%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG050+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 : n015.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 08:25:20 AM UTC 2026
% Result : Theorem 26.69s 7.47s
% Output : Refutation 27.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 38 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 237 ( 44 ~; 32 |; 5 &; 144 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 17 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(aVector0_decl,type,
aVector0: $i > $o ).
thf(aDimensionOf0_decl,type,
aDimensionOf0: $i > $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(xs_decl,type,
xs: $i ).
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(sz0z00_decl,type,
sz0z00: $i ).
thf(sdtasasdt0_decl,type,
sdtasasdt0: $i > $i > $i ).
thf(aScalar0_decl,type,
aScalar0: $i > $o ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( B @ aVector0 )
& ( A @ aVector0 ) )
=> ( ( ( ( B @ aDimensionOf0 )
= sz00 )
& ( ( A @ aDimensionOf0 )
= ( B @ aDimensionOf0 ) ) )
=> ( ( B @ ( A @ sdtasasdt0 ) )
= sz0z00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSPZ) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( ( B @ aVector0 )
& ( A @ aVector0 ) )
=> ( ( ( ( B @ aDimensionOf0 )
= sz00 )
& ( ( A @ aDimensionOf0 )
= ( B @ aDimensionOf0 ) ) )
=> ( ( B @ ( A @ sdtasasdt0 ) )
= sz0z00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtasasdt0 ) )
= sz0z00 )
| ( ( B @ aDimensionOf0 )
!= sz00 )
| ( ( A @ aDimensionOf0 )
!= ( B @ aDimensionOf0 ) )
| ~ ( B @ aVector0 )
| ~ ( A @ aVector0 ) ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( B @ aVector0 )
| ~ ( A @ aVector0 )
| ( ( B @ ( A @ sdtasasdt0 ) )
= sz0z00 )
| ( ( B @ aDimensionOf0 )
!= sz00 )
| ( ( A @ aDimensionOf0 )
!= ( B @ aDimensionOf0 ) ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(23,axiom,
sz0z00 @ aScalar0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
thf(106,plain,
sz0z00 @ aScalar0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ aScalar0 )
=> ( A @ ( A @ sdtlseqdt0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERef) ).
thf(177,plain,
! [A: $i] :
( ( A @ aScalar0 )
=> ( A @ ( A @ sdtlseqdt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(178,plain,
! [A: $i] :
( ( A @ ( A @ sdtlseqdt0 ) )
| ~ ( A @ aScalar0 ) ),
inference(cnf,[status(esa)],[177]) ).
thf(560,plain,
! [A: $i] :
( ( ( sz0z00 @ aScalar0 )
!= ( A @ aScalar0 ) )
| ( A @ ( A @ sdtlseqdt0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,178]) ).
thf(561,plain,
! [A: $i] :
( ( ( sz0z00 @ aScalar0 )
!= ( A @ aScalar0 ) )
| ( A @ ( A @ sdtlseqdt0 ) ) ),
inference(simp,[status(thm)],[560]) ).
thf(562,plain,
sz0z00 @ ( sz0z00 @ sdtlseqdt0 ),
inference(pattern_uni,[status(thm)],[561:[bind(A,$thf( sz0z00 ))]]) ).
thf(1,conjecture,
( ( ( ( xs @ aDimensionOf0 )
!= sz00 )
=> ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) )
=> ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( ( xs @ aDimensionOf0 )
!= sz00 )
=> ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) )
=> ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(41,plain,
~ ( ( ( ( xs @ aDimensionOf0 )
!= sz00 )
=> ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) )
=> ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,plain,
( ~ ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
& ( ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
| ( ( xs @ aDimensionOf0 )
= sz00 ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(44,plain,
~ ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) ),
inference(cnfConj,[status(thm)],[42]) ).
thf(671,plain,
( ( ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
!= ( sz0z00 @ ( sz0z00 @ sdtlseqdt0 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[562,44]) ).
thf(672,plain,
( ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
!= ( sz0z00 @ ( sz0z00 @ sdtlseqdt0 ) ) ),
inference(simp,[status(thm)],[671]) ).
thf(673,plain,
( ( ( xs @ ( xs @ sdtasasdt0 ) )
!= sz0z00 )
| ( sz0z00 != sz0z00 ) ),
inference(simp,[status(thm)],[672]) ).
thf(674,plain,
( ( xs @ ( xs @ sdtasasdt0 ) )
!= sz0z00 ),
inference(simp,[status(thm)],[673]) ).
thf(4929,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtasasdt0 ) )
!= ( xs @ ( xs @ sdtasasdt0 ) ) )
| ( sz0z00 != sz0z00 )
| ~ ( B @ aVector0 )
| ~ ( A @ aVector0 )
| ( ( B @ aDimensionOf0 )
!= sz00 )
| ( ( A @ aDimensionOf0 )
!= ( B @ aDimensionOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[93,674]) ).
thf(4930,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ sdtasasdt0 ) )
!= ( xs @ ( xs @ sdtasasdt0 ) ) )
| ~ ( B @ aVector0 )
| ~ ( A @ aVector0 )
| ( ( B @ aDimensionOf0 )
!= sz00 )
| ( ( A @ aDimensionOf0 )
!= ( B @ aDimensionOf0 ) ) ),
inference(simp,[status(thm)],[4929]) ).
thf(4931,plain,
( ~ ( xs @ aVector0 )
| ~ ( xs @ aVector0 )
| ( ( xs @ aDimensionOf0 )
!= sz00 )
| ( ( xs @ aDimensionOf0 )
!= ( xs @ aDimensionOf0 ) ) ),
inference(pattern_uni,[status(thm)],[4930:[bind(A,$thf( xs )),bind(B,$thf( xs ))]]) ).
thf(4942,plain,
( ~ ( xs @ aVector0 )
| ( ( xs @ aDimensionOf0 )
!= sz00 ) ),
inference(simp,[status(thm)],[4931]) ).
thf(33,axiom,
xs @ aVector0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1542) ).
thf(165,plain,
xs @ aVector0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(43,plain,
( ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
| ( ( xs @ aDimensionOf0 )
= sz00 ) ),
inference(cnfConj,[status(thm)],[42]) ).
thf(45,plain,
( ( xs @ ( xs @ sdtasasdt0 ) @ ( sz0z00 @ sdtlseqdt0 ) )
| ( ( xs @ aDimensionOf0 )
= sz00 ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(183,plain,
( $false
| ( ( xs @ aDimensionOf0 )
= sz00 ) ),
inference(rewrite,[status(thm)],[45,44]) ).
thf(184,plain,
( ( xs @ aDimensionOf0 )
= sz00 ),
inference(simp,[status(thm)],[183]) ).
thf(5120,plain,
( ~ $true
| ( sz00 != sz00 ) ),
inference(rewrite,[status(thm)],[4942,165,184]) ).
thf(5121,plain,
$false,
inference(simp,[status(thm)],[5120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG050+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.13/0.39 % Computer : n015.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 05:55:58 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 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
% 0.89/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.21 % [INFO] Parsing done (229ms).
% 1.48/1.22 % [INFO] Running in sequential loop mode.
% 2.39/1.63 % [INFO] eprover registered as external prover.
% 2.39/1.64 % [INFO] Scanning for conjecture ...
% 2.61/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.61/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 38 axioms. Running axiom selection ...
% 2.80/1.84 % [INFO] Axiom selection finished. Selected 38 axioms (removed 0 axioms).
% 3.04/1.90 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/1.92 % [INFO] Problem is first-order (TPTP FOF).
% 3.04/1.93 % [INFO] Type checking passed.
% 3.04/1.94 % [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 ...
% 26.69/7.47 % [INFO] Killing All external provers ...
% 26.69/7.47 % Time passed: 6931ms (effective reasoning time: 6239ms)
% 26.69/7.47 % 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)>
% 26.69/7.47 % Axioms used in derivation (4): mDefSPZ, mSZeroSc, mLERef, m__1542
% 26.69/7.47 % No. of inferences in proof: 33
% 26.69/7.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6931 ms resp. 6239 ms w/o parsing
% 27.18/7.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.18/7.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------