%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO011-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:05:18 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 198 ( 59 ~; 123 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(colinear_type,type,
colinear: ( $i * $i * $i ) > $o ).
tff(lower_dimension_point_3_type,type,
lower_dimension_point_3: $i ).
tff(lower_dimension_point_2_type,type,
lower_dimension_point_2: $i ).
tff(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(1,plain,
( colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
<=> colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
tff(3,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X) )
<=> ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z)
| between(Z,X,Y) ) )),
rewrite(( ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z)
| between(Z,X,Y) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
tff(10,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
<=> ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension3) ).
tff(16,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
<=> ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension2) ).
tff(19,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
<=> ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension1) ).
tff(22,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )
<=> ( between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,22,19,16,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO011-2 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.19/0.34 % Computer : n003.cluster.edu
% 0.19/0.34 % Model : x86_64 x86_64
% 0.19/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.34 % Memory : 8042.1875MB
% 0.19/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Thu Jun 19 14:02:54 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------