%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP022-2 : 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 05:06:52 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 67 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 89 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 11 ~; 7 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 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; 0-2 aty)
% Number of variables : 72 ( 65 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(identity_type,type,
identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(identity,X) = X )
<=> ( multiply(identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(identity,X) = X )
<=> ! [X: $i] : ( multiply(identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
tff(5,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(identity,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(identity,a) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = identity )
<=> ( multiply(inverse(X),X) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
tff(14,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( multiply(inverse(X),X) = identity ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(inverse(a)),inverse(a)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
multiply(inverse(inverse(a)),inverse(a)) = identity,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
identity = multiply(inverse(inverse(a)),inverse(a)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
multiply(identity,a) = multiply(multiply(inverse(inverse(a)),inverse(a)),a),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
multiply(multiply(inverse(inverse(a)),inverse(a)),a) = multiply(identity,a),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) )
| ( multiply(multiply(inverse(inverse(a)),inverse(a)),a) = multiply(inverse(inverse(a)),multiply(inverse(a),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
multiply(multiply(inverse(inverse(a)),inverse(a)),a) = multiply(inverse(inverse(a)),multiply(inverse(a),a)),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
multiply(inverse(inverse(a)),multiply(inverse(a),a)) = multiply(multiply(inverse(inverse(a)),inverse(a)),a),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ ! [X: $i] : ( multiply(identity,X) = X )
| ( multiply(identity,inverse(identity)) = inverse(identity) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
multiply(identity,inverse(identity)) = inverse(identity),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
^ [X: $i] :
refl(( ( multiply(X,inverse(X)) = identity )
<=> ( multiply(X,inverse(X)) = identity ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
tff(38,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [X: $i] : ( multiply(X,inverse(X)) = identity ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = identity )
| ( multiply(identity,inverse(identity)) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
multiply(identity,inverse(identity)) = identity,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
identity = multiply(identity,inverse(identity)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = identity )
| ( multiply(inverse(a),a) = identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
multiply(inverse(a),a) = identity,
inference(unit_resolution,[status(thm)],[44,16]) ).
tff(46,plain,
multiply(inverse(a),a) = inverse(identity),
inference(transitivity,[status(thm)],[45,43,33]) ).
tff(47,plain,
multiply(inverse(inverse(a)),multiply(inverse(a),a)) = multiply(inverse(inverse(a)),inverse(identity)),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
multiply(inverse(inverse(a)),inverse(identity)) = multiply(inverse(inverse(a)),multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
inverse(identity) = multiply(identity,inverse(identity)),
inference(symmetry,[status(thm)],[33]) ).
tff(50,plain,
inverse(identity) = identity,
inference(transitivity,[status(thm)],[49,42]) ).
tff(51,plain,
multiply(inverse(inverse(a)),inverse(identity)) = multiply(inverse(inverse(a)),identity),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
multiply(inverse(inverse(a)),identity) = multiply(inverse(inverse(a)),inverse(identity)),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
^ [X: $i] :
refl(( ( multiply(X,identity) = X )
<=> ( multiply(X,identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [X: $i] : ( multiply(X,identity) = X )
<=> ! [X: $i] : ( multiply(X,identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
! [X: $i] : ( multiply(X,identity) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
tff(57,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X: $i] : ( multiply(X,identity) = X ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [X: $i] : ( multiply(X,identity) = X )
| ( multiply(inverse(inverse(a)),identity) = inverse(inverse(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
multiply(inverse(inverse(a)),identity) = inverse(inverse(a)),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
inverse(inverse(a)) = multiply(inverse(inverse(a)),identity),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
inverse(inverse(a)) = a,
inference(transitivity,[status(thm)],[62,52,48,31,21,9]) ).
tff(64,plain,
( ( inverse(inverse(a)) != a )
<=> ( inverse(inverse(a)) != a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
inverse(inverse(a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_inverse_is_original) ).
tff(66,plain,
inverse(inverse(a)) != a,
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
$false,
inference(unit_resolution,[status(thm)],[66,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP022-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 15:32:03 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% See solution above
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------