TSTP Solution File: ITP209^1 by Leo-III-SAT---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : ITP209^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 : Tue May 7 10:36:38 EDT 2024
% Result : Theorem 5.03s 2.41s
% Output : Refutation 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 19 unt; 5 typ; 0 def)
% Number of atoms : 21 ( 20 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 148 ( 7 ~; 1 |; 0 &; 140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 ^ 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(a2_type,type,
a2: a ).
thf(b_type,type,
b: a ).
thf(c_type,type,
c: a ).
thf(f_type,type,
f: a > a > a ).
thf(4,axiom,
! [A: a,B: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_commute) ).
thf(16,plain,
! [A: a,B: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [B: a,A: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [B: a,A: a] :
( ( f @ A @ B )
= ( f @ B @ A ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(1,conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ ( f @ a2 @ c ) @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
( ( f @ ( f @ a2 @ c ) @ b )
!= ( f @ ( f @ a2 @ b ) @ c ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(52,plain,
! [B: a,A: a] :
( ( ( f @ A @ B )
!= ( f @ ( f @ a2 @ b ) @ c ) )
| ( ( f @ B @ A )
!= ( f @ ( f @ a2 @ c ) @ b ) ) ),
inference(paramod_ordered,[status(thm)],[18,14]) ).
thf(53,plain,
( ( f @ ( f @ a2 @ b ) @ c )
!= ( f @ b @ ( f @ a2 @ c ) ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( b )),bind(B,$thf( f @ a2 @ c ))]]) ).
thf(6,axiom,
! [A: a,B: a,C: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_right__assoc) ).
thf(22,plain,
! [A: a,B: a,C: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [C: a,B: a,A: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [C: a,B: a,A: a] :
( ( f @ ( f @ A @ B ) @ C )
= ( f @ A @ ( f @ B @ C ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(232,plain,
( ( f @ b @ ( f @ a2 @ c ) )
!= ( f @ a2 @ ( f @ b @ c ) ) ),
inference(rewrite,[status(thm)],[53,24]) ).
thf(5,axiom,
! [A: a,B: a,C: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_left__commute) ).
thf(19,plain,
! [A: a,B: a,C: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
! [C: a,B: a,A: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [C: a,B: a,A: a] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ B @ ( f @ A @ C ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(233,plain,
$false,
inference(simplifyReflect,[status(thm)],[232,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : ITP209^1 : TPTP v8.1.2. Released v8.1.0.
% 0.18/0.18 % Command : run_Leo-III %s %d
% 0.18/0.41 % Computer : n014.cluster.edu
% 0.18/0.41 % Model : x86_64 x86_64
% 0.18/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41 % Memory : 8042.1875MB
% 0.18/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.41 % CPULimit : 300
% 0.18/0.41 % WCLimit : 300
% 0.18/0.41 % DateTime : Mon May 6 22:05:24 EDT 2024
% 0.18/0.41 % CPUTime :
% 1.07/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.14 % [INFO] Parsing done (147ms).
% 1.37/1.15 % [INFO] Running in sequential loop mode.
% 1.81/1.38 % [INFO] nitpick registered as external prover.
% 1.81/1.39 % [INFO] Scanning for conjecture ...
% 1.99/1.45 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.99/1.47 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.08/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.51 % [INFO] Type checking passed.
% 2.08/1.52 % [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 ...
% 5.03/2.41 % [INFO] Killing All external provers ...
% 5.03/2.41 % Time passed: 1839ms (effective reasoning time: 1257ms)
% 5.03/2.41 % 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)>
% 5.03/2.41 % Axioms used in derivation (3): fact_1_commute, fact_3_right__assoc, fact_2_left__commute
% 5.03/2.41 % No. of inferences in proof: 20
% 5.03/2.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1839 ms resp. 1257 ms w/o parsing
% 5.03/2.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.03/2.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------