%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO012-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:00:08 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 32
% Syntax : Number of formulae : 80 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 110 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 44 ( 13 ~; 9 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 94 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(x_type,type,
x: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(multiplicative_identity_type,type,
multiplicative_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( multiply(multiplicative_identity,X) = X )
<=> ( multiply(multiplicative_identity,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
<=> ! [X: $i] : ( multiply(multiplicative_identity,X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
<=> ! [X: $i] : ( multiply(multiplicative_identity,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
tff(5,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(multiplicative_identity,X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
| ( multiply(multiplicative_identity,x) = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(multiplicative_identity,x) = x,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( add(X,inverse(X)) = multiplicative_identity )
<=> ( add(X,inverse(X)) = multiplicative_identity ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
tff(14,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
| ( add(inverse(x),inverse(inverse(x))) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
add(inverse(x),inverse(inverse(x))) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiply(add(inverse(x),inverse(inverse(x))),x) = multiply(multiplicative_identity,x),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(inverse(x),inverse(inverse(x))),x) = add(multiply(inverse(x),x),multiply(inverse(inverse(x)),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
multiply(add(inverse(x),inverse(inverse(x))),x) = add(multiply(inverse(x),x),multiply(inverse(inverse(x)),x)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
add(multiply(inverse(x),x),multiply(inverse(inverse(x)),x)) = multiply(add(inverse(x),inverse(inverse(x))),x),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(X,Y) = multiply(Y,X) )
<=> ( multiply(X,Y) = multiply(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
<=> ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
tff(34,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(x,inverse(inverse(x))) = multiply(inverse(inverse(x)),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
multiply(x,inverse(inverse(x))) = multiply(inverse(inverse(x)),x),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
^ [X: $i] :
refl(( ( multiply(inverse(X),X) = additive_identity )
<=> ( multiply(inverse(X),X) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = additive_identity ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $i] : ( multiply(inverse(X),X) = additive_identity )
<=> ! [X: $i] : ( multiply(inverse(X),X) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [X: $i] : ( multiply(inverse(X),X) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse2) ).
tff(43,plain,
! [X: $i] : ( multiply(inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i] : ( multiply(inverse(X),X) = additive_identity ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i] : ( multiply(inverse(X),X) = additive_identity ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [X: $i] : ( multiply(inverse(X),X) = additive_identity )
| ( multiply(inverse(x),x) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
multiply(inverse(x),x) = additive_identity,
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
additive_identity = multiply(inverse(x),x),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
^ [X: $i] :
refl(( ( multiply(X,inverse(X)) = additive_identity )
<=> ( multiply(X,inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
tff(53,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
| ( multiply(inverse(x),inverse(inverse(x))) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
multiply(inverse(x),inverse(inverse(x))) = additive_identity,
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
multiply(inverse(x),inverse(inverse(x))) = multiply(inverse(x),x),
inference(transitivity,[status(thm)],[57,48]) ).
tff(59,plain,
add(multiply(inverse(x),inverse(inverse(x))),multiply(x,inverse(inverse(x)))) = add(multiply(inverse(x),x),multiply(inverse(inverse(x)),x)),
inference(monotonicity,[status(thm)],[58,38]) ).
tff(60,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(inverse(x),x),inverse(inverse(x))) = add(multiply(inverse(x),inverse(inverse(x))),multiply(x,inverse(inverse(x)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
multiply(add(inverse(x),x),inverse(inverse(x))) = add(multiply(inverse(x),inverse(inverse(x))),multiply(x,inverse(inverse(x)))),
inference(unit_resolution,[status(thm)],[60,26]) ).
tff(62,plain,
^ [X: $i] :
refl(( ( add(inverse(X),X) = multiplicative_identity )
<=> ( add(inverse(X),X) = multiplicative_identity ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
<=> ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
<=> ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse2) ).
tff(66,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
| ( add(inverse(x),x) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
add(inverse(x),x) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
multiplicative_identity = add(inverse(x),x),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
multiply(multiplicative_identity,inverse(inverse(x))) = multiply(add(inverse(x),x),inverse(inverse(x))),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [X: $i] : ( multiply(multiplicative_identity,X) = X )
| ( multiply(multiplicative_identity,inverse(inverse(x))) = inverse(inverse(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
multiply(multiplicative_identity,inverse(inverse(x))) = inverse(inverse(x)),
inference(unit_resolution,[status(thm)],[73,7]) ).
tff(75,plain,
inverse(inverse(x)) = multiply(multiplicative_identity,inverse(inverse(x))),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
inverse(inverse(x)) = x,
inference(transitivity,[status(thm)],[75,72,61,59,29,19,9]) ).
tff(77,plain,
( ( inverse(inverse(x)) != x )
<=> ( inverse(inverse(x)) != x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
tff(79,plain,
inverse(inverse(x)) != x,
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
$false,
inference(unit_resolution,[status(thm)],[79,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO012-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 11:37:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------