TSTP Solution File: NUM755_8 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM755_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 10:45:32 EDT 2024
% Result : Theorem 3.67s 1.96s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 42 ( 10 unt; 8 typ; 0 def)
% Number of atoms : 84 ( 5 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 308 ( 44 ~; 15 |; 0 &; 224 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 ^ 58 !; 0 ?; 58 :)
% 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(moref_type,type,
moref: frac > frac > $o ).
thf(pf_type,type,
pf: frac > frac > frac ).
thf(eq_type,type,
eq: frac > frac > $o ).
thf(lessf_type,type,
lessf: frac > frac > $o ).
thf(8,axiom,
! [A: frac,B: frac] :
( ~ ( eq @ A @ B )
=> ( ~ ( moref @ A @ B )
=> ( lessf @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41a) ).
thf(25,plain,
! [A: frac,B: frac] :
( ~ ( eq @ A @ B )
=> ( ~ ( moref @ A @ B )
=> ( lessf @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,plain,
! [B: frac,A: frac] :
( ( eq @ A @ B )
| ( moref @ A @ B )
| ( lessf @ A @ B ) ),
inference(cnf,[status(esa)],[25]) ).
thf(7,axiom,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62c) ).
thf(22,plain,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,plain,
! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ! [C: frac] : ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(miniscope,[status(thm)],[22]) ).
thf(24,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(3,axiom,
moref @ ( pf @ x @ z ) @ ( pf @ y @ z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(10,plain,
moref @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: frac,B: frac] :
~ ( ( ( eq @ A @ B )
=> ~ ( moref @ A @ B ) )
=> ~ ~ ( ( ( moref @ A @ B )
=> ~ ( lessf @ A @ B ) )
=> ~ ( ( lessf @ A @ B )
=> ~ ( eq @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41b) ).
thf(12,plain,
! [A: frac,B: frac] :
~ ( ( ( eq @ A @ B )
=> ~ ( moref @ A @ B ) )
=> ( ( ( moref @ A @ B )
=> ~ ( lessf @ A @ B ) )
=> ~ ( ( lessf @ A @ B )
=> ~ ( eq @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,plain,
~ ( ! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ~ ( moref @ A @ B ) )
=> ( ! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ~ ( lessf @ A @ B ) )
=> ~ ! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ~ ( eq @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(15,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( lessf @ A @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(18,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( lessf @ A @ B ) ),
inference(simp,[status(thm)],[15]) ).
thf(33,plain,
! [B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= ( moref @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,18]) ).
thf(34,plain,
~ ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( pf @ x @ z )),bind(B,$thf( pf @ y @ z ))]]) ).
thf(60,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ( ( lessf @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
!= ( lessf @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,34]) ).
thf(61,plain,
~ ( lessf @ x @ y ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(68,plain,
! [B: frac,A: frac] :
( ( eq @ A @ B )
| ( moref @ A @ B )
| ( ( lessf @ A @ B )
!= ( lessf @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[26,61]) ).
thf(69,plain,
( ( eq @ x @ y )
| ( moref @ x @ y ) ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(1,conjecture,
moref @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63a) ).
thf(2,negated_conjecture,
~ ( moref @ x @ y ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( moref @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62b) ).
thf(19,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac] : ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(16,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( moref @ A @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(29,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= ( moref @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,16]) ).
thf(30,plain,
~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( pf @ x @ z )),bind(B,$thf( pf @ y @ z ))]]) ).
thf(41,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
!= ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,30]) ).
thf(42,plain,
~ ( eq @ x @ y ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(85,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[69,9,42]) ).
thf(86,plain,
$false,
inference(simp,[status(thm)],[85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM755_8 : TPTP v8.1.2. Released v8.0.0.
% 0.07/0.14 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 6 19:25:39 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.83/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.11/0.95 % [INFO] Parsing done (135ms).
% 1.11/0.96 % [INFO] Running in sequential loop mode.
% 1.57/1.21 % [INFO] nitpick registered as external prover.
% 1.57/1.21 % [INFO] Scanning for conjecture ...
% 1.65/1.28 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.65/1.30 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.65/1.33 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.90/1.33 % [INFO] Type checking passed.
% 1.90/1.33 % [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 ...
% 3.67/1.96 % [INFO] Killing All external provers ...
% 3.67/1.96 % Time passed: 1494ms (effective reasoning time: 991ms)
% 3.67/1.96 % 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)>
% 3.67/1.96 % Axioms used in derivation (5): satz41b, m, satz62b, satz62c, satz41a
% 3.67/1.96 % No. of inferences in proof: 34
% 3.67/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1494 ms resp. 991 ms w/o parsing
% 3.67/2.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.67/2.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------