TSTP Solution File: GRP777+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP777+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 11:15:22 EDT 2023
% Result : Theorem 11.39s 3.06s
% Output : Refutation 11.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 29 ( 22 unt; 7 typ; 0 def)
% Number of atoms : 22 ( 21 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 134 ( 2 ~; 0 |; 0 &; 132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 39 ( 0 ^; 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(bigC_type,type,
bigC: $i > $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(product_type,type,
product: $i > $i > $i ).
thf(quotient_type,type,
quotient: $i > $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( product @ ( quotient @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( product @ ( quotient @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( product @ ( product @ D @ C ) @ ( product @ B @ A ) )
= ( product @ ( product @ D @ B ) @ ( product @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
thf(27,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( product @ ( product @ D @ C ) @ ( product @ B @ A ) )
= ( product @ ( product @ D @ B ) @ ( product @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i] :
( ( bigC @ a @ b @ A )
= ( bigC @ c @ c @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( bigC @ a @ b @ A )
= ( bigC @ c @ c @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ! [A: $i] :
( ( bigC @ a @ b @ A )
= ( bigC @ c @ c @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
( ( product @ ( product @ a @ c ) @ ( product @ c @ b ) )
= ( product @ a @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
thf(39,plain,
( ( product @ ( product @ a @ c ) @ ( product @ c @ b ) )
= ( product @ a @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( product @ B @ ( difference @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( product @ B @ ( difference @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( difference @ B @ ( product @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
thf(15,plain,
! [A: $i,B: $i] :
( ( difference @ B @ ( product @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( quotient @ ( product @ B @ A ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( quotient @ ( product @ B @ A ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( product @ ( product @ ( product @ B @ A ) @ A ) @ ( product @ A @ ( product @ A @ B ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( product @ ( product @ ( product @ B @ A ) @ A ) @ ( product @ A @ ( product @ A @ B ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( bigC @ C @ B @ A )
= ( product @ ( product @ C @ B ) @ ( product @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
thf(36,plain,
! [A: $i,B: $i,C: $i] :
( ( bigC @ C @ B @ A )
= ( product @ ( product @ C @ B ) @ ( product @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
thf(30,plain,
! [A: $i] :
( ( product @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1684,plain,
$false,
inference(e,[status(thm)],[24,27,12,39,18,15,21,33,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP777+1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri May 19 01:34:55 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.97 % [INFO] Parsing done (110ms).
% 1.25/0.97 % [INFO] Running in sequential loop mode.
% 1.62/1.16 % [INFO] eprover registered as external prover.
% 1.62/1.16 % [INFO] cvc4 registered as external prover.
% 1.62/1.17 % [INFO] Scanning for conjecture ...
% 1.71/1.22 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.84/1.24 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.87/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.26 % [INFO] Type checking passed.
% 1.87/1.26 % [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 ...
% 11.39/3.05 % External prover 'e' found a proof!
% 11.39/3.05 % [INFO] Killing All external provers ...
% 11.39/3.05 % Time passed: 2521ms (effective reasoning time: 2077ms)
% 11.39/3.05 % 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)>
% 11.39/3.06 % Axioms used in derivation (9): sos06, sos03, sos09, sos02, sos05, sos08, sos04, sos07, sos01
% 11.39/3.06 % No. of inferences in proof: 22
% 11.39/3.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2521 ms resp. 2077 ms w/o parsing
% 11.39/3.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.39/3.09 % [INFO] Killing All external provers ...
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