%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 07:45:01 AM UTC 2026
% Result : Unsatisfiable 9.62s 3.41s
% Output : CNFRefutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 64 ( 7 unt; 20 nHn; 64 RR)
% Number of literals : 264 ( 0 equ; 188 neg)
% Maximal clause size : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 70 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1,negated_conjecture,
e(exist) ).
cnf(clause_2,negated_conjecture,
~ f(exist) ).
cnf(clause_3,axiom,
( ~ a(X0)
| d(X0)
| c(X0) ) ).
cnf(clause_6,axiom,
( ~ c(X1)
| ~ c(X0)
| ~ r(X2,X1)
| ~ r(X2,X0)
| ~ e(X2)
| equalish(X0,X1) ) ).
cnf(clause_7,axiom,
( ~ e(X0)
| r3least(X0) ) ).
cnf(clause_8,axiom,
( ~ r(X1,X0)
| ~ e(X1)
| a(X0) ) ).
cnf(clause_19,axiom,
( ~ equalish(u2r2(X0),u2r1(X0))
| ~ r3least(X0) ) ).
cnf(clause_20,axiom,
( ~ equalish(u2r3(X0),u2r1(X0))
| ~ r3least(X0) ) ).
cnf(clause_21,axiom,
( ~ equalish(u2r3(X0),u2r2(X0))
| ~ r3least(X0) ) ).
cnf(clause_22,axiom,
( ~ r3least(X0)
| r(X0,u2r1(X0)) ) ).
cnf(clause_23,axiom,
( ~ r3least(X0)
| r(X0,u2r2(X0)) ) ).
cnf(clause_24,axiom,
( ~ r3least(X0)
| r(X0,u2r3(X0)) ) ).
cnf(clause_31,axiom,
( ~ d(X2)
| ~ d(X1)
| ~ r(X0,X2)
| ~ r(X0,X1)
| equalish(X1,X2)
| f(X0) ) ).
cnf(c0,plain,
e(exist),
inference(clausification,[status(esa)],[clause_1]) ).
cnf(c1,plain,
~ f(exist),
inference(clausification,[status(esa)],[clause_2]) ).
cnf(c2,plain,
( ~ a(X0)
| d(X0)
| c(X0) ),
inference(clausification,[status(esa)],[clause_3]) ).
cnf(c5,plain,
( ~ c(X1)
| ~ r(X0,X2)
| ~ e(X0)
| ~ c(X2)
| equalish(X1,X2)
| ~ r(X0,X1) ),
inference(clausification,[status(esa)],[clause_6]) ).
cnf(c6,plain,
( ~ e(X0)
| r3least(X0) ),
inference(clausification,[status(esa)],[clause_7]) ).
cnf(c7,plain,
( ~ r(X1,X0)
| ~ e(X1)
| a(X0) ),
inference(clausification,[status(esa)],[clause_8]) ).
cnf(c18,plain,
( ~ equalish(u2r2(X0),u2r1(X0))
| ~ r3least(X0) ),
inference(clausification,[status(esa)],[clause_19]) ).
cnf(c19,plain,
( ~ equalish(u2r3(X0),u2r1(X0))
| ~ r3least(X0) ),
inference(clausification,[status(esa)],[clause_20]) ).
cnf(c20,plain,
( ~ equalish(u2r3(X0),u2r2(X0))
| ~ r3least(X0) ),
inference(clausification,[status(esa)],[clause_21]) ).
cnf(c21,plain,
( ~ r3least(X0)
| r(X0,u2r1(X0)) ),
inference(clausification,[status(esa)],[clause_22]) ).
cnf(c22,plain,
( ~ r3least(X0)
| r(X0,u2r2(X0)) ),
inference(clausification,[status(esa)],[clause_23]) ).
cnf(c23,plain,
( ~ r3least(X0)
| r(X0,u2r3(X0)) ),
inference(clausification,[status(esa)],[clause_24]) ).
cnf(c30,plain,
( ~ d(X1)
| ~ d(X2)
| ~ r(X0,X2)
| equalish(X2,X1)
| ~ r(X0,X1)
| f(X0) ),
inference(clausification,[status(esa)],[clause_31]) ).
cnf(d0,plain,
r3least(exist),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d1,plain,
( a(u2r2(X0))
| ~ e(X0)
| ~ r3least(X0) ),
inference(resolution,[status(thm)],[c22,c7]) ).
cnf(d2,plain,
( d(u2r2(X0))
| c(u2r2(X0))
| ~ r3least(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( a(u2r1(X0))
| ~ e(X0)
| ~ r3least(X0) ),
inference(resolution,[status(thm)],[c21,c7]) ).
cnf(d4,plain,
( d(u2r1(X0))
| c(u2r1(X0))
| ~ r3least(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( ~ r3least(X0)
| equalish(X1,u2r1(X0))
| ~ r(X0,X1)
| ~ d(u2r1(X0))
| ~ d(X1)
| f(X0) ),
inference(resolution,[status(thm)],[c30,c21]) ).
cnf(d6,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ r(X0,u2r2(X0))
| ~ d(u2r1(X0))
| ~ d(u2r2(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d5,c18]) ).
cnf(d7,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ d(u2r1(X0))
| ~ d(u2r2(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d6,c22]) ).
cnf(d8,plain,
( ~ r3least(X0)
| c(u2r1(X0))
| ~ e(X0)
| ~ r3least(X0)
| ~ d(u2r2(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
( ~ r3least(X0)
| c(u2r2(X0))
| ~ e(X0)
| ~ r3least(X0)
| c(u2r1(X0))
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( equalish(u2r3(X0),X1)
| ~ r(X0,X1)
| ~ c(u2r3(X0))
| ~ c(X1)
| ~ e(X0)
| ~ r3least(X0) ),
inference(resolution,[status(thm)],[c23,c5]) ).
cnf(d11,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ r(X0,u2r1(X0))
| ~ c(u2r3(X0))
| ~ c(u2r1(X0))
| ~ e(X0) ),
inference(resolution,[status(thm)],[d10,c19]) ).
cnf(d12,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ c(u2r3(X0))
| ~ c(u2r1(X0))
| ~ e(X0) ),
inference(resolution,[status(thm)],[d11,c21]) ).
cnf(d13,plain,
( a(u2r3(X0))
| ~ e(X0)
| ~ r3least(X0) ),
inference(resolution,[status(thm)],[c23,c7]) ).
cnf(d14,plain,
( d(u2r3(X0))
| c(u2r3(X0))
| ~ r3least(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
( ~ r3least(X0)
| equalish(X1,u2r2(X0))
| ~ r(X0,X1)
| ~ d(u2r2(X0))
| ~ d(X1)
| f(X0) ),
inference(resolution,[status(thm)],[c30,c22]) ).
cnf(d16,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ r(X0,u2r3(X0))
| ~ d(u2r2(X0))
| ~ d(u2r3(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d15,c20]) ).
cnf(d17,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ d(u2r3(X0))
| ~ d(u2r2(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d16,c23]) ).
cnf(d18,plain,
( ~ r3least(X0)
| c(u2r3(X0))
| ~ e(X0)
| ~ r3least(X0)
| ~ d(u2r2(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
( ~ r3least(X0)
| c(u2r2(X0))
| ~ e(X0)
| ~ r3least(X0)
| c(u2r3(X0))
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
( ~ r3least(X0)
| ~ c(u2r1(X0))
| ~ e(X0)
| ~ r3least(X0)
| c(u2r2(X0))
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d19,d12]) ).
cnf(d21,plain,
( ~ r3least(X0)
| c(u2r2(X0))
| f(X0)
| ~ e(X0)
| ~ r3least(X0)
| c(u2r2(X0))
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d20,d9]) ).
cnf(d22,plain,
( equalish(u2r2(X0),X1)
| ~ r(X0,X1)
| ~ c(u2r2(X0))
| ~ c(X1)
| ~ e(X0)
| ~ r3least(X0) ),
inference(resolution,[status(thm)],[c22,c5]) ).
cnf(d23,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ r(X0,u2r1(X0))
| ~ c(u2r2(X0))
| ~ c(u2r1(X0))
| ~ e(X0) ),
inference(resolution,[status(thm)],[d22,c18]) ).
cnf(d24,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ c(u2r1(X0))
| ~ c(u2r2(X0))
| ~ e(X0) ),
inference(resolution,[status(thm)],[d23,c21]) ).
cnf(d25,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ r(X0,u2r2(X0))
| ~ c(u2r3(X0))
| ~ c(u2r2(X0))
| ~ e(X0) ),
inference(resolution,[status(thm)],[d10,c20]) ).
cnf(d26,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ c(u2r3(X0))
| ~ c(u2r2(X0))
| ~ e(X0) ),
inference(resolution,[status(thm)],[d25,c22]) ).
cnf(d27,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ r(X0,u2r3(X0))
| ~ d(u2r1(X0))
| ~ d(u2r3(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d5,c19]) ).
cnf(d28,plain,
( ~ r3least(X0)
| ~ r3least(X0)
| ~ d(u2r3(X0))
| ~ d(u2r1(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d27,c23]) ).
cnf(d29,plain,
( ~ r3least(X0)
| c(u2r3(X0))
| ~ e(X0)
| ~ r3least(X0)
| ~ d(u2r1(X0))
| f(X0) ),
inference(resolution,[status(thm)],[d28,d14]) ).
cnf(d30,plain,
( ~ r3least(X0)
| c(u2r1(X0))
| ~ e(X0)
| ~ r3least(X0)
| c(u2r3(X0))
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d29,d4]) ).
cnf(d31,plain,
( ~ r3least(X0)
| ~ c(u2r2(X0))
| ~ e(X0)
| ~ r3least(X0)
| c(u2r1(X0))
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
( ~ r3least(X0)
| c(u2r1(X0))
| f(X0)
| ~ e(X0)
| ~ r3least(X0)
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d21,d31]) ).
cnf(d33,plain,
( ~ r3least(X0)
| ~ c(u2r2(X0))
| ~ e(X0)
| ~ r3least(X0)
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d32,d24]) ).
cnf(d34,plain,
( ~ r3least(X0)
| f(X0)
| ~ e(X0)
| ~ r3least(X0)
| f(X0)
| ~ e(X0) ),
inference(resolution,[status(thm)],[d33,d21]) ).
cnf(d35,plain,
( f(exist)
| ~ e(exist) ),
inference(resolution,[status(thm)],[d34,d0]) ).
cnf(d36,plain,
f(exist),
inference(resolution,[status(thm)],[c0,d35]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[c1,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS010-1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.66 % Computer : n019.cluster.edu
% 0.19/0.66 % Model : x86_64 x86_64
% 0.19/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.66 % Memory : 8046.5625MB
% 0.19/0.66 % OS : Linux 6.8.0-71-generic
% 0.23/0.66 % CPULimit : 300
% 0.23/0.66 % WCLimit : 300
% 0.23/0.66 % DateTime : Fri Sep 25 19:32:36 UTC 2026
% 0.23/0.67 % CPUTime :
% 0.23/0.67 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.62/3.41 % SZS status Unsatisfiable for theBenchmark.p
% 9.62/3.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------