%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM713^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n009.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 08:18:03 AM UTC 2026
% Result : Theorem 8.29s 3.43s
% Output : Refutation 8.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 26 unt; 0 typ; 1 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 211 ( 29 ~; 6 |; 0 &; 176 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 41 !; 2 ?; 44 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(z_decl,type,
z: nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(ts_decl,type,
ts: nat > nat > nat ).
thf(sk1_decl,type,
sk1: nat ).
thf(sk1_def,definition,
( sk1
= ( @+[A: nat] :
( x
= ( pl @ y @ A ) ) ) ) ).
thf(3,axiom,
~ ! [A: nat] :
( x
!= ( pl @ y @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(12,plain,
~ ! [A: nat] :
( x
!= ( pl @ y @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
~ ! [A: nat] :
( x
!= ( pl @ y @ A ) ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
~ ~ ? [A: nat] :
( x
= ( pl @ y @ A ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
( x
= ( pl @ y @ sk1 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
( ( pl @ y @ sk1 )
= x ),
inference(lifteq,[status(thm)],[15]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ts @ A @ ( pl @ B @ C ) )
= ( pl @ ( ts @ A @ B ) @ ( ts @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz30) ).
thf(21,plain,
! [A: nat,B: nat,C: nat] :
( ( ts @ A @ ( pl @ B @ C ) )
= ( pl @ ( ts @ A @ B ) @ ( ts @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [C: nat,B: nat,A: nat] :
( ( ts @ A @ ( pl @ B @ C ) )
= ( pl @ ( ts @ A @ B ) @ ( ts @ A @ C ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [C: nat,B: nat,A: nat] :
( ( ts @ A @ ( pl @ B @ C ) )
= ( pl @ ( ts @ A @ B ) @ ( ts @ A @ C ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(31,plain,
! [C: nat,B: nat,A: nat] :
( ( ( ts @ A @ x )
= ( pl @ ( ts @ A @ B ) @ ( ts @ A @ C ) ) )
| ( ( pl @ y @ sk1 )
!= ( pl @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,23]) ).
thf(32,plain,
! [A: nat] :
( ( ts @ A @ x )
= ( pl @ ( ts @ A @ y ) @ ( ts @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( sk1 ))]]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).
thf(18,plain,
! [A: nat,B: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [B: nat,A: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [B: nat,A: nat] :
( ( ts @ A @ B )
= ( ts @ B @ A ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(83,plain,
! [C: nat,B: nat,A: nat] :
( ( ( pl @ ( ts @ A @ y ) @ ( ts @ A @ sk1 ) )
= ( ts @ C @ B ) )
| ( ( ts @ A @ x )
!= ( ts @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[32,20]) ).
thf(84,plain,
! [A: nat] :
( ( pl @ ( ts @ A @ y ) @ ( ts @ A @ sk1 ) )
= ( ts @ x @ A ) ),
inference(pattern_uni,[status(thm)],[83:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( x ))]]) ).
thf(1,conjecture,
~ ! [A: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz32a) ).
thf(2,negated_conjecture,
~ ~ ! [A: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ~ ! [A: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [A: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ A ) ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
~ ? [A: nat] :
( ( ts @ x @ z )
= ( pl @ ( ts @ y @ z ) @ A ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
! [A: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [A: nat] :
( ( ts @ x @ z )
!= ( pl @ ( ts @ y @ z ) @ A ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(577,plain,
! [B: nat,A: nat] :
( ( ( ts @ x @ A )
!= ( ts @ x @ z ) )
| ( ( pl @ ( ts @ A @ y ) @ ( ts @ A @ sk1 ) )
!= ( pl @ ( ts @ y @ z ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[84,11]) ).
thf(652,plain,
! [B: nat,A: nat] :
( ( x != x )
| ( A != z )
| ( ( ts @ A @ y )
!= ( ts @ y @ z ) )
| ( ( ts @ A @ sk1 )
!= B ) ),
inference(simp,[status(thm)],[577]) ).
thf(667,plain,
( ( ts @ z @ y )
!= ( ts @ y @ z ) ),
inference(simp,[status(thm)],[652]) ).
thf(687,plain,
$false,
inference(simplifyReflect,[status(thm)],[667,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM713^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.11/0.21 % Computer : n009.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 12:44:45 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (188ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 1.86/1.39 % [INFO] eprover registered as external prover.
% 2.06/1.40 % [INFO] Scanning for conjecture ...
% 2.24/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.24/1.54 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.24/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.55 % [INFO] Type checking passed.
% 2.24/1.56 % [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 ...
% 8.29/3.43 % [INFO] Killing All external provers ...
% 8.29/3.43 % Time passed: 3068ms (effective reasoning time: 2428ms)
% 8.29/3.43 % 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)>
% 8.29/3.43 % Axioms used in derivation (3): m, satz30, satz29
% 8.29/3.43 % No. of inferences in proof: 29
% 8.29/3.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3068 ms resp. 2428 ms w/o parsing
% 8.29/3.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.29/3.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------