%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD020-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 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 05:04:55 AM UTC 2025
% Result : Unsatisfiable 11.49s 11.68s
% Output : Proof 11.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 102
% Syntax : Number of formulae : 226 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 1318 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1986 ( 937 ~; 933 |; 0 &)
% ( 116 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 43 ( 43 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 531 ( 503 !; 0 ?; 531 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(m_type,type,
m: $i ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(a_type,type,
a: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( defined(m)
<=> defined(m) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
defined(m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_is_defined) ).
tff(3,plain,
defined(m),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( defined(a)
<=> defined(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
tff(6,plain,
defined(a),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
<=> ( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
rewrite(( ( defined(add(X,Y))
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] :
( defined(add(X,Y))
| ~ defined(X)
| ~ defined(Y) )
<=> ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [Y: $i,X: $i] :
( defined(add(X,Y))
| ~ defined(X)
| ~ defined(Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
tff(13,plain,
! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(m)
| defined(add(m,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(m)
| defined(add(m,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(m)
| defined(add(m,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(m)
| defined(add(m,a)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
defined(add(m,a)),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( defined(additive_inverse(X))
| ~ defined(X) )
<=> ( defined(additive_inverse(X))
| ~ defined(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
<=> ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
<=> ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
tff(25,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(add(m,a)))
| ~ defined(add(m,a)) )
<=> ( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(add(m,a)))
| ~ defined(add(m,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(add(m,a)))
| ~ defined(add(m,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(add(m,a)))
| ~ defined(add(m,a)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
defined(additive_inverse(add(m,a))),
inference(unit_resolution,[status(thm)],[30,27,20]) ).
tff(32,plain,
( equalish(add(m,a),a)
<=> equalish(add(m,a),a) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
equalish(add(m,a),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_equals_a_3) ).
tff(34,plain,
equalish(add(m,a),a),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( equalish(add(X,Z),add(Y,Z))
| ~ defined(Z) )
<=> ( ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ) )),
( ( equalish(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| equalish(add(X,Z),add(Y,Z))
| ~ equalish(X,Y) ) )),
rewrite(( ( ~ defined(Z)
| equalish(add(X,Z),add(Y,Z))
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ) )),
( ( equalish(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [Z: $i,Y: $i,X: $i] :
( equalish(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [Z: $i,Y: $i,X: $i] :
( equalish(add(X,Z),add(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
tff(41,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ equalish(add(m,a),a)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ equalish(add(m,a),a)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ defined(additive_inverse(add(m,a)))
| ~ equalish(add(m,a),a)
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) )
<=> ( ~ equalish(add(m,a),a)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ equalish(add(m,a),a)
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ equalish(add(m,a),a)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ equalish(add(m,a),a)
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ equalish(add(m,a),a)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ equalish(add(m,a),a)
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ equalish(add(m,a),a)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a)))),
inference(unit_resolution,[status(thm)],[50,44,34,31]) ).
tff(52,plain,
( defined(additive_identity)
<=> defined(additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
tff(54,plain,
defined(additive_identity),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
^ [X: $i] :
refl(( ( equalish(add(additive_identity,X),X)
| ~ defined(X) )
<=> ( equalish(add(additive_identity,X),X)
| ~ defined(X) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
<=> ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
<=> ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
tff(59,plain,
! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_identity),additive_identity) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( equalish(add(additive_identity,additive_identity),additive_identity)
| ~ defined(additive_identity) )
<=> ( ~ defined(additive_identity)
| equalish(add(additive_identity,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,additive_identity),additive_identity)
| ~ defined(additive_identity) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_identity),additive_identity) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,additive_identity),additive_identity)
| ~ defined(additive_identity) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_identity),additive_identity) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,additive_identity),additive_identity)
| ~ defined(additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
equalish(add(additive_identity,additive_identity),additive_identity),
inference(unit_resolution,[status(thm)],[67,61,54]) ).
tff(69,plain,
^ [Y: $i,X: $i] :
refl(( ( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ( equalish(X,Y)
| ~ equalish(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
tff(73,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,add(additive_identity,additive_identity))
| ~ equalish(add(additive_identity,additive_identity),additive_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,add(additive_identity,additive_identity))
| ~ equalish(add(additive_identity,additive_identity),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,add(additive_identity,additive_identity))
| ~ equalish(add(additive_identity,additive_identity),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,add(additive_identity,additive_identity))
| ~ equalish(add(additive_identity,additive_identity),additive_identity) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
equalish(additive_identity,add(additive_identity,additive_identity)),
inference(unit_resolution,[status(thm)],[78,75,68]) ).
tff(80,plain,
^ [X: $i] :
refl(( ( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
<=> ( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
<=> ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
<=> ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
tff(84,plain,
! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
( ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(add(m,a))
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity) )
<=> ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(add(m,a))
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| ~ defined(add(m,a)) )
<=> ( ~ defined(add(m,a))
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| ~ defined(add(m,a)) )
<=> ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(add(m,a))
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| ~ defined(add(m,a)) )
<=> ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(add(m,a))
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| ~ defined(add(m,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(add(m,a))
| equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity),
inference(unit_resolution,[status(thm)],[92,86,20]) ).
tff(94,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( equalish(X,Z)
| ~ equalish(X,Y) )
<=> ( ~ equalish(X,Y)
| equalish(X,Z) ) )),
( ( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) ) )),
rewrite(( ( ~ equalish(X,Y)
| equalish(X,Z)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) )),
( ( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [Z: $i,Y: $i,X: $i] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [Z: $i,Y: $i,X: $i] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
tff(99,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(additive_identity,add(additive_identity,additive_identity))
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(additive_identity,add(additive_identity,additive_identity))
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(additive_identity,add(additive_identity,additive_identity))
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(additive_identity,add(additive_identity,additive_identity))
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)),
inference(unit_resolution,[status(thm)],[105,102,93,79]) ).
tff(107,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity))
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity))
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ( equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a))))
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)) )
<=> ( ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity))
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a))))
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity))
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a)))) ) ),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a))))
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity))
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a)))) ) ),
inference(transitivity,[status(thm)],[109,107]) ).
tff(111,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a))))
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(additive_identity,additive_identity))
| equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a)))) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a)))),
inference(unit_resolution,[status(thm)],[112,75,106]) ).
tff(114,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a))))
| ~ equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a))))
| equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a))))
| ~ equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a))))
| equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a))))
| ~ equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a))))
| equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),add(a,additive_inverse(add(m,a))))
| ~ equalish(add(additive_identity,additive_identity),add(add(m,a),additive_inverse(add(m,a))))
| equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a)))) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a)))),
inference(unit_resolution,[status(thm)],[116,102,113,51]) ).
tff(118,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ defined(m)
| ~ equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a))))
| equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ defined(m)
| ~ equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a))))
| equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ defined(m)
| ~ equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a))))
| equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(add(X,Z),add(Y,Z)) )
| ~ defined(m)
| ~ equalish(add(additive_identity,additive_identity),add(a,additive_inverse(add(m,a))))
| equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m)) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m)),
inference(unit_resolution,[status(thm)],[120,44,3,117]) ).
tff(122,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(additive_inverse(add(m,a)))
| defined(add(a,additive_inverse(add(m,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(additive_inverse(add(m,a)))
| defined(add(a,additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
( ( ~ defined(additive_inverse(add(m,a)))
| ~ defined(a)
| defined(add(a,additive_inverse(add(m,a)))) )
<=> ( ~ defined(a)
| ~ defined(additive_inverse(add(m,a)))
| defined(add(a,additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ defined(a)
| defined(add(a,additive_inverse(add(m,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(additive_inverse(add(m,a)))
| defined(add(a,additive_inverse(add(m,a)))) ) ),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ defined(a)
| defined(add(a,additive_inverse(add(m,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(additive_inverse(add(m,a)))
| defined(add(a,additive_inverse(add(m,a)))) ) ),
inference(transitivity,[status(thm)],[124,122]) ).
tff(126,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ defined(a)
| defined(add(a,additive_inverse(add(m,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(a)
| ~ defined(additive_inverse(add(m,a)))
| defined(add(a,additive_inverse(add(m,a)))) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
defined(add(a,additive_inverse(add(m,a)))),
inference(unit_resolution,[status(thm)],[127,16,6,31]) ).
tff(129,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) )
<=> ( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) )
<=> ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) )
<=> ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
^ [Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( equalish(add(X,Y),add(Y,X))
| ~ defined(X) )
<=> ( ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) )),
( ( equalish(add(X,Y),add(Y,X))
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(X)
| equalish(add(X,Y),add(Y,X))
| ~ defined(Y) ) )),
rewrite(( ( ~ defined(X)
| equalish(add(X,Y),add(Y,X))
| ~ defined(Y) )
<=> ( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) )),
( ( equalish(add(X,Y),add(Y,X))
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) )),
inference(bind,[status(th)],[]) ).
tff(133,plain,
( ! [Y: $i,X: $i] :
( equalish(add(X,Y),add(Y,X))
| ~ defined(X)
| ~ defined(Y) )
<=> ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [Y: $i,X: $i] :
( equalish(add(X,Y),add(Y,X))
| ~ defined(X)
| ~ defined(Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
tff(135,plain,
! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) ),
inference(modus_ponens,[status(thm)],[137,130]) ).
tff(139,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) )
| ~ defined(m)
| ~ defined(add(a,additive_inverse(add(m,a))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a))))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) )
| ~ defined(m)
| ~ defined(add(a,additive_inverse(add(m,a))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) )
| ~ defined(m)
| ~ defined(add(a,additive_inverse(add(m,a))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,Y),add(Y,X)) )
| ~ defined(m)
| ~ defined(add(a,additive_inverse(add(m,a))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a))))) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
( ~ defined(add(a,additive_inverse(add(m,a))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a))))) ),
inference(unit_resolution,[status(thm)],[141,138,3]) ).
tff(143,plain,
equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a))))),
inference(unit_resolution,[status(thm)],[142,128]) ).
tff(144,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
<=> ( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(X) )
<=> ( ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) )),
( ( equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(Y) ) )),
rewrite(( ( ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(Y) )
<=> ( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) )),
( ( equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(X)
| ~ defined(Y) )
<=> ( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) )),
( ( equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(X)
| ~ defined(Y)
| ~ defined(Z) )
<=> ( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(Z) ) )),
rewrite(( ( ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(Z) )
<=> ( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) )),
( ( equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(X)
| ~ defined(Y)
| ~ defined(Z) )
<=> ( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [Z: $i,Y: $i,X: $i] :
( equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(X)
| ~ defined(Y)
| ~ defined(Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [Z: $i,Y: $i,X: $i] :
( equalish(add(X,add(Y,Z)),add(add(X,Y),Z))
| ~ defined(X)
| ~ defined(Y)
| ~ defined(Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_addition) ).
tff(150,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(a)
| ~ defined(m)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(a)
| ~ defined(m)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ( ~ defined(additive_inverse(add(m,a)))
| ~ defined(a)
| ~ defined(m)
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) )
<=> ( ~ defined(a)
| ~ defined(m)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ defined(a)
| ~ defined(m)
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(a)
| ~ defined(m)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) ) ),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ defined(a)
| ~ defined(m)
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(a)
| ~ defined(m)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) ) ),
inference(transitivity,[status(thm)],[156,154]) ).
tff(158,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(additive_inverse(add(m,a)))
| ~ defined(a)
| ~ defined(m)
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(a)
| ~ defined(m)
| ~ defined(additive_inverse(add(m,a)))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
( ~ defined(additive_inverse(add(m,a)))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))) ),
inference(unit_resolution,[status(thm)],[159,153,6,3]) ).
tff(161,plain,
equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a)))),
inference(unit_resolution,[status(thm)],[160,31]) ).
tff(162,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| ~ equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a))))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| ~ equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a))))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| ~ equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a))))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(m,a),additive_inverse(add(m,a))),additive_identity)
| ~ equalish(add(m,add(a,additive_inverse(add(m,a)))),add(add(m,a),additive_inverse(add(m,a))))
| equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity),
inference(unit_resolution,[status(thm)],[164,102,93,161]) ).
tff(166,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity)
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a)))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity)
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a)))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity)
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a)))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(m,add(a,additive_inverse(add(m,a)))),additive_identity)
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),add(m,add(a,additive_inverse(add(m,a)))))
| equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity),
inference(unit_resolution,[status(thm)],[168,102,165,143]) ).
tff(170,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,plain,
( ( ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) )
<=> ( ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) ) ),
inference(monotonicity,[status(thm)],[171]) ).
tff(173,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) ) ),
inference(transitivity,[status(thm)],[172,170]) ).
tff(174,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(additive_identity,additive_identity),m),add(add(a,additive_inverse(add(m,a))),m))
| ~ equalish(add(add(a,additive_inverse(add(m,a))),m),additive_identity)
| equalish(add(add(additive_identity,additive_identity),m),additive_identity) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
equalish(add(add(additive_identity,additive_identity),m),additive_identity),
inference(unit_resolution,[status(thm)],[175,102,169,121]) ).
tff(177,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(m)
| ~ defined(additive_identity)
| defined(add(additive_identity,m)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(m)
| ~ defined(additive_identity)
| defined(add(additive_identity,m)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(m)
| ~ defined(additive_identity)
| defined(add(additive_identity,m)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) )
| ~ defined(m)
| ~ defined(additive_identity)
| defined(add(additive_identity,m)) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
defined(add(additive_identity,m)),
inference(unit_resolution,[status(thm)],[179,16,54,3]) ).
tff(181,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m)) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(182,plain,
( ( equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m))
| ~ defined(add(additive_identity,m)) )
<=> ( ~ defined(add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(183,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m))
| ~ defined(add(additive_identity,m)) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m)) ) ),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m))
| ~ defined(add(additive_identity,m)) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m)) ) ),
inference(transitivity,[status(thm)],[183,181]) ).
tff(185,plain,
( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m))
| ~ defined(add(additive_identity,m)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m)) ),
inference(modus_ponens,[status(thm)],[185,184]) ).
tff(187,plain,
equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m)),
inference(unit_resolution,[status(thm)],[186,61,180]) ).
tff(188,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(m)
| equalish(add(additive_identity,m),m) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(m)
| equalish(add(additive_identity,m),m) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ( equalish(add(additive_identity,m),m)
| ~ defined(m) )
<=> ( ~ defined(m)
| equalish(add(additive_identity,m),m) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,m),m)
| ~ defined(m) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(m)
| equalish(add(additive_identity,m),m) ) ),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,m),m)
| ~ defined(m) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(m)
| equalish(add(additive_identity,m),m) ) ),
inference(transitivity,[status(thm)],[190,188]) ).
tff(192,plain,
( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,m),m)
| ~ defined(m) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(m)
| equalish(add(additive_identity,m),m) ),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
equalish(add(additive_identity,m),m),
inference(unit_resolution,[status(thm)],[193,61,3]) ).
tff(195,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,m),m)
| ~ equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),m) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,m),m)
| ~ equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),m) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,m),m)
| ~ equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),m) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,m),m)
| ~ equalish(add(additive_identity,add(additive_identity,m)),add(additive_identity,m))
| equalish(add(additive_identity,add(additive_identity,m)),m) ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
equalish(add(additive_identity,add(additive_identity,m)),m),
inference(unit_resolution,[status(thm)],[197,102,194,187]) ).
tff(199,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),m)
| equalish(m,add(additive_identity,add(additive_identity,m))) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),m)
| equalish(m,add(additive_identity,add(additive_identity,m))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(200,plain,
( ( equalish(m,add(additive_identity,add(additive_identity,m)))
| ~ equalish(add(additive_identity,add(additive_identity,m)),m) )
<=> ( ~ equalish(add(additive_identity,add(additive_identity,m)),m)
| equalish(m,add(additive_identity,add(additive_identity,m))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(m,add(additive_identity,add(additive_identity,m)))
| ~ equalish(add(additive_identity,add(additive_identity,m)),m) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),m)
| equalish(m,add(additive_identity,add(additive_identity,m))) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(m,add(additive_identity,add(additive_identity,m)))
| ~ equalish(add(additive_identity,add(additive_identity,m)),m) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),m)
| equalish(m,add(additive_identity,add(additive_identity,m))) ) ),
inference(transitivity,[status(thm)],[201,199]) ).
tff(203,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(m,add(additive_identity,add(additive_identity,m)))
| ~ equalish(add(additive_identity,add(additive_identity,m)),m) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),m)
| equalish(m,add(additive_identity,add(additive_identity,m))) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
equalish(m,add(additive_identity,add(additive_identity,m))),
inference(unit_resolution,[status(thm)],[204,75,198]) ).
tff(206,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(m)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(m)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
( ( ~ defined(m)
| ~ defined(additive_identity)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) )
<=> ( ~ defined(m)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(208,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(m)
| ~ defined(additive_identity)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(m)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) ) ),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(m)
| ~ defined(additive_identity)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(m)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) ) ),
inference(transitivity,[status(thm)],[208,206]) ).
tff(210,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(m)
| ~ defined(additive_identity)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(211,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ defined(Y)
| ~ defined(X)
| equalish(add(X,add(Y,Z)),add(add(X,Y),Z)) )
| ~ defined(m)
| ~ defined(additive_identity)
| equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m)),
inference(unit_resolution,[status(thm)],[211,153,54,3]) ).
tff(213,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m))
| ~ equalish(m,add(additive_identity,add(additive_identity,m)))
| equalish(m,add(add(additive_identity,additive_identity),m)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m))
| ~ equalish(m,add(additive_identity,add(additive_identity,m)))
| equalish(m,add(add(additive_identity,additive_identity),m)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m))
| ~ equalish(m,add(additive_identity,add(additive_identity,m)))
| equalish(m,add(add(additive_identity,additive_identity),m)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(215,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,add(additive_identity,m)),add(add(additive_identity,additive_identity),m))
| ~ equalish(m,add(additive_identity,add(additive_identity,m)))
| equalish(m,add(add(additive_identity,additive_identity),m)) ),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
equalish(m,add(add(additive_identity,additive_identity),m)),
inference(unit_resolution,[status(thm)],[215,102,212,205]) ).
tff(217,plain,
( ~ equalish(m,additive_identity)
<=> ~ equalish(m,additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,axiom,
~ equalish(m,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_not_equal_to_additive_identity_4) ).
tff(219,plain,
~ equalish(m,additive_identity),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(m,additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(m,additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(221,plain,
( ( ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| equalish(m,additive_identity) )
<=> ( equalish(m,additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(222,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| equalish(m,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(m,additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity) ) ),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| equalish(m,additive_identity) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(m,additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity) ) ),
inference(transitivity,[status(thm)],[222,220]) ).
tff(224,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| equalish(m,additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(m,additive_identity)
| ~ equalish(m,add(add(additive_identity,additive_identity),m))
| ~ equalish(add(add(additive_identity,additive_identity),m),additive_identity) ),
inference(modus_ponens,[status(thm)],[224,223]) ).
tff(226,plain,
$false,
inference(unit_resolution,[status(thm)],[225,102,219,216,176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : FLD020-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 13:33:56 EDT 2025
% 0.11/0.32 % CPUTime :
% 11.49/11.68 % SZS status Unsatisfiable
% 11.49/11.68 % SZS output start Proof
% See solution above
% 11.57/11.74 % E exiting
%------------------------------------------------------------------------------