%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO056-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:05:27 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 29 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 2 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 50 ( 45 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(reflection_type,type,
reflection: ( $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(extension_type,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
( ( u = v )
<=> ( u = v ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
u = v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_equals_v) ).
tff(3,plain,
u = v,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
reflection(u,v) = reflection(v,v),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
reflection(v,v) = reflection(u,v),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
^ [V: $i,U: $i] :
refl(( ( reflection(U,V) = extension(U,V,U,V) )
<=> ( reflection(U,V) = extension(U,V,U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
<=> ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
<=> ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-2.ax',reflection) ).
tff(10,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ~ ! [V: $i,U: $i] : ( reflection(U,V) = extension(U,V,U,V) )
| ( reflection(v,v) = extension(v,v,v,v) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(14,plain,
reflection(v,v) = extension(v,v,v,v),
inference(unit_resolution,[status(thm)],[13,12]) ).
tff(15,plain,
extension(v,v,v,v) = reflection(v,v),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( V = extension(U,V,W,W) )
<=> ( V = extension(U,V,W,W) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) )
<=> ! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) )
<=> ! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
tff(20,plain,
! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [W: $i,V: $i,U: $i] : ( V = extension(U,V,W,W) )
| ( v = extension(v,v,v,v) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
v = extension(v,v,v,v),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
v = reflection(u,v),
inference(transitivity,[status(thm)],[24,15,5]) ).
tff(26,plain,
( ( v != reflection(u,v) )
<=> ( v != reflection(u,v) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
v != reflection(u,v),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_reflection) ).
tff(28,plain,
v != reflection(u,v),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO056-3 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:12:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% See solution above
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------