TSTP Solution File: BOO023-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : BOO023-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 10:11:58 EDT 2023
% Result : Unsatisfiable 3.03s 1.74s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 16
% Syntax : Number of formulae : 25 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 17 ( 16 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 104 ( 2 ~; 0 |; 0 &; 102 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(add_type,type,
add: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(n1_type,type,
n1: $i ).
thf(pixley_type,type,
pixley: $i > $i > $i > $i ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( pixley @ A @ B @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( pixley @ A @ B @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ C ) )
= ( add @ ( multiply @ B @ A ) @ ( multiply @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( add @ B @ C ) )
= ( add @ ( multiply @ B @ A ) @ ( multiply @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( pixley @ A @ A @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( pixley @ A @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,negated_conjecture,
( ( add @ a @ ( multiply @ b @ c ) )
!= ( multiply @ ( add @ a @ b ) @ ( add @ a @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_add_multiply_property) ).
thf(9,plain,
( ( add @ a @ ( multiply @ b @ c ) )
!= ( multiply @ ( add @ a @ b ) @ ( add @ a @ c ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( pixley @ A @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( pixley @ A @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( pixley @ A @ B @ C )
= ( add @ ( multiply @ A @ ( inverse @ B ) ) @ ( add @ ( multiply @ A @ C ) @ ( multiply @ ( inverse @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley_defn) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( pixley @ A @ B @ C )
= ( add @ ( multiply @ A @ ( inverse @ B ) ) @ ( add @ ( multiply @ A @ C ) @ ( multiply @ ( inverse @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
thf(16,plain,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(39,plain,
$false,
inference(e,[status(thm)],[24,14,20,9,22,12,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : BOO023-1 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 18 21:19:35 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.85/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.93 % [INFO] Parsing done (113ms).
% 1.16/0.94 % [INFO] Running in sequential loop mode.
% 1.44/1.16 % [INFO] eprover registered as external prover.
% 1.44/1.16 % [INFO] cvc4 registered as external prover.
% 1.44/1.16 % [INFO] Scanning for conjecture ...
% 1.70/1.22 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.70/1.24 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.82/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.82/1.25 % [INFO] Type checking passed.
% 1.82/1.25 % [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 ...
% 3.03/1.73 % External prover 'e' found a proof!
% 3.03/1.73 % [INFO] Killing All external provers ...
% 3.03/1.73 % Time passed: 1243ms (effective reasoning time: 791ms)
% 3.03/1.73 % 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)>
% 3.03/1.74 % Axioms used in derivation (7): multiply_add, pixley3, pixley_defn, pixley1, pixley2, additive_inverse, multiply_add_property
% 3.03/1.74 % No. of inferences in proof: 17
% 3.03/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1243 ms resp. 791 ms w/o parsing
% 3.03/1.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.03/1.76 % [INFO] Killing All external provers ...
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