%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : QUA004^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n010.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 08:21:21 AM UTC 2026
% Result : Theorem 5.70s 2.77s
% Output : Refutation 6.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 25 ( 25 unt; 0 typ; 7 def)
% Number of atoms : 54 ( 35 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 78 ( 2 ~; 2 |; 8 &; 66 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 49 ( 22 ^; 19 !; 8 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(emptyset_decl,type,
emptyset: $i > $o ).
thf(union_decl,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i > $o ).
thf(zero_decl,type,
zero: $i ).
thf(sup_decl,type,
sup: ( $i > $o ) > $i ).
thf(supset_decl,type,
supset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(unionset_decl,type,
unionset: ( ( $i > $o ) > $o ) > $i > $o ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(crossmult_decl,type,
crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(one_decl,type,
one: $i ).
thf(emptyset_def,definition,
( emptyset
= ( ^ [A: $i] : $false ) ) ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i,B: $i] : ( B = A ) ) ) ).
thf(supset_def,definition,
( supset
= ( ^ [A: ( $i > $o ) > $o,B: $i] :
? [C: $i > $o] :
( ( A @ C )
& ( ( sup @ C )
= B ) ) ) ) ).
thf(unionset_def,definition,
( unionset
= ( ^ [A: ( $i > $o ) > $o,B: $i] :
? [C: $i > $o] :
( ( A @ C )
& ( C @ B ) ) ) ) ).
thf(addition_def,definition,
( addition
= ( ^ [A: $i,B: $i] : ( sup @ ( union @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ).
thf(crossmult_def,definition,
( crossmult
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_idemp) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i] :
( ( sup
@ ^ [B: $i] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i > $o,B: $i > $o] :
( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
= ( sup @ ( crossmult @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_def) ).
thf(24,plain,
! [A: $i > $o,B: $i > $o] :
( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
= ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_def) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( leq @ A @ B )
= ( ( sup
@ ^ [C: $i] :
( ( C = A )
| ( C = B ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
( ( sup @ emptyset )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sup_es) ).
thf(13,plain,
( ( sup
@ ^ [A: $i] : $false )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_neutral_right) ).
thf(27,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: ( $i > $o ) > $o] :
( ( sup @ ( supset @ A ) )
= ( sup @ ( unionset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sup_set) ).
thf(18,plain,
! [A: ( $i > $o ) > $o] :
( ( sup
@ ^ [B: $i] :
? [C: $i > $o] :
( ( A @ C )
& ( ( sup @ C )
= B ) ) )
= ( sup
@ ^ [B: $i] :
? [C: $i > $o] :
( ( A @ C )
& ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_neutral_left) ).
thf(30,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i] :
( ( sup @ ( singleton @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sup_singleset) ).
thf(15,plain,
! [A: $i] :
( ( sup
@ ^ [B: $i] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(35,plain,
$false,
inference(e,[status(thm)],[10,24,21,13,27,18,30,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : QUA004^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % 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
% 0.11/0.20 % Computer : n010.cluster.edu
% 0.11/0.20 % Model : x86_64 x86_64
% 0.11/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.20 % Memory : 8046.5625MB
% 0.11/0.20 % OS : Linux 6.8.0-71-generic
% 0.11/0.20 % CPULimit : 300
% 0.11/0.20 % WCLimit : 300
% 0.11/0.20 % DateTime : Tue Sep 29 13:29:26 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 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
% 1.00/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/1.01 % [INFO] Parsing done (214ms).
% 1.48/1.03 % [INFO] Running in sequential loop mode.
% 2.03/1.42 % [INFO] eprover registered as external prover.
% 2.03/1.43 % [INFO] Scanning for conjecture ...
% 2.21/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.21/1.58 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.21/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.39/1.60 % [INFO] Type checking passed.
% 2.39/1.60 % [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 ...
% 5.70/2.77 % External prover 'e' found a proof!
% 5.70/2.77 % [INFO] Killing All external provers ...
% 5.70/2.77 % Time passed: 2423ms (effective reasoning time: 1734ms)
% 5.70/2.77 % 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)>
% 5.70/2.77 % Axioms used in derivation (7): multiplication_neutral_left, sup_es, sup_set, multiplication_def, multiplication_neutral_right, order_def, sup_singleset
% 5.70/2.77 % No. of inferences in proof: 18
% 5.70/2.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2423 ms resp. 1734 ms w/o parsing
% 6.05/2.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.05/2.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------