TSTP Solution File: GRP776+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 3.62s 1.86s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 28
% Syntax : Number of formulae : 49 ( 7 unt; 9 typ; 0 def)
% Number of atoms : 88 ( 28 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 227 ( 5 ~; 3 |; 15 &; 174 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 ^; 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_type,type,
f: $i > $i ).
thf(eh_type,type,
eh: $i ).
thf(eg_type,type,
eg: $i ).
thf(g_type,type,
g: $i > $o ).
thf(inv_type,type,
inv: $i > $i ).
thf(opp_type,type,
opp: $i > $i ).
thf(h_type,type,
h: $i > $o ).
thf(sum_type,type,
sum: $i > $i > $i ).
thf(product_type,type,
product: $i > $i > $i ).
thf(17,axiom,
h @ eg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
thf(65,plain,
h @ eg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [A: $i] :
( ( g @ A )
=> ( ( product @ ( inv @ A ) @ A )
= eh ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
thf(41,plain,
! [A: $i] :
( ( g @ A )
=> ( ( product @ ( inv @ A ) @ A )
= eh ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( f @ ( product @ B @ A ) )
= ( sum @ ( f @ B ) @ ( f @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( f @ ( product @ B @ A ) )
= ( sum @ ( f @ B ) @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
g @ eh,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
thf(66,plain,
g @ eh,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i] :
( ( g @ A )
=> ( ( product @ eh @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
thf(35,plain,
! [A: $i] :
( ( g @ A )
=> ( ( product @ eh @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( h @ B )
=> ( h @ ( opp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( h @ B )
=> ( h @ ( opp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: $i] :
( ( h @ A )
=> ( ( sum @ A @ ( opp @ A ) )
= eg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
thf(51,plain,
! [A: $i] :
( ( h @ A )
=> ( ( sum @ A @ ( opp @ A ) )
= eg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( g @ A )
=> ( g @ ( inv @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
thf(57,plain,
! [A: $i] :
( ( g @ A )
=> ( g @ ( inv @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( h @ C )
& ( h @ B )
& ( h @ A ) )
=> ( ( sum @ ( sum @ C @ B ) @ A )
= ( sum @ C @ ( sum @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] :
( ( ( h @ C )
& ( h @ B )
& ( h @ A ) )
=> ( ( sum @ ( sum @ C @ B ) @ A )
= ( sum @ C @ ( sum @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( g @ C )
& ( g @ B )
& ( g @ A ) )
=> ( ( product @ ( product @ C @ B ) @ A )
= ( product @ C @ ( product @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( ( g @ C )
& ( g @ B )
& ( g @ A ) )
=> ( ( product @ ( product @ C @ B ) @ A )
= ( product @ C @ ( product @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
! [A: $i] :
( ( h @ A )
=> ( ( sum @ eg @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
thf(70,plain,
! [A: $i] :
( ( h @ A )
=> ( ( sum @ eg @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( f @ eh )
= eg )
& ( ~ ( g @ A )
| ( ( f @ ( inv @ A ) )
= ( opp @ ( f @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( f @ eh )
= eg )
& ( ~ ( g @ A )
| ( ( f @ ( inv @ A ) )
= ( opp @ ( f @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ( ( f @ eh )
= eg )
& ( ~ ( g @ A )
| ( ( f @ ( inv @ A ) )
= ( opp @ ( f @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i] :
( ( g @ A )
=> ( ( product @ A @ eh )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
thf(44,plain,
! [A: $i] :
( ( g @ A )
=> ( ( product @ A @ eh )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i] :
( ( h @ A )
=> ( ( sum @ A @ eg )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos14) ).
thf(59,plain,
! [A: $i] :
( ( h @ A )
=> ( ( sum @ A @ eg )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( h @ B )
& ( h @ A ) )
=> ( h @ ( sum @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( h @ B )
& ( h @ A ) )
=> ( h @ ( sum @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i] :
( ( h @ A )
=> ( ( sum @ ( opp @ A ) @ A )
= eg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
thf(54,plain,
! [A: $i] :
( ( h @ A )
=> ( ( sum @ ( opp @ A ) @ A )
= eg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( g @ A )
=> ( h @ ( f @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
thf(49,plain,
! [A: $i] :
( ( g @ A )
=> ( h @ ( f @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( g @ B )
& ( g @ A ) )
=> ( g @ ( product @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( ( g @ B )
& ( g @ A ) )
=> ( g @ ( product @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i] :
( ( g @ A )
=> ( ( product @ A @ ( inv @ A ) )
= eh ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
thf(62,plain,
! [A: $i] :
( ( g @ A )
=> ( ( product @ A @ ( inv @ A ) )
= eh ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(79,plain,
$false,
inference(e,[status(thm)],[65,41,32,66,35,67,51,57,29,38,70,21,44,59,27,54,49,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP776+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 01:38:19 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.30/1.03 % [INFO] Parsing done (139ms).
% 1.30/1.03 % [INFO] Running in sequential loop mode.
% 1.69/1.23 % [INFO] eprover registered as external prover.
% 1.69/1.23 % [INFO] cvc4 registered as external prover.
% 1.69/1.24 % [INFO] Scanning for conjecture ...
% 1.79/1.29 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 2.03/1.33 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.03/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.36 % [INFO] Type checking passed.
% 2.03/1.36 % [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 ...
% 3.62/1.85 % External prover 'e' found a proof!
% 3.62/1.85 % [INFO] Killing All external provers ...
% 3.62/1.85 % Time passed: 1331ms (effective reasoning time: 816ms)
% 3.62/1.85 % 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)>
% 3.62/1.85 % Axioms used in derivation (18): sos14, sos06, sos13, sos10, sos09, sos02, sos11, sos08, sos12, sos04, sos15, sos17, sos03, sos16, sos05, sos07, sos01, sos18
% 3.62/1.85 % No. of inferences in proof: 40
% 3.62/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1331 ms resp. 816 ms w/o parsing
% 3.62/1.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.62/1.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------