_0 @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_relset_1 ) ) ) ) ) @ ( B @ u1_orders_2 @ ( A @ u1_orders_2 @ k2_xboole_0 ) @ k2_xboole_0 ) ) )
& ( ( C @ u1_struct_0 )
= ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_xboole_0 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ! [B: $i] :
( ( B @ l1_orders_2 )
=> ! [C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( C @ r2_hidden ) )
& ( B @ ( A @ k1_latsum_1 ) @ u1_orders_2 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_xboole_0 ) @ m1_subset_1 ) )
& ( A @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_xboole_0 ) @ v13_waybel_0 ) ) )
=> ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_latsum_1) ).
thf(231,plain,
! [A: $i] :
( ( A @ l1_orders_2 )
=> ! [B: $i] :
( ( B @ l1_orders_2 )
=> ! [C: $i,D: $i] :
( ( ( B @ u1_struct_0 @ ( C @ r2_hidden ) )
& ( B @ ( A @ k1_latsum_1 ) @ u1_orders_2 @ ( D @ ( C @ k4_tarski ) @ r2_hidden ) )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_xboole_0 ) @ m1_subset_1 ) )
& ( A @ ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ k3_xboole_0 ) @ v13_waybel_0 ) ) )
=> ( B @ u1_struct_0 @ ( D @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(16,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(99,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(75,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(58,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(40,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(214,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)],[40]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(168,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ r2_hidden ) )
<=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(183,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) )
=> ( C
= ( B @ ( A @ k4_xboole_0 ) ) ) )
& ( ( C
= ( B @ ( A @ k4_xboole_0 ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) )
=> ( C @ ( D @ r2_hidden ) ) )
& ( ( C @ ( D @ r2_hidden ) )
=> ( ~ ( B @ ( D @ r2_hidden ) )
& ( A @ ( D @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31825,plain,
$false,
inference(e,[status(thm)],[101,170,174,157,97,48,177,143,210,68,93,228,78,216,164,106,84,233,60,109,225,212,73,237,161,180,71,159,172,113,219,81,103,140,66,155,112,145,231,99,87,75,58,214,168,183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU412+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 09:33:23 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.59/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.98/0.82 % [INFO] Parsing done (126ms).
% 0.98/0.83 % [INFO] Running in sequential loop mode.
% 1.65/1.04 % [INFO] eprover registered as external prover.
% 1.65/1.04 % [INFO] Scanning for conjecture ...
% 1.65/1.13 % [INFO] Found a conjecture (or negated_conjecture) and 56 axioms. Running axiom selection ...
% 2.07/1.22 % [INFO] Axiom selection finished. Selected 45 axioms (removed 11 axioms).
% 2.07/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/1.30 % [INFO] Type checking passed.
% 2.30/1.31 % [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 ...
% 62.53/12.59 % External prover 'e' found a proof!
% 62.53/12.59 % [INFO] Killing All external provers ...
% 62.53/12.60 % Time passed: 12114ms (effective reasoning time: 11763ms)
% 62.53/12.60 % 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)>
% 53.03/12.60 % Axioms used in derivation (45): redefinition_m2_relset_1, dt_k7_relset_1, t2_boole, dt_k1_latsum_1, t6_boole, existence_m1_relset_1, dt_g1_orders_2, abstractness_v1_orders_2, t106_zfmisc_1, existence_m2_relset_1, dt_l1_orders_2, t2_subset, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k3_xboole_0, t1_boole, fc1_xboole_0, t1_subset, dt_m2_relset_1, commutativity_k3_xboole_0, t17_latsum_1, fc2_xboole_0, dt_u1_orders_2, commutativity_k2_xboole_0, t5_subset, t4_boole, t4_subset, fc3_xboole_0, d2_xboole_0, t7_boole, existence_l1_orders_2, t3_subset, cc1_relset_1, existence_m1_subset_1, free_g1_orders_2, dt_k5_relat_1, reflexivity_r1_tarski, d4_xboole_0, redefinition_k7_relset_1, t8_boole, rc1_xboole_0, existence_l1_struct_0, d2_latsum_1, t3_boole
% 53.03/12.60 % No. of inferences in proof: 94
% 53.03/12.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12114 ms resp. 11763 ms w/o parsing
% 53.03/12.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 53.03/12.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------