%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT299+2 : 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 : n012.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 07:47:05 AM UTC 2026
% Result : ContradictoryAxioms 69.44s 22.62s
% Output : Refutation 69.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 20 unt; 0 typ; 4 def)
% Number of atoms : 158 ( 77 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 389 ( 52 ~; 32 |; 38 &; 245 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 117 ( 3 ^; 100 !; 10 ?; 117 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(r2_tarski_decl,type,
r2_tarski: $i > $i > $o ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk43_decl,type,
sk43: $i > $i > $i ).
thf(sk102_decl,type,
sk102: $i > $i ).
thf(sk198_decl,type,
sk198: $i > $i ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ r2_hidden ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk102_def,definition,
( sk102
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ) ) ).
thf(sk198_def,definition,
( sk198
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ) ) ) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
<=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(1025,plain,
! [A: $i,B: $i] :
( ( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1026,plain,
( ! [A: $i,B: $i] :
( ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) )
=> ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
=> ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 ) ) ) ),
inference(miniscope,[status(thm)],[1025]) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( D != k1_xboole_0 ) )
& ( ( ( D @ ( C @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( C != k1_xboole_0 ) )
& ( ( B = k1_xboole_0 )
| ( A = k1_xboole_0 )
| ( ( B @ ( A @ k2_zfmisc_1 ) )
!= k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[1026]) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[1027]) ).
thf(1034,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 )
| ( B != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[1030]) ).
thf(1035,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
= k1_xboole_0 ),
inference(simp,[status(thm)],[1034]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
thf(1184,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ k2_zfmisc_1 ) )
= ( B @ ( B @ k2_zfmisc_1 ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(1185,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(cnf,[status(esa)],[1184]) ).
thf(1186,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( A @ k2_zfmisc_1 ) )
!= ( B @ ( B @ k2_zfmisc_1 ) ) ) ),
inference(lifteq,[status(thm)],[1185]) ).
thf(1187,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ k2_zfmisc_1 ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1186]) ).
thf(1188,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk43 ) )
= A ),
inference(cnf,[status(esa)],[1187]) ).
thf(40846,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ ( B @ sk43 ) )
= A ),
inference(lifteq,[status(thm)],[1188]) ).
thf(40871,plain,
! [C: $i,B: $i,A: $i] :
( ( ( k1_xboole_0 @ ( A @ k2_zfmisc_1 ) )
!= ( C @ ( B @ k2_zfmisc_1 ) ) )
| ( ( k1_xboole_0 @ ( C @ sk43 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1035,40846]) ).
thf(40872,plain,
! [A: $i] :
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk43 ) )
= A ),
inference(pattern_uni,[status(thm)],[40871:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( k1_xboole_0 ))]]) ).
thf(447,axiom,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(3053,plain,
! [A: $i] :
? [B: $i] :
( ! [C: $i] :
~ ( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(3054,plain,
! [A: $i] :
? [B: $i] :
( ~ ? [C: $i] :
( ~ ( B @ ( C @ r2_hidden ) )
& ~ ( B @ ( C @ r2_tarski ) )
& ( B @ ( C @ r1_tarski ) ) )
& ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
=> ( B @ ( C @ k1_zfmisc_1 @ r2_hidden ) ) )
& ! [C: $i,D: $i] :
( ( ( C @ ( D @ r1_tarski ) )
& ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( D @ r2_hidden ) ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(miniscope,[status(thm)],[3053]) ).
thf(3055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ sk198 @ ( E @ r2_hidden ) )
| ( A @ sk198 @ ( E @ r2_tarski ) )
| ~ ( A @ sk198 @ ( E @ r1_tarski ) ) )
& ( ( A @ sk198 @ ( D @ k1_zfmisc_1 @ r2_hidden ) )
| ~ ( A @ sk198 @ ( D @ r2_hidden ) ) )
& ( ( A @ sk198 @ ( C @ r2_hidden ) )
| ~ ( B @ ( C @ r1_tarski ) )
| ~ ( A @ sk198 @ ( B @ r2_hidden ) ) )
& ( A @ sk198 @ ( A @ r2_hidden ) ) ),
inference(cnf,[status(esa)],[3054]) ).
thf(3056,plain,
! [A: $i] : ( A @ sk198 @ ( A @ r2_hidden ) ),
inference(cnfConj,[status(thm)],[3055]) ).
thf(57,axiom,
! [A: $i] :
( ( A = k1_xboole_0 )
<=> ! [B: $i] :
~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(940,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)],[57]) ).
thf(941,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) )
=> ( A = k1_xboole_0 ) )
& ! [A: $i] :
( ( A = k1_xboole_0 )
=> ~ ? [B: $i] : ( A @ ( B @ r2_hidden ) ) ) ),
inference(miniscope,[status(thm)],[940]) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = k1_xboole_0 )
| ( C @ ( C @ sk22 @ r2_hidden ) ) )
& ( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ) ),
inference(cnf,[status(esa)],[941]) ).
thf(943,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(cnfConj,[status(thm)],[942]) ).
thf(945,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2_hidden ) )
| ( A != k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[943]) ).
thf(946,plain,
! [A: $i] :
~ ( k1_xboole_0 @ ( A @ r2_hidden ) ),
inference(simp,[status(thm)],[945]) ).
thf(25369,plain,
! [B: $i,A: $i] :
( ( ( A @ sk198 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3056,946]) ).
thf(25370,plain,
! [B: $i,A: $i] :
( ( A @ sk198 @ ( A @ r2_hidden ) )
!= ( k1_xboole_0 @ ( B @ r2_hidden ) ) ),
inference(simp,[status(thm)],[25369]) ).
thf(25373,plain,
! [B: $i,A: $i] :
( ( ( A @ sk198 )
!= k1_xboole_0 )
| ( A != B ) ),
inference(simp,[status(thm)],[25370]) ).
thf(25380,plain,
! [A: $i] :
( ( A @ sk198 )
!= k1_xboole_0 ),
inference(simp,[status(thm)],[25373]) ).
thf(41052,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk198 ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk43 ) )
!= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[40872,25380]) ).
thf(41053,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk43 ) )
!= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[41052:[bind(A,$thf( C @ sk198 )),bind(B,$thf( C ))]]) ).
thf(250,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(1896,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)],[250]) ).
thf(1897,plain,
! [A: $i] :
( ( A @ sk102 @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( A @ sk102 @ m1_subset_1 ) ) ),
inference(cnf,[status(esa)],[1896]) ).
thf(1899,plain,
! [A: $i] : ( A @ sk102 @ v1_xboole_0 ),
inference(cnfConj,[status(thm)],[1897]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(721,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(722,plain,
! [A: $i] :
( ( A = k1_xboole_0 )
| ~ ( A @ v1_xboole_0 ) ),
inference(cnf,[status(esa)],[721]) ).
thf(723,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
| ( A = k1_xboole_0 ) ),
inference(lifteq,[status(thm)],[722]) ).
thf(20489,plain,
! [B: $i,A: $i] :
( ( ( A @ sk102 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ~ $true
| ( B = k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[1899,723]) ).
thf(20490,plain,
! [B: $i,A: $i] :
( ( ( A @ sk102 @ v1_xboole_0 )
!= ( B @ v1_xboole_0 ) )
| ( B = k1_xboole_0 ) ),
inference(simp,[status(thm)],[20489]) ).
thf(20491,plain,
! [A: $i] :
( ( A @ sk102 )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[20490:[bind(A,$thf( C )),bind(B,$thf( C @ sk102 ))]]) ).
thf(20524,plain,
! [A: $i] :
( ( A @ sk102 )
= k1_xboole_0 ),
inference(simp,[status(thm)],[20491]) ).
thf(41048,plain,
! [B: $i,A: $i] :
( ( A
!= ( B @ sk102 ) )
| ( ( k1_xboole_0 @ ( k1_xboole_0 @ sk43 ) )
= k1_xboole_0 ) ),
inference(paramod_ordered,[status(thm)],[40872,20524]) ).
thf(41049,plain,
( ( k1_xboole_0 @ ( k1_xboole_0 @ sk43 ) )
= k1_xboole_0 ),
inference(pattern_uni,[status(thm)],[41048:[bind(A,$thf( C @ sk102 )),bind(B,$thf( C ))]]) ).
thf(43123,plain,
k1_xboole_0 != k1_xboole_0,
inference(rewrite,[status(thm)],[41053,41049]) ).
thf(43124,plain,
$false,
inference(simp,[status(thm)],[43123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT299+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % 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
% 0.05/5.32 % Computer : n012.cluster.edu
% 0.05/5.32 % Model : x86_64 x86_64
% 0.05/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.32 % Memory : 8046.5625MB
% 0.05/5.32 % OS : Linux 6.8.0-71-generic
% 0.05/5.32 % CPULimit : 300
% 0.05/5.32 % WCLimit : 300
% 0.05/5.32 % DateTime : Fri Sep 25 20:35:57 UTC 2026
% 0.05/5.33 % CPUTime :
% 0.05/5.33 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
% 0.08/5.61 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.08/5.98 % [INFO] Parsing done (375ms).
% 0.08/5.99 % [INFO] Running in sequential loop mode.
% 2.32/6.18 % [INFO] eprover registered as external prover.
% 2.32/6.19 % [INFO] Scanning for conjecture ...
% 2.83/6.35 % [INFO] Found a conjecture (or negated_conjecture) and 2934 axioms. Running axiom selection ...
% 4.09/6.66 % [INFO] Axiom selection finished. Selected 667 axioms (removed 2267 axioms).
% 4.91/6.97 % [INFO] Problem is first-order (TPTP FOF).
% 4.91/6.99 % [INFO] Type checking passed.
% 4.91/7.00 % [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 ...
% 69.44/22.62 % [INFO] Killing All external provers ...
% 69.44/22.62 % Time passed: 17221ms (effective reasoning time: 16626ms)
% 69.44/22.62 % Axioms used in derivation (6): t113_zfmisc_1, t115_zfmisc_1, d1_xboole_0, t136_zfmisc_1, t6_boole, rc2_subset_1
% 69.44/22.62 % No. of inferences in proof: 50
% 69.44/22.62 % SZS status ContradictoryAxioms for /export/starexec/sandbox2/benchmark/theBenchmark.p : 17221 ms resp. 16626 ms w/o parsing
% 69.44/22.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.44/22.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------