%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : QUA011^1 : 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 : n019.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 20.93s 5.84s
% Output : Refutation 20.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 40 unt; 0 typ; 4 def)
% Number of atoms : 124 ( 86 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 216 ( 31 ~; 14 |; 16 &; 155 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 89 ( 39 ^; 33 !; 16 ?; 89 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(emptyset_decl,type,
emptyset: $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(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(crossmult_decl,type,
crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(emptyset_def,definition,
( emptyset
= ( ^ [A: $i] : $false ) ) ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i,B: $i] : ( B = A ) ) ) ).
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(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
!= zero ) ) ) ).
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(16,plain,
! [A: $i] :
( ( sup
@ ^ [B: $i] : ( B = A ) )
= A ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [A: $i] :
( ( sup
@ ^ [B: $i] : ( B = A ) )
= A ),
inference(lifteq,[status(thm)],[16]) ).
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(14,plain,
( ( sup
@ ^ [A: $i] : $false )
= zero ),
inference(lifteq,[status(thm)],[13]) ).
thf(39,plain,
! [A: $i] :
( ( A = zero )
| ( ( sup
@ ^ [B: $i] : ( B = A ) )
!= ( sup
@ ^ [B: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[17,14]) ).
thf(43,plain,
! [A: $i] :
( ( A = zero )
| ( ( ^ [B: $i] : ( B = A ) )
!= ( ^ [B: $i] : $false ) ) ),
inference(simp,[status(thm)],[39]) ).
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(25,plain,
! [B: $i > $o,A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: $i > $o,A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(285,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( multiplication @ zero @ ( sup @ B ) )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) )
| ( ( sup
@ ^ [C: $i] : $false )
!= ( sup @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,26]) ).
thf(286,plain,
! [A: $i > $o] :
( ( multiplication @ zero @ ( sup @ A ) )
= ( sup
@ ^ [B: $i] :
? [C: $i,D: $i] :
( $false
& ( A @ D )
& ( B
= ( multiplication @ C @ D ) ) ) ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(361,plain,
! [A: $i > $o] :
( ( multiplication @ zero @ ( sup @ A ) )
= ( sup
@ ^ [B: $i] : $false ) ),
inference(simp,[status(thm)],[286]) ).
thf(368,plain,
! [A: $i > $o] :
( ( multiplication @ zero @ ( sup @ A ) )
= zero ),
inference(rewrite,[status(thm)],[361,14]) ).
thf(369,plain,
! [A: $i > $o] :
( ( ( multiplication @ zero @ zero )
= zero )
| ( ( sup
@ ^ [B: $i] : $false )
!= ( sup @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,368]) ).
thf(370,plain,
( ( multiplication @ zero @ zero )
= zero ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(1,conjecture,
! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_anni) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= zero ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
( ( multiplication @ ( sup @ sk1 ) @ zero )
!= zero ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
( ( multiplication @ ( sup @ sk1 ) @ zero )
!= zero ),
inference(lifteq,[status(thm)],[11]) ).
thf(411,plain,
( ( zero != zero )
| ( ( multiplication @ ( sup @ sk1 ) @ zero )
!= ( multiplication @ zero @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[370,12]) ).
thf(412,plain,
( ( multiplication @ ( sup @ sk1 ) @ zero )
!= ( multiplication @ zero @ zero ) ),
inference(simp,[status(thm)],[411]) ).
thf(431,plain,
( ( ( sup @ sk1 )
!= zero )
| ( zero != zero ) ),
inference(simp,[status(thm)],[412]) ).
thf(437,plain,
( ( sup @ sk1 )
!= zero ),
inference(simp,[status(thm)],[431]) ).
thf(737,plain,
! [A: $i] :
( ( ( ^ [B: $i] : ( B = A ) )
!= ( ^ [B: $i] : $false ) )
| ( zero != zero )
| ( A
!= ( sup @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[43,437]) ).
thf(738,plain,
! [A: $i] :
( ( ( ^ [B: $i] : ( B = A ) )
!= ( ^ [B: $i] : $false ) )
| ( A
!= ( sup @ sk1 ) ) ),
inference(simp,[status(thm)],[737]) ).
thf(739,plain,
( ( ^ [A: $i] :
( A
= ( sup @ sk1 ) ) )
!= ( ^ [A: $i] : $false ) ),
inference(pattern_uni,[status(thm)],[738:[bind(A,$thf( sup @ sk1 ))]]) ).
thf(764,plain,
( sk16
= ( sup @ sk1 ) ),
inference(func_ext,[status(esa)],[739]) ).
thf(773,plain,
( ( sup @ sk1 )
= sk16 ),
inference(lifteq,[status(thm)],[764]) ).
thf(287,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( multiplication @ ( sup @ A ) @ zero )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) )
| ( ( sup
@ ^ [C: $i] : $false )
!= ( sup @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,26]) ).
thf(288,plain,
! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= ( sup
@ ^ [B: $i] :
? [C: $i,D: $i] :
( ( A @ C )
& $false
& ( B
= ( multiplication @ C @ D ) ) ) ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : $false ))]]) ).
thf(363,plain,
! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= ( sup
@ ^ [B: $i] : $false ) ),
inference(simp,[status(thm)],[288]) ).
thf(1358,plain,
! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= zero ),
inference(rewrite,[status(thm)],[363,14]) ).
thf(1376,plain,
! [A: $i > $o] :
( ( ( multiplication @ sk16 @ zero )
= zero )
| ( ( sup @ sk1 )
!= ( sup @ A ) ) ),
inference(paramod_ordered,[status(thm)],[773,1358]) ).
thf(1377,plain,
( ( multiplication @ sk16 @ zero )
= zero ),
inference(pattern_uni,[status(thm)],[1376:[bind(A,$thf( sk1 ))]]) ).
thf(780,plain,
( ( multiplication @ sk16 @ zero )
!= zero ),
inference(rewrite,[status(thm)],[12,773]) ).
thf(913,plain,
! [A: $i] :
( ( ( ^ [B: $i] : ( B = A ) )
!= ( ^ [B: $i] : $false ) )
| ( zero != zero )
| ( A
!= ( multiplication @ sk16 @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[43,780]) ).
thf(914,plain,
! [A: $i] :
( ( ( ^ [B: $i] : ( B = A ) )
!= ( ^ [B: $i] : $false ) )
| ( A
!= ( multiplication @ sk16 @ zero ) ) ),
inference(simp,[status(thm)],[913]) ).
thf(915,plain,
( ( ^ [A: $i] :
( A
= ( multiplication @ sk16 @ zero ) ) )
!= ( ^ [A: $i] : $false ) ),
inference(pattern_uni,[status(thm)],[914:[bind(A,$thf( multiplication @ sk16 @ zero ))]]) ).
thf(957,plain,
( sk18
= ( multiplication @ sk16 @ zero ) ),
inference(func_ext,[status(esa)],[915]) ).
thf(973,plain,
( ( multiplication @ sk16 @ zero )
= sk18 ),
inference(lifteq,[status(thm)],[957]) ).
thf(1426,plain,
sk18 = zero,
inference(rewrite,[status(thm)],[1377,973]) ).
thf(994,plain,
sk18 != zero,
inference(rewrite,[status(thm)],[780,973]) ).
thf(1427,plain,
$false,
inference(simplifyReflect,[status(thm)],[1426,994]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : QUA011^1 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.12/0.22 % Computer : n019.cluster.edu
% 0.12/0.22 % Model : x86_64 x86_64
% 0.12/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.22 % Memory : 8046.5625MB
% 0.12/0.22 % OS : Linux 6.8.0-71-generic
% 0.12/0.22 % CPULimit : 300
% 0.12/0.22 % WCLimit : 300
% 0.12/0.22 % DateTime : Tue Sep 29 13:29:17 UTC 2026
% 0.12/0.22 % CPUTime :
% 0.12/0.22 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
% 0.96/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/1.00 % [INFO] Parsing done (196ms).
% 1.13/1.01 % [INFO] Running in sequential loop mode.
% 2.00/1.41 % [INFO] eprover registered as external prover.
% 2.00/1.42 % [INFO] Scanning for conjecture ...
% 2.17/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.17/1.57 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.17/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.17/1.59 % [INFO] Type checking passed.
% 2.17/1.59 % [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 ...
% 20.93/5.83 % [INFO] Killing All external provers ...
% 20.93/5.83 % Time passed: 5465ms (effective reasoning time: 4814ms)
% 20.93/5.83 % 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)>
% 20.93/5.84 % Axioms used in derivation (3): sup_singleset, sup_es, multiplication_def
% 20.93/5.84 % No. of inferences in proof: 48
% 20.93/5.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5465 ms resp. 4814 ms w/o parsing
% 20.93/5.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.93/5.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------