%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD071-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 187 ( 88 ~; 84 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(less_or_equal_type,type,
less_or_equal: ( $i * $i ) > $o ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(additive_identity_type,type,
additive_identity: $i ).
tff(1,plain,
( ~ less_or_equal(additive_identity,multiply(a,b))
<=> ~ less_or_equal(additive_identity,multiply(a,b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ less_or_equal(additive_identity,multiply(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_5) ).
tff(3,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( less_or_equal(additive_identity,b)
<=> less_or_equal(additive_identity,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_4) ).
tff(6,plain,
less_or_equal(additive_identity,b),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( less_or_equal(additive_identity,a)
<=> less_or_equal(additive_identity,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
tff(9,plain,
less_or_equal(additive_identity,a),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i] :
refl(( ( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
<=> ( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [Z: $i,Y: $i] :
trans(monotonicity(rewrite(( ( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y) )
<=> ( ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) )),
( ( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,Z) )
<=> ( ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Z) ) )),
rewrite(( ( ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Z) )
<=> ( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) )),
( ( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,Z) )
<=> ( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Z: $i,Y: $i] :
( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,Z) )
<=> ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [Z: $i,Y: $i] :
( less_or_equal(additive_identity,multiply(Y,Z))
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_multiplication) ).
tff(16,plain,
! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) )
<=> ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,multiply(a,b)) )
<=> ( less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,multiply(a,b)) )
<=> ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,multiply(a,b)) )
<=> ( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a)
| less_or_equal(additive_identity,multiply(a,b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Z: $i,Y: $i] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) )
| less_or_equal(additive_identity,multiply(a,b))
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(additive_identity,a) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD071-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 13:46:16 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.39 % SZS status Unsatisfiable
% 0.22/0.39 % SZS output start Proof
% See solution above
% 0.22/0.39 % E exiting
%------------------------------------------------------------------------------