TSTP Solution File: NUM686^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 10:45:12 EDT 2024
% Result : Theorem 8.55s 2.93s
% Output : Refutation 8.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 6 unt; 8 typ; 0 def)
% Number of atoms : 118 ( 10 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 316 ( 20 ~; 12 |; 0 &; 275 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 57 ( 0 ^ 57 !; 0 ?; 57 :)
% 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(some_type,type,
some: ( nat > $o ) > $o ).
thf(diffprop_type,type,
diffprop: nat > nat > nat > $o ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6) ).
thf(17,plain,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,plain,
! [B: nat,A: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [B: nat,A: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(3,axiom,
some @ ( diffprop @ x @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(9,plain,
some @ ( diffprop @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ A @ B ) )
=> ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz19a) ).
thf(14,plain,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ A @ B ) )
=> ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,plain,
! [A: nat,B: nat] :
( ( some @ ( diffprop @ A @ B ) )
=> ! [C: nat] : ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( some @ ( diffprop @ A @ B ) )
| ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(141,plain,
! [C: nat,B: nat,A: nat] :
( ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) )
| ( ( some @ ( diffprop @ x @ y ) )
!= ( some @ ( diffprop @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,16]) ).
thf(142,plain,
! [A: nat] : ( some @ ( diffprop @ ( pl @ x @ A ) @ ( pl @ y @ A ) ) ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(168,plain,
! [A: nat] : ( some @ ( diffprop @ ( pl @ x @ A ) @ ( pl @ y @ A ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(201,plain,
! [C: nat,B: nat,A: nat] :
( ( some @ ( diffprop @ ( pl @ x @ C ) @ ( pl @ A @ B ) ) )
| ( ( pl @ B @ A )
!= ( pl @ y @ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,168]) ).
thf(202,plain,
! [A: nat] : ( some @ ( diffprop @ ( pl @ x @ A ) @ ( pl @ A @ y ) ) ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( A ))]]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(11,plain,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,plain,
! [A: nat,B: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ! [C: nat] :
( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(miniscope,[status(thm)],[11]) ).
thf(13,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( some @ ( diffprop @ B @ A ) )
| ~ ( some @ ( diffprop @ C @ B ) )
| ( some @ ( diffprop @ C @ A ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(1,conjecture,
some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz21) ).
thf(2,negated_conjecture,
~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(68,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( some @ ( diffprop @ B @ A ) )
| ~ ( some @ ( diffprop @ C @ B ) )
| ( ( some @ ( diffprop @ C @ A ) )
!= ( some @ ( diffprop @ ( pl @ x @ z ) @ ( pl @ y @ u ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,8]) ).
thf(69,plain,
! [A: nat] :
( ~ ( some @ ( diffprop @ A @ ( pl @ y @ u ) ) )
| ~ ( some @ ( diffprop @ ( pl @ x @ z ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( pl @ y @ u )),bind(B,$thf( B )),bind(C,$thf( pl @ x @ z ))]]) ).
thf(73,plain,
! [A: nat] :
( ~ ( some @ ( diffprop @ A @ ( pl @ y @ u ) ) )
| ~ ( some @ ( diffprop @ ( pl @ x @ z ) @ A ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(445,plain,
! [B: nat,A: nat] :
( ~ ( some @ ( diffprop @ B @ ( pl @ y @ u ) ) )
| ( ( some @ ( diffprop @ ( pl @ x @ A ) @ ( pl @ A @ y ) ) )
!= ( some @ ( diffprop @ ( pl @ x @ z ) @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[202,73]) ).
thf(446,plain,
~ ( some @ ( diffprop @ ( pl @ z @ y ) @ ( pl @ y @ u ) ) ),
inference(pattern_uni,[status(thm)],[445:[bind(A,$thf( z )),bind(B,$thf( pl @ z @ y ))]]) ).
thf(4,axiom,
some @ ( diffprop @ z @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(10,plain,
some @ ( diffprop @ z @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(139,plain,
! [C: nat,B: nat,A: nat] :
( ( some @ ( diffprop @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) )
| ( ( some @ ( diffprop @ z @ u ) )
!= ( some @ ( diffprop @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,16]) ).
thf(140,plain,
! [A: nat] : ( some @ ( diffprop @ ( pl @ z @ A ) @ ( pl @ u @ A ) ) ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( z )),bind(B,$thf( u ))]]) ).
thf(166,plain,
! [A: nat] : ( some @ ( diffprop @ ( pl @ z @ A ) @ ( pl @ u @ A ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(180,plain,
! [C: nat,B: nat,A: nat] :
( ( some @ ( diffprop @ ( pl @ z @ C ) @ ( pl @ A @ B ) ) )
| ( ( pl @ B @ A )
!= ( pl @ u @ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,166]) ).
thf(181,plain,
! [A: nat] : ( some @ ( diffprop @ ( pl @ z @ A ) @ ( pl @ A @ u ) ) ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( A )),bind(B,$thf( u )),bind(C,$thf( A ))]]) ).
thf(498,plain,
~ $true,
inference(rewrite,[status(thm)],[446,181]) ).
thf(499,plain,
$false,
inference(simp,[status(thm)],[498]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : NUM686^1 : TPTP v8.1.2. Released v3.7.0.
% 0.03/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 6 19:47:24 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.94/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/1.06 % [INFO] Parsing done (163ms).
% 1.17/1.07 % [INFO] Running in sequential loop mode.
% 1.78/1.42 % [INFO] nitpick registered as external prover.
% 1.78/1.42 % [INFO] Scanning for conjecture ...
% 1.99/1.51 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 2.04/1.55 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.04/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.58 % [INFO] Type checking passed.
% 2.04/1.58 % [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 ...
% 8.34/2.92 % [INFO] Killing All external provers ...
% 8.55/2.93 % Time passed: 2453ms (effective reasoning time: 1850ms)
% 8.55/2.93 % 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)>
% 8.55/2.93 % Axioms used in derivation (5): n, m, satz15, satz19a, satz6
% 8.55/2.93 % No. of inferences in proof: 36
% 8.55/2.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2453 ms resp. 1850 ms w/o parsing
% 8.55/3.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.55/3.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------