%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP006-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:06:49 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 48 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 263 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 393 ( 188 ~; 181 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 10 ( 10 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; 2 con; 0-1 aty)
% Number of variables : 107 ( 99 !; 0 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(the_element_type,type,
the_element: $i ).
tff(identity_type,type,
identity: $i ).
tff(an_element_type,type,
an_element: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(( product(X,inverse(X),identity)
<=> product(X,inverse(X),identity) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
tff(5,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(the_element,inverse(the_element),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
product(the_element,inverse(the_element),identity),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( an_element(the_element)
<=> an_element(the_element) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
an_element(the_element),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_of_set) ).
tff(12,plain,
an_element(the_element),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
<=> ( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ an_element(X)
| ~ an_element(Y)
| ~ product(X,inverse(Y),Z) )
<=> ( ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ) )),
( ( ~ an_element(X)
| ~ an_element(Y)
| ~ product(X,inverse(Y),Z)
| an_element(Z) )
<=> ( ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X)
| an_element(Z) ) )),
rewrite(( ( ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X)
| an_element(Z) )
<=> ( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ) )),
( ( ~ an_element(X)
| ~ an_element(Y)
| ~ product(X,inverse(Y),Z)
| an_element(Z) )
<=> ( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ an_element(X)
| ~ an_element(Y)
| ~ product(X,inverse(Y),Z)
| an_element(Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ an_element(X)
| ~ an_element(Y)
| ~ product(X,inverse(Y),Z)
| an_element(Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
tff(19,plain,
! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element)
| ~ an_element(the_element) )
<=> ( an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element)
| ~ an_element(the_element) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element)
| ~ an_element(the_element) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element)
| ~ an_element(the_element) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(identity)
| ~ product(the_element,inverse(the_element),identity)
| ~ an_element(the_element) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
an_element(identity),
inference(unit_resolution,[status(thm)],[28,22,12,9]) ).
tff(30,plain,
( ~ an_element(inverse(the_element))
<=> ~ an_element(inverse(the_element)) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
~ an_element(inverse(the_element)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_inverse_is_in_set) ).
tff(32,plain,
~ an_element(inverse(the_element)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(inverse(the_element))
| ~ an_element(the_element)
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(inverse(the_element))
| ~ an_element(the_element)
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( an_element(inverse(the_element))
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(the_element)
| ~ an_element(identity) )
<=> ( an_element(inverse(the_element))
| ~ an_element(the_element)
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(inverse(the_element))
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(the_element)
| ~ an_element(identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(inverse(the_element))
| ~ an_element(the_element)
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(identity) ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(inverse(the_element))
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(the_element)
| ~ an_element(identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(inverse(the_element))
| ~ an_element(the_element)
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(identity) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(inverse(the_element))
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(the_element)
| ~ an_element(identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( an_element(Z)
| ~ product(X,inverse(Y),Z)
| ~ an_element(Y)
| ~ an_element(X) )
| an_element(inverse(the_element))
| ~ an_element(the_element)
| ~ product(identity,inverse(the_element),inverse(the_element))
| ~ an_element(identity) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
~ product(identity,inverse(the_element),inverse(the_element)),
inference(unit_resolution,[status(thm)],[38,22,12,32,29]) ).
tff(40,plain,
^ [X: $i] :
refl(( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
tff(44,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(the_element),inverse(the_element)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,46,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP006-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 15:31:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------