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 ... 
%------------------------------------------------------------------------------