%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM551+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 : n013.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 08:09:08 AM UTC 2026
% Result : Theorem 96.75s 48.55s
% Output : Refutation 96.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 102 ( 26 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 218 ( 42 ~; 30 |; 18 &; 119 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 1 ^; 25 !; 8 ?; 35 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_decl,type,
slcrc0: $i ).
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(isFinite0_decl,type,
isFinite0: $i > $o ).
thf(sbrdtbr0_decl,type,
sbrdtbr0: $i > $i ).
thf(xQ_decl,type,
xQ: $i ).
thf(xk_decl,type,
xk: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ aElementOf0 ) ) ) ) ).
thf(35,axiom,
! [A: $i] :
( ( A = slcrc0 )
<=> ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
& ( A @ aSet0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
thf(195,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)],[35]) ).
thf(196,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)],[195]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = slcrc0 )
| ( C @ ( C @ sk6 @ aElementOf0 ) )
| ~ ( C @ aSet0 ) )
& ( ~ ( A @ ( B @ aElementOf0 ) )
| ( A != slcrc0 ) )
& ( ( A @ aSet0 )
| ( A != slcrc0 ) ) ),
inference(cnf,[status(esa)],[196]) ).
thf(200,plain,
! [A: $i] :
( ( A = slcrc0 )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnfConj,[status(thm)],[197]) ).
thf(205,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(lifteq,[status(thm)],[200]) ).
thf(206,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 )
| ( A = slcrc0 ) ),
inference(simp,[status(thm)],[205]) ).
thf(54,axiom,
xQ != slcrc0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2313) ).
thf(346,plain,
xQ != slcrc0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(347,plain,
xQ != slcrc0,
inference(polarity_switch,[status(thm)],[346]) ).
thf(348,plain,
xQ != slcrc0,
inference(lifteq,[status(thm)],[347]) ).
thf(30239,plain,
! [A: $i] :
( ( A != xQ )
| ( slcrc0 != slcrc0 )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[206,348]) ).
thf(30240,plain,
! [A: $i] :
( ( A != xQ )
| ( A @ ( A @ sk6 @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[30239]) ).
thf(30241,plain,
( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
| ~ ( xQ @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[30240:[bind(A,$thf( xQ ))]]) ).
thf(52,axiom,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2291) ).
thf(304,plain,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(305,plain,
( ( ( xQ @ sbrdtbr0 )
= xk )
& ( xQ @ isFinite0 )
& ( xQ @ aSet0 ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
xQ @ aSet0,
inference(cnfConj,[status(thm)],[305]) ).
thf(32160,plain,
( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
| ~ $true ),
inference(rewrite,[status(thm)],[30241,306]) ).
thf(32161,plain,
xQ @ ( xQ @ sk6 @ aElementOf0 ),
inference(simp,[status(thm)],[32160]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(230,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(231,plain,
! [B: $i,A: $i] :
( ( B @ aElement0 )
| ~ ( A @ ( B @ aElementOf0 ) )
| ~ ( A @ aSet0 ) ),
inference(cnf,[status(esa)],[230]) ).
thf(43405,plain,
! [B: $i,A: $i] :
( ( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ $true
| ~ ( A @ aSet0 ) ),
inference(paramod_ordered,[status(thm)],[32161,231]) ).
thf(43406,plain,
! [B: $i,A: $i] :
( ( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
!= ( A @ ( B @ aElementOf0 ) ) )
| ( B @ aElement0 )
| ~ ( A @ aSet0 ) ),
inference(simp,[status(thm)],[43405]) ).
thf(43407,plain,
( ( xQ @ sk6 @ aElement0 )
| ~ ( xQ @ aSet0 ) ),
inference(pattern_uni,[status(thm)],[43406:[bind(A,$thf( xQ )),bind(B,$thf( xQ @ sk6 ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(70,plain,
~ ? [A: $i] :
( ( xQ @ ( A @ aElementOf0 ) )
& ( A @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(71,plain,
! [A: $i] :
( ~ ( xQ @ ( A @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(cnf,[status(esa)],[70]) ).
thf(32252,plain,
! [A: $i] :
( ( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
!= ( xQ @ ( A @ aElementOf0 ) ) )
| ~ $true
| ~ ( A @ aElement0 ) ),
inference(paramod_ordered,[status(thm)],[32161,71]) ).
thf(32253,plain,
! [A: $i] :
( ( ( xQ @ ( xQ @ sk6 @ aElementOf0 ) )
!= ( xQ @ ( A @ aElementOf0 ) ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[32252]) ).
thf(32254,plain,
~ ( xQ @ sk6 @ aElement0 ),
inference(pattern_uni,[status(thm)],[32253:[bind(A,$thf( xQ @ sk6 ))]]) ).
thf(68708,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[43407,306,32254]) ).
thf(68709,plain,
$false,
inference(simp,[status(thm)],[68708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM551+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.20/10.48 % Computer : n013.cluster.edu
% 0.20/10.48 % Model : x86_64 x86_64
% 0.20/10.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/10.48 % Memory : 8046.5625MB
% 0.20/10.48 % OS : Linux 6.8.0-71-generic
% 0.20/10.49 % CPULimit : 300
% 0.20/10.49 % WCLimit : 300
% 0.20/10.49 % DateTime : Sat Sep 26 03:11:50 UTC 2026
% 0.20/10.49 % CPUTime :
% 0.20/10.49 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
% 1.42/11.32 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.00/11.67 % [INFO] Parsing done (350ms).
% 2.00/11.69 % [INFO] Running in sequential loop mode.
% 3.41/12.23 % [INFO] eprover registered as external prover.
% 3.41/12.24 % [INFO] Scanning for conjecture ...
% 3.64/12.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.64/12.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.64/12.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.64/12.37 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.64/12.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.85/12.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.85/12.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.85/12.42 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.85/12.44 % [INFO] Found a conjecture (or negated_conjecture) and 67 axioms. Running axiom selection ...
% 4.12/12.53 % [INFO] Axiom selection finished. Selected 67 axioms (removed 0 axioms).
% 4.12/12.56 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.12/12.57 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.12/12.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.12/12.58 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.12/12.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.12/12.59 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/12.60 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/12.61 % [INFO] Definitions in FOF are currently treated as axioms.
% 4.37/12.63 % [INFO] Problem is first-order (TPTP FOF).
% 4.37/12.65 % [INFO] Type checking passed.
% 4.37/12.65 % [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 ...
% 96.75/48.54 % [INFO] Killing All external provers ...
% 96.75/48.55 % Time passed: 37851ms (effective reasoning time: 36844ms)
% 96.75/48.55 % 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)>
% 96.75/48.55 % Axioms used in derivation (4): mDefEmp, m__2313, m__2291, mEOfElem
% 96.75/48.55 % No. of inferences in proof: 35
% 96.75/48.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 37851 ms resp. 36844 ms w/o parsing
% 96.75/48.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 96.75/48.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------