%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD006-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:04:51 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 35
% Syntax : Number of formulae : 76 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 331 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 457 ( 213 ~; 208 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 11 ( 11 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 : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 141 ( 133 !; 0 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(additive_inverse_type,type,
additive_inverse: $i > $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ( defined(additive_inverse(X))
| ~ defined(X) )
<=> ( defined(additive_inverse(X))
| ~ defined(X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
<=> ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
<=> ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
tff(5,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( defined(additive_identity)
<=> defined(additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
tff(10,plain,
defined(additive_identity),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(additive_identity))
| ~ defined(additive_identity) )
<=> ( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(additive_identity))
| ~ defined(additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(additive_identity))
| ~ defined(additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [X: $i] :
( defined(additive_inverse(X))
| ~ defined(X) )
| defined(additive_inverse(additive_identity))
| ~ defined(additive_identity) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
defined(additive_inverse(additive_identity)),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,axiom,
! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
tff(19,plain,
! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_inverse(additive_identity))
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_inverse(additive_identity))
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) )
<=> ( ~ defined(additive_inverse(additive_identity))
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_inverse(additive_identity))
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) )
<=> ( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_inverse(additive_identity))
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity))
| ~ defined(additive_inverse(additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [X: $i] :
( equalish(add(additive_identity,X),X)
| ~ defined(X) )
| ~ defined(additive_inverse(additive_identity))
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)),
inference(unit_resolution,[status(thm)],[27,21,14]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,axiom,
! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
tff(33,plain,
! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) )
<=> ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ( equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity)
| ~ defined(additive_identity) )
<=> ( ~ defined(additive_identity)
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity)
| ~ defined(additive_identity) )
<=> ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity)
| ~ defined(additive_identity) )
<=> ( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity)
| ~ defined(additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [X: $i] :
( equalish(add(X,additive_inverse(X)),additive_identity)
| ~ defined(X) )
| ~ defined(additive_identity)
| equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),
inference(unit_resolution,[status(thm)],[41,35,10]) ).
tff(43,plain,
^ [Y: $i,X: $i] :
refl(( ( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ( equalish(X,Y)
| ~ equalish(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(44,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)],[43]) ).
tff(45,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(46,axiom,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
tff(47,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity))),
inference(unit_resolution,[status(thm)],[52,49,42]) ).
tff(54,plain,
( ~ equalish(additive_inverse(additive_identity),additive_identity)
<=> ~ equalish(additive_inverse(additive_identity),additive_identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
~ equalish(additive_inverse(additive_identity),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_not_equal_to_additive_identity_1) ).
tff(56,plain,
~ equalish(additive_inverse(additive_identity),additive_identity),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_inverse(additive_identity),additive_identity)
| ~ equalish(additive_identity,additive_inverse(additive_identity)) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_inverse(additive_identity),additive_identity)
| ~ equalish(additive_identity,additive_inverse(additive_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_inverse(additive_identity),additive_identity)
| ~ equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(additive_inverse(additive_identity),additive_identity)
| ~ equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ equalish(additive_identity,additive_inverse(additive_identity)),
inference(unit_resolution,[status(thm)],[59,49,56]) ).
tff(61,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(62,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(63,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(64,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)],[63]) ).
tff(65,axiom,
! [Z: $i,Y: $i,X: $i] :
( equalish(X,Z)
| ~ equalish(X,Y)
| ~ equalish(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
tff(66,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(additive_identity,additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(additive_identity,additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ( ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| equalish(additive_identity,additive_inverse(additive_identity)) )
<=> ( equalish(additive_identity,additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| equalish(additive_identity,additive_inverse(additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(additive_identity,additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| equalish(additive_identity,additive_inverse(additive_identity)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(additive_identity,additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| equalish(additive_identity,additive_inverse(additive_identity)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) )
| equalish(additive_identity,additive_inverse(additive_identity))
| ~ equalish(additive_identity,add(additive_identity,additive_inverse(additive_identity)))
| ~ equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,69,60,53,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : FLD006-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.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 13:32:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% See solution above
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------