%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : BOO012-4 : TPTP v9.0.0. Released v1.1.0.
% 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 05:00:08 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 89 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 119 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 47 ( 16 ~; 12 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 6 ( 6 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 : 109 ( 99 !; 0 ?; 109 :)
% 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(X,multiplicative_identity) = X )
<=> ( multiply(X,multiplicative_identity) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
<=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
<=> ! [X: $i] : ( multiply(X,multiplicative_identity) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
tff(5,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( multiply(X,multiplicative_identity) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(x,multiplicative_identity) = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
multiply(x,multiplicative_identity) = 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/BOO004-0.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(x,inverse(x)) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
add(x,inverse(x)) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiplicative_identity = add(x,inverse(x)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
multiply(multiplicative_identity,multiplicative_identity) = multiply(add(x,inverse(x)),add(x,inverse(x))),
inference(monotonicity,[status(thm)],[19,19]) ).
tff(21,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(multiplicative_identity,multiplicative_identity) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
multiply(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[21,7]) ).
tff(23,plain,
multiplicative_identity = multiply(multiplicative_identity,multiplicative_identity),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
multiplicative_identity = multiply(add(x,inverse(x)),add(x,inverse(x))),
inference(transitivity,[status(thm)],[23,20]) ).
tff(25,plain,
multiply(x,multiplicative_identity) = multiply(x,multiply(add(x,inverse(x)),add(x,inverse(x)))),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
multiply(x,multiply(add(x,inverse(x)),add(x,inverse(x)))) = multiply(x,multiplicative_identity),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
| ( add(inverse(x),inverse(inverse(x))) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
add(inverse(x),inverse(inverse(x))) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[27,16]) ).
tff(29,plain,
add(inverse(x),inverse(inverse(x))) = multiply(add(x,inverse(x)),add(x,inverse(x))),
inference(transitivity,[status(thm)],[28,23,20]) ).
tff(30,plain,
multiply(x,add(inverse(x),inverse(inverse(x)))) = multiply(x,multiply(add(x,inverse(x)),add(x,inverse(x)))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
tff(35,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(x,add(inverse(x),inverse(inverse(x)))) = add(multiply(x,inverse(x)),multiply(x,inverse(inverse(x)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
multiply(x,add(inverse(x),inverse(inverse(x)))) = add(multiply(x,inverse(x)),multiply(x,inverse(inverse(x)))),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
add(multiply(x,inverse(x)),multiply(x,inverse(inverse(x)))) = multiply(x,add(inverse(x),inverse(inverse(x)))),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
^ [Y: $i,X: $i] :
refl(( ( multiply(X,Y) = multiply(Y,X) )
<=> ( multiply(X,Y) = multiply(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(42,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)],[41]) ).
tff(43,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(44,axiom,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
tff(45,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(inverse(inverse(x)),x) = multiply(x,inverse(inverse(x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
multiply(inverse(inverse(x)),x) = multiply(x,inverse(inverse(x))),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
^ [X: $i] :
refl(( ( multiply(X,inverse(X)) = additive_identity )
<=> ( multiply(X,inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
tff(54,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
| ( multiply(x,inverse(x)) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
multiply(x,inverse(x)) = additive_identity,
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
additive_identity = multiply(x,inverse(x)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
| ( multiply(inverse(x),inverse(inverse(x))) = additive_identity ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
multiply(inverse(x),inverse(inverse(x))) = additive_identity,
inference(unit_resolution,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(inverse(x),inverse(inverse(x))) = multiply(inverse(inverse(x)),inverse(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
multiply(inverse(x),inverse(inverse(x))) = multiply(inverse(inverse(x)),inverse(x)),
inference(unit_resolution,[status(thm)],[62,47]) ).
tff(64,plain,
multiply(inverse(inverse(x)),inverse(x)) = multiply(inverse(x),inverse(inverse(x))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
multiply(inverse(inverse(x)),inverse(x)) = multiply(x,inverse(x)),
inference(transitivity,[status(thm)],[64,61,59]) ).
tff(66,plain,
add(multiply(inverse(inverse(x)),inverse(x)),multiply(inverse(inverse(x)),x)) = add(multiply(x,inverse(x)),multiply(x,inverse(inverse(x)))),
inference(monotonicity,[status(thm)],[65,49]) ).
tff(67,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(inverse(inverse(x)),add(inverse(x),x)) = add(multiply(inverse(inverse(x)),inverse(x)),multiply(inverse(inverse(x)),x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
multiply(inverse(inverse(x)),add(inverse(x),x)) = add(multiply(inverse(inverse(x)),inverse(x)),multiply(inverse(inverse(x)),x)),
inference(unit_resolution,[status(thm)],[67,37]) ).
tff(69,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
tff(73,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(x,inverse(x)) = add(inverse(x),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
add(x,inverse(x)) = add(inverse(x),x),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
multiply(add(x,inverse(x)),add(x,inverse(x))) = multiply(multiplicative_identity,multiplicative_identity),
inference(symmetry,[status(thm)],[20]) ).
tff(79,plain,
multiply(add(x,inverse(x)),add(x,inverse(x))) = add(inverse(x),x),
inference(transitivity,[status(thm)],[78,22,19,77]) ).
tff(80,plain,
multiply(inverse(inverse(x)),multiply(add(x,inverse(x)),add(x,inverse(x)))) = multiply(inverse(inverse(x)),add(inverse(x),x)),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
multiply(inverse(inverse(x)),multiplicative_identity) = multiply(inverse(inverse(x)),multiply(add(x,inverse(x)),add(x,inverse(x)))),
inference(monotonicity,[status(thm)],[24]) ).
tff(82,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(inverse(inverse(x)),multiplicative_identity) = inverse(inverse(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
multiply(inverse(inverse(x)),multiplicative_identity) = inverse(inverse(x)),
inference(unit_resolution,[status(thm)],[82,7]) ).
tff(84,plain,
inverse(inverse(x)) = multiply(inverse(inverse(x)),multiplicative_identity),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
inverse(inverse(x)) = x,
inference(transitivity,[status(thm)],[84,81,80,68,66,40,30,26,9]) ).
tff(86,plain,
( ( inverse(inverse(x)) != x )
<=> ( inverse(inverse(x)) != x ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
tff(88,plain,
inverse(inverse(x)) != x,
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
$false,
inference(unit_resolution,[status(thm)],[88,85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO012-4 : TPTP v9.0.0. Released v1.1.0.
% 0.06/0.11 % 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 11:37:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------