TSTP Solution File: COM008+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : COM008+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 10:13:52 EDT 2023
% Result : Theorem 3.67s 1.86s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 18
% Syntax : Number of formulae : 31 ( 6 unt; 7 typ; 0 def)
% Number of atoms : 60 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 146 ( 2 ~; 2 |; 18 &; 108 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 38 !; 6 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(goal_type,type,
goal: $o ).
thf(transitive_reflexive_rewrite_type,type,
transitive_reflexive_rewrite: $i > $i > $o ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(a_type,type,
a: $i ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(rewrite_type,type,
rewrite: $i > $i > $o ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_in_transitive_reflexive_rewrite) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i] :
( ( ( transitive_reflexive_rewrite @ b @ A )
& ( transitive_reflexive_rewrite @ c @ A ) )
=> goal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',found) ).
thf(14,plain,
! [A: $i] :
( ( ( transitive_reflexive_rewrite @ b @ A )
& ( transitive_reflexive_rewrite @ c @ A ) )
=> goal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(20,plain,
! [A: $i] : ( equalish @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
goal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_to_be_proved) ).
thf(2,negated_conjecture,
~ goal,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ goal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
( ( transitive_reflexive_rewrite @ a @ b )
& ( transitive_reflexive_rewrite @ a @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
thf(17,plain,
( ( transitive_reflexive_rewrite @ a @ b )
& ( transitive_reflexive_rewrite @ a @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( equalish @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( equalish @ A @ B )
=> ( equalish @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( rewrite @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_in_transitive_reflexive_rewrite) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( rewrite @ A @ B )
=> ( transitive_reflexive_rewrite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ B @ C ) )
=> ( transitive_reflexive_rewrite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_transitive_reflexive_rewrite) ).
thf(28,plain,
! [A: $i,B: $i,C: $i] :
( ( ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ B @ C ) )
=> ( transitive_reflexive_rewrite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ a @ A )
& ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ih_cfl) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ a @ A )
& ( transitive_reflexive_rewrite @ A @ B )
& ( transitive_reflexive_rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( transitive_reflexive_rewrite @ A @ B )
=> ( ( equalish @ A @ B )
| ? [C: $i] :
( ( rewrite @ A @ C )
& ( transitive_reflexive_rewrite @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equalish_or_rewrite) ).
thf(36,plain,
! [A: $i,B: $i] :
( ( transitive_reflexive_rewrite @ A @ B )
=> ( ( equalish @ A @ B )
| ? [C: $i] :
( ( rewrite @ A @ C )
& ( transitive_reflexive_rewrite @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ A @ B )
& ( rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lo_cfl) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rewrite @ A @ B )
& ( rewrite @ A @ C ) )
=> ? [D: $i] :
( ( transitive_reflexive_rewrite @ B @ D )
& ( transitive_reflexive_rewrite @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,plain,
$false,
inference(e,[status(thm)],[24,14,20,13,17,22,26,28,33,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM008+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n003.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 19 03:17:46 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (123ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.64/1.20 % [INFO] eprover registered as external prover.
% 1.64/1.20 % [INFO] cvc4 registered as external prover.
% 1.64/1.20 % [INFO] Scanning for conjecture ...
% 1.84/1.25 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.90/1.27 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.90/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 1.90/1.30 % [INFO] Type checking passed.
% 1.90/1.31 % [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 ...
% 3.67/1.85 % External prover 'e' found a proof!
% 3.67/1.85 % [INFO] Killing All external provers ...
% 3.67/1.85 % Time passed: 1335ms (effective reasoning time: 867ms)
% 3.67/1.85 % 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)>
% 3.67/1.85 % Axioms used in derivation (10): transitivity_of_transitive_reflexive_rewrite, reflexivity, found, equalish_or_rewrite, rewrite_in_transitive_reflexive_rewrite, lo_cfl, assumption, equality_in_transitive_reflexive_rewrite, ih_cfl, symmetry
% 3.67/1.85 % No. of inferences in proof: 24
% 3.67/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1335 ms resp. 867 ms w/o parsing
% 3.67/1.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.67/1.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------