%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM688_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 : n019.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 08:09:38 AM UTC 2026
% Result : Theorem 5.81s 3.04s
% Output : Refutation 5.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 266 ( 29 ~; 23 |; 0 &; 200 @)
% ( 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 : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(z_decl,type,
z: nat ).
thf(u_decl,type,
u: nat ).
thf(more_decl,type,
more: nat > nat > $o ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(7,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ more ) )
=> ( ( D @ ( C @ more ) )
=> ( D @ ( B @ pl ) @ ( C @ ( A @ pl ) @ more ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).
thf(19,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( B @ ( A @ more ) )
=> ( ( D @ ( C @ more ) )
=> ( D @ ( B @ pl ) @ ( C @ ( A @ pl ) @ more ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ more ) )
=> ! [C: nat,D: nat] :
( ( D @ ( C @ more ) )
=> ( D @ ( B @ pl ) @ ( C @ ( A @ pl ) @ more ) ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( D @ ( B @ pl ) @ ( C @ ( A @ pl ) @ more ) )
| ~ ( D @ ( C @ more ) )
| ~ ( B @ ( A @ more ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(1,conjecture,
u @ ( y @ pl ) @ ( z @ ( x @ pl ) @ more ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz22b) ).
thf(2,negated_conjecture,
~ ( u @ ( y @ pl ) @ ( z @ ( x @ pl ) @ more ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( u @ ( y @ pl ) @ ( z @ ( x @ pl ) @ more ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(156,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( D @ ( B @ pl ) @ ( C @ ( A @ pl ) @ more ) )
!= ( u @ ( y @ pl ) @ ( z @ ( x @ pl ) @ more ) ) )
| ~ $true
| ~ ( D @ ( C @ more ) )
| ~ ( B @ ( A @ more ) ) ),
inference(paramod_ordered,[status(thm)],[21,8]) ).
thf(157,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( D @ ( B @ pl ) @ ( C @ ( A @ pl ) @ more ) )
!= ( u @ ( y @ pl ) @ ( z @ ( x @ pl ) @ more ) ) )
| ~ ( D @ ( C @ more ) )
| ~ ( B @ ( A @ more ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(158,plain,
( ~ ( u @ ( z @ more ) )
| ~ ( y @ ( x @ more ) ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(3,axiom,
y @ ( x @ more ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(9,plain,
y @ ( x @ more ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
( ~ ( u @ ( z @ more ) )
=> ( z = u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(10,plain,
( ~ ( u @ ( z @ more ) )
=> ( z = u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,plain,
( ( z = u )
| ( u @ ( z @ more ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
( ( u @ ( z @ more ) )
| ( u = z ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(25,plain,
( ( u != u )
| ~ ( z @ ( y @ pl ) @ ( z @ ( x @ pl ) @ more ) )
| ( u @ ( z @ more ) ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(26,plain,
( ~ ( z @ ( y @ pl ) @ ( z @ ( x @ pl ) @ more ) )
| ( u @ ( z @ more ) ) ),
inference(pattern_uni,[status(thm)],[25:[]]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A = B )
=> ( ( D @ ( C @ more ) )
=> ( B @ ( D @ pl ) @ ( A @ ( C @ pl ) @ more ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19h) ).
thf(14,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A = B )
=> ( ( D @ ( C @ more ) )
=> ( B @ ( D @ pl ) @ ( A @ ( C @ pl ) @ more ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ! [C: nat,D: nat] :
( ( D @ ( C @ more ) )
=> ( B @ ( D @ pl ) @ ( A @ ( C @ pl ) @ more ) ) ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( D @ pl ) @ ( A @ ( C @ pl ) @ more ) )
| ~ ( D @ ( C @ more ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( B @ ( D @ pl ) @ ( A @ ( C @ pl ) @ more ) )
| ~ ( D @ ( C @ more ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(18,plain,
! [C: nat,B: nat,A: nat] :
( ( A @ ( C @ pl ) @ ( A @ ( B @ pl ) @ more ) )
| ~ ( C @ ( B @ more ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(42,plain,
! [C: nat,B: nat,A: nat] :
( ( ( y @ ( x @ more ) )
!= ( C @ ( B @ more ) ) )
| ( A @ ( C @ pl ) @ ( A @ ( B @ pl ) @ more ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9,18]) ).
thf(43,plain,
! [C: nat,B: nat,A: nat] :
( ( ( y @ ( x @ more ) )
!= ( C @ ( B @ more ) ) )
| ( A @ ( C @ pl ) @ ( A @ ( B @ pl ) @ more ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(44,plain,
! [A: nat] : ( A @ ( y @ pl ) @ ( A @ ( x @ pl ) @ more ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( A )),bind(B,$thf( x )),bind(C,$thf( y ))]]) ).
thf(58,plain,
( ~ $true
| ( u @ ( z @ more ) ) ),
inference(rewrite,[status(thm)],[26,44]) ).
thf(59,plain,
u @ ( z @ more ),
inference(simp,[status(thm)],[58]) ).
thf(218,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[158,9,59]) ).
thf(219,plain,
$false,
inference(simp,[status(thm)],[218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM688_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % 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
% 0.13/0.41 % Computer : n019.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 03:45:33 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.18 % [INFO] Parsing done (189ms).
% 1.27/1.19 % [INFO] Running in sequential loop mode.
% 2.00/1.60 % [INFO] eprover registered as external prover.
% 2.00/1.61 % [INFO] Scanning for conjecture ...
% 2.18/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.18/1.74 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.18/1.76 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.18/1.77 % [INFO] Type checking passed.
% 2.18/1.77 % [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 ...
% 5.81/3.03 % [INFO] Killing All external provers ...
% 5.81/3.03 % Time passed: 2478ms (effective reasoning time: 1830ms)
% 5.81/3.03 % 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)>
% 5.81/3.03 % Axioms used in derivation (4): satz21, m, n, satz19h
% 5.81/3.04 % No. of inferences in proof: 31
% 5.81/3.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2478 ms resp. 1830 ms w/o parsing
% 5.81/3.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.81/3.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------