TSTP Solution File: ANA003-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA003-2 : TPTP v8.1.2. Released v1.0.0.
% 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 10:08:43 EDT 2023
% Result : Unsatisfiable 3.71s 1.84s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 34
% Syntax : Number of formulae : 52 ( 9 unt; 17 typ; 0 def)
% Number of atoms : 75 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 358 ( 44 ~; 40 |; 0 &; 274 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 17 usr; 6 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_than_type,type,
less_than: $i > $i > $o ).
thf(n0_type,type,
n0: $i ).
thf(fp31_type,type,
fp31: $i > $i ).
thf(absolute_type,type,
absolute: $i > $i ).
thf(add_type,type,
add: $i > $i > $i ).
thf(minus_type,type,
minus: $i > $i ).
thf(a_type,type,
a: $i ).
thf(f_type,type,
f: $i > $i ).
thf(l1_type,type,
l1: $i ).
thf(fp32_type,type,
fp32: $i > $i ).
thf(g_type,type,
g: $i > $i ).
thf(l2_type,type,
l2: $i ).
thf(b_type,type,
b: $i ).
thf(fp33_type,type,
fp33: $i > $i ).
thf(equalish_type,type,
equalish: $i > $i > $o ).
thf(minimum_type,type,
minimum: $i > $i > $i ).
thf(half_type,type,
half: $i > $i ).
thf(6,negated_conjecture,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
thf(20,plain,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ( less_than @ ( absolute @ ( add @ ( fp33 @ A ) @ ( minus @ a ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ n0 @ B )
| ( less_than @ ( minimum @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_3) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ n0 @ B )
| ( less_than @ ( minimum @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ A ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ A ) ) @ ( minus @ l2 ) ) ) ) @ b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
thf(22,plain,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ ( add @ ( absolute @ ( add @ ( f @ ( fp33 @ A ) ) @ ( minus @ l1 ) ) ) @ ( absolute @ ( add @ ( g @ ( fp33 @ A ) ) @ ( minus @ l2 ) ) ) ) @ b ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ n0 @ B )
| ( less_than @ ( minimum @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_2) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ n0 @ B )
| ( less_than @ ( minimum @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ C )
| ( less_than @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_than) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ C )
| ( less_than @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,negated_conjecture,
less_than @ n0 @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).
thf(18,plain,
less_than @ n0 @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(31,plain,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ ( half @ B ) )
| ~ ( less_than @ C @ ( half @ B ) )
| ( less_than @ ( add @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ ( half @ B ) )
| ~ ( less_than @ C @ ( half @ B ) )
| ( less_than @ ( add @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ( less_than @ n0 @ ( fp32 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).
thf(23,plain,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ( less_than @ n0 @ ( fp32 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ( less_than @ n0 @ ( fp31 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).
thf(19,plain,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ( less_than @ n0 @ ( fp31 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ( less_than @ n0 @ ( half @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(47,plain,
! [A: $i] :
( ~ ( less_than @ n0 @ A )
| ( less_than @ n0 @ ( half @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp32 @ A ) )
| ( less_than @ ( absolute @ ( add @ ( g @ B ) @ ( minus @ l2 ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp32 @ A ) )
| ( less_than @ ( absolute @ ( add @ ( g @ B ) @ ( minus @ l2 ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ n0 @ B )
| ( less_than @ n0 @ ( minimum @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_1) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ n0 @ B )
| ( less_than @ n0 @ ( minimum @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp31 @ A ) )
| ( less_than @ ( absolute @ ( add @ ( f @ B ) @ ( minus @ l1 ) ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ n0 @ A )
| ~ ( less_than @ ( absolute @ ( add @ B @ ( minus @ a ) ) ) @ ( fp31 @ A ) )
| ( less_than @ ( absolute @ ( add @ ( f @ B ) @ ( minus @ l1 ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i] :
~ ( less_than @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_less_than) ).
thf(33,plain,
! [A: $i] :
~ ( less_than @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,axiom,
! [A: $i] : ( equalish @ ( add @ n0 @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(32,plain,
! [A: $i] : ( equalish @ ( add @ n0 @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ ( add @ ( absolute @ A ) @ ( absolute @ B ) ) @ C )
| ( less_than @ ( absolute @ ( add @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_17) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ ( add @ ( absolute @ A ) @ ( absolute @ B ) ) @ C )
| ( less_than @ ( absolute @ ( add @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(52,plain,
$false,
inference(e,[status(thm)],[20,41,22,39,35,18,31,43,23,19,47,24,37,21,33,32,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA003-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n026.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 18:13:51 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.01 % [INFO] Parsing done (129ms).
% 1.37/1.01 % [INFO] Running in sequential loop mode.
% 1.79/1.23 % [INFO] eprover registered as external prover.
% 1.79/1.23 % [INFO] cvc4 registered as external prover.
% 1.79/1.23 % [INFO] Scanning for conjecture ...
% 1.88/1.31 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 2.08/1.34 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.08/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.36 % [INFO] Type checking passed.
% 2.08/1.36 % [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 ...
% 3.71/1.84 % External prover 'e' found a proof!
% 3.71/1.84 % [INFO] Killing All external provers ...
% 3.71/1.84 % Time passed: 1296ms (effective reasoning time: 821ms)
% 3.71/1.84 % 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)>
% 3.71/1.84 % Axioms used in derivation (10): axiom_7, axiom_2_2, left_identity, axiom_3, right_identity, transitivity_of_less_than, axiom_2_1, c_17, reflexivity_of_less_than, axiom_2_3
% 3.71/1.84 % No. of inferences in proof: 35
% 3.71/1.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1296 ms resp. 821 ms w/o parsing
% 3.71/1.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.71/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------