%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM531+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n004.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 08:09:04 AM UTC 2026
% Result : Theorem 2.79s 1.54s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 76 ( 21 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 137 ( 34 ~; 15 |; 17 &; 60 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 1 ^; 17 !; 5 ?; 25 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_decl,type,
slcrc0: $i ).
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(isCountable0_decl,type,
isCountable0: $i > $o ).
thf(isFinite0_decl,type,
isFinite0: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ isCountable0 )
& ( A @ aSet0 ) )
=> ( A != slcrc0 ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ aElementOf0 ) ) ) ) ).
thf(3,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
thf(17,plain,
! [A: $i] :
( ( ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) )
=> ( A = slcrc0 ) )
& ( ( A = slcrc0 )
=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,plain,
( ! [A: $i] :
( ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) )
=> ( A = slcrc0 ) )
& ! [A: $i] :
( ( A = slcrc0 )
=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = slcrc0 )
| ( C @ ( C @ sk2 @ aElementOf0 ) )
| ~ ( C @ aSet0 ) )
& ( ~ ( A @ ( B @ aElementOf0 ) )
| ( A != slcrc0 ) )
& ( ( A @ aSet0 )
| ( A != slcrc0 ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(23,plain,
! [A: $i] :
( ( A @ aSet0 )
| ( A != slcrc0 ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(24,plain,
slcrc0 @ aSet0,
inference(simp,[status(thm)],[23]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ isCountable0 )
& ( A @ aSet0 ) )
=> ~ ( A @ isFinite0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
thf(36,plain,
! [A: $i] :
( ( ( A @ isCountable0 )
& ( A @ aSet0 ) )
=> ~ ( A @ isFinite0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ isFinite0 )
| ~ ( A @ isCountable0 )
| ~ ( A @ aSet0 ) ),
inference(cnf,[status(esa)],[36]) ).
thf(40,plain,
! [A: $i] :
( ( ( slcrc0 @ aSet0 )
!= ( A @ aSet0 ) )
| ~ ( A @ isFinite0 )
| ~ ( A @ isCountable0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24,37]) ).
thf(41,plain,
! [A: $i] :
( ( ( slcrc0 @ aSet0 )
!= ( A @ aSet0 ) )
| ~ ( A @ isFinite0 )
| ~ ( A @ isCountable0 ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
( ~ ( slcrc0 @ isFinite0 )
| ~ ( slcrc0 @ isCountable0 ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( slcrc0 ))]]) ).
thf(8,axiom,
slcrc0 @ isFinite0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
thf(34,plain,
slcrc0 @ isFinite0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ isCountable0 )
& ( A @ aSet0 ) )
=> ( A != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ isCountable0 )
& ( A @ aSet0 ) )
=> ( A != slcrc0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i] :
( ( ( A @ isCountable0 )
& ( A @ aSet0 ) )
=> ( A != slcrc0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
( ( sk1 = slcrc0 )
& ( sk1 @ isCountable0 )
& ( sk1 @ aSet0 ) ),
inference(cnf,[status(esa)],[11]) ).
thf(14,plain,
sk1 @ isCountable0,
inference(cnfConj,[status(thm)],[12]) ).
thf(15,plain,
sk1 = slcrc0,
inference(cnfConj,[status(thm)],[12]) ).
thf(16,plain,
sk1 = slcrc0,
inference(lifteq,[status(thm)],[15]) ).
thf(39,plain,
slcrc0 @ isCountable0,
inference(rewrite,[status(thm)],[14,16]) ).
thf(79,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[42,34,39]) ).
thf(80,plain,
$false,
inference(simp,[status(thm)],[79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM531+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n004.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 03:07:52 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 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
% 0.68/0.74 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.83 % [INFO] Parsing done (98ms).
% 0.91/0.84 % [INFO] Running in sequential loop mode.
% 1.37/1.04 % [INFO] eprover registered as external prover.
% 1.37/1.04 % [INFO] Scanning for conjecture ...
% 1.37/1.07 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.37/1.09 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 1.37/1.11 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.37/1.11 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.37/1.11 % [INFO] Problem is first-order (TPTP FOF).
% 1.37/1.12 % [INFO] Type checking passed.
% 1.37/1.12 % [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 ...
% 2.79/1.54 % [INFO] Killing All external provers ...
% 2.79/1.54 % Time passed: 1023ms (effective reasoning time: 697ms)
% 2.79/1.54 % 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)>
% 2.79/1.54 % Axioms used in derivation (3): mDefEmp, mCountNFin, mEmpFin
% 2.79/1.54 % No. of inferences in proof: 25
% 2.79/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1023 ms resp. 697 ms w/o parsing
% 2.79/1.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.79/1.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------