TSTP Solution File: NUM746^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM746^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 10:45:28 EDT 2024
% Result : Theorem 19.28s 4.02s
% Output : Refutation 19.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 5 unt; 6 typ; 0 def)
% Number of atoms : 140 ( 9 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 382 ( 54 ~; 43 |; 0 &; 254 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 61 ( 0 ^ 61 !; 0 ?; 61 :)
% 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(3,axiom,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(12,plain,
( ~ ( lessf @ x @ y )
=> ( eq @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
( ( lessf @ x @ y )
| ( eq @ x @ y ) ),
inference(cnf,[status(esa)],[12]) ).
thf(4,axiom,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(14,plain,
( ~ ( lessf @ y @ z )
=> ( eq @ y @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
( ( lessf @ y @ z )
| ( eq @ y @ z ) ),
inference(cnf,[status(esa)],[14]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).
thf(17,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac] :
( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( eq @ A @ C ) ),
inference(cnf,[status(esa)],[18]) ).
thf(1,conjecture,
( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz52) ).
thf(2,negated_conjecture,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( ~ ( lessf @ x @ z )
=> ( eq @ x @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
~ ( eq @ x @ z ),
inference(cnf,[status(esa)],[9]) ).
thf(34,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( ( eq @ A @ C )
!= ( eq @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[19,10]) ).
thf(35,plain,
! [A: frac] :
( ~ ( eq @ x @ A )
| ~ ( eq @ A @ z ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).
thf(46,plain,
! [A: frac] :
( ~ ( eq @ x @ A )
| ~ ( eq @ A @ z ) ),
inference(simp,[status(thm)],[35]) ).
thf(71,plain,
! [A: frac] :
( ( lessf @ x @ y )
| ~ ( eq @ A @ z )
| ( ( eq @ x @ y )
!= ( eq @ x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[13,46]) ).
thf(72,plain,
( ( lessf @ x @ y )
| ~ ( eq @ y @ z ) ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( y ))]]) ).
thf(102,plain,
( ( lessf @ y @ z )
| ( lessf @ x @ y )
| ( ( eq @ y @ z )
!= ( eq @ y @ z ) ) ),
inference(paramod_ordered,[status(thm)],[15,72]) ).
thf(103,plain,
( ( lessf @ y @ z )
| ( lessf @ x @ y ) ),
inference(pattern_uni,[status(thm)],[102:[]]) ).
thf(8,axiom,
! [A: frac,B: frac,C: frac] :
( ( ~ ( lessf @ A @ B )
=> ( eq @ A @ B ) )
=> ( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz51a) ).
thf(24,plain,
! [A: frac,B: frac,C: frac] :
( ( ~ ( lessf @ A @ B )
=> ( eq @ A @ B ) )
=> ( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,plain,
! [A: frac,B: frac] :
( ( ~ ( lessf @ A @ B )
=> ( eq @ A @ B ) )
=> ! [C: frac] :
( ( lessf @ B @ C )
=> ( lessf @ A @ C ) ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(27,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnf,[status(esa)],[25]) ).
thf(322,plain,
! [C: frac,B: frac,A: frac] :
( ( lessf @ x @ y )
| ~ ( eq @ A @ B )
| ( lessf @ A @ C )
| ( ( lessf @ y @ z )
!= ( lessf @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[103,27]) ).
thf(323,plain,
! [A: frac] :
( ( lessf @ x @ y )
| ~ ( eq @ A @ y )
| ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(4339,plain,
! [A: frac] :
( ( lessf @ x @ y )
| ( lessf @ A @ z )
| ( ( eq @ x @ y )
!= ( eq @ A @ y ) ) ),
inference(paramod_ordered,[status(thm)],[13,323]) ).
thf(4340,plain,
( ( lessf @ x @ y )
| ( lessf @ x @ z ) ),
inference(pattern_uni,[status(thm)],[4339:[bind(A,$thf( x ))]]) ).
thf(11,plain,
~ ( lessf @ x @ z ),
inference(cnf,[status(esa)],[9]) ).
thf(4352,plain,
( ( lessf @ x @ y )
| $false ),
inference(rewrite,[status(thm)],[4340,11]) ).
thf(4353,plain,
lessf @ x @ y,
inference(simp,[status(thm)],[4352]) ).
thf(7,axiom,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( ( ~ ( lessf @ B @ C )
=> ( eq @ B @ C ) )
=> ( lessf @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz51b) ).
thf(20,plain,
! [A: frac,B: frac,C: frac] :
( ( lessf @ A @ B )
=> ( ( ~ ( lessf @ B @ C )
=> ( eq @ B @ C ) )
=> ( lessf @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,plain,
! [A: frac,B: frac] :
( ( lessf @ A @ B )
=> ! [C: frac] :
( ( ~ ( lessf @ B @ C )
=> ( eq @ B @ C ) )
=> ( lessf @ A @ C ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( eq @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnf,[status(esa)],[21]) ).
thf(68,plain,
! [C: frac,B: frac,A: frac] :
( ( lessf @ y @ z )
| ~ ( lessf @ A @ B )
| ( lessf @ A @ C )
| ( ( eq @ y @ z )
!= ( eq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,22]) ).
thf(69,plain,
! [A: frac] :
( ( lessf @ y @ z )
| ~ ( lessf @ A @ y )
| ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(4384,plain,
! [A: frac] :
( ( lessf @ y @ z )
| ( lessf @ A @ z )
| ( ( lessf @ x @ y )
!= ( lessf @ A @ y ) ) ),
inference(paramod_ordered,[status(thm)],[4353,69]) ).
thf(4385,plain,
( ( lessf @ y @ z )
| ( lessf @ x @ z ) ),
inference(pattern_uni,[status(thm)],[4384:[bind(A,$thf( x ))]]) ).
thf(23,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( lessf @ A @ C ) ),
inference(cnf,[status(esa)],[21]) ).
thf(186,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( lessf @ A @ B )
| ~ ( lessf @ B @ C )
| ( ( lessf @ A @ C )
!= ( lessf @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[23,11]) ).
thf(187,plain,
! [A: frac] :
( ~ ( lessf @ x @ A )
| ~ ( lessf @ A @ z ) ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).
thf(192,plain,
! [A: frac] :
( ~ ( lessf @ x @ A )
| ~ ( lessf @ A @ z ) ),
inference(simp,[status(thm)],[187]) ).
thf(4394,plain,
! [A: frac] :
( ~ ( lessf @ A @ z )
| ( ( lessf @ x @ y )
!= ( lessf @ x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[4353,192]) ).
thf(4395,plain,
~ ( lessf @ y @ z ),
inference(pattern_uni,[status(thm)],[4394:[bind(A,$thf( y ))]]) ).
thf(4651,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[4385,11,4395]) ).
thf(4652,plain,
$false,
inference(simp,[status(thm)],[4651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM746^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n028.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 19:25:54 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (109ms).
% 1.20/0.96 % [INFO] Running in sequential loop mode.
% 1.46/1.15 % [INFO] nitpick registered as external prover.
% 1.46/1.16 % [INFO] Scanning for conjecture ...
% 1.69/1.20 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.69/1.22 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.81/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.85/1.24 % [INFO] Type checking passed.
% 1.85/1.24 % [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 ...
% 19.28/4.00 % [INFO] Killing All external provers ...
% 19.28/4.01 % Time passed: 3484ms (effective reasoning time: 3043ms)
% 19.28/4.01 % 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)>
% 19.28/4.02 % Axioms used in derivation (5): satz51b, satz39, satz51a, l, k
% 19.28/4.02 % No. of inferences in proof: 48
% 19.28/4.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3484 ms resp. 3043 ms w/o parsing
% 19.28/4.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.28/4.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------