%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:10:36 AM UTC 2026
% Result : Unsatisfiable 22.36s 3.34s
% Output : CNFRefutation 22.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 15 unt; 0 nHn; 15 RR)
% Number of literals : 51 ( 0 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_equation,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))) ).
cnf(reflexivity,axiom,
equalish(X0,X0) ).
cnf(transitivity,axiom,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ) ).
cnf(commutativity_of_addition,axiom,
equalish(add(X0,X1),add(X1,X0)) ).
cnf(associativity_of_addition,axiom,
equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2)) ).
cnf(addition_inverts_subtraction1,axiom,
equalish(subtract(add(X0,X1),X1),X0) ).
cnf(addition_inverts_subtraction2,axiom,
equalish(X0,subtract(add(X0,X1),X1)) ).
cnf(add_substitution1,axiom,
( equalish(X2,add(X1,X3))
| ~ equalish(X2,add(X0,X3))
| ~ equalish(X0,X1) ) ).
cnf(subtract_substitution1,axiom,
( equalish(X2,subtract(X1,X3))
| ~ equalish(X2,subtract(X0,X3))
| ~ equalish(X0,X1) ) ).
cnf(subtract_substitution2,axiom,
( equalish(X2,subtract(X3,X1))
| ~ equalish(X2,subtract(X3,X0))
| ~ equalish(X0,X1) ) ).
cnf(c0,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(clausification,[status(esa)],[prove_equation]) ).
cnf(c1,plain,
equalish(X0,X0),
inference(clausification,[status(esa)],[reflexivity]) ).
cnf(c2,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity]) ).
cnf(c3,plain,
equalish(add(X0,X1),add(X1,X0)),
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c4,plain,
equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2)),
inference(clausification,[status(esa)],[associativity_of_addition]) ).
cnf(c5,plain,
equalish(subtract(add(X0,X1),X1),X0),
inference(clausification,[status(esa)],[addition_inverts_subtraction1]) ).
cnf(c6,plain,
equalish(X0,subtract(add(X0,X1),X1)),
inference(clausification,[status(esa)],[addition_inverts_subtraction2]) ).
cnf(c9,plain,
( equalish(X2,add(X1,X3))
| ~ equalish(X2,add(X0,X3))
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[add_substitution1]) ).
cnf(c11,plain,
( equalish(X2,subtract(X1,X3))
| ~ equalish(X2,subtract(X0,X3))
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[subtract_substitution1]) ).
cnf(c12,plain,
( equalish(X2,subtract(X3,X1))
| ~ equalish(X2,subtract(X3,X0))
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[subtract_substitution2]) ).
cnf(d0,plain,
( ~ equalish(add(X0,X1),X3)
| equalish(add(X0,add(X1,X2)),add(X3,X2)) ),
inference(resolution,[status(thm)],[c9,c4]) ).
cnf(d1,plain,
( ~ equalish(X0,subtract(add(X1,X2),X2))
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d2,plain,
( equalish(X0,subtract(X2,X1))
| ~ equalish(add(X0,X1),X2) ),
inference(resolution,[status(thm)],[c11,c6]) ).
cnf(d3,plain,
equalish(X0,subtract(add(X1,X0),X1)),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( equalish(X2,subtract(add(X0,X2),X1))
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ equalish(add(X2,X3),X0)
| equalish(add(X0,X1),add(X2,add(X3,X1))) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
~ equalish(add(a,b),add(a,b)),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c1,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 01:51:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.36/3.34 % SZS status Unsatisfiable for theBenchmark.p
% 22.36/3.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------