TSTP Solution File: BOO012-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : BOO012-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Tue Sep 6 17:18:41 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 46
% Syntax : Number of formulae : 111 ( 75 unt; 6 typ; 0 def)
% Number of atoms : 153 ( 143 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 54 ( 15 ~; 11 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 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 : 162 ( 146 !; 0 ?; 162 :)
% 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/BOO003-0.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(inverse(X),X) = multiplicative_identity )
<=> ( add(inverse(X),X) = multiplicative_identity ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
<=> ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
<=> ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse2) ).
tff(14,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( add(inverse(X),X) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( add(inverse(X),X) = multiplicative_identity )
| ( add(inverse(inverse(x)),inverse(x)) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
add(inverse(inverse(x)),inverse(x)) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
multiplicative_identity = add(inverse(inverse(x)),inverse(x)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
multiply(x,multiplicative_identity) = multiply(x,add(inverse(inverse(x)),inverse(x))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
multiply(x,add(inverse(inverse(x)),inverse(x))) = multiply(x,multiplicative_identity),
inference(symmetry,[status(thm)],[20]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,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/BOO003-0.ax',distributivity4) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) )
| ( multiply(x,add(inverse(inverse(x)),inverse(x))) = add(multiply(x,inverse(inverse(x))),multiply(x,inverse(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
multiply(x,add(inverse(inverse(x)),inverse(x))) = add(multiply(x,inverse(inverse(x))),multiply(x,inverse(x))),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
add(multiply(x,inverse(inverse(x))),multiply(x,inverse(x))) = multiply(x,add(inverse(inverse(x)),inverse(x))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ( multiply(X,inverse(X)) = additive_identity )
<=> ( multiply(X,inverse(X)) = additive_identity ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
<=> ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
tff(36,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] : ( multiply(X,inverse(X)) = additive_identity ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
| ( multiply(inverse(x),inverse(inverse(x))) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
multiply(inverse(x),inverse(inverse(x))) = additive_identity,
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
additive_identity = multiply(inverse(x),inverse(inverse(x))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [X: $i] : ( multiply(X,inverse(X)) = additive_identity )
| ( multiply(x,inverse(x)) = additive_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
multiply(x,inverse(x)) = additive_identity,
inference(unit_resolution,[status(thm)],[42,38]) ).
tff(44,plain,
multiply(x,inverse(x)) = multiply(inverse(x),inverse(inverse(x))),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
add(multiply(x,inverse(inverse(x))),multiply(x,inverse(x))) = add(multiply(x,inverse(inverse(x))),multiply(inverse(x),inverse(inverse(x)))),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
add(multiply(x,inverse(inverse(x))),multiply(inverse(x),inverse(inverse(x)))) = add(multiply(x,inverse(inverse(x))),multiply(x,inverse(x))),
inference(symmetry,[status(thm)],[45]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,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(51,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) )
| ( multiply(add(x,inverse(x)),inverse(inverse(x))) = add(multiply(x,inverse(inverse(x))),multiply(inverse(x),inverse(inverse(x)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
multiply(add(x,inverse(x)),inverse(inverse(x))) = add(multiply(x,inverse(inverse(x))),multiply(inverse(x),inverse(inverse(x)))),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ~ ! [X: $i] : ( multiply(X,multiplicative_identity) = X )
| ( multiply(add(inverse(inverse(x)),x),multiplicative_identity) = add(inverse(inverse(x)),x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
multiply(add(inverse(inverse(x)),x),multiplicative_identity) = add(inverse(inverse(x)),x),
inference(unit_resolution,[status(thm)],[56,7]) ).
tff(58,plain,
multiply(add(inverse(inverse(x)),x),add(inverse(inverse(x)),inverse(x))) = multiply(add(inverse(inverse(x)),x),multiplicative_identity),
inference(monotonicity,[status(thm)],[18]) ).
tff(59,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
<=> ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
tff(63,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) )
| ( add(inverse(inverse(x)),multiply(x,inverse(x))) = multiply(add(inverse(inverse(x)),x),add(inverse(inverse(x)),inverse(x))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
add(inverse(inverse(x)),multiply(x,inverse(x))) = multiply(add(inverse(inverse(x)),x),add(inverse(inverse(x)),inverse(x))),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
additive_identity = multiply(x,inverse(x)),
inference(symmetry,[status(thm)],[43]) ).
tff(69,plain,
add(inverse(inverse(x)),additive_identity) = add(inverse(inverse(x)),multiply(x,inverse(x))),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
^ [X: $i] :
refl(
( ( add(X,additive_identity) = X )
<=> ( add(X,additive_identity) = X ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X: $i] : ( add(X,additive_identity) = X )
<=> ! [X: $i] : ( add(X,additive_identity) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
! [X: $i] : ( add(X,additive_identity) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
tff(74,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [X: $i] : ( add(X,additive_identity) = X ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [X: $i] : ( add(X,additive_identity) = X )
| ( add(inverse(inverse(x)),additive_identity) = inverse(inverse(x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
add(inverse(inverse(x)),additive_identity) = inverse(inverse(x)),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
inverse(inverse(x)) = add(inverse(inverse(x)),additive_identity),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
inverse(inverse(x)) = add(inverse(inverse(x)),x),
inference(transitivity,[status(thm)],[79,69,67,58,57]) ).
tff(81,plain,
^ [X: $i] :
refl(
( ( add(X,inverse(X)) = multiplicative_identity )
<=> ( add(X,inverse(X)) = multiplicative_identity ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
<=> ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
tff(85,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( ~ ! [X: $i] : ( add(X,inverse(X)) = multiplicative_identity )
| ( add(x,inverse(x)) = multiplicative_identity ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
add(x,inverse(x)) = multiplicative_identity,
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
multiply(add(x,inverse(x)),inverse(inverse(x))) = multiply(multiplicative_identity,add(inverse(inverse(x)),x)),
inference(monotonicity,[status(thm)],[89,80]) ).
tff(91,plain,
multiply(multiplicative_identity,add(inverse(inverse(x)),x)) = multiply(add(x,inverse(x)),inverse(inverse(x))),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
^ [Y: $i,X: $i] :
refl(
( ( multiply(X,Y) = multiply(Y,X) )
<=> ( multiply(X,Y) = multiply(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(93,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)],[92]) ).
tff(94,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(95,axiom,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
tff(96,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
( ~ ! [Y: $i,X: $i] : ( multiply(X,Y) = multiply(Y,X) )
| ( multiply(add(inverse(inverse(x)),x),multiplicative_identity) = multiply(multiplicative_identity,add(inverse(inverse(x)),x)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
multiply(add(inverse(inverse(x)),x),multiplicative_identity) = multiply(multiplicative_identity,add(inverse(inverse(x)),x)),
inference(unit_resolution,[status(thm)],[99,98]) ).
tff(101,plain,
inverse(inverse(x)) = x,
inference(transitivity,[status(thm)],[79,69,67,58,100,91,55,46,31,21,9]) ).
tff(102,plain,
( ( inverse(inverse(x)) != x )
<=> ( inverse(inverse(x)) != x ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
tff(104,plain,
inverse(inverse(x)) != x,
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
$false,
inference(unit_resolution,[status(thm)],[104,101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO012-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 02:47:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------