TSTP Solution File: GEO067-2 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : GEO067-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 10:31:06 EDT 2024
% Result : Unsatisfiable 168.06s 32.20s
% Output : Refutation 168.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 46 ( 11 unt; 7 typ; 0 def)
% Number of atoms : 96 ( 17 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 370 ( 55 ~; 49 |; 0 &; 266 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 98 ( 0 ^ 98 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(colinear_type,type,
colinear: $i > $i > $i > $o ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(z_type,type,
z: $i ).
thf(equidistant_type,type,
equidistant: $i > $i > $i > $i > $o ).
thf(extension_type,type,
extension: $i > $i > $i > $i > $i ).
thf(between_type,type,
between: $i > $i > $i > $o ).
thf(1,negated_conjecture,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_1) ).
thf(25,plain,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(27,plain,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ( x = y ) ),
inference(cnf,[status(esa)],[25]) ).
thf(28,plain,
( ( y = x )
| ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(2,negated_conjecture,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ~ ( colinear @ x @ z @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_2) ).
thf(26,plain,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ~ ( colinear @ x @ z @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,plain,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ~ ( colinear @ x @ z @ y ) ),
inference(cnf,[status(esa)],[26]) ).
thf(121,plain,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ~ ( colinear @ x @ z @ x )
| ( y != y ) ),
inference(paramod_ordered,[status(thm)],[28,29]) ).
thf(122,plain,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ~ ( colinear @ x @ z @ x ) ),
inference(pattern_uni,[status(thm)],[121:[]]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( equidistant @ A @ B @ C @ C ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(1869,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ( ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D )
!= ( equidistant @ E @ F @ G @ G ) ) ),
inference(paramod_ordered,[status(thm)],[36,34]) ).
thf(1870,plain,
! [C: $i,B: $i,A: $i] :
( ( extension @ A @ B @ C @ C )
= B ),
inference(pattern_uni,[status(thm)],[1869:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( K )),bind(D,$thf( K )),bind(E,$thf( I )),bind(F,$thf( extension @ H @ I @ K @ K )),bind(G,$thf( K ))]]) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ( extension @ A @ B @ C @ C )
= B ),
inference(simp,[status(thm)],[1870]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2279,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( between @ D @ E @ B )
| ( ( extension @ A @ B @ C @ C )
!= ( extension @ D @ E @ F @ G ) ) ),
inference(paramod_ordered,[status(thm)],[2190,69]) ).
thf(2280,plain,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
inference(pattern_uni,[status(thm)],[2279:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( C )),bind(G,$thf( C ))]]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
inference(cnf,[status(esa)],[74]) ).
thf(45426,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( colinear @ C @ D @ E )
| ( ( between @ A @ B @ B )
!= ( between @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2280,75]) ).
thf(45427,plain,
! [B: $i,A: $i] : ( colinear @ A @ B @ B ),
inference(pattern_uni,[status(thm)],[45426:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( B ))]]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity3) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
inference(cnf,[status(esa)],[70]) ).
thf(42662,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( colinear @ D @ E @ C )
| ( ( between @ A @ B @ B )
!= ( between @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2280,71]) ).
thf(42663,plain,
! [B: $i,A: $i] : ( colinear @ B @ B @ A ),
inference(pattern_uni,[status(thm)],[42662:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( B ))]]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity2) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
inference(cnf,[status(esa)],[76]) ).
thf(48636,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( colinear @ E @ C @ D )
| ( ( between @ A @ B @ B )
!= ( between @ C @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[2280,77]) ).
thf(48637,plain,
! [B: $i,A: $i] : ( colinear @ B @ A @ B ),
inference(pattern_uni,[status(thm)],[48636:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( B ))]]) ).
thf(68604,plain,
( ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[122,45427,42663,48637]) ).
thf(68605,plain,
$false,
inference(simp,[status(thm)],[68604]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO067-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue May 7 01:34:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.95/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/1.02 % [INFO] Parsing done (137ms).
% 1.32/1.03 % [INFO] Running in sequential loop mode.
% 1.88/1.26 % [INFO] nitpick registered as external prover.
% 1.88/1.26 % [INFO] Scanning for conjecture ...
% 2.00/1.32 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 2.19/1.36 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.28/1.39 % [INFO] Problem is propositional (TPTP CNF).
% 2.28/1.40 % [INFO] Type checking passed.
% 2.28/1.40 % [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 ...
% 168.06/32.19 % [INFO] Killing All external provers ...
% 168.06/32.20 % Time passed: 31653ms (effective reasoning time: 31158ms)
% 168.06/32.20 % 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)>
% 168.06/32.20 % Axioms used in derivation (6): colinearity3, colinearity1, segment_construction2, segment_construction1, identity_for_equidistance, colinearity2
% 168.06/32.20 % No. of inferences in proof: 39
% 168.06/32.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 31653 ms resp. 31158 ms w/o parsing
% 168.06/32.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 168.06/32.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------