TSTP Solution File: NUM691^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 : Tue May 7 10:45:14 EDT 2024
% Result : Theorem 9.36s 3.09s
% Output : Refutation 9.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 9 unt; 7 typ; 0 def)
% Number of atoms : 122 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 404 ( 57 ~; 38 |; 0 &; 284 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 0 ^ 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_type,type,
x: nat ).
thf(y_type,type,
y: nat ).
thf(z_type,type,
z: nat ).
thf(u_type,type,
u: nat ).
thf(more_type,type,
more: nat > nat > $o ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(7,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( more @ A @ B )
=> ( ( ~ ( more @ C @ D )
=> ( C = D ) )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22b) ).
thf(25,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( more @ A @ B )
=> ( ( ~ ( more @ C @ D )
=> ( C = D ) )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
! [A: nat,B: nat] :
( ( more @ A @ B )
=> ! [C: nat,D: nat] :
( ( ~ ( more @ C @ D )
=> ( C = D ) )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[25]) ).
thf(27,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( C != D )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(29,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( C != D )
| ~ ( more @ A @ B )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(30,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(1,conjecture,
( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz23) ).
thf(2,negated_conjecture,
~ ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( ~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) )
=> ( ( pl @ x @ z )
= ( pl @ y @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
inference(cnf,[status(esa)],[8]) ).
thf(4,axiom,
( ~ ( more @ z @ u )
=> ( z = u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(15,plain,
( ~ ( more @ z @ u )
=> ( z = u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
( ( more @ z @ u )
| ( z = u ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
( ( u = z )
| ( more @ z @ u ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ~ ( more @ A @ B )
=> ( A = B ) )
=> ( ( more @ C @ D )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22a) ).
thf(19,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ~ ( more @ A @ B )
=> ( A = B ) )
=> ( ( more @ C @ D )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [A: nat,B: nat] :
( ( ~ ( more @ A @ B )
=> ( A = B ) )
=> ! [C: nat,D: nat] :
( ( more @ C @ D )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( more @ C @ D )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(44,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( more @ C @ D )
| ( ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) )
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,10]) ).
thf(45,plain,
( ~ ( more @ x @ y )
| ~ ( more @ z @ u ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(136,plain,
( ( u = z )
| ~ ( more @ x @ y )
| ( ( more @ z @ u )
!= ( more @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[17,45]) ).
thf(137,plain,
( ( u = z )
| ~ ( more @ x @ y ) ),
inference(pattern_uni,[status(thm)],[136:[]]) ).
thf(3,axiom,
( ~ ( more @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(12,plain,
( ~ ( more @ x @ y )
=> ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
( ( more @ x @ y )
| ( x = y ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
( ( y = x )
| ( more @ x @ y ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(9,plain,
( ( pl @ x @ z )
!= ( pl @ y @ u ) ),
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
( ( pl @ y @ u )
!= ( pl @ x @ z ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(31,plain,
( ( y != x )
| ( u != z ) ),
inference(simp,[status(thm)],[11]) ).
thf(39,plain,
( ( more @ x @ y )
| ( u != z )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[14,31]) ).
thf(40,plain,
( ( more @ x @ y )
| ( u != z ) ),
inference(pattern_uni,[status(thm)],[39:[]]) ).
thf(81,plain,
( ( more @ z @ u )
| ( more @ x @ y )
| ( u != u ) ),
inference(paramod_ordered,[status(thm)],[17,40]) ).
thf(82,plain,
( ( more @ z @ u )
| ( more @ x @ y ) ),
inference(pattern_uni,[status(thm)],[81:[]]) ).
thf(22,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( A != B )
| ~ ( more @ C @ D )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(23,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( A != B )
| ~ ( more @ C @ D )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ D ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(24,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ B @ C )
| ( more @ ( pl @ A @ B ) @ ( pl @ A @ C ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(32,plain,
( ( more @ x @ y )
| ~ ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[14,10]) ).
thf(33,plain,
( ( more @ x @ y )
| ~ ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) ) ),
inference(pattern_uni,[status(thm)],[32:[]]) ).
thf(799,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ B @ C )
| ( more @ x @ y )
| ( ( more @ ( pl @ A @ B ) @ ( pl @ A @ C ) )
!= ( more @ ( pl @ x @ z ) @ ( pl @ x @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,33]) ).
thf(800,plain,
( ~ ( more @ z @ u )
| ( more @ x @ y ) ),
inference(pattern_uni,[status(thm)],[799:[bind(A,$thf( x )),bind(B,$thf( z )),bind(C,$thf( u ))]]) ).
thf(951,plain,
( ( more @ x @ y )
| ( ( more @ z @ u )
!= ( more @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[82,800]) ).
thf(952,plain,
more @ x @ y,
inference(pattern_uni,[status(thm)],[951:[]]) ).
thf(964,plain,
( ( u = z )
| ~ $true ),
inference(rewrite,[status(thm)],[137,952]) ).
thf(965,plain,
u = z,
inference(simp,[status(thm)],[964]) ).
thf(1019,plain,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
inference(rewrite,[status(thm)],[10,965]) ).
thf(1085,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) )
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,1019]) ).
thf(1086,plain,
~ ( more @ x @ y ),
inference(pattern_uni,[status(thm)],[1085:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(1093,plain,
~ $true,
inference(rewrite,[status(thm)],[1086,952]) ).
thf(1094,plain,
$false,
inference(simp,[status(thm)],[1093]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : NUM691^1 : TPTP v8.1.2. Released v3.7.0.
% 0.02/0.12 % Command : run_Leo-III %s %d
% 0.10/0.32 % Computer : n006.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon May 6 19:39:09 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.91/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.04 % [INFO] Parsing done (119ms).
% 1.17/1.05 % [INFO] Running in sequential loop mode.
% 1.51/1.29 % [INFO] nitpick registered as external prover.
% 1.51/1.29 % [INFO] Scanning for conjecture ...
% 1.67/1.35 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.77/1.37 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.77/1.40 % [INFO] Problem is higher-order (TPTP THF).
% 1.77/1.40 % [INFO] Type checking passed.
% 1.77/1.40 % [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 ...
% 9.36/3.08 % [INFO] Killing All external provers ...
% 9.36/3.09 % Time passed: 2622ms (effective reasoning time: 2029ms)
% 9.36/3.09 % 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)>
% 9.36/3.09 % Axioms used in derivation (4): satz22b, n, satz22a, m
% 9.36/3.09 % No. of inferences in proof: 49
% 9.36/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2622 ms resp. 2029 ms w/o parsing
% 9.47/3.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.47/3.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------