%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU430+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 : n016.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 08:38:52 AM UTC 2026
% Result : Theorem 4.36s 3.11s
% Output : Refutation 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 52 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 136 ( 20 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 341 ( 23 ~; 2 |; 39 &; 234 @)
% ( 6 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 0 ^; 81 !; 17 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k5_setfam_1_decl,type,
k5_setfam_1: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(v3_relat_1_decl,type,
v3_relat_1: $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k3_tarski_decl,type,
k3_tarski: $i > $i ).
thf(23,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(125,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ( ( A = k1_xboole_0 )
=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(16,axiom,
( ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(78,plain,
( ( k1_xboole_0 @ v3_relat_1 )
& ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(85,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
? [A: $i] :
( ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(39,plain,
? [A: $i] :
( ( A @ v3_relat_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( A @ k1_zfmisc_1 @ ( B @ ( A @ k5_setfam_1 ) @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(43,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(55,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(51,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(138,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,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(88,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)],[19]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k3_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) )
=> ( B
= ( A @ k3_tarski ) ) )
& ( ( B
= ( A @ k3_tarski ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ? [D: $i] :
( ( A @ ( D @ r2_hidden ) )
& ( D @ ( C @ r2_hidden ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(65,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(53,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,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(141,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)],[26]) ).
thf(24,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(134,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,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(73,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)],[14]) ).
thf(9,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(59,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)],[9]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k5_setfam_1 ) )
= k1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( C = k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,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(75,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)],[15]) ).
thf(22,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(119,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)],[22]) ).
thf(5,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(47,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( A @ k1_zfmisc_1 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( ( B @ ( A @ k5_setfam_1 ) )
= ( B @ k3_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(83,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(148,plain,
$false,
inference(e,[status(thm)],[125,78,85,71,39,63,43,55,51,138,88,92,65,53,141,134,73,59,27,75,119,47,68,90,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU430+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
% 0.14/0.78 % Computer : n016.cluster.edu
% 0.14/0.78 % Model : x86_64 x86_64
% 0.14/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.78 % Memory : 8046.5625MB
% 0.14/0.78 % OS : Linux 6.8.0-71-generic
% 0.14/0.78 % CPULimit : 300
% 0.14/0.78 % WCLimit : 300
% 0.14/0.78 % DateTime : Sat Sep 26 09:50:17 UTC 2026
% 0.14/0.78 % CPUTime :
% 0.14/0.78 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
% 0.88/1.36 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.57 % [INFO] Parsing done (208ms).
% 1.18/1.58 % [INFO] Running in sequential loop mode.
% 1.87/1.98 % [INFO] eprover registered as external prover.
% 1.87/1.99 % [INFO] Scanning for conjecture ...
% 2.10/2.10 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 2.27/2.17 % [INFO] Axiom selection finished. Selected 24 axioms (removed 4 axioms).
% 2.41/2.21 % [INFO] Problem is first-order (TPTP FOF).
% 2.41/2.21 % [INFO] Type checking passed.
% 2.41/2.22 % [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 ...
% 4.36/3.10 % External prover 'e' found a proof!
% 4.36/3.10 % [INFO] Killing All external provers ...
% 4.36/3.10 % Time passed: 2184ms (effective reasoning time: 1513ms)
% 4.36/3.10 % 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)>
% 4.36/3.11 % Axioms used in derivation (24): cc1_relat_1, d1_xboole_0, t5_subset, redefinition_k5_setfam_1, rc1_subset_1, rc2_relat_1, dt_k5_setfam_1, t8_boole, antisymmetry_r2_hidden, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc2_subset_1, t4_subset, d4_tarski, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, rc1_relat_1, reflexivity_r1_tarski, t2_subset, fc12_relat_1
% 4.36/3.11 % No. of inferences in proof: 52
% 4.36/3.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2184 ms resp. 1513 ms w/o parsing
% 4.68/3.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.68/3.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------