%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM799^1 : 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 : 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 : Wed Sep 30 08:18:13 AM UTC 2026
% Result : Theorem 13.25s 3.97s
% Output : Refutation 13.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 11 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 11 ( 10 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 85 ( 4 ~; 0 |; 0 &; 81 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-4 aty)
% Number of variables : 30 ( 25 ^; 2 !; 3 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(four_decl,type,
four: ( $i > $i ) > $i > $i ).
thf(five_decl,type,
five: ( $i > $i ) > $i > $i ).
thf(seven_decl,type,
seven: ( $i > $i ) > $i > $i ).
thf(plus_decl,type,
plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(mult_decl,type,
mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).
thf(four_def,definition,
( four
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ).
thf(five_def,definition,
( five
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ) ).
thf(seven_def,definition,
( seven
= ( ^ [A: $i > $i,B: $i] : ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ ( A @ B ) ) ) ) ) ) ) ) ) ).
thf(plus_def,definition,
( plus
= ( ^ [A: ( $i > $i ) > $i > $i,B: ( $i > $i ) > $i > $i,C: $i > $i,D: $i] : ( A @ C @ ( B @ C @ D ) ) ) ) ).
thf(mult_def,definition,
( mult
= ( ^ [A: ( $i > $i ) > $i > $i,B: ( $i > $i ) > $i > $i,C: $i > $i] : ( A @ ( B @ C ) ) ) ) ).
thf(1,conjecture,
? [A: ( $i > $i ) > $i > $i] :
( ( mult @ A @ four )
= ( plus @ five @ seven ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $i ) > $i > $i] :
( ( mult @ A @ four )
= ( plus @ five @ seven ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $i ) > $i > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) )
= ( ^ [B: $i > $i,C: $i] : ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $i ) > $i > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) )
!= ( ^ [B: $i > $i,C: $i] : ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $i ) > $i > $i] :
( ( ^ [B: $i > $i] :
( A
@ ^ [C: $i] : ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) )
!= ( ^ [B: $i > $i,C: $i] : ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ ( B @ C ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
$false,
inference(pre_uni,[status(thm)],[5:[bind(A,$thf( ^ [B: $i > $i] : ^ [C: $i] : ( B @ ( B @ ( B @ C ) ) ) ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM799^1 : 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
% 0.09/0.21 % Computer : n006.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 13:00:09 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.68/0.57 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/0.77 % [INFO] Parsing done (196ms).
% 1.13/0.78 % [INFO] Running in sequential loop mode.
% 2.01/1.12 % [INFO] eprover registered as external prover.
% 2.01/1.12 % [INFO] Scanning for conjecture ...
% 2.41/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.41/1.25 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.41/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 2.41/1.26 % [INFO] Type checking passed.
% 2.41/1.26 % [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 ...
% 13.25/3.96 % [INFO] Killing All external provers ...
% 13.25/3.97 % Time passed: 3668ms (effective reasoning time: 3182ms)
% 13.25/3.97 % 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)>
% 13.25/3.97 % Axioms used in derivation (0):
% 13.25/3.97 % No. of inferences in proof: 6
% 13.25/3.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3668 ms resp. 3182 ms w/o parsing
% 13.25/4.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.25/4.02 % [INFO] Killing All external provers ...
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