TSTP Solution File: NUN133-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUN133-1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 11:46:22 EDT 2023
% Result : Unsatisfiable 3.10s 1.78s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 45 ( 37 unt; 8 typ; 0 def)
% Number of atoms : 37 ( 36 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 208 ( 2 ~; 0 |; 0 &; 206 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(times_type,type,
times: $i > $i > $i ).
thf(sum_type,type,
sum: $i > $i ).
thf(s_type,type,
s: $i > $i ).
thf(a_type,type,
a: $i ).
thf(cubes_type,type,
cubes: $i > $i ).
thf('\'+\'_type',type,
'\'+\'': $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(one_type,type,
one: $i ).
thf(17,axiom,
( ( cubes @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cubes_zero) ).
thf(52,plain,
( ( cubes @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
( ( times @ ( sum @ a ) @ ( sum @ a ) )
= ( cubes @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction_hypothesis) ).
thf(46,plain,
( ( times @ ( sum @ a ) @ ( sum @ a ) )
= ( cubes @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [A: $i] :
( ( times @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_one) ).
thf(54,plain,
! [A: $i] :
( ( times @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i] :
( ( sum @ ( s @ A ) )
= ( '\'+\'' @ ( s @ A ) @ ( sum @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_s) ).
thf(48,plain,
! [A: $i] :
( ( sum @ ( s @ A ) )
= ( '\'+\'' @ ( s @ A ) @ ( sum @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( times @ A @ B )
= ( times @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_comm) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( times @ A @ B )
= ( times @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( times @ A @ ( times @ B @ C ) )
= ( times @ ( times @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_assoc) ).
thf(42,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)],[12]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( '\'+\'' @ A @ B )
= ( '\'+\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_comm) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( '\'+\'' @ A @ B )
= ( '\'+\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] :
( ( cubes @ ( s @ A ) )
= ( '\'+\'' @ ( times @ ( s @ A ) @ ( times @ ( s @ A ) @ ( s @ A ) ) ) @ ( cubes @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cubes_s) ).
thf(28,plain,
! [A: $i] :
( ( cubes @ ( s @ A ) )
= ( '\'+\'' @ ( times @ ( s @ A ) @ ( times @ ( s @ A ) @ ( s @ A ) ) ) @ ( cubes @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
( ( sum @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_zero) ).
thf(38,plain,
( ( sum @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i] :
( ( times @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(32,plain,
! [A: $i] :
( ( times @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( times @ ( s @ A ) @ B )
= ( '\'+\'' @ B @ ( times @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_s) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( times @ ( s @ A ) @ B )
= ( '\'+\'' @ B @ ( times @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) )
= ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_assoc) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) )
= ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( times @ ( '\'+\'' @ A @ B ) @ C )
= ( '\'+\'' @ ( times @ A @ C ) @ ( times @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr_001) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( times @ ( '\'+\'' @ A @ B ) @ C )
= ( '\'+\'' @ ( times @ A @ C ) @ ( times @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( '\'+\'' @ ( sum @ A ) @ ( sum @ A ) )
= ( times @ A @ ( s @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_sum) ).
thf(40,plain,
! [A: $i] :
( ( '\'+\'' @ ( sum @ A ) @ ( sum @ A ) )
= ( times @ A @ ( s @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i] :
( ( '\'+\'' @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
thf(26,plain,
! [A: $i] :
( ( '\'+\'' @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( '\'+\'' @ ( s @ A ) @ B )
= ( s @ ( '\'+\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_s) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( '\'+\'' @ ( s @ A ) @ B )
= ( s @ ( '\'+\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( times @ A @ ( '\'+\'' @ B @ C ) )
= ( '\'+\'' @ ( times @ A @ B ) @ ( times @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distr) ).
thf(30,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)],[6]) ).
thf(1,negated_conjecture,
( ( times @ ( sum @ ( s @ a ) ) @ ( sum @ ( s @ a ) ) )
!= ( cubes @ ( s @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(19,plain,
( ( times @ ( sum @ ( s @ a ) ) @ ( sum @ ( s @ a ) ) )
!= ( cubes @ ( s @ a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(66,plain,
$false,
inference(cvc4,[status(thm)],[52,46,54,48,50,42,24,28,38,32,34,22,44,40,26,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUN133-1 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n009.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 21:12:18 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.99 % [INFO] Parsing done (118ms).
% 1.21/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.20 % [INFO] eprover registered as external prover.
% 1.70/1.20 % [INFO] cvc4 registered as external prover.
% 1.70/1.20 % [INFO] Scanning for conjecture ...
% 1.70/1.26 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.88/1.30 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 1.88/1.31 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/1.32 % [INFO] Type checking passed.
% 1.88/1.32 % [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 ...
% 3.10/1.78 % External prover 'cvc4' found a proof!
% 3.10/1.78 % [INFO] Killing All external provers ...
% 3.10/1.78 % Time passed: 1239ms (effective reasoning time: 782ms)
% 3.10/1.78 % 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)>
% 3.10/1.78 % Axioms used in derivation (17): distr_001, sum_zero, cubes_s, plus_zero, times_assoc, induction_hypothesis, sum_s, plus_comm, times_comm, plus_s, cubes_zero, distr, times_zero, plus_sum, times_s, plus_assoc, times_one
% 3.10/1.78 % No. of inferences in proof: 37
% 3.10/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1239 ms resp. 782 ms w/o parsing
% 3.46/1.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.46/1.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------