TSTP Solution File: RNG046+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG046+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:49:10 EDT 2023
% Result : Theorem 3.85s 1.95s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 33 ( 7 unt; 7 typ; 0 def)
% Number of atoms : 89 ( 37 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 328 ( 2 ~; 0 |; 46 &; 263 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(sdtasdt0_type,type,
sdtasdt0: $i > $i > $i ).
thf(smndt0_type,type,
smndt0: $i > $i ).
thf(xx_type,type,
xx: $i ).
thf(xy_type,type,
xy: $i ).
thf(aScalar0_type,type,
aScalar0: $i > $o ).
thf(sz0z00_type,type,
sz0z00: $i ).
thf(sdtpldt0_type,type,
sdtpldt0: $i > $i > $i ).
thf(1,conjecture,
( ( sdtasdt0 @ ( smndt0 @ xx ) @ ( smndt0 @ xy ) )
= ( sdtasdt0 @ xx @ xy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
( ( sdtasdt0 @ ( smndt0 @ xx ) @ ( smndt0 @ xy ) )
!= ( sdtasdt0 @ xx @ xy ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
( ( sdtasdt0 @ ( smndt0 @ xx ) @ ( smndt0 @ xy ) )
!= ( sdtasdt0 @ xx @ xy ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNegSc) ).
thf(61,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( aScalar0 @ ( smndt0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr) ).
thf(53,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtasdt0 @ A @ ( sdtpldt0 @ B @ C ) )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ B ) @ ( sdtasdt0 @ A @ C ) ) )
& ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtpldt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ ( sdtpldt0 @ C @ D ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ A @ D ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ B @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistr2) ).
thf(58,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C )
& ( aScalar0 @ D ) )
=> ( ( sdtasdt0 @ ( sdtpldt0 @ A @ B ) @ ( sdtpldt0 @ C @ D ) )
= ( sdtpldt0 @ ( sdtpldt0 @ ( sdtasdt0 @ A @ C ) @ ( sdtasdt0 @ A @ D ) ) @ ( sdtpldt0 @ ( sdtasdt0 @ B @ C ) @ ( sdtasdt0 @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScSort) ).
thf(19,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
& ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
& ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArith) ).
thf(20,plain,
! [A: $i,B: $i,C: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B )
& ( aScalar0 @ C ) )
=> ( ( ( sdtpldt0 @ ( sdtpldt0 @ A @ B ) @ C )
= ( sdtpldt0 @ A @ ( sdtpldt0 @ B @ C ) ) )
& ( ( sdtpldt0 @ A @ B )
= ( sdtpldt0 @ B @ A ) )
& ( ( sdtasdt0 @ ( sdtasdt0 @ A @ B ) @ C )
= ( sdtasdt0 @ A @ ( sdtasdt0 @ B @ C ) ) )
& ( ( sdtasdt0 @ A @ B )
= ( sdtasdt0 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
thf(29,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( aScalar0 @ ( sdtasdt0 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ ( smndt0 @ B ) )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) )
& ( ( sdtasdt0 @ ( smndt0 @ A ) @ B )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMNeg) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( aScalar0 @ A )
& ( aScalar0 @ B ) )
=> ( ( ( sdtasdt0 @ A @ ( smndt0 @ B ) )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) )
& ( ( sdtasdt0 @ ( smndt0 @ A ) @ B )
= ( smndt0 @ ( sdtasdt0 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
( ( aScalar0 @ xx )
& ( aScalar0 @ xy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
thf(63,plain,
( ( aScalar0 @ xx )
& ( aScalar0 @ xy ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
aScalar0 @ sz0z00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSZeroSc) ).
thf(16,plain,
aScalar0 @ sz0z00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i] :
( ( aScalar0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz0z00 )
= A )
& ( ( sdtpldt0 @ sz0z00 @ A )
= A )
& ( ( sdtasdt0 @ A @ sz0z00 )
= sz0z00 )
& ( ( sdtasdt0 @ sz0z00 @ A )
= sz0z00 )
& ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz0z00 )
& ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz0z00 )
& ( ( smndt0 @ ( smndt0 @ A ) )
= A )
& ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mScZero) ).
thf(31,plain,
! [A: $i] :
( ( aScalar0 @ A )
=> ( ( ( sdtpldt0 @ A @ sz0z00 )
= A )
& ( ( sdtpldt0 @ sz0z00 @ A )
= A )
& ( ( sdtasdt0 @ A @ sz0z00 )
= sz0z00 )
& ( ( sdtasdt0 @ sz0z00 @ A )
= sz0z00 )
& ( ( sdtpldt0 @ A @ ( smndt0 @ A ) )
= sz0z00 )
& ( ( sdtpldt0 @ ( smndt0 @ A ) @ A )
= sz0z00 )
& ( ( smndt0 @ ( smndt0 @ A ) )
= A )
& ( ( smndt0 @ sz0z00 )
= sz0z00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(104,plain,
$false,
inference(cvc4,[status(thm)],[14,61,53,17,58,19,20,29,48,63,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG046+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 19:55:46 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.94/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.02 % [INFO] Parsing done (134ms).
% 1.23/1.03 % [INFO] Running in sequential loop mode.
% 1.78/1.22 % [INFO] eprover registered as external prover.
% 1.78/1.23 % [INFO] cvc4 registered as external prover.
% 1.78/1.23 % [INFO] Scanning for conjecture ...
% 1.88/1.28 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.88/1.32 % [INFO] Axiom selection finished. Selected 11 axioms (removed 7 axioms).
% 2.09/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.09/1.36 % [INFO] Type checking passed.
% 2.09/1.36 % [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 ...
% 3.85/1.95 % External prover 'cvc4' found a proof!
% 3.85/1.95 % [INFO] Killing All external provers ...
% 3.85/1.95 % Time passed: 1439ms (effective reasoning time: 918ms)
% 3.85/1.95 % 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)>
% 3.85/1.95 % Axioms used in derivation (11): mArith, mMulSc, mMNeg, mScSort, mDistr, mSZeroSc, mDistr2, mNegSc, mSumSc, m__799, mScZero
% 3.85/1.95 % No. of inferences in proof: 26
% 3.85/1.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1439 ms resp. 918 ms w/o parsing
% 3.85/1.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.85/1.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------