%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS003_1 : TPTP v9.3.1. Released v5.0.0.
% 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 : n017.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 07:44:29 AM UTC 2026
% Result : Theorem 3.35s 7.35s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 159 ( 10 ~; 9 |; 8 &; 110 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(unreal_type,type,
unreal: $tType ).
thf(real_type,type,
real: $tType ).
thf(u1r1_decl,type,
u1r1: unreal > real ).
thf(u1r2_decl,type,
u1r2: unreal > real ).
thf(u3r1_decl,type,
u3r1: unreal > real ).
thf(u3r2_decl,type,
u3r2: unreal > real ).
thf(exist_decl,type,
exist: unreal ).
thf(f_decl,type,
f: unreal > $o ).
thf(d_decl,type,
d: unreal > $o ).
thf(e_decl,type,
e: unreal > $o ).
thf(s1most_decl,type,
s1most: unreal > $o ).
thf(s_decl,type,
s: unreal > real > $o ).
thf(c_decl,type,
c: unreal > $o ).
thf(equalish_decl,type,
equalish: real > real > $o ).
thf(s2least_decl,type,
s2least: unreal > $o ).
thf(5,axiom,
! [A: unreal] :
~ ( ( A @ u1r1 @ ( A @ u1r2 @ equalish ) )
& ( A @ s2least ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(25,plain,
! [A: unreal] :
~ ( ( A @ u1r1 @ ( A @ u1r2 @ equalish ) )
& ( A @ s2least ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: unreal] :
( ( A @ u3r1 @ ( A @ u3r2 @ equalish ) )
=> ( A @ s1most ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
thf(41,plain,
! [A: unreal] :
( ( A @ u3r1 @ ( A @ u3r2 @ equalish ) )
=> ( A @ s1most ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: unreal] :
( ( A @ f )
=> ( A @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
thf(49,plain,
! [A: unreal] :
( ( A @ f )
=> ( A @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: unreal] :
( ( A @ u3r1 @ ( A @ s ) )
| ( A @ s1most ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
thf(43,plain,
! [A: unreal] :
( ( A @ u3r1 @ ( A @ s ) )
| ( A @ s1most ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: unreal] :
( ( A @ s2least )
=> ( A @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(23,plain,
! [A: unreal] :
( ( A @ s2least )
=> ( A @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: unreal] :
( ( A @ e )
=> ( A @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
thf(47,plain,
! [A: unreal] :
( ( A @ e )
=> ( A @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: unreal] :
( ( A @ c )
=> ( A @ s2least ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(21,plain,
! [A: unreal] :
( ( A @ c )
=> ( A @ s2least ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: unreal] :
( ( A @ s2least )
=> ( A @ u1r1 @ ( A @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(28,plain,
! [A: unreal] :
( ( A @ s2least )
=> ( A @ u1r1 @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: real,B: real,C: unreal] :
( ( ( A @ ( C @ s ) )
& ( B @ ( C @ s ) )
& ( C @ s1most ) )
=> ( A @ ( B @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
thf(38,plain,
! [A: real,B: real,C: unreal] :
( ( ( A @ ( C @ s ) )
& ( B @ ( C @ s ) )
& ( C @ s1most ) )
=> ( A @ ( B @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: unreal] :
( ( A @ u3r2 @ ( A @ s ) )
| ( A @ s1most ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
thf(45,plain,
! [A: unreal] :
( ( A @ u3r2 @ ( A @ s ) )
| ( A @ s1most ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
( ~ ( exist @ f )
| ~ ( exist @ e ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1__clause_2) ).
thf(2,negated_conjecture,
~ ( ~ ( exist @ f )
| ~ ( exist @ e ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ( ~ ( exist @ f )
| ~ ( exist @ e ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: real,B: real,C: unreal] :
( ( ( A @ ( C @ s ) )
& ( B @ ( C @ s ) ) )
=> ( ( A @ ( B @ equalish ) )
| ( C @ s2least ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(32,plain,
! [A: real,B: real,C: unreal] :
( ( ( A @ ( C @ s ) )
& ( B @ ( C @ s ) ) )
=> ( ( A @ ( B @ equalish ) )
| ( C @ s2least ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: unreal] :
( ( A @ d )
=> ( A @ s1most ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(34,plain,
! [A: unreal] :
( ( A @ d )
=> ( A @ s1most ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: unreal] :
( ( A @ s1most )
=> ( A @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(36,plain,
! [A: unreal] :
( ( A @ s1most )
=> ( A @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: unreal] :
( ( A @ s2least )
=> ( A @ u1r2 @ ( A @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(30,plain,
! [A: unreal] :
( ( A @ s2least )
=> ( A @ u1r2 @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[25,41,49,43,23,47,21,28,38,45,17,32,34,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS003_1 : TPTP v9.3.1. Released v5.0.0.
% 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
% 0.14/5.40 % Computer : n017.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.40 % DateTime : Fri Sep 25 19:27:23 UTC 2026
% 0.14/5.40 % CPUTime :
% 0.14/5.40 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
% 0.17/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/6.19 % [INFO] Parsing done (183ms).
% 1.36/6.20 % [INFO] Running in sequential loop mode.
% 2.00/6.60 % [INFO] eprover registered as external prover.
% 2.00/6.61 % [INFO] Scanning for conjecture ...
% 2.17/6.71 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.17/6.74 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.17/6.78 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.17/6.79 % [INFO] Type checking passed.
% 2.17/6.79 % [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 ...
% 3.35/7.34 % External prover 'e' found a proof!
% 3.35/7.34 % [INFO] Killing All external provers ...
% 3.35/7.34 % Time passed: 1793ms (effective reasoning time: 1135ms)
% 3.35/7.34 % 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)>
% 3.35/7.35 % Axioms used in derivation (14): clause_5, clause_16, clause_9, clause_14, clause_4, clause_13, clause_6, clause_12, clause_8, clause_15, clause_7, clause_10, clause_11, clause_3
% 3.35/7.35 % No. of inferences in proof: 32
% 3.35/7.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1793 ms resp. 1135 ms w/o parsing
% 3.67/7.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.67/7.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------