TSTP Solution File: LDA007-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LDA007-2 : TPTP v8.1.2. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:34:20 EDT 2023
% Result : Unsatisfiable 3.04s 1.64s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 36
% Syntax : Number of formulae : 57 ( 31 unt; 16 typ; 0 def)
% Number of atoms : 51 ( 36 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 186 ( 10 ~; 10 |; 0 &; 166 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 13 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(f_type,type,
f: $i > $i > $i ).
thf(t_type,type,
t: $i ).
thf(tsk_type,type,
tsk: $i ).
thf(tt_ts_type,type,
tt_ts: $i ).
thf(tk_type,type,
tk: $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(a_type,type,
a: $i > $i > $i ).
thf(critical_point_type,type,
critical_point: $i > $i ).
thf(k_type,type,
k: $i ).
thf(ts_type,type,
ts: $i ).
thf(sk_type,type,
sk: $i ).
thf(s_type,type,
s: $i ).
thf(ttk_type,type,
ttk: $i ).
thf(tt_type,type,
tt: $i ).
thf(stk_type,type,
stk: $i ).
thf(st_type,type,
st: $i ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( f @ A @ ( f @ B @ C ) )
= ( f @ ( f @ A @ B ) @ ( f @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
( ts
= ( f @ t @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(52,plain,
( ts
= ( f @ t @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
( stk
= ( f @ st @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(61,plain,
( stk
= ( f @ st @ k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( less @ A @ ( critical_point @ B ) )
| ( less @ A @ ( a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( less @ A @ ( critical_point @ B ) )
| ( less @ A @ ( a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
( sk
= ( f @ s @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(44,plain,
( sk
= ( f @ s @ k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
( tk
= ( f @ t @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(54,plain,
( tk
= ( f @ t @ k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( a @ A @ B )
!= B )
| ( ( a @ ( f @ C @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ A @ B )
!= B )
| ( ( a @ ( f @ C @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( critical_point @ ( f @ A @ B ) )
= ( a @ A @ ( critical_point @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( critical_point @ ( f @ A @ B ) )
= ( a @ A @ ( critical_point @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( a @ A @ ( a @ B @ C ) )
= ( a @ ( f @ A @ B ) @ ( a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1a) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( a @ A @ ( a @ B @ C ) )
= ( a @ ( f @ A @ B ) @ ( a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,axiom,
! [A: $i] :
~ ( less @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
thf(24,plain,
! [A: $i] :
~ ( less @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
( ttk
= ( f @ tt @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(46,plain,
( ttk
= ( f @ tt @ k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( less @ ( a @ C @ A ) @ ( a @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less @ A @ B )
| ( less @ ( a @ C @ A ) @ ( a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
( k
= ( critical_point @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(38,plain,
( k
= ( critical_point @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
( ( f @ t @ tsk )
!= ( f @ tt_ts @ tk ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
thf(21,plain,
( ( f @ t @ tsk )
!= ( f @ tt_ts @ tk ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
( tt
= ( f @ t @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(48,plain,
( tt
= ( f @ t @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
( st
= ( f @ s @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(63,plain,
( st
= ( f @ s @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
( tt_ts
= ( f @ tt @ ts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(50,plain,
( tt_ts
= ( f @ tt @ ts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( less @ A @ ( critical_point @ B ) )
| ( ( a @ B @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( less @ A @ ( critical_point @ B ) )
| ( ( a @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
( tsk
= ( f @ ts @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(40,plain,
( tsk
= ( f @ ts @ k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( A
= ( a @ B @ A ) )
| ( less @ A @ ( a @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A
= ( a @ B @ A ) )
| ( less @ A @ ( a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(83,plain,
$false,
inference(e,[status(thm)],[56,52,61,34,44,54,58,36,42,24,46,29,38,21,48,63,50,31,40,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LDA007-2 : TPTP v8.1.2. Bugfixed v2.6.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 20:49:51 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.85/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.94 % [INFO] Parsing done (111ms).
% 1.22/0.95 % [INFO] Running in sequential loop mode.
% 1.50/1.15 % [INFO] eprover registered as external prover.
% 1.50/1.15 % [INFO] cvc4 registered as external prover.
% 1.50/1.16 % [INFO] Scanning for conjecture ...
% 1.79/1.21 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 1.89/1.25 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 1.89/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.89/1.27 % [INFO] Type checking passed.
% 1.89/1.27 % [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 ...
% 3.04/1.63 % External prover 'e' found a proof!
% 3.04/1.63 % [INFO] Killing All external provers ...
% 3.04/1.64 % Time passed: 1128ms (effective reasoning time: 680ms)
% 3.04/1.64 % 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)>
% 3.04/1.64 % Axioms used in derivation (19): clause_2, clause_1, clause_8, b4, clause_9, clause_6, a1, clause_3, a2, c3, clause_5, a1a, c2, b1, c1, clause_7, clause_10, clause_4, d2
% 3.04/1.64 % No. of inferences in proof: 41
% 3.04/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1128 ms resp. 680 ms w/o parsing
% 3.22/1.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.22/1.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------