TSTP Solution File: GRP194+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 11:13:28 EDT 2023
% Result : Theorem 3.04s 1.69s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 25 ( 6 unt; 7 typ; 0 def)
% Number of atoms : 48 ( 9 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 172 ( 2 ~; 0 |; 14 &; 140 @)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 0 ^; 29 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(left_zero_type,type,
left_zero: $i > $i > $o ).
thf(h_type,type,
h: $i ).
thf(phi_type,type,
phi: $i > $i ).
thf(f_left_zero_type,type,
f_left_zero: $i ).
thf(group_member_type,type,
group_member: $i > $i > $o ).
thf(multiply_type,type,
multiply: $i > $i > $i > $i ).
thf(f_type,type,
f: $i ).
thf(1,conjecture,
left_zero @ h @ ( phi @ f_left_zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_zero_h) ).
thf(2,negated_conjecture,
~ ( left_zero @ h @ ( phi @ f_left_zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ( left_zero @ h @ ( phi @ f_left_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( left_zero @ A @ B )
<=> ( ( group_member @ B @ A )
& ! [C: $i] :
( ( group_member @ C @ A )
=> ( ( multiply @ A @ B @ C )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( ( left_zero @ A @ B )
=> ( ( group_member @ B @ A )
& ! [C: $i] :
( ( group_member @ C @ A )
=> ( ( multiply @ A @ B @ C )
= B ) ) ) )
& ( ( ( group_member @ B @ A )
& ! [C: $i] :
( ( group_member @ C @ A )
=> ( ( multiply @ A @ B @ C )
= B ) ) )
=> ( left_zero @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [A: $i] :
( ( group_member @ A @ h )
=> ? [B: $i] :
( ( group_member @ B @ f )
& ( ( phi @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
thf(21,plain,
! [A: $i] :
( ( group_member @ A @ h )
=> ? [B: $i] :
( ( group_member @ B @ f )
& ( ( phi @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( group_member @ B @ A )
& ( group_member @ C @ A )
& ( group_member @ D @ A ) )
=> ( ( multiply @ A @ ( multiply @ A @ B @ C ) @ D )
= ( multiply @ A @ B @ ( multiply @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(13,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( group_member @ B @ A )
& ( group_member @ C @ A )
& ( group_member @ D @ A ) )
=> ( ( multiply @ A @ ( multiply @ A @ B @ C ) @ D )
= ( multiply @ A @ B @ ( multiply @ A @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
left_zero @ f @ f_left_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero_for_f) ).
thf(35,plain,
left_zero @ f @ f_left_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( group_member @ A @ f )
& ( group_member @ B @ f ) )
=> ( ( multiply @ h @ ( phi @ A ) @ ( phi @ B ) )
= ( phi @ ( multiply @ f @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ( group_member @ A @ f )
& ( group_member @ B @ f ) )
=> ( ( multiply @ h @ ( phi @ A ) @ ( phi @ B ) )
= ( phi @ ( multiply @ f @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i] :
( ( group_member @ A @ f )
=> ( group_member @ ( phi @ A ) @ h ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
thf(16,plain,
! [A: $i] :
( ( group_member @ A @ f )
=> ( group_member @ ( phi @ A ) @ h ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( group_member @ B @ A )
& ( group_member @ C @ A ) )
=> ( group_member @ ( multiply @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function) ).
thf(11,plain,
! [A: $i,B: $i,C: $i] :
( ( ( group_member @ B @ A )
& ( group_member @ C @ A ) )
=> ( group_member @ ( multiply @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(38,plain,
$false,
inference(e,[status(thm)],[10,25,21,13,35,18,16,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:00:06 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.96 % [INFO] Parsing done (117ms).
% 1.18/0.97 % [INFO] Running in sequential loop mode.
% 1.51/1.18 % [INFO] eprover registered as external prover.
% 1.51/1.18 % [INFO] cvc4 registered as external prover.
% 1.72/1.18 % [INFO] Scanning for conjecture ...
% 1.82/1.23 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.90/1.25 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.90/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 1.90/1.28 % [INFO] Type checking passed.
% 1.90/1.28 % [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 ...
% 3.04/1.69 % External prover 'e' found a proof!
% 3.04/1.69 % [INFO] Killing All external provers ...
% 3.04/1.69 % Time passed: 1170ms (effective reasoning time: 714ms)
% 3.04/1.69 % 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)>
% 3.04/1.69 % Axioms used in derivation (7): associativity, homomorphism1, surjective, left_zero_for_f, total_function, homomorphism2, left_zero
% 3.04/1.69 % No. of inferences in proof: 18
% 3.04/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1170 ms resp. 714 ms w/o parsing
% 3.04/1.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.04/1.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------