TSTP Solution File: BOO002-1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : BOO002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 07:28:37 EDT 2024
% Result : Unsatisfiable 2.53s 1.54s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of formulae : 15 ( 11 unt; 4 typ; 0 def)
% Number of atoms : 11 ( 10 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 60 ( 2 ~; 0 |; 0 &; 58 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 22 ( 0 ^ 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(b_type,type,
b: $i ).
thf(1,negated_conjecture,
( ( multiply @ a @ ( inverse @ a ) @ b )
!= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(6,plain,
( ( multiply @ a @ ( inverse @ a ) @ b )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B @ C ) @ D @ ( multiply @ A @ B @ E ) )
= ( multiply @ A @ B @ ( multiply @ C @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(9,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B @ C ) @ D @ ( multiply @ A @ B @ E ) )
= ( multiply @ A @ B @ ( multiply @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ A @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_2) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( multiply @ A @ B @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_1) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( multiply @ A @ B @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ A ) @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( multiply @ ( inverse @ A ) @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
$false,
inference(e,[status(thm)],[6,9,13,11,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n019.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 : Mon May 6 14:12:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.84/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.98/0.92 % [INFO] Parsing done (108ms).
% 0.98/0.93 % [INFO] Running in sequential loop mode.
% 1.56/1.15 % [INFO] eprover registered as external prover.
% 1.56/1.15 % [INFO] cvc4 registered as external prover.
% 1.56/1.16 % [INFO] Scanning for conjecture ...
% 1.64/1.21 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.64/1.23 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.79/1.23 % [INFO] Problem is propositional (TPTP CNF).
% 1.79/1.24 % [INFO] Type checking passed.
% 1.79/1.24 % [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 ...
% 2.33/1.53 % External prover 'e' found a proof!
% 2.33/1.53 % [INFO] Killing All external provers ...
% 2.33/1.53 % Time passed: 1039ms (effective reasoning time: 597ms)
% 2.33/1.53 % 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)>
% 2.33/1.53 % Axioms used in derivation (4): associativity, ternary_multiply_2, ternary_multiply_1, left_inverse
% 2.53/1.53 % No. of inferences in proof: 11
% 2.53/1.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1039 ms resp. 597 ms w/o parsing
% 2.53/1.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.53/1.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------