%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL203-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 07:54:02 AM UTC 2026
% Result : Unsatisfiable 133.38s 39.54s
% Output : CNFRefutation 133.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 4 RR)
% Number of literals : 75 ( 74 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 156 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(axiom_1_2,axiom,
axiom(implies(or(X0,X0),X0)) = true ).
cnf(axiom_1_3,axiom,
axiom(implies(X0,or(X1,X0))) = true ).
cnf(axiom_1_4,axiom,
axiom(implies(or(X0,X1),or(X1,X0))) = true ).
cnf(axiom_1_5,axiom,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) = true ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) = true ).
cnf(implies_definition,axiom,
implies(X0,X1) = or(not(X0),X1) ).
cnf(rule_1,axiom,
ifeq(axiom(X0),true,theorem(X0),true) = true ).
cnf(rule_2,axiom,
ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true ).
cnf(prove_this,negated_conjecture,
theorem(implies(not(or(p,q)),or(not(p),not(q)))) != true ).
cnf(c0,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
axiom(implies(or(X0,X0),X0)) = true,
inference(clausification,[status(esa)],[axiom_1_2]) ).
cnf(c2,plain,
axiom(implies(X0,or(X1,X0))) = true,
inference(clausification,[status(esa)],[axiom_1_3]) ).
cnf(c3,plain,
axiom(implies(or(X0,X1),or(X1,X0))) = true,
inference(clausification,[status(esa)],[axiom_1_4]) ).
cnf(c4,plain,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) = true,
inference(clausification,[status(esa)],[axiom_1_5]) ).
cnf(c5,plain,
axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) = true,
inference(clausification,[status(esa)],[axiom_1_6]) ).
cnf(c6,plain,
implies(X0,X1) = or(not(X0),X1),
inference(clausification,[status(esa)],[implies_definition]) ).
cnf(c7,plain,
ifeq(axiom(X0),true,theorem(X0),true) = true,
inference(clausification,[status(esa)],[rule_1]) ).
cnf(c8,plain,
ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
inference(clausification,[status(esa)],[rule_2]) ).
cnf(c9,plain,
theorem(implies(not(or(p,q)),or(not(p),not(q)))) != true,
inference(clausification,[status(esa)],[prove_this]) ).
cnf(d0,plain,
theorem(implies(not(or(p,q)),implies(p,not(q)))) != true,
inference(demodulation,[status(thm)],[c9,c6]) ).
cnf(d1,plain,
axiom(implies(or(X2,implies(X0,X1)),or(not(X0),or(X2,X1)))) = true,
inference(superposition,[status(thm)],[c6,c4]) ).
cnf(d2,plain,
axiom(implies(or(X1,implies(X0,X2)),implies(X0,or(X1,X2)))) = true,
inference(demodulation,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
ifeq(true,true,theorem(implies(or(X0,implies(X1,X2)),implies(X1,or(X0,X2)))),true) = true,
inference(superposition,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
theorem(implies(or(X0,implies(X1,X2)),implies(X1,or(X0,X2)))) = true,
inference(demodulation,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
ifeq(true,true,ifeq(theorem(or(X0,implies(X1,X2))),true,theorem(implies(X1,or(X0,X2))),true),true) = true,
inference(superposition,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
ifeq(theorem(or(X0,implies(X1,X2))),true,theorem(implies(X1,or(X0,X2))),true) = true,
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
ifeq(true,true,theorem(implies(X0,or(X1,X0))),true) = true,
inference(superposition,[status(thm)],[c2,c7]) ).
cnf(d8,plain,
theorem(implies(X0,or(X1,X0))) = true,
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
ifeq(true,true,ifeq(theorem(X0),true,theorem(or(X1,X0)),true),true) = true,
inference(superposition,[status(thm)],[d8,c8]) ).
cnf(d10,plain,
ifeq(theorem(X0),true,theorem(or(X1,X0)),true) = true,
inference(demodulation,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
ifeq(true,true,theorem(implies(or(X0,X1),or(X1,X0))),true) = true,
inference(superposition,[status(thm)],[c3,c7]) ).
cnf(d12,plain,
theorem(implies(or(X0,X1),or(X1,X0))) = true,
inference(demodulation,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
theorem(implies(implies(X0,X1),or(X1,not(X0)))) = true,
inference(superposition,[status(thm)],[c6,d12]) ).
cnf(d14,plain,
theorem(implies(implies(X1,not(X0)),implies(X0,not(X1)))) = true,
inference(superposition,[status(thm)],[c6,d13]) ).
cnf(d15,plain,
ifeq(true,true,ifeq(theorem(implies(X0,not(X1))),true,theorem(implies(X1,not(X0))),true),true) = true,
inference(superposition,[status(thm)],[d14,c8]) ).
cnf(d16,plain,
ifeq(theorem(implies(X0,not(X1))),true,theorem(implies(X1,not(X0))),true) = true,
inference(demodulation,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
ifeq(theorem(implies(implies(X0,or(X1,X0)),X2)),true,ifeq(true,true,theorem(X2),true),true) = true,
inference(superposition,[status(thm)],[d8,c8]) ).
cnf(d18,plain,
ifeq(theorem(implies(implies(X1,or(X2,X1)),X0)),true,theorem(X0),true) = true,
inference(demodulation,[status(thm)],[d17,c0]) ).
cnf(d19,plain,
ifeq(true,true,theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),true) = true,
inference(superposition,[status(thm)],[c5,c7]) ).
cnf(d20,plain,
theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) = true,
inference(demodulation,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
ifeq(true,true,ifeq(theorem(implies(X0,X1)),true,theorem(implies(or(X2,X0),or(X2,X1))),true),true) = true,
inference(superposition,[status(thm)],[d20,c8]) ).
cnf(d22,plain,
ifeq(theorem(implies(X0,X1)),true,theorem(implies(or(X2,X0),or(X2,X1))),true) = true,
inference(demodulation,[status(thm)],[d21,c0]) ).
cnf(d23,plain,
ifeq(true,true,ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true),true) = true,
inference(superposition,[status(thm)],[d12,c8]) ).
cnf(d24,plain,
ifeq(theorem(or(X0,X1)),true,theorem(or(X1,X0)),true) = true,
inference(demodulation,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
ifeq(theorem(implies(X0,X1)),true,theorem(or(X1,not(X0))),true) = true,
inference(superposition,[status(thm)],[c6,d24]) ).
cnf(d26,plain,
ifeq(true,true,theorem(implies(or(X0,X0),X0)),true) = true,
inference(superposition,[status(thm)],[c1,c7]) ).
cnf(d27,plain,
theorem(implies(or(X0,X0),X0)) = true,
inference(demodulation,[status(thm)],[d26,c0]) ).
cnf(d28,plain,
ifeq(true,true,ifeq(theorem(or(X0,X0)),true,theorem(X0),true),true) = true,
inference(superposition,[status(thm)],[d27,c8]) ).
cnf(d29,plain,
ifeq(theorem(or(X0,X0)),true,theorem(X0),true) = true,
inference(demodulation,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
axiom(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))) = true,
inference(superposition,[status(thm)],[c6,c4]) ).
cnf(d31,plain,
axiom(implies(implies(X0,or(X2,X1)),or(X2,implies(X0,X1)))) = true,
inference(demodulation,[status(thm)],[d30,c6]) ).
cnf(d32,plain,
ifeq(true,true,theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),true) = true,
inference(superposition,[status(thm)],[d31,c7]) ).
cnf(d33,plain,
theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))) = true,
inference(demodulation,[status(thm)],[d32,c0]) ).
cnf(d34,plain,
ifeq(true,true,theorem(or(X1,implies(X0,X0))),true) = true,
inference(superposition,[status(thm)],[d33,d18]) ).
cnf(d35,plain,
theorem(or(X0,implies(X1,X1))) = true,
inference(demodulation,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
ifeq(true,true,theorem(implies(X0,X0)),true) = true,
inference(superposition,[status(thm)],[d35,d29]) ).
cnf(d37,plain,
theorem(implies(X0,X0)) = true,
inference(demodulation,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
ifeq(true,true,theorem(or(X0,not(X0))),true) = true,
inference(superposition,[status(thm)],[d37,d25]) ).
cnf(d39,plain,
theorem(or(X0,not(X0))) = true,
inference(demodulation,[status(thm)],[d38,c0]) ).
cnf(d40,plain,
theorem(implies(X0,not(not(X0)))) = true,
inference(superposition,[status(thm)],[c6,d39]) ).
cnf(d41,plain,
ifeq(true,true,theorem(implies(or(X1,X0),or(X1,not(not(X0))))),true) = true,
inference(superposition,[status(thm)],[d40,d22]) ).
cnf(d42,plain,
theorem(implies(or(X0,X1),or(X0,not(not(X1))))) = true,
inference(demodulation,[status(thm)],[d41,c0]) ).
cnf(d43,plain,
theorem(implies(implies(X0,X1),or(not(X0),not(not(X1))))) = true,
inference(superposition,[status(thm)],[c6,d42]) ).
cnf(d44,plain,
theorem(implies(implies(X0,X1),implies(X0,not(not(X1))))) = true,
inference(demodulation,[status(thm)],[d43,c6]) ).
cnf(d45,plain,
ifeq(true,true,theorem(implies(X0,not(not(or(X1,X0))))),true) = true,
inference(superposition,[status(thm)],[d44,d18]) ).
cnf(d46,plain,
theorem(implies(X0,not(not(or(X1,X0))))) = true,
inference(demodulation,[status(thm)],[d45,c0]) ).
cnf(d47,plain,
ifeq(true,true,theorem(implies(not(or(X1,X0)),not(X0))),true) = true,
inference(superposition,[status(thm)],[d46,d16]) ).
cnf(d48,plain,
theorem(implies(not(or(X0,X1)),not(X1))) = true,
inference(demodulation,[status(thm)],[d47,c0]) ).
cnf(d49,plain,
ifeq(true,true,theorem(or(X2,implies(not(or(X0,X1)),not(X1)))),true) = true,
inference(superposition,[status(thm)],[d48,d10]) ).
cnf(d50,plain,
theorem(or(X0,implies(not(or(X1,X2)),not(X2)))) = true,
inference(demodulation,[status(thm)],[d49,c0]) ).
cnf(d51,plain,
ifeq(true,true,theorem(implies(not(or(X1,X2)),or(X0,not(X2)))),true) = true,
inference(superposition,[status(thm)],[d50,d6]) ).
cnf(d52,plain,
theorem(implies(not(or(X0,X1)),or(X2,not(X1)))) = true,
inference(demodulation,[status(thm)],[d51,c0]) ).
cnf(d53,plain,
theorem(implies(not(or(X2,X1)),implies(X0,not(X1)))) = true,
inference(superposition,[status(thm)],[c6,d52]) ).
cnf(d54,plain,
$false,
inference(resolution,[status(thm)],[d53,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL203-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n005.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 22:00:08 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 133.38/39.54 % SZS status Unsatisfiable for theBenchmark.p
% 133.38/39.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------