%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ROB030-1 : TPTP v9.0.0. Released v3.1.0.
% 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 05:24:20 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 16 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 14 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 1 ( 1 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(negate_type,type,
negate: $i > $i ).
tff(d_type,type,
d: $i ).
tff(add_type,type,
add: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(1,plain,
( ( add(c,d) = d )
<=> ( add(c,d) = d ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
add(c,d) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion) ).
tff(3,plain,
add(c,d) = d,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
d = add(c,d),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
negate(d) = negate(add(c,d)),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
negate(add(c,d)) = negate(d),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
^ [B: $i,A: $i] :
refl(( ( negate(add(A,B)) != negate(B) )
<=> ( negate(add(A,B)) != negate(B) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) )
<=> ! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) )
<=> ! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_absorption_within_negation) ).
tff(11,plain,
! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ~ ! [B: $i,A: $i] : ( negate(add(A,B)) != negate(B) )
| ( negate(add(c,d)) != negate(d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
negate(add(c,d)) != negate(d),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
$false,
inference(unit_resolution,[status(thm)],[15,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ROB030-1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.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 03:32:16 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------