TSTP Solution File: ROB013-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ROB013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 : Tue Sep 20 03:22:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 35 ( 22 unt; 5 typ; 0 def)
% Number of atoms : 42 ( 39 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 2 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 3 ( 2 >; 1 *; 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 : 40 ( 36 !; 0 ?; 40 :)
% 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/sandbox/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,
^ [Y: $i,X: $i] :
refl(
( ( add(X,Y) = add(Y,X) )
<=> ( add(X,Y) = add(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(11,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)],[10]) ).
tff(12,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(13,axiom,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
tff(14,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( add(X,Y) = add(Y,X) )
| ( add(negate(b),a) = add(a,negate(b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
add(negate(b),a) = add(a,negate(b)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
add(a,negate(b)) = add(negate(b),a),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
negate(add(a,negate(b))) = negate(add(negate(b),a)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
add(negate(add(a,b)),negate(add(a,negate(b)))) = add(negate(add(a,b)),negate(add(negate(b),a))),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
add(negate(add(a,b)),negate(add(negate(b),a))) = add(negate(add(a,b)),negate(add(a,negate(b)))),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
negate(add(negate(add(a,b)),negate(add(negate(b),a)))) = negate(add(negate(add(a,b)),negate(add(a,negate(b))))),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
negate(add(negate(add(a,b)),negate(add(negate(b),a)))) = a,
inference(transitivity,[status(thm)],[23,9]) ).
tff(25,plain,
( ( negate(add(c,negate(add(negate(b),a)))) != a )
<=> ( negate(add(negate(add(a,b)),negate(add(negate(b),a)))) != a ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ( negate(add(c,negate(add(negate(b),a)))) != a )
<=> ( negate(add(c,negate(add(negate(b),a)))) != a ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
negate(add(c,negate(add(negate(b),a)))) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_result) ).
tff(28,plain,
negate(add(c,negate(add(negate(b),a)))) != a,
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
negate(add(negate(add(a,b)),negate(add(negate(b),a)))) != a,
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
$false,
inference(unit_resolution,[status(thm)],[29,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ROB013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 23:01:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------