TSTP Solution File: BOO026-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : BOO026-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 3.05s 1.73s
% Output : Refutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 18
% Syntax : Number of formulae : 30 ( 23 unt; 7 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 206 ( 2 ~; 0 |; 0 &; 204 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(n1_type,type,
n1: $i ).
thf(n0_type,type,
n0: $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( add @ ( multiply @ A @ ( inverse @ B ) ) @ ( add @ ( multiply @ A @ B ) @ ( multiply @ ( inverse @ B ) @ B ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( add @ ( multiply @ A @ ( inverse @ B ) ) @ ( add @ ( multiply @ A @ B ) @ ( multiply @ ( inverse @ B ) @ B ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ ( inverse @ A ) ) @ ( multiply @ ( add @ A @ B ) @ ( add @ ( inverse @ A ) @ B ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1_dual) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ ( inverse @ A ) ) @ ( multiply @ ( add @ A @ B ) @ ( add @ ( inverse @ A ) @ B ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
thf(17,plain,
! [A: $i] :
( ( add @ A @ ( inverse @ A ) )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( add @ ( multiply @ A @ ( inverse @ B ) ) @ ( add @ ( multiply @ A @ A ) @ ( multiply @ ( inverse @ B ) @ A ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( add @ ( multiply @ A @ ( inverse @ B ) ) @ ( add @ ( multiply @ A @ A ) @ ( multiply @ ( inverse @ B ) @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( multiply @ ( add @ a @ b ) @ b )
!= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add) ).
thf(12,plain,
( ( multiply @ ( add @ a @ b ) @ b )
!= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ ( inverse @ B ) ) @ ( multiply @ ( add @ A @ B ) @ ( add @ ( inverse @ B ) @ B ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2_dual) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ ( inverse @ B ) ) @ ( multiply @ ( add @ A @ B ) @ ( add @ ( inverse @ B ) @ B ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( add @ ( multiply @ A @ ( inverse @ A ) ) @ ( add @ ( multiply @ A @ B ) @ ( multiply @ ( inverse @ A ) @ B ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( add @ ( multiply @ A @ ( inverse @ A ) ) @ ( add @ ( multiply @ A @ B ) @ ( multiply @ ( inverse @ A ) @ B ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( multiply @ B @ C ) )
= ( multiply @ ( add @ B @ A ) @ ( add @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( add @ A @ ( multiply @ B @ C ) )
= ( multiply @ ( add @ B @ A ) @ ( add @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,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(15,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)],[2]) ).
thf(5,axiom,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse) ).
thf(21,plain,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ ( inverse @ B ) ) @ ( multiply @ ( add @ A @ A ) @ ( add @ ( inverse @ B ) @ A ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley3_dual) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( multiply @ ( add @ A @ ( inverse @ B ) ) @ ( multiply @ ( add @ A @ A ) @ ( add @ ( inverse @ B ) @ A ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[25,29,17,27,12,31,23,19,15,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO026-1 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n022.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Thu May 18 21:03:48 EDT 2023
% 0.17/0.38 % CPUTime :
% 1.01/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.03 % [INFO] Parsing done (129ms).
% 1.33/1.03 % [INFO] Running in sequential loop mode.
% 1.78/1.24 % [INFO] eprover registered as external prover.
% 1.78/1.24 % [INFO] cvc4 registered as external prover.
% 1.78/1.24 % [INFO] Scanning for conjecture ...
% 1.78/1.29 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.78/1.31 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.04/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 2.04/1.34 % [INFO] Type checking passed.
% 2.04/1.34 % [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 ...
% 3.05/1.72 % External prover 'e' found a proof!
% 3.05/1.72 % [INFO] Killing All external provers ...
% 3.05/1.72 % Time passed: 1187ms (effective reasoning time: 689ms)
% 3.05/1.72 % 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)>
% 3.05/1.73 % Axioms used in derivation (10): pixley3, pixley1, pixley2, pixley2_dual, additive_inverse, multiply_add_property, pixley3_dual, pixley1_dual, add_multiply_property, multiplicative_inverse
% 3.05/1.73 % No. of inferences in proof: 23
% 3.05/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1187 ms resp. 689 ms w/o parsing
% 3.05/1.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.05/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------