%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO079-1 : TPTP v9.0.0. Released v1.1.0.
% 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 05:05:31 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 28 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 103 ( 49 ~; 44 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-6 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 104 ( 96 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(parallel_type,type,
parallel: ( $i * $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(a_type,type,
a: $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(eq_type,type,
eq: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(trapezoid_type,type,
trapezoid: ( $i * $i * $i * $i ) > $o ).
tff(1,plain,
( ~ eq(a,c,b,c,a,d)
<=> ~ eq(a,c,b,c,a,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ eq(a,c,b,c,a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_angles_equal) ).
tff(3,plain,
~ eq(a,c,b,c,a,d),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) )
<=> ( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interior_angles_are_equal) ).
tff(8,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) )
| ~ parallel(b,c,a,d)
| eq(a,c,b,c,a,d) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) )
| ~ parallel(b,c,a,d)
| eq(a,c,b,c,a,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) )
| ~ parallel(b,c,a,d)
| eq(a,c,b,c,a,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ parallel(U,V,X,Y)
| eq(X,V,U,V,X,Y) )
| ~ parallel(b,c,a,d)
| eq(a,c,b,c,a,d) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ parallel(b,c,a,d),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( trapezoid(a,b,c,d)
<=> trapezoid(a,b,c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
trapezoid(a,b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_trapezoid) ).
tff(17,plain,
trapezoid(a,b,c,d),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) )
<=> ( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trapezoid_definition) ).
tff(22,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) )
| ~ trapezoid(a,b,c,d)
| parallel(b,c,a,d) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) )
| ~ trapezoid(a,b,c,d)
| parallel(b,c,a,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) )
| ~ trapezoid(a,b,c,d)
| parallel(b,c,a,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ trapezoid(U,V,W,X)
| parallel(V,W,U,X) )
| ~ trapezoid(a,b,c,d)
| parallel(b,c,a,d) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
$false,
inference(unit_resolution,[status(thm)],[27,24,17,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO079-1 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:16:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------