%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM761_8 : TPTP v9.3.1. Released v8.0.0.
% 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 08:09:54 AM UTC 2026
% Result : Theorem 2.67s 1.61s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 70 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 259 ( 31 ~; 20 |; 0 &; 194 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(x_decl,type,
x: frac ).
thf(y_decl,type,
y: frac ).
thf(z_decl,type,
z: frac ).
thf(u_decl,type,
u: frac ).
thf(moref_decl,type,
moref: frac > frac > $o ).
thf(eq_decl,type,
eq: frac > frac > $o ).
thf(pf_decl,type,
pf: frac > frac > frac ).
thf(7,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( B @ ( A @ moref ) )
=> ( ( D @ ( C @ moref ) )
=> ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz64) ).
thf(16,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( B @ ( A @ moref ) )
=> ( ( D @ ( C @ moref ) )
=> ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,plain,
! [A: frac,B: frac] :
( ( B @ ( A @ moref ) )
=> ! [C: frac,D: frac] :
( ( D @ ( C @ moref ) )
=> ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ) ),
inference(miniscope,[status(thm)],[16]) ).
thf(18,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
| ~ ( D @ ( C @ moref ) )
| ~ ( B @ ( A @ moref ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(1,conjecture,
u @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz65a) ).
thf(2,negated_conjecture,
~ ( u @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( u @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(77,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ( ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
!= ( u @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ) )
| ~ $true
| ~ ( D @ ( C @ moref ) )
| ~ ( B @ ( A @ moref ) ) ),
inference(paramod_ordered,[status(thm)],[18,8]) ).
thf(78,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ( ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
!= ( u @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ) )
| ~ ( D @ ( C @ moref ) )
| ~ ( B @ ( A @ moref ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
( ~ ( u @ ( z @ moref ) )
| ~ ( y @ ( x @ moref ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(3,axiom,
( ~ ( y @ ( x @ moref ) )
=> ( y @ ( x @ eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(9,plain,
( ~ ( y @ ( x @ moref ) )
=> ( y @ ( x @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,plain,
( ( y @ ( x @ eq ) )
| ( y @ ( x @ moref ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( B @ ( A @ eq ) )
=> ( ( D @ ( C @ moref ) )
=> ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62g) ).
thf(13,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( B @ ( A @ eq ) )
=> ( ( D @ ( C @ moref ) )
=> ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,plain,
! [A: frac,B: frac] :
( ( B @ ( A @ eq ) )
=> ! [C: frac,D: frac] :
( ( D @ ( C @ moref ) )
=> ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) ) ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
| ~ ( D @ ( C @ moref ) )
| ~ ( B @ ( A @ eq ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(28,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ( ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
!= ( u @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ) )
| ~ $true
| ~ ( D @ ( C @ moref ) )
| ~ ( B @ ( A @ eq ) ) ),
inference(paramod_ordered,[status(thm)],[15,8]) ).
thf(29,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ( ( D @ ( B @ pf ) @ ( C @ ( A @ pf ) @ moref ) )
!= ( u @ ( y @ pf ) @ ( z @ ( x @ pf ) @ moref ) ) )
| ~ ( D @ ( C @ moref ) )
| ~ ( B @ ( A @ eq ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(30,plain,
( ~ ( u @ ( z @ moref ) )
| ~ ( y @ ( x @ eq ) ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(4,axiom,
u @ ( z @ moref ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(11,plain,
u @ ( z @ moref ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,plain,
( ~ $true
| ~ ( y @ ( x @ eq ) ) ),
inference(rewrite,[status(thm)],[30,11]) ).
thf(37,plain,
~ ( y @ ( x @ eq ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
( $false
| ( y @ ( x @ moref ) ) ),
inference(rewrite,[status(thm)],[10,37]) ).
thf(39,plain,
y @ ( x @ moref ),
inference(simp,[status(thm)],[38]) ).
thf(98,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[79,39,11]) ).
thf(99,plain,
$false,
inference(simp,[status(thm)],[98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM761_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.07/0.33 % Computer : n012.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 26 04:01:36 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 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
% 0.49/0.65 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.75 % [INFO] Parsing done (100ms).
% 0.64/0.76 % [INFO] Running in sequential loop mode.
% 0.94/0.97 % [INFO] eprover registered as external prover.
% 0.94/0.97 % [INFO] Scanning for conjecture ...
% 1.16/1.03 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.16/1.05 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.16/1.06 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.16/1.06 % [INFO] Type checking passed.
% 1.16/1.07 % [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 ...
% 2.67/1.60 % [INFO] Killing All external provers ...
% 2.67/1.60 % Time passed: 1188ms (effective reasoning time: 841ms)
% 2.67/1.60 % 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)>
% 2.67/1.60 % Axioms used in derivation (4): satz64, m, satz62g, n
% 2.67/1.60 % No. of inferences in proof: 28
% 2.67/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1188 ms resp. 841 ms w/o parsing
% 2.67/1.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.67/1.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------