%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM647^1 : 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 : n026.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 08:17:52 AM UTC 2026
% Result : Theorem 3.46s 1.68s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 25 ( 24 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 71 ( 10 ~; 3 |; 0 &; 56 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 22 !; 1 ?; 24 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(z_decl,type,
z: nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(sk1_decl,type,
sk1: nat > nat > nat ).
thf(sk1_def,definition,
( sk1
= ( @+[A: nat > nat > nat] :
! [B: nat,C: nat] :
( ( A @ B @ ( pl @ B @ C ) )
= C ) ) ) ).
thf(3,axiom,
( ( pl @ x @ y )
= ( pl @ x @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i) ).
thf(8,plain,
( ( pl @ x @ y )
= ( pl @ x @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
( ( pl @ x @ z )
= ( pl @ x @ y ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( B != C )
=> ( ( pl @ A @ B )
!= ( pl @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz8) ).
thf(11,plain,
! [A: nat,B: nat,C: nat] :
( ( B != C )
=> ( ( pl @ A @ B )
!= ( pl @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,plain,
! [C: nat,B: nat,A: nat] :
( ( B = C )
| ( ( pl @ A @ B )
!= ( pl @ A @ C ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [C: nat,B: nat,A: nat] :
( ( B = C )
| ( ( pl @ A @ B )
!= ( pl @ A @ C ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(14,plain,
? [A: nat > nat > nat] :
! [B: nat,C: nat] :
( ( A @ B @ ( pl @ B @ C ) )
= C ),
inference(detectInverse,[status(thm)],[13]) ).
thf(15,plain,
! [B: nat,A: nat] :
( ( sk1 @ A @ ( pl @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [B: nat,A: nat] :
( ( sk1 @ A @ ( pl @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[15]) ).
thf(17,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ A @ ( pl @ x @ y ) )
= B )
| ( ( pl @ x @ z )
!= ( pl @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,16]) ).
thf(18,plain,
( ( sk1 @ x @ ( pl @ x @ y ) )
= z ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).
thf(19,plain,
z = y,
inference(rewrite,[status(thm)],[18,16]) ).
thf(1,conjecture,
y = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz8a) ).
thf(2,negated_conjecture,
y != z,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
y != z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
z != y,
inference(lifteq,[status(thm)],[6]) ).
thf(20,plain,
$false,
inference(simplifyReflect,[status(thm)],[19,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM647^1 : 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
% 0.09/0.22 % Computer : n026.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 12:32:57 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.70/0.57 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.03/0.69 % [INFO] Parsing done (119ms).
% 1.16/0.70 % [INFO] Running in sequential loop mode.
% 1.53/0.95 % [INFO] eprover registered as external prover.
% 1.53/0.95 % [INFO] Scanning for conjecture ...
% 1.53/1.00 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.53/1.02 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.53/1.03 % [INFO] Problem is higher-order (TPTP THF).
% 1.53/1.03 % [INFO] Type checking passed.
% 1.53/1.04 % [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 ...
% 3.46/1.67 % [INFO] Killing All external provers ...
% 3.46/1.68 % Time passed: 1362ms (effective reasoning time: 969ms)
% 3.46/1.68 % 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)>
% 3.46/1.68 % Axioms used in derivation (2): i, satz8
% 3.46/1.68 % No. of inferences in proof: 18
% 3.46/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1362 ms resp. 969 ms w/o parsing
% 3.73/1.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.73/1.75 % [INFO] Killing All external provers ...
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