TSTP Solution File: PUZ133+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : PUZ133+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:47:46 EDT 2023
% Result : Theorem 4.54s 2.15s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 21
% Syntax : Number of formulae : 33 ( 5 unt; 11 typ; 0 def)
% Number of atoms : 84 ( 31 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 325 ( 14 ~; 0 |; 36 &; 249 @)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 ^; 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(queens_p_type,type,
queens_p: $o ).
thf(q_type,type,
q: $i > $i ).
thf(p_type,type,
p: $i > $i ).
thf(perm_type,type,
perm: $i > $i ).
thf(queens_q_type,type,
queens_q: $o ).
thf(le_type,type,
le: $i > $i > $o ).
thf(s_type,type,
s: $i > $i ).
thf(n0_type,type,
n0: $i ).
thf(n_type,type,
n: $i ).
thf(plus_type,type,
plus: $i > $i > $i ).
thf(minus_type,type,
minus: $i > $i > $i ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( plus @ A @ B )
= ( plus @ C @ D ) )
<=> ( ( minus @ A @ C )
= ( minus @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1) ).
thf(46,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( plus @ A @ B )
= ( plus @ C @ D ) )
=> ( ( minus @ A @ C )
= ( minus @ D @ B ) ) )
& ( ( ( minus @ A @ C )
= ( minus @ D @ B ) )
=> ( ( plus @ A @ B )
= ( plus @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( minus @ A @ B )
= ( minus @ C @ D ) )
<=> ( ( minus @ A @ C )
= ( minus @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus1) ).
thf(53,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( minus @ A @ B )
= ( minus @ C @ D ) )
=> ( ( minus @ A @ C )
= ( minus @ B @ D ) ) )
& ( ( ( minus @ A @ C )
= ( minus @ B @ D ) )
=> ( ( minus @ A @ B )
= ( minus @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
( queens_p
=> ! [A: $i,B: $i] :
( ( ( le @ ( s @ n0 ) @ A )
& ( le @ A @ n )
& ( le @ ( s @ A ) @ B )
& ( le @ B @ n ) )
=> ( ( ( p @ A )
!= ( p @ B ) )
& ( ( plus @ ( p @ A ) @ A )
!= ( plus @ ( p @ B ) @ B ) )
& ( ( minus @ ( p @ A ) @ A )
!= ( minus @ ( p @ B ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_p) ).
thf(17,plain,
( queens_p
=> ! [A: $i,B: $i] :
( ( ( le @ ( s @ n0 ) @ A )
& ( le @ A @ n )
& ( le @ ( s @ A ) @ B )
& ( le @ B @ n ) )
=> ( ( ( p @ A )
!= ( p @ B ) )
& ( ( plus @ ( p @ A ) @ A )
!= ( plus @ ( p @ B ) @ B ) )
& ( ( minus @ ( p @ A ) @ A )
!= ( minus @ ( p @ B ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
( ( queens_p
& ! [A: $i] :
( ( q @ A )
= ( p @ ( perm @ A ) ) ) )
=> queens_q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_sym) ).
thf(2,negated_conjecture,
~ ( ( queens_p
& ! [A: $i] :
( ( q @ A )
= ( p @ ( perm @ A ) ) ) )
=> queens_q ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ( ( queens_p
& ! [A: $i] :
( ( q @ A )
= ( p @ ( perm @ A ) ) ) )
=> queens_q ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( minus @ B @ A )
= ( minus @ ( perm @ A ) @ ( perm @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation_another_one) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( minus @ B @ A )
= ( minus @ ( perm @ A ) @ ( perm @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i] :
( ( ( le @ ( s @ n0 ) @ A )
& ( le @ A @ n ) )
=> ( ( le @ ( s @ n0 ) @ ( perm @ A ) )
& ( le @ ( perm @ A ) @ n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation_range) ).
thf(36,plain,
! [A: $i] :
( ( ( le @ ( s @ n0 ) @ A )
& ( le @ A @ n ) )
=> ( ( le @ ( s @ n0 ) @ ( perm @ A ) )
& ( le @ ( perm @ A ) @ n ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( le @ A @ B )
& ( le @ B @ C ) )
=> ( le @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',le_trans) ).
thf(42,plain,
! [A: $i,B: $i,C: $i] :
( ( ( le @ A @ B )
& ( le @ B @ C ) )
=> ( le @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] :
( ( ( le @ ( s @ n0 ) @ A )
& ( le @ A @ n ) )
=> ( ( perm @ A )
= ( minus @ ( s @ n ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation) ).
thf(24,plain,
! [A: $i] :
( ( ( le @ ( s @ n0 ) @ A )
& ( le @ A @ n ) )
=> ( ( perm @ A )
= ( minus @ ( s @ n ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] : ( le @ A @ ( s @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_le) ).
thf(44,plain,
! [A: $i] : ( le @ A @ ( s @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
( ! [A: $i,B: $i] :
( ( ( le @ ( s @ n0 ) @ A )
& ( le @ A @ n )
& ( le @ ( s @ A ) @ B )
& ( le @ B @ n )
& ( ( le @ ( s @ A ) @ B )
<=> ( le @ ( s @ ( perm @ B ) ) @ ( perm @ A ) ) ) )
=> ( ( ( q @ A )
!= ( q @ B ) )
& ( ( plus @ ( q @ A ) @ A )
!= ( plus @ ( q @ B ) @ B ) )
& ( ( minus @ ( q @ A ) @ A )
!= ( minus @ ( q @ B ) @ B ) ) ) )
=> queens_q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_q) ).
thf(27,plain,
( ! [A: $i,B: $i] :
( ( ( le @ ( s @ n0 ) @ A )
& ( le @ A @ n )
& ( le @ ( s @ A ) @ B )
& ( le @ B @ n )
& ( ( le @ ( s @ A ) @ B )
=> ( le @ ( s @ ( perm @ B ) ) @ ( perm @ A ) ) )
& ( ( le @ ( s @ ( perm @ B ) ) @ ( perm @ A ) )
=> ( le @ ( s @ A ) @ B ) ) )
=> ( ( ( q @ A )
!= ( q @ B ) )
& ( ( plus @ ( q @ A ) @ A )
!= ( plus @ ( q @ B ) @ B ) )
& ( ( minus @ ( q @ A ) @ A )
!= ( minus @ ( q @ B ) @ B ) ) ) )
=> queens_q ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(239,plain,
$false,
inference(cvc4,[status(thm)],[46,53,17,12,39,36,42,24,44,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ133+2 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 20:02:25 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.96/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.04 % [INFO] Parsing done (137ms).
% 1.43/1.05 % [INFO] Running in sequential loop mode.
% 1.73/1.25 % [INFO] eprover registered as external prover.
% 1.73/1.25 % [INFO] cvc4 registered as external prover.
% 1.73/1.25 % [INFO] Scanning for conjecture ...
% 1.83/1.31 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 2.03/1.34 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 2.03/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.03/1.37 % [INFO] Type checking passed.
% 2.03/1.37 % [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 ...
% 4.54/2.14 % External prover 'cvc4' found a proof!
% 4.54/2.14 % [INFO] Killing All external provers ...
% 4.54/2.15 % Time passed: 1625ms (effective reasoning time: 1095ms)
% 4.54/2.15 % 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)>
% 4.54/2.15 % Axioms used in derivation (9): permutation, queens_q, queens_p, plus1, permutation_range, succ_le, le_trans, minus1, permutation_another_one
% 4.54/2.15 % No. of inferences in proof: 22
% 4.54/2.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1625 ms resp. 1095 ms w/o parsing
% 4.77/2.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.77/2.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------