%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/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 06:46:24 AM UTC 2026
% Result : Theorem 4.39s 2.65s
% Output : Refutation 4.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 52 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 21 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 334 ( 27 ~; 2 |; 49 &; 209 @)
% ( 3 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 86 ( 0 ^; 65 !; 21 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(m1_pboole_decl,type,
m1_pboole: $i > $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_closure3_decl,type,
k1_closure3: $i > $i > $i ).
thf(k1_funct_1_decl,type,
k1_funct_1: $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(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(v1_fraenkel_decl,type,
v1_fraenkel: $i > $o ).
thf(a_2_0_closure3_decl,type,
a_2_0_closure3: $i > $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(24,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( C
= ( B @ ( A @ k1_closure3 ) ) )
<=> ( C
= ( B @ ( A @ a_2_0_closure3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_closure3) ).
thf(115,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( ( C
= ( B @ ( A @ a_2_0_closure3 ) ) )
=> ( C
= ( B @ ( A @ k1_closure3 ) ) ) )
& ( ( C
= ( B @ ( A @ k1_closure3 ) ) )
=> ( C
= ( B @ ( A @ a_2_0_closure3 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(23,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(110,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(89,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(70,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(25,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(124,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(14,axiom,
? [A: $i] :
( ( A @ v1_fraenkel )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_closure2) ).
thf(73,plain,
? [A: $i] :
( ( A @ v1_fraenkel )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(81,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(108,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(35,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
<=> ( B @ ( C @ r2_hidden ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(95,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ r2_hidden ) )
=> ( A @ ( C @ r2_hidden ) ) )
& ( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(127,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(51,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(46,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(93,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(57,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pboole ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) )
<=> ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_closure3) ).
thf(60,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ m1_pboole ) )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) ) )
& ( ( C @ ( B @ a_2_0_closure3 ) @ ( A @ r2_hidden ) )
=> ? [D: $i] :
( ( ( D @ ( C @ k1_funct_1 ) )
!= k1_xboole_0 )
& ( A = D )
& ( B @ ( D @ m1_subset_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_fraenkel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_closure2) ).
thf(44,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_fraenkel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( A @ k1_closure3 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= k1_xboole_0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_closure3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( A @ k1_closure3 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= k1_xboole_0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ! [B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( A @ ( C @ m1_subset_1 ) )
=> ( ~ ( B @ ( A @ k1_closure3 ) @ ( C @ r2_hidden ) )
=> ( ( C @ ( B @ k1_funct_1 ) )
= k1_xboole_0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(71,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(49,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)],[7]) ).
thf(4,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(40,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(55,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(132,plain,
$false,
inference(e,[status(thm)],[115,110,106,89,70,124,73,81,108,35,95,127,51,83,46,93,57,60,85,44,27,71,49,40,55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.40 % Computer : n018.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sat Sep 26 21:38:37 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.19 % [INFO] Parsing done (203ms).
% 1.42/1.21 % [INFO] Running in sequential loop mode.
% 2.14/1.62 % [INFO] eprover registered as external prover.
% 2.14/1.62 % [INFO] Scanning for conjecture ...
% 2.33/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 2.52/1.81 % [INFO] Axiom selection finished. Selected 24 axioms (removed 4 axioms).
% 2.52/1.85 % [INFO] Problem is first-order (TPTP FOF).
% 2.52/1.86 % [INFO] Type checking passed.
% 2.52/1.87 % [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 ...
% 4.39/2.64 % External prover 'e' found a proof!
% 4.39/2.64 % [INFO] Killing All external provers ...
% 4.39/2.65 % Time passed: 2103ms (effective reasoning time: 1430ms)
% 4.39/2.65 % 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)>
% 4.39/2.65 % Axioms used in derivation (24): d3_closure3, rc3_funct_1, t6_boole, t2_tarski, cc1_closure2, rc2_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, fraenkel_a_2_0_closure3, rc1_funct_1, t7_boole, cc1_funct_1, dt_m1_pboole, existence_m1_pboole, cc2_funct_1, existence_m1_subset_1, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, t2_subset, rc1_closure2
% 4.39/2.65 % No. of inferences in proof: 52
% 4.39/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2103 ms resp. 1430 ms w/o parsing
% 4.70/2.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.70/2.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------