%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM670_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : n006.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 08:09:33 AM UTC 2026
% Result : Theorem 6.32s 3.27s
% Output : Refutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 28 unt; 0 typ; 1 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 198 ( 28 ~; 4 |; 0 &; 166 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 ^; 42 !; 2 ?; 45 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(z_decl,type,
z: nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(sk1_decl,type,
sk1: nat ).
thf(sk1_def,definition,
( sk1
= ( @+[A: nat] :
( x
= ( A @ ( y @ pl ) ) ) ) ) ).
thf(3,axiom,
~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(12,plain,
~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
~ ! [A: nat] :
( x
!= ( A @ ( y @ pl ) ) ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
~ ~ ? [A: nat] :
( x
= ( A @ ( y @ pl ) ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
( x
= ( sk1 @ ( y @ pl ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
( ( sk1 @ ( y @ pl ) )
= x ),
inference(lifteq,[status(thm)],[15]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ pl ) )
= ( A @ ( B @ pl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(18,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ pl ) )
= ( A @ ( B @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ pl ) )
= ( A @ ( B @ pl ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [B: nat,A: nat] :
( ( B @ ( A @ pl ) )
= ( A @ ( B @ pl ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(59,plain,
! [B: nat,A: nat] :
( ( ( sk1 @ ( y @ pl ) )
!= ( B @ ( A @ pl ) ) )
| ( ( A @ ( B @ pl ) )
= x ) ),
inference(paramod_ordered,[status(thm)],[16,20]) ).
thf(60,plain,
( ( y @ ( sk1 @ pl ) )
= x ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( y )),bind(B,$thf( sk1 ))]]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ pl ) @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
thf(21,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ pl ) @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( B @ ( A @ pl ) @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( B @ ( A @ pl ) @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(117,plain,
! [C: nat,B: nat,A: nat] :
( ( ( y @ ( sk1 @ pl ) )
!= ( B @ ( A @ pl ) ) )
| ( ( C @ ( x @ pl ) )
= ( C @ ( B @ pl ) @ ( A @ pl ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,23]) ).
thf(118,plain,
! [A: nat] :
( ( A @ ( y @ pl ) @ ( sk1 @ pl ) )
= ( A @ ( x @ pl ) ) ),
inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( sk1 )),bind(B,$thf( y ))]]) ).
thf(134,plain,
! [A: nat] :
( ( A @ ( y @ pl ) @ ( sk1 @ pl ) )
= ( A @ ( x @ pl ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(1,conjecture,
~ ! [A: nat] :
( ( z @ ( x @ pl ) )
!= ( A @ ( z @ ( y @ pl ) @ pl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(2,negated_conjecture,
~ ~ ! [A: nat] :
( ( z @ ( x @ pl ) )
!= ( A @ ( z @ ( y @ pl ) @ pl ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ~ ! [A: nat] :
( ( z @ ( x @ pl ) )
!= ( A @ ( z @ ( y @ pl ) @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [A: nat] :
( ( z @ ( x @ pl ) )
!= ( A @ ( z @ ( y @ pl ) @ pl ) ) ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
~ ? [A: nat] :
( ( z @ ( x @ pl ) )
= ( A @ ( z @ ( y @ pl ) @ pl ) ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
! [A: nat] :
( ( z @ ( x @ pl ) )
!= ( A @ ( z @ ( y @ pl ) @ pl ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [A: nat] :
( ( A @ ( z @ ( y @ pl ) @ pl ) )
!= ( z @ ( x @ pl ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(55,plain,
! [C: nat,B: nat,A: nat] :
( ( ( A @ ( B @ pl ) )
!= ( C @ ( z @ ( y @ pl ) @ pl ) ) )
| ( ( B @ ( A @ pl ) )
!= ( z @ ( x @ pl ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,11]) ).
thf(56,plain,
! [A: nat] :
( ( z @ ( y @ pl ) @ ( A @ pl ) )
!= ( z @ ( x @ pl ) ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( A )),bind(B,$thf( z @ ( y @ pl ) )),bind(C,$thf( A ))]]) ).
thf(394,plain,
! [B: nat,A: nat] :
( ( ( A @ ( y @ pl ) @ ( sk1 @ pl ) )
!= ( z @ ( y @ pl ) @ ( B @ pl ) ) )
| ( ( A @ ( x @ pl ) )
!= ( z @ ( x @ pl ) ) ) ),
inference(paramod_ordered,[status(thm)],[134,56]) ).
thf(395,plain,
( ( z @ ( x @ pl ) )
!= ( z @ ( x @ pl ) ) ),
inference(pattern_uni,[status(thm)],[394:[bind(A,$thf( z )),bind(B,$thf( sk1 ))]]) ).
thf(471,plain,
$false,
inference(simp,[status(thm)],[395]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM670_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.13/0.39 % Computer : n006.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 03:40:55 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.18 % [INFO] Parsing done (185ms).
% 1.26/1.19 % [INFO] Running in sequential loop mode.
% 1.81/1.59 % [INFO] eprover registered as external prover.
% 2.00/1.60 % [INFO] Scanning for conjecture ...
% 2.17/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.17/1.74 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.17/1.76 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.17/1.76 % [INFO] Type checking passed.
% 2.17/1.77 % [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 ...
% 6.32/3.26 % [INFO] Killing All external provers ...
% 6.32/3.27 % Time passed: 2716ms (effective reasoning time: 2063ms)
% 6.32/3.27 % 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)>
% 6.32/3.27 % Axioms used in derivation (3): m, satz6, satz5
% 6.32/3.27 % No. of inferences in proof: 31
% 6.32/3.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2716 ms resp. 2063 ms w/o parsing
% 6.63/3.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.63/3.31 % [INFO] Killing All external provers ...
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