%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM688^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n017.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 08:17:59 AM UTC 2026
% Result : Theorem 6.24s 2.97s
% Output : Refutation 6.24s
% 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] :
( ( more @ A @ B )
=> ( ( more @ C @ D )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz21) ).
thf(19,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( more @ A @ B )
=> ( ( more @ C @ D )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [A: nat,B: nat] :
( ( more @ A @ B )
=> ! [C: nat,D: nat] :
( ( more @ C @ D )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( more @ C @ D )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(1,conjecture,
more @ ( pl @ x @ z ) @ ( pl @ y @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22b) ).
thf(2,negated_conjecture,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(156,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( more @ C @ D )
| ~ $true
| ( ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) )
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,8]) ).
thf(157,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( more @ C @ D )
| ( ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) )
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(158,plain,
( ~ ( more @ x @ y )
| ~ ( more @ z @ u ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(3,axiom,
more @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(9,plain,
more @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
( ~ ( more @ z @ u )
=> ( z = u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(10,plain,
( ~ ( more @ z @ u )
=> ( z = u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,plain,
( ( more @ z @ u )
| ( z = u ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
( ( u = z )
| ( more @ z @ u ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(25,plain,
( ( more @ z @ u )
| ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
| ( u != u ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(26,plain,
( ( more @ z @ u )
| ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ),
inference(pattern_uni,[status(thm)],[25:[]]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A = B )
=> ( ( more @ C @ D )
=> ( more @ ( pl @ C @ A ) @ ( pl @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19h) ).
thf(14,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( A = B )
=> ( ( more @ C @ D )
=> ( more @ ( pl @ C @ A ) @ ( pl @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ! [C: nat,D: nat] :
( ( more @ C @ D )
=> ( more @ ( pl @ C @ A ) @ ( pl @ D @ B ) ) ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( A != B )
| ~ ( more @ C @ D )
| ( more @ ( pl @ C @ A ) @ ( pl @ D @ B ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( A != B )
| ~ ( more @ C @ D )
| ( more @ ( pl @ C @ A ) @ ( pl @ D @ B ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(18,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ B @ C )
| ( more @ ( pl @ B @ A ) @ ( pl @ C @ A ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(42,plain,
! [C: nat,B: nat,A: nat] :
( ~ $true
| ( more @ ( pl @ B @ A ) @ ( pl @ C @ A ) )
| ( ( more @ x @ y )
!= ( more @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9,18]) ).
thf(43,plain,
! [C: nat,B: nat,A: nat] :
( ( more @ ( pl @ B @ A ) @ ( pl @ C @ A ) )
| ( ( more @ x @ y )
!= ( more @ B @ C ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(44,plain,
! [A: nat] : ( more @ ( pl @ x @ A ) @ ( pl @ y @ A ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( A )),bind(B,$thf( x )),bind(C,$thf( y ))]]) ).
thf(58,plain,
( ( more @ z @ u )
| ~ $true ),
inference(rewrite,[status(thm)],[26,44]) ).
thf(59,plain,
more @ z @ u,
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 : NUM688^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.10/0.21 % Computer : n017.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 12:34:43 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.91/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/0.99 % [INFO] Parsing done (195ms).
% 1.26/1.01 % [INFO] Running in sequential loop mode.
% 2.06/1.41 % [INFO] eprover registered as external prover.
% 2.06/1.42 % [INFO] Scanning for conjecture ...
% 2.24/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.24/1.53 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.24/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.57 % [INFO] Type checking passed.
% 2.24/1.57 % [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 ...
% 6.24/2.97 % [INFO] Killing All external provers ...
% 6.24/2.97 % Time passed: 2613ms (effective reasoning time: 1950ms)
% 6.24/2.97 % 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)>
% 6.24/2.97 % Axioms used in derivation (4): satz21, m, n, satz19h
% 6.24/2.97 % No. of inferences in proof: 31
% 6.24/2.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2613 ms resp. 1950 ms w/o parsing
% 6.24/3.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.24/3.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------