TSTP Solution File: GRP028-4 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP028-4 : TPTP v8.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 : Mon May 20 21:02:59 EDT 2024
% Result : Unsatisfiable 4.67s 2.54s
% Output : Refutation 4.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 11 unt; 4 typ; 0 def)
% Number of atoms : 49 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 202 ( 30 ~; 21 |; 0 &; 151 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 64 ( 0 ^ 64 !; 0 ?; 64 :)
% Comments :
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thf(product_type,type,
product: $i > $i > $i > $o ).
thf(not_identity_type,type,
not_identity: $i > $i ).
thf(left_solution_type,type,
left_solution: $i > $i > $i ).
thf(right_solution_type,type,
right_solution: $i > $i > $i ).
thf(5,axiom,
! [B: $i,A: $i] : ( product @ A @ ( right_solution @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_soln) ).
thf(13,plain,
! [B: $i,A: $i] : ( product @ A @ ( right_solution @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( product @ ( left_solution @ A @ B ) @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_soln) ).
thf(12,plain,
! [B: $i,A: $i] : ( product @ ( left_solution @ A @ B ) @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).
thf(8,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
inference(cnf,[status(esa)],[8]) ).
thf(41,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ( product @ C @ D @ F )
| ( ( product @ A @ E @ F )
!= ( product @ A @ B @ C ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ C @ D )
| ~ ( product @ C @ B @ C )
| ( product @ D @ B @ D ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( F ))]]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ C @ D )
| ~ ( product @ C @ B @ C )
| ( product @ D @ B @ D ) ),
inference(simp,[status(thm)],[43]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( product @ ( not_identity @ A ) @ A @ ( not_identity @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_identity) ).
thf(6,plain,
! [A: $i] :
~ ( product @ ( not_identity @ A ) @ A @ ( not_identity @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
! [A: $i] :
~ ( product @ ( not_identity @ A ) @ A @ ( not_identity @ A ) ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(76,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ C @ D )
| ~ ( product @ C @ B @ C )
| ( ( product @ D @ B @ D )
!= ( product @ ( not_identity @ E ) @ E @ ( not_identity @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,7]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( product @ A @ C @ ( not_identity @ B ) )
| ~ ( product @ C @ B @ C ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( not_identity @ B )),bind(E,$thf( B ))]]) ).
thf(105,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ E @ D @ E )
| ( ( product @ ( left_solution @ A @ B ) @ A @ B )
!= ( product @ C @ E @ ( not_identity @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,77]) ).
thf(106,plain,
! [B: $i,A: $i] :
~ ( product @ A @ B @ A ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( F )),bind(B,$thf( not_identity @ H )),bind(C,$thf( left_solution @ F @ ( not_identity @ H ) )),bind(D,$thf( H )),bind(E,$thf( F ))]]) ).
thf(122,plain,
! [B: $i,A: $i] :
~ ( product @ A @ B @ A ),
inference(simp,[status(thm)],[106]) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( product @ A @ ( right_solution @ A @ B ) @ B )
!= ( product @ C @ D @ C ) ),
inference(paramod_ordered,[status(thm)],[13,122]) ).
thf(128,plain,
$false,
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( right_solution @ F @ F ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP028-4 : TPTP v8.2.0. Released v2.6.0.
% 0.05/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n024.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 04:39:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.99/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.10 % [INFO] Parsing done (153ms).
% 1.29/1.12 % [INFO] Running in sequential loop mode.
% 1.84/1.49 % [INFO] nitpick registered as external prover.
% 1.84/1.50 % [INFO] Scanning for conjecture ...
% 2.03/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.03/1.61 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.03/1.62 % [INFO] Problem is propositional (TPTP CNF).
% 2.03/1.62 % [INFO] Type checking passed.
% 2.03/1.63 % [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 ...
% 4.67/2.53 % [INFO] Killing All external provers ...
% 4.67/2.54 % Time passed: 2065ms (effective reasoning time: 1413ms)
% 4.67/2.54 % Axioms used in derivation (3): right_soln, left_soln, associativity1
% 4.67/2.54 % No. of inferences in proof: 20
% 4.67/2.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2065 ms resp. 1413 ms w/o parsing
% 4.67/2.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.67/2.58 % [INFO] Killing All external provers ...
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