%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ROB010-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:24:18 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.35s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 34 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 3 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_type,type,
a: $i ).
tff(negate_type,type,
negate: $i > $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
<=> ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
<=> ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
<=> ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).
tff(5,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X )
| ( negate(add(negate(add(a,b)),negate(add(a,negate(b))))) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
negate(add(negate(add(a,b)),negate(add(a,negate(b))))) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( negate(add(a,negate(b))) = c )
<=> ( negate(add(a,negate(b))) = c ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
negate(add(a,negate(b))) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
tff(12,plain,
negate(add(a,negate(b))) = c,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [Y: $i,X: $i] :
refl(( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
<=> ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
tff(17,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(b,a) = add(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
add(b,a) = add(a,b),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
add(a,b) = add(b,a),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
negate(add(a,b)) = negate(add(b,a)),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
add(negate(add(a,b)),negate(add(a,negate(b)))) = add(negate(add(b,a)),c),
inference(monotonicity,[status(thm)],[23,12]) ).
tff(25,plain,
add(negate(add(b,a)),c) = add(negate(add(a,b)),negate(add(a,negate(b)))),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(c,negate(add(b,a))) = add(negate(add(b,a)),c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
add(c,negate(add(b,a))) = add(negate(add(b,a)),c),
inference(unit_resolution,[status(thm)],[26,19]) ).
tff(28,plain,
add(c,negate(add(b,a))) = add(negate(add(a,b)),negate(add(a,negate(b)))),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
negate(add(c,negate(add(b,a)))) = negate(add(negate(add(a,b)),negate(add(a,negate(b))))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
negate(add(c,negate(add(b,a)))) = a,
inference(transitivity,[status(thm)],[29,9]) ).
tff(31,plain,
( ( negate(add(c,negate(add(b,a)))) != a )
<=> ( negate(add(c,negate(add(b,a)))) != a ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
negate(add(c,negate(add(b,a)))) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_result) ).
tff(33,plain,
negate(add(c,negate(add(b,a)))) != a,
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ROB010-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.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 : Fri Jun 20 03:29:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.35 % SZS status Unsatisfiable
% 0.11/0.35 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------