%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:58:41 AM UTC 2026
% Result : Theorem 6.36s 2.07s
% Output : CNFRefutation 6.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 28 ~; 31 |; 5 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(assumption,axiom,
( 'reflexive$urewrite'(a,c)
& 'reflexive$urewrite'(a,b) ) ).
fof(goal_ax,axiom,
! [X0] :
( ( 'reflexive$urewrite'(c,X0)
& 'reflexive$urewrite'(b,X0) )
=> goal ) ).
fof(reflexivity,axiom,
! [X0] : equalish(X0,X0) ).
fof(symmtery,axiom,
! [X0,X1] :
( equalish(X0,X1)
=> equalish(X1,X0) ) ).
fof(substitution,axiom,
! [X0,X1,X2] :
( ( 'reflexive$urewrite'(X1,X2)
& equalish(X0,X1) )
=> 'reflexive$urewrite'(X0,X2) ) ).
fof(equalish_in_reflexive_rewrite,axiom,
! [X0,X1] :
( equalish(X0,X1)
=> 'reflexive$urewrite'(X0,X1) ) ).
fof(rewrite_in_reflexive_rewrite,axiom,
! [X0,X1] :
( rewrite(X0,X1)
=> 'reflexive$urewrite'(X0,X1) ) ).
fof(equalish_or_rewrite,axiom,
! [X0,X1] :
( 'reflexive$urewrite'(X0,X1)
=> ( rewrite(X0,X1)
| equalish(X0,X1) ) ) ).
fof(rewrite_diamond,axiom,
! [X0,X1,X2] :
( ( rewrite(X0,X2)
& rewrite(X0,X1) )
=> ? [X3] :
( rewrite(X2,X3)
& rewrite(X1,X3) ) ) ).
fof(goal_to_be_proved,conjecture,
goal ).
fof(negated_conjecture,negated_conjecture,
~ goal,
inference(negate_conjecture,[status(cth)],[goal_to_be_proved]) ).
cnf(c0,plain,
'reflexive$urewrite'(a,b),
inference(clausification,[status(esa)],[assumption]) ).
cnf(c1,plain,
'reflexive$urewrite'(a,c),
inference(clausification,[status(esa)],[assumption]) ).
cnf(c2,plain,
( goal
| ~ 'reflexive$urewrite'(c,X0)
| ~ 'reflexive$urewrite'(b,X0) ),
inference(clausification,[status(esa)],[goal_ax]) ).
cnf(c3,plain,
equalish(X0,X0),
inference(clausification,[status(esa)],[reflexivity]) ).
cnf(c4,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmtery]) ).
cnf(c5,plain,
( 'reflexive$urewrite'(X0,X2)
| ~ 'reflexive$urewrite'(X1,X2)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[substitution]) ).
cnf(c6,plain,
( 'reflexive$urewrite'(X0,X1)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[equalish_in_reflexive_rewrite]) ).
cnf(c7,plain,
( 'reflexive$urewrite'(X0,X1)
| ~ rewrite(X0,X1) ),
inference(clausification,[status(esa)],[rewrite_in_reflexive_rewrite]) ).
cnf(c8,plain,
( rewrite(X0,X1)
| equalish(X0,X1)
| ~ 'reflexive$urewrite'(X0,X1) ),
inference(clausification,[status(esa)],[equalish_or_rewrite]) ).
cnf(c9,plain,
( rewrite(X1,sK16(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(clausification,[status(esa)],[rewrite_diamond]) ).
cnf(c10,plain,
( rewrite(X2,sK16(X1,X2))
| ~ rewrite(X0,X2)
| ~ rewrite(X0,X1) ),
inference(clausification,[status(esa)],[rewrite_diamond]) ).
cnf(c11,plain,
~ goal,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'reflexive$urewrite'(c,X0)
| ~ 'reflexive$urewrite'(b,X0) ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d1,plain,
( rewrite(a,c)
| equalish(a,c) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d2,plain,
( equalish(c,a)
| rewrite(a,c) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( ~ 'reflexive$urewrite'(a,X0)
| 'reflexive$urewrite'(c,X0)
| rewrite(a,c) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( rewrite(a,c)
| 'reflexive$urewrite'(c,b) ),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
( rewrite(a,b)
| equalish(a,b) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d6,plain,
( equalish(b,a)
| rewrite(a,b) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( ~ 'reflexive$urewrite'(a,X0)
| 'reflexive$urewrite'(b,X0)
| rewrite(a,b) ),
inference(resolution,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
( rewrite(a,b)
| 'reflexive$urewrite'(b,c) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
'reflexive$urewrite'(X0,X0),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d10,plain,
~ 'reflexive$urewrite'(b,c),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
rewrite(a,b),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( ~ rewrite(a,X0)
| rewrite(b,sK16(X0,b)) ),
inference(resolution,[status(thm)],[d11,c10]) ).
cnf(d13,plain,
( 'reflexive$urewrite'(b,sK16(X0,b))
| ~ rewrite(a,X0) ),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
( ~ rewrite(a,X0)
| rewrite(X0,sK16(X0,b)) ),
inference(resolution,[status(thm)],[d11,c9]) ).
cnf(d15,plain,
( 'reflexive$urewrite'(X0,sK16(X0,b))
| ~ rewrite(a,X0) ),
inference(resolution,[status(thm)],[d14,c7]) ).
cnf(d16,plain,
( ~ 'reflexive$urewrite'(b,sK16(c,b))
| ~ rewrite(a,c) ),
inference(resolution,[status(thm)],[d15,d0]) ).
cnf(d17,plain,
( ~ rewrite(a,c)
| ~ rewrite(a,c) ),
inference(resolution,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
'reflexive$urewrite'(c,b),
inference(resolution,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
~ 'reflexive$urewrite'(b,b),
inference(resolution,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d9,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM007+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 23:20:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.36/2.07 % SZS status Theorem for theBenchmark.p
% 6.36/2.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------