TSTP Solution File: RNG045+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG045+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Tue Sep 20 03:17:54 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 62 ( 20 unt; 7 typ; 0 def)
% Number of atoms : 415 ( 154 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 685 ( 348 ~; 232 |; 68 &)
% ( 31 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 90 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xv_type,type,
xv: $i ).
tff(xy_type,type,
xy: $i ).
tff(xu_type,type,
xu: $i ).
tff(xx_type,type,
xx: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(1,plain,
( aScalar0(xv)
<=> aScalar0(xv) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aScalar0(xx)
& aScalar0(xy)
& aScalar0(xu)
& aScalar0(xv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__674) ).
tff(3,plain,
aScalar0(xv),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aScalar0(xv),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aScalar0(xu)
<=> aScalar0(xu) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( aScalar0(xx)
& aScalar0(xy)
& aScalar0(xu) ),
inference(and_elim,[status(thm)],[2]) ).
tff(7,plain,
aScalar0(xu),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aScalar0(xu),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
( aScalar0(xy)
<=> aScalar0(xy) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( aScalar0(xx)
& aScalar0(xy) ),
inference(and_elim,[status(thm)],[6]) ).
tff(11,plain,
aScalar0(xy),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
aScalar0(xy),
inference(modus_ponens,[status(thm)],[11,9]) ).
tff(13,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ~ ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ~ ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(
( ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) )
<=> ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
rewrite(
( ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
rewrite(
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
tff(21,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
inference(modus_ponens,[status(thm)],[24,14]) ).
tff(26,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xy)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) )
<=> ( ~ aScalar0(xy)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xy)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xy)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xy)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xy)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ ( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) ) ),
inference(unit_resolution,[status(thm)],[31,25,12,8,4]) ).
tff(33,plain,
( ( sdtasdt0(xy,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) )
| ( sdtasdt0(sdtpldt0(xy,xu),xv) != sdtpldt0(sdtasdt0(xy,xv),sdtasdt0(xu,xv)) )
| ( sdtasdt0(xy,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) ) ),
inference(tautology,[status(thm)],]) ).
tff(34,plain,
sdtasdt0(xy,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
( aScalar0(xx)
<=> aScalar0(xx) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
aScalar0(xx),
inference(and_elim,[status(thm)],[10]) ).
tff(37,plain,
aScalar0(xx),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xx)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xx)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xx)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) )
<=> ( ~ aScalar0(xx)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xx)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xx)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xx)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xx)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xx)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W0,W1),W2) != sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) )
| ~ aScalar0(xx)
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ ( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) ) ),
inference(unit_resolution,[status(thm)],[43,25,37,8,4]) ).
tff(45,plain,
( ( sdtasdt0(xx,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xu),xv) != sdtpldt0(sdtasdt0(xx,xv),sdtasdt0(xu,xv)) )
| ( sdtasdt0(xx,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) ) ),
inference(tautology,[status(thm)],]) ).
tff(46,plain,
sdtasdt0(xx,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(monotonicity,[status(thm)],[46,34]) ).
tff(48,plain,
( ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) )
<=> ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__733) ).
tff(50,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(transitivity,[status(thm)],[50,47]) ).
tff(52,plain,
( ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) )
<=> ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(54,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
$false,
inference(unit_resolution,[status(thm)],[54,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG045+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 21:58:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------