%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU406+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 : n005.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 08:38:42 AM UTC 2026
% Result : Theorem 6.59s 3.63s
% Output : Refutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 42 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 19 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 330 ( 35 ~; 7 |; 36 &; 232 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 70 !; 6 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k2_xboole_0_decl,type,
k2_xboole_0: $i > $i > $i ).
thf(k4_xboole_0_decl,type,
k4_xboole_0: $i > $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(7,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(42,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,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(46,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)],[9]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ k4_xboole_0 ) @ ( A @ k2_xboole_0 ) )
= ( B @ ( A @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,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(85,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)],[14]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(33,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(73,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k4_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(45,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_latsum_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( B @ r2_hidden ) )
& ( D @ ( A @ r2_hidden ) ) )
& ~ ( ( D @ ( C @ k4_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k4_xboole_0 ) @ ( A @ r2_hidden ) ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( B @ r2_hidden ) )
& ( D @ ( C @ k2_xboole_0 ) @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(76,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,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(103,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)],[21]) ).
thf(3,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(31,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,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)],[15]) ).
thf(6,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(40,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(82,plain,
! [A: $i] :
( ( A @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
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(36,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(20,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(100,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_xboole_0 ) )
= ( A @ ( B @ k2_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,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(97,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)],[19]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(79,plain,
! [A: $i] :
( ( A @ ( k1_xboole_0 @ k4_xboole_0 ) )
= k1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(94,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_xboole_0 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(109,plain,
$false,
inference(e,[status(thm)],[42,46,89,85,33,73,45,22,76,103,31,87,40,82,36,100,92,97,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU406+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.12 % 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
% 0.23/0.47 % Computer : n005.cluster.edu
% 0.23/0.47 % Model : x86_64 x86_64
% 0.23/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.47 % Memory : 8046.5625MB
% 0.23/0.47 % OS : Linux 6.8.0-71-generic
% 0.23/0.47 % CPULimit : 300
% 0.23/0.47 % WCLimit : 300
% 0.23/0.47 % DateTime : Sat Sep 26 09:27:31 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 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
% 1.45/1.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.79/1.60 % [INFO] Parsing done (281ms).
% 2.08/1.62 % [INFO] Running in sequential loop mode.
% 3.14/2.20 % [INFO] eprover registered as external prover.
% 3.14/2.21 % [INFO] Scanning for conjecture ...
% 3.35/2.36 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 3.55/2.45 % [INFO] Axiom selection finished. Selected 19 axioms (removed 4 axioms).
% 3.55/2.49 % [INFO] Problem is first-order (TPTP FOF).
% 3.77/2.50 % [INFO] Type checking passed.
% 3.77/2.51 % [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 ...
% 6.59/3.62 % External prover 'e' found a proof!
% 6.59/3.62 % [INFO] Killing All external provers ...
% 6.59/3.62 % Time passed: 2937ms (effective reasoning time: 1995ms)
% 6.59/3.62 % 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)>
% 6.59/3.62 % Axioms used in derivation (19): t1_boole, fc2_xboole_0, t6_boole, commutativity_k2_xboole_0, t7_boole, existence_m1_subset_1, t2_subset, idempotence_k2_xboole_0, t3_boole, rc2_xboole_0, fc1_xboole_0, t1_subset, t4_boole, fc3_xboole_0, d2_xboole_0, t8_boole, rc1_xboole_0, t39_xboole_1, antisymmetry_r2_hidden
% 6.59/3.62 % No. of inferences in proof: 42
% 6.59/3.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2937 ms resp. 1995 ms w/o parsing
% 6.92/3.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.92/3.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------