%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP023-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:06:52 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 40 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 35 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 130 ( 61 ~; 53 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 88 ( 78 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
( ( identity = inverse(identity) )
<=> ( inverse(identity) = identity ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( inverse(identity) = identity )
<=> ( identity = inverse(identity) ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( inverse(identity) != identity )
<=> ( identity != inverse(identity) ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( ( inverse(identity) != identity )
<=> ( inverse(identity) != identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
inverse(identity) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_id_is_id) ).
tff(6,plain,
inverse(identity) != identity,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
identity != inverse(identity),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
^ [X: $i] :
refl(( product(X,inverse(X),identity)
<=> product(X,inverse(X),identity) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [X: $i] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
tff(12,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(identity,inverse(identity),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
product(identity,inverse(identity),identity),
inference(unit_resolution,[status(thm)],[15,14]) ).
tff(17,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
tff(23,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( identity = inverse(identity) )
| ~ product(identity,inverse(identity),inverse(identity))
| ~ product(identity,inverse(identity),identity) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( identity = inverse(identity) )
| ~ product(identity,inverse(identity),inverse(identity))
| ~ product(identity,inverse(identity),identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( identity = inverse(identity) )
| ~ product(identity,inverse(identity),inverse(identity))
| ~ product(identity,inverse(identity),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( Z = W )
| ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| ( identity = inverse(identity) )
| ~ product(identity,inverse(identity),inverse(identity))
| ~ product(identity,inverse(identity),identity) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ( identity = inverse(identity) )
| ~ product(identity,inverse(identity),inverse(identity)) ),
inference(unit_resolution,[status(thm)],[29,26,16]) ).
tff(31,plain,
~ product(identity,inverse(identity),inverse(identity)),
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
^ [X: $i] :
refl(( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
tff(36,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(identity),inverse(identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
$false,
inference(unit_resolution,[status(thm)],[39,38,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP023-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 15:29:41 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% See solution above
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------