%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD071-4 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:05:09 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 29 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 289 ( 137 ~; 133 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_or_equal_type,type,
less_or_equal: ( $i * $i ) > $o ).
tff(u_type,type,
u: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
( ~ less_or_equal(additive_identity,u)
<=> ~ less_or_equal(additive_identity,u) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_7) ).
tff(3,plain,
~ less_or_equal(additive_identity,u),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( product(a,b,u)
<=> product(a,b,u) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
product(a,b,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
tff(6,plain,
product(a,b,u),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( less_or_equal(additive_identity,b)
<=> less_or_equal(additive_identity,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_5) ).
tff(9,plain,
less_or_equal(additive_identity,b),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( less_or_equal(additive_identity,a)
<=> less_or_equal(additive_identity,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_4) ).
tff(12,plain,
less_or_equal(additive_identity,a),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
<=> ( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X) )
<=> ( ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) )),
( ( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X)
| ~ less_or_equal(additive_identity,Y) )
<=> ( ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y) ) )),
rewrite(( ( ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y) )
<=> ( ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) )),
( ( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X)
| ~ less_or_equal(additive_identity,Y) )
<=> ( ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) )),
( ( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X)
| ~ less_or_equal(additive_identity,Y)
| ~ product(X,Y,Z) )
<=> ( ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z)
| ~ product(X,Y,Z) ) )),
rewrite(( ( ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z)
| ~ product(X,Y,Z) )
<=> ( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) )),
( ( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X)
| ~ less_or_equal(additive_identity,Y)
| ~ product(X,Y,Z) )
<=> ( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [Z: $i,Y: $i,X: $i] :
( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X)
| ~ less_or_equal(additive_identity,Y)
| ~ product(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [Z: $i,Y: $i,X: $i] :
( less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,X)
| ~ less_or_equal(additive_identity,Y)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_multiplication) ).
tff(19,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
| less_or_equal(additive_identity,u)
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
| less_or_equal(additive_identity,u)
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,u) )
<=> ( less_or_equal(additive_identity,u)
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,u) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
| less_or_equal(additive_identity,u)
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,u) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
| less_or_equal(additive_identity,u)
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,u) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) )
| less_or_equal(additive_identity,u)
| ~ product(a,b,u)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,22,12,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : FLD071-4 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 13:46:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.38 % E exiting
%------------------------------------------------------------------------------