%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA003-2 : 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 : n003.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 06:50:34 AM UTC 2026
% Result : Unsatisfiable 36.73s 6.62s
% Output : CNFRefutation 36.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 43 ( 4 unt; 0 nHn; 43 RR)
% Number of literals : 132 ( 0 equ; 103 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_less_than,axiom,
( 'less$uthan'(X0,X2)
| ~ 'less$uthan'(X1,X2)
| ~ 'less$uthan'(X0,X1) ) ).
cnf(axiom_2_1,axiom,
( 'less$uthan'(n0,minimum(X0,X1))
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(n0,X0) ) ).
cnf(axiom_2_2,axiom,
( 'less$uthan'(minimum(X0,X1),X0)
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(n0,X0) ) ).
cnf(axiom_2_3,axiom,
( 'less$uthan'(minimum(X0,X1),X1)
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(n0,X0) ) ).
cnf(axiom_3,axiom,
( 'less$uthan'(add(X0,X2),X1)
| ~ 'less$uthan'(X2,half(X1))
| ~ 'less$uthan'(X0,half(X1)) ) ).
cnf(axiom_7,axiom,
( 'less$uthan'(n0,half(X0))
| ~ 'less$uthan'(n0,X0) ) ).
cnf(c_10,negated_conjecture,
( 'less$uthan'(n0,fp31(X0))
| ~ 'less$uthan'(n0,X0) ) ).
cnf(c_11,negated_conjecture,
( 'less$uthan'(absolute(add(f(X1),minus(l1))),X0)
| ~ 'less$uthan'(absolute(add(X1,minus(a))),fp31(X0))
| ~ 'less$uthan'(n0,X0) ) ).
cnf(c_12,negated_conjecture,
( 'less$uthan'(n0,fp32(X0))
| ~ 'less$uthan'(n0,X0) ) ).
cnf(c_13,negated_conjecture,
( 'less$uthan'(absolute(add(g(X1),minus(l2))),X0)
| ~ 'less$uthan'(absolute(add(X1,minus(a))),fp32(X0))
| ~ 'less$uthan'(n0,X0) ) ).
cnf(c_14,negated_conjecture,
'less$uthan'(n0,b) ).
cnf(c_15,negated_conjecture,
( 'less$uthan'(absolute(add(fp33(X0),minus(a))),X0)
| ~ 'less$uthan'(n0,X0) ) ).
cnf(c_16,negated_conjecture,
( ~ 'less$uthan'(add(absolute(add(f(fp33(X0)),minus(l1))),absolute(add(g(fp33(X0)),minus(l2)))),b)
| ~ 'less$uthan'(n0,X0) ) ).
cnf(c3,plain,
( 'less$uthan'(X0,X2)
| ~ 'less$uthan'(X1,X2)
| ~ 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less_than]) ).
cnf(c4,plain,
( 'less$uthan'(n0,minimum(X0,X1))
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[axiom_2_1]) ).
cnf(c5,plain,
( 'less$uthan'(minimum(X0,X1),X0)
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[axiom_2_2]) ).
cnf(c6,plain,
( 'less$uthan'(minimum(X0,X1),X1)
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[axiom_2_3]) ).
cnf(c7,plain,
( 'less$uthan'(add(X0,X2),X1)
| ~ 'less$uthan'(X2,half(X1))
| ~ 'less$uthan'(X0,half(X1)) ),
inference(clausification,[status(esa)],[axiom_3]) ).
cnf(c9,plain,
( 'less$uthan'(n0,half(X0))
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[axiom_7]) ).
cnf(c10,plain,
( 'less$uthan'(n0,fp31(X0))
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[c_10]) ).
cnf(c11,plain,
( 'less$uthan'(absolute(add(f(X1),minus(l1))),X0)
| ~ 'less$uthan'(absolute(add(X1,minus(a))),fp31(X0))
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[c_11]) ).
cnf(c12,plain,
( 'less$uthan'(n0,fp32(X0))
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[c_12]) ).
cnf(c13,plain,
( 'less$uthan'(absolute(add(g(X1),minus(l2))),X0)
| ~ 'less$uthan'(absolute(add(X1,minus(a))),fp32(X0))
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[c_13]) ).
cnf(c14,plain,
'less$uthan'(n0,b),
inference(clausification,[status(esa)],[c_14]) ).
cnf(c15,plain,
( 'less$uthan'(absolute(add(fp33(X0),minus(a))),X0)
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[c_15]) ).
cnf(c16,plain,
( ~ 'less$uthan'(add(absolute(add(f(fp33(X0)),minus(l1))),absolute(add(g(fp33(X0)),minus(l2)))),b)
| ~ 'less$uthan'(n0,X0) ),
inference(clausification,[status(esa)],[c_16]) ).
cnf(d0,plain,
( 'less$uthan'(minimum(X0,X1),X2)
| ~ 'less$uthan'(X0,X2)
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(n0,X0) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d1,plain,
( 'less$uthan'(absolute(add(fp33(X0),minus(a))),X1)
| ~ 'less$uthan'(X0,X1)
| ~ 'less$uthan'(n0,X0) ),
inference(resolution,[status(thm)],[c15,c3]) ).
cnf(d2,plain,
( 'less$uthan'(absolute(add(f(fp33(X0)),minus(l1))),X1)
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(X0,fp31(X1)) ),
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d3,plain,
( ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(X1,fp32(X0))
| 'less$uthan'(absolute(add(g(fp33(X1)),minus(l2))),X0)
| ~ 'less$uthan'(n0,X0) ),
inference(resolution,[status(thm)],[c13,d1]) ).
cnf(d4,plain,
( ~ 'less$uthan'(absolute(add(f(fp33(X0)),minus(l1))),half(b))
| ~ 'less$uthan'(absolute(add(g(fp33(X0)),minus(l2))),half(b))
| ~ 'less$uthan'(n0,X0) ),
inference(resolution,[status(thm)],[c16,c7]) ).
cnf(d5,plain,
( ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(X0,fp32(half(b)))
| ~ 'less$uthan'(absolute(add(f(fp33(X0)),minus(l1))),half(b))
| ~ 'less$uthan'(n0,X0) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(X0,fp31(half(b)))
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(X0,fp32(half(b))) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(n0,X1)
| ~ 'less$uthan'(X0,fp32(half(b)))
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,minimum(X0,X1))
| ~ 'less$uthan'(minimum(X0,X1),fp31(half(b))) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(n0,fp31(half(b)))
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,minimum(X0,fp31(half(b))))
| ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(n0,fp31(half(b)))
| ~ 'less$uthan'(X0,fp32(half(b))) ),
inference(resolution,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
( ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(n0,fp31(half(b)))
| ~ 'less$uthan'(n0,fp31(half(b)))
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(X0,fp32(half(b))) ),
inference(resolution,[status(thm)],[d8,c4]) ).
cnf(d10,plain,
( ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(X0,fp32(half(b))) ),
inference(resolution,[status(thm)],[d9,c10]) ).
cnf(d11,plain,
( ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(n0,fp32(half(b)))
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,minimum(X0,fp32(half(b)))) ),
inference(resolution,[status(thm)],[d10,c6]) ).
cnf(d12,plain,
( ~ 'less$uthan'(n0,X0)
| ~ 'less$uthan'(n0,fp32(half(b)))
| ~ 'less$uthan'(n0,fp32(half(b)))
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,X0) ),
inference(resolution,[status(thm)],[d11,c4]) ).
cnf(d13,plain,
( ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,half(b))
| ~ 'less$uthan'(n0,X0) ),
inference(resolution,[status(thm)],[d12,c12]) ).
cnf(d14,plain,
( ~ 'less$uthan'(n0,b)
| ~ 'less$uthan'(n0,X0) ),
inference(resolution,[status(thm)],[d13,c9]) ).
cnf(d15,plain,
~ 'less$uthan'(n0,X0),
inference(resolution,[status(thm)],[c14,d14]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,c14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n003.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 22:03:39 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.73/6.62 % SZS status Unsatisfiable for theBenchmark.p
% 36.73/6.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------