TSTP Solution File: ANA133-1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : ANA133-1 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n027.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 : Mon Jun 24 04:16:41 EDT 2024
% Result : Unsatisfiable 7.27s 2.67s
% Output : Refutation 7.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 44 ( 35 unt; 9 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 164 ( 2 ~; 0 |; 0 &; 162 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 ^ 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_type,type,
d: $i > $i ).
thf(times_type,type,
times: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(cos_type,type,
cos: $i > $i ).
thf('\'+\'_type',type,
'\'+\'': $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(minus_type,type,
minus: $i > $i ).
thf(one_type,type,
one: $i ).
thf(sin_type,type,
sin: $i > $i ).
thf(6,axiom,
( ( d @ one )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_one) ).
thf(29,plain,
( ( d @ one )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( times @ A @ B )
= ( times @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_times) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( times @ A @ B )
= ( times @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
( ( d @ x )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_x) ).
thf(45,plain,
( ( d @ x )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) )
= ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associtivity_of_plus) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) )
= ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i] :
( ( times @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(49,plain,
! [A: $i] :
( ( times @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
( ( d @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_zero) ).
thf(39,plain,
( ( d @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( d @ ( sin @ A ) )
= ( times @ ( cos @ A ) @ ( d @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_sin) ).
thf(35,plain,
! [A: $i] :
( ( d @ ( sin @ A ) )
= ( times @ ( cos @ A ) @ ( d @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( d @ A )
!= ( times @ x @ ( cos @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(18,plain,
! [A: $i] :
( ( d @ A )
!= ( times @ x @ ( cos @ x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [A: $i] :
( ( d @ ( cos @ A ) )
= ( minus @ ( times @ ( sin @ A ) @ ( d @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_cos) ).
thf(31,plain,
! [A: $i] :
( ( d @ ( cos @ A ) )
= ( minus @ ( times @ ( sin @ A ) @ ( d @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i] :
( ( times @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
thf(43,plain,
! [A: $i] :
( ( times @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i] :
( ( '\'+\'' @ A @ ( minus @ A ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus) ).
thf(23,plain,
! [A: $i] :
( ( '\'+\'' @ A @ ( minus @ A ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( d @ ( times @ A @ B ) )
= ( '\'+\'' @ ( times @ A @ ( d @ B ) ) @ ( times @ B @ ( d @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_times) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( d @ ( times @ A @ B ) )
= ( '\'+\'' @ ( times @ A @ ( d @ B ) ) @ ( times @ B @ ( d @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( d @ ( '\'+\'' @ A @ B ) )
= ( '\'+\'' @ ( d @ A ) @ ( d @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',derivative_of_plus) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( d @ ( '\'+\'' @ A @ B ) )
= ( '\'+\'' @ ( d @ A ) @ ( d @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( times @ A @ ( times @ B @ C ) )
= ( times @ ( times @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_times) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( times @ A @ ( times @ B @ C ) )
= ( times @ ( times @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( '\'+\'' @ A @ B )
= ( '\'+\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_plus) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( '\'+\'' @ A @ B )
= ( '\'+\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( '\'+\'' @ zero @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
thf(21,plain,
! [A: $i] :
( ( '\'+\'' @ zero @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( times @ A @ ( '\'+\'' @ B @ C ) )
= ( '\'+\'' @ ( times @ A @ B ) @ ( times @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( times @ A @ ( '\'+\'' @ B @ C ) )
= ( '\'+\'' @ ( times @ A @ B ) @ ( times @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1056,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,49,39,35,18,31,43,23,51,47,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA133-1 : TPTP v8.2.0. Released v8.1.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 04:15:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.03 % [INFO] Parsing done (119ms).
% 1.33/1.04 % [INFO] Running in sequential loop mode.
% 1.72/1.25 % [INFO] eprover registered as external prover.
% 1.72/1.25 % [INFO] Scanning for conjecture ...
% 1.91/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 1.91/1.35 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.91/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 2.11/1.36 % [INFO] Type checking passed.
% 2.11/1.37 % [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 ...
% 7.27/2.66 % External prover 'e' found a proof!
% 7.27/2.67 % [INFO] Killing All external provers ...
% 7.27/2.67 % Time passed: 2137ms (effective reasoning time: 1621ms)
% 7.27/2.67 % Axioms used in derivation (16): commutativity_of_plus, minus, derivative_of_times, derivative_of_zero, commutativity_of_times, derivative_of_cos, derivative_of_x, times_zero, derivative_of_sin, derivative_of_plus, associtivity_of_plus, distributivity, plus_zero, derivative_of_one, associativity_of_times, times_one
% 7.27/2.67 % No. of inferences in proof: 35
% 7.27/2.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2137 ms resp. 1621 ms w/o parsing
% 7.67/2.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.67/2.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------