TSTP Solution File: NUM742^1 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : NUM742^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 21 01:36:06 EDT 2024
% Result : Theorem 13.29s 4.08s
% Output : Refutation 13.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 45 ( 13 unt; 6 typ; 0 def)
% Number of atoms : 96 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 247 ( 28 ~; 26 |; 0 &; 174 @)
% ( 0 <=>; 19 =>; 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 : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 ^ 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(x_type,type,
x: frac ).
thf(y_type,type,
y: frac ).
thf(z_type,type,
z: frac ).
thf(lessf_type,type,
lessf: frac > frac > $o ).
thf(eq_type,type,
eq: frac > frac > $o ).
thf(4,axiom,
lessf @ y @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(13,plain,
lessf @ y @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(11,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
( ( lessf @ x @ y )
| ( eq @ x @ y ) ),
inference(cnf,[status(esa)],[11]) ).
thf(7,axiom,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).
thf(18,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( eq @ B @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(111,plain,
! [B: frac,A: frac] :
( ( lessf @ x @ y )
| ( eq @ B @ A )
| ( ( eq @ x @ y )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12,19]) ).
thf(112,plain,
( ( lessf @ x @ y )
| ( eq @ y @ x ) ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(8,axiom,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz50) ).
thf(20,plain,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,plain,
! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ! [C: frac] :
( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnf,[status(esa)],[21]) ).
thf(159,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ( lessf @ A @ C )
| ( ( lessf @ y @ z )
!= ( lessf @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13,22]) ).
thf(160,plain,
! [A: frac] :
( ~ ( lessf @ A @ y )
| ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(1,conjecture,
lessf @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz51a) ).
thf(2,negated_conjecture,
~ ( lessf @ x @ z ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ( lessf @ x @ z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(181,plain,
! [A: frac] :
( ~ ( lessf @ A @ y )
| ( ( lessf @ A @ z )
!= ( lessf @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[160,10]) ).
thf(182,plain,
~ ( lessf @ x @ y ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( x ))]]) ).
thf(206,plain,
( $false
| ( eq @ y @ x ) ),
inference(rewrite,[status(thm)],[112,182]) ).
thf(207,plain,
eq @ y @ x,
inference(simp,[status(thm)],[206]) ).
thf(9,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
thf(23,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,plain,
! [A: frac] : ( eq @ A @ A ),
inference(cnf,[status(esa)],[23]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( lessf @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( lessf @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz45) ).
thf(15,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( lessf @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( lessf @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,plain,
! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ! [C: frac] :
( ( eq @ A @ C )
=> ! [D: frac] :
( ( eq @ B @ D )
=> ( lessf @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[15]) ).
thf(17,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( lessf @ C @ D ) ),
inference(cnf,[status(esa)],[16]) ).
thf(31,plain,
! [E: frac,D: frac,C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ C )
| ~ ( eq @ B @ D )
| ( lessf @ D @ E )
| ( ( eq @ A @ A )
!= ( eq @ C @ E ) ) ),
inference(paramod_ordered,[status(thm)],[24,17]) ).
thf(32,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ A )
| ~ ( eq @ B @ C )
| ( lessf @ C @ A ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(39,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ A )
| ~ ( eq @ B @ C )
| ( lessf @ C @ A ) ),
inference(simp,[status(thm)],[32]) ).
thf(308,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ B @ A )
| ( lessf @ C @ A )
| ( ( eq @ y @ x )
!= ( eq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[207,39]) ).
thf(309,plain,
! [A: frac] :
( ~ ( lessf @ y @ A )
| ( lessf @ x @ A ) ),
inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( x ))]]) ).
thf(1128,plain,
! [A: frac] :
( ( lessf @ x @ A )
| ( ( lessf @ y @ z )
!= ( lessf @ y @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13,309]) ).
thf(1129,plain,
lessf @ x @ z,
inference(pattern_uni,[status(thm)],[1128:[bind(A,$thf( z ))]]) ).
thf(1141,plain,
$false,
inference(rewrite,[status(thm)],[1129,10]) ).
thf(1142,plain,
$false,
inference(simp,[status(thm)],[1141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM742^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 20 05:25:39 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.17/1.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.29 % [INFO] Parsing done (184ms).
% 1.51/1.31 % [INFO] Running in sequential loop mode.
% 2.12/1.73 % [INFO] nitpick registered as external prover.
% 2.12/1.74 % [INFO] Scanning for conjecture ...
% 2.40/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.43/1.86 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.43/1.89 % [INFO] Problem is higher-order (TPTP THF).
% 2.43/1.89 % [INFO] Type checking passed.
% 2.43/1.90 % [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 ...
% 13.29/4.07 % [INFO] Killing All external provers ...
% 13.29/4.08 % Time passed: 3533ms (effective reasoning time: 2763ms)
% 13.29/4.08 % 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)>
% 13.29/4.08 % Axioms used in derivation (6): satz50, satz37, l, satz45, satz38, k
% 13.29/4.08 % No. of inferences in proof: 39
% 13.29/4.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3533 ms resp. 2763 ms w/o parsing
% 13.29/4.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.29/4.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------