%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 08:10:37 AM UTC 2026
% Result : Unsatisfiable 58.38s 11.64s
% Output : CNFRefutation 58.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 20 unt; 0 nHn; 15 RR)
% Number of literals : 50 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_equation,negated_conjecture,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)) ).
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(addition_inverts_subtraction1,axiom,
equalish(subtract(add(X0,X1),X1),X0) ).
cnf(addition_inverts_subtraction2,axiom,
equalish(X0,subtract(add(X0,X1),X1)) ).
cnf(commutativity1,axiom,
equalish(add(subtract(X0,X1),X2),subtract(add(X0,X2),X1)) ).
cnf(commutativity2,axiom,
equalish(subtract(add(X0,X1),X2),add(subtract(X0,X2),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(c0,plain,
~ equalish(add(a,subtract(b,c)),add(subtract(a,c),b)),
inference(clausification,[status(esa)],[prove_equation]) ).
cnf(c2,plain,
( equalish(X2,X1)
| ~ equalish(X2,X0)
| ~ 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(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(c7,plain,
equalish(add(subtract(X0,X1),X2),subtract(add(X0,X2),X1)),
inference(clausification,[status(esa)],[commutativity1]) ).
cnf(c8,plain,
equalish(subtract(add(X0,X1),X2),add(subtract(X0,X2),X1)),
inference(clausification,[status(esa)],[commutativity2]) ).
cnf(c9,plain,
( equalish(X0,add(X3,X2))
| ~ equalish(X1,X3)
| ~ equalish(X0,add(X1,X2)) ),
inference(clausification,[status(esa)],[add_substitution1]) ).
cnf(c11,plain,
( equalish(X0,subtract(X3,X2))
| ~ equalish(X1,X3)
| ~ equalish(X0,subtract(X1,X2)) ),
inference(clausification,[status(esa)],[subtract_substitution1]) ).
cnf(d0,plain,
( ~ equalish(subtract(add(X0,X2),X2),X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d1,plain,
equalish(X0,add(subtract(X0,X1),X1)),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( ~ equalish(subtract(X0,X2),X1)
| equalish(X0,add(X1,X2)) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( ~ equalish(add(X1,X0),X2)
| equalish(add(X0,X1),X2) ),
inference(resolution,[status(thm)],[c2,c3]) ).
cnf(d4,plain,
( ~ equalish(subtract(add(X0,X2),X1),X3)
| equalish(add(subtract(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d5,plain,
equalish(add(subtract(X0,X1),X1),X0),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
equalish(add(X0,subtract(X1,X0)),X1),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ equalish(X0,subtract(add(X3,subtract(X1,X3)),X2))
| equalish(X0,subtract(X1,X2)) ),
inference(resolution,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
equalish(add(X0,subtract(X1,X2)),subtract(add(X1,X0),X2)),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d9,plain,
( ~ equalish(add(subtract(X0,X2),X1),X3)
| equalish(subtract(add(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d10,plain,
equalish(subtract(add(X0,subtract(X1,X2)),X3),subtract(add(X1,subtract(X0,X3)),X2)),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
equalish(subtract(add(X0,subtract(X1,X2)),X1),subtract(X0,X2)),
inference(resolution,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
equalish(add(X0,subtract(X1,X2)),add(subtract(X0,X2),X1)),
inference(resolution,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n006.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Sat Sep 26 01:51:42 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.52 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.38/11.64 % SZS status Unsatisfiable for theBenchmark.p
% 58.38/11.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------