%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ150^18 : TPTP v9.3.1. Released v8.1.0.
% 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 : Wed Sep 30 08:20:50 AM UTC 2026
% Result : Theorem 3.92s 1.72s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 31 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 176 ( 5 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 359 ( 5 ~; 15 |; 3 &; 298 @)
% ( 0 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 5 con; 0-3 aty)
% Number of variables : 65 ( 12 ^; 50 !; 3 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mindex_type,type,
mindex: $tType ).
thf(mrel_decl,type,
mrel: mindex > mworld > mworld > $o ).
thf('#c_decl',type,
'#c': mindex ).
thf('#b_decl',type,
'#b': mindex ).
thf('#a_decl',type,
'#a': mindex ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mnot_decl,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mor_decl,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mbox_decl,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(mdia_decl,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(c0_decl,type,
c0: mworld > $o ).
thf(c1_decl,type,
c1: mworld > $o ).
thf(b0_decl,type,
b0: mworld > $o ).
thf(c2_decl,type,
c2: mworld > $o ).
thf(b1_decl,type,
b1: mworld > $o ).
thf(a0_decl,type,
a0: mworld > $o ).
thf(b2_decl,type,
b2: mworld > $o ).
thf(a1_decl,type,
a1: mworld > $o ).
thf(a2_decl,type,
a2: mworld > $o ).
thf(cb_decl,type,
cb: mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
thf(mor_def,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mindex,B: mworld > $o,C: mworld] :
! [D: mworld] :
( ( mrel @ A @ C @ D )
=> ( B @ D ) ) ) ) ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: mindex,B: mworld > $o,C: mworld] :
? [D: mworld] :
( ( mrel @ A @ C @ D )
& ( B @ D ) ) ) ) ).
thf(5,axiom,
! [A: mworld,B: mworld] : ( mrel @ '#a' @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#a_universal') ).
thf(24,plain,
! [A: mworld,B: mworld] : ( mrel @ '#a' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
mlocal @ ( mbox @ '#b' @ ( mnot @ ( mdia @ '#a' @ ( mdia @ '#b' @ ( mbox @ '#c' @ ( mnot @ a0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mbox @ '#b' @ ( mnot @ ( mdia @ '#a' @ ( mdia @ '#b' @ ( mbox @ '#c' @ ( mnot @ a0 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: mworld] :
( ( mrel @ '#b' @ mactual @ A )
=> ~ ? [B: mworld] :
( ( mrel @ '#a' @ A @ B )
& ? [C: mworld] :
( ( mrel @ '#b' @ B @ C )
& ! [D: mworld] :
( ( mrel @ '#c' @ C @ D )
=> ~ ( a0 @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mworld,B: mworld] : ( mrel @ '#c' @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#c_universal') ).
thf(20,plain,
! [A: mworld,B: mworld] : ( mrel @ '#c' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: mworld,B: mworld] : ( mrel @ '#b' @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_universal') ).
thf(22,plain,
! [A: mworld,B: mworld] : ( mrel @ '#b' @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
mlocal @ ( mbox @ '#b' @ ( mbox @ '#a' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_knows_b_a_c) ).
thf(28,plain,
! [A: mworld] :
( ( mrel @ '#b' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '#a' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
mlocal @ ( mbox @ '#b' @ ( mbox @ '#c' @ ( mor @ ( mbox @ '#a' @ a0 ) @ ( mor @ ( mbox @ '#a' @ a1 ) @ ( mbox @ '#a' @ a2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_knows_b_c_a) ).
thf(38,plain,
! [A: mworld] :
( ( mrel @ '#b' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '#c' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '#a' @ B @ C )
=> ( a0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#a' @ B @ C )
=> ( a1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#a' @ B @ C )
=> ( a2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
mlocal @ ( mbox @ '#a' @ ( mbox @ '#c' @ ( mor @ ( mbox @ '#b' @ b0 ) @ ( mor @ ( mbox @ '#b' @ b1 ) @ ( mbox @ '#b' @ b2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_knows_a_c_b) ).
thf(32,plain,
! [A: mworld] :
( ( mrel @ '#a' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '#c' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '#b' @ B @ C )
=> ( b0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#b' @ B @ C )
=> ( b1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#b' @ B @ C )
=> ( b2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
mlocal @ ( mbox @ '#c' @ ( mbox @ '#a' @ ( mor @ ( mbox @ '#b' @ cb ) @ ( mor @ ( mbox @ '#b' @ b1 ) @ ( mbox @ '#b' @ b2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_knows_c_a_b) ).
thf(34,plain,
! [A: mworld] :
( ( mrel @ '#c' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '#a' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '#b' @ B @ C )
=> ( cb @ C ) )
| ! [C: mworld] :
( ( mrel @ '#b' @ B @ C )
=> ( b1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#b' @ B @ C )
=> ( b2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
mlocal @ a0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_a0) ).
thf(40,plain,
a0 @ mactual,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
mlocal @ ( mbox @ '#a' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_knows_a_b_c) ).
thf(26,plain,
! [A: mworld] :
( ( mrel @ '#a' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '#b' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
mlocal @ ( mbox @ '#c' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#a' @ a0 ) @ ( mor @ ( mbox @ '#a' @ a1 ) @ ( mbox @ '#a' @ a2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_knows_c_b_a) ).
thf(36,plain,
! [A: mworld] :
( ( mrel @ '#c' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '#b' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '#a' @ B @ C )
=> ( a0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#a' @ B @ C )
=> ( a1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#a' @ B @ C )
=> ( a2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
mlocal @ ( mbox @ '#a' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_knows_a_b_c_0) ).
thf(30,plain,
! [A: mworld] :
( ( mrel @ '#a' @ mactual @ A )
=> ! [B: mworld] :
( ( mrel @ '#b' @ A @ B )
=> ( ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c0 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c1 @ C ) )
| ! [C: mworld] :
( ( mrel @ '#c' @ B @ C )
=> ( c2 @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[24,14,20,22,28,38,32,34,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ150^18 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.10/0.20 % Computer : n003.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:29:28 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.65/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.07/0.64 % [INFO] Parsing done (126ms).
% 1.07/0.65 % [INFO] Running in sequential loop mode.
% 1.54/0.86 % [INFO] eprover registered as external prover.
% 1.54/0.86 % [INFO] Scanning for conjecture ...
% 1.79/0.94 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.79/0.98 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.79/1.00 % [INFO] Problem is higher-order (TPTP THF).
% 1.79/1.01 % [INFO] Type checking passed.
% 1.79/1.01 % [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 ...
% 3.92/1.72 % External prover 'e' found a proof!
% 3.92/1.72 % [INFO] Killing All external provers ...
% 3.92/1.72 % Time passed: 1431ms (effective reasoning time: 1066ms)
% 3.92/1.72 % 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)>
% 3.92/1.72 % Axioms used in derivation (11): mrel_#b_universal, axiom_knows_a_b_c, axiom_a0, axiom_knows_b_c_a, axiom_knows_a_c_b, mrel_#a_universal, axiom_knows_c_a_b, axiom_knows_c_b_a, mrel_#c_universal, axiom_knows_a_b_c_0, axiom_knows_b_a_c
% 3.92/1.72 % No. of inferences in proof: 26
% 3.92/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1431 ms resp. 1066 ms w/o parsing
% 3.92/1.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.92/1.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------