%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 07:24:37 AM UTC 2026
% Result : Unsatisfiable 52.35s 24.59s
% Output : CNFRefutation 52.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of clauses : 79 ( 79 unt; 0 nHn; 5 RR)
% Number of literals : 79 ( 78 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos01,axiom,
product(X0,one) = X0 ).
cnf(sos02,axiom,
product(one,X0) = X0 ).
cnf(sos03,axiom,
product(X0,difference(X0,X1)) = X1 ).
cnf(sos04,axiom,
difference(X0,product(X0,X1)) = X1 ).
cnf(sos05,axiom,
quotient(product(X0,X1),X1) = X0 ).
cnf(sos06,axiom,
product(quotient(X0,X1),X1) = X0 ).
cnf(sos07,axiom,
difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0) ).
cnf(sos08,axiom,
difference(product(X0,X1),product(X0,product(X1,X2))) = quotient(quotient(product(X2,product(X0,X1)),X1),X0) ).
cnf(sos09,axiom,
i(X0) = difference(X0,one) ).
cnf(sos10,axiom,
j(X0) = quotient(one,X0) ).
cnf(sos11,axiom,
product(i(X0),X0) = product(X0,j(X0)) ).
cnf(sos12,axiom,
eta(X0) = product(i(X0),X0) ).
cnf(sos13,axiom,
product(i(i(X0)),X1) = product(eta(X0),product(X0,X1)) ).
cnf(sos16,axiom,
product(eta(X0),product(X1,X2)) = product(product(eta(X0),X1),X2) ).
cnf(sos19,axiom,
t(X0,X1) = quotient(product(X0,X1),X0) ).
cnf(goals,negated_conjecture,
product(j(j(x0)),j(product(x1,x0))) != j(x1) ).
cnf(c0,plain,
product(X0,one) = X0,
inference(clausification,[status(esa)],[sos01]) ).
cnf(c1,plain,
product(one,X0) = X0,
inference(clausification,[status(esa)],[sos02]) ).
cnf(c2,plain,
product(X0,difference(X0,X1)) = X1,
inference(clausification,[status(esa)],[sos03]) ).
cnf(c3,plain,
difference(X0,product(X0,X1)) = X1,
inference(clausification,[status(esa)],[sos04]) ).
cnf(c4,plain,
quotient(product(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[sos05]) ).
cnf(c5,plain,
product(quotient(X0,X1),X1) = X0,
inference(clausification,[status(esa)],[sos06]) ).
cnf(c6,plain,
difference(X0,product(product(X0,X1),X2)) = quotient(product(X1,product(X2,X0)),X0),
inference(clausification,[status(esa)],[sos07]) ).
cnf(c7,plain,
difference(product(X0,X1),product(X0,product(X1,X2))) = quotient(quotient(product(X2,product(X0,X1)),X1),X0),
inference(clausification,[status(esa)],[sos08]) ).
cnf(c8,plain,
i(X0) = difference(X0,one),
inference(clausification,[status(esa)],[sos09]) ).
cnf(c9,plain,
j(X0) = quotient(one,X0),
inference(clausification,[status(esa)],[sos10]) ).
cnf(c10,plain,
product(i(X0),X0) = product(X0,j(X0)),
inference(clausification,[status(esa)],[sos11]) ).
cnf(c11,plain,
eta(X0) = product(i(X0),X0),
inference(clausification,[status(esa)],[sos12]) ).
cnf(c12,plain,
product(i(i(X0)),X1) = product(eta(X0),product(X0,X1)),
inference(clausification,[status(esa)],[sos13]) ).
cnf(c15,plain,
product(eta(X0),product(X1,X2)) = product(product(eta(X0),X1),X2),
inference(clausification,[status(esa)],[sos16]) ).
cnf(c18,plain,
t(X0,X1) = quotient(product(X0,X1),X0),
inference(clausification,[status(esa)],[sos19]) ).
cnf(c20,plain,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
inference(clausification,[status(esa)],[goals]) ).
cnf(d0,plain,
product(j(X0),X0) = one,
inference(superposition,[status(thm)],[c9,c5]) ).
cnf(d1,plain,
quotient(one,X0) = j(X0),
inference(superposition,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
quotient(X1,difference(X0,X1)) = X0,
inference(superposition,[status(thm)],[c2,c4]) ).
cnf(d3,plain,
X0 = j(difference(X0,one)),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
X0 = j(i(X0)),
inference(demodulation,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
quotient(X0,one) = X0,
inference(superposition,[status(thm)],[c0,c4]) ).
cnf(d6,plain,
X0 = product(X0,one),
inference(superposition,[status(thm)],[c4,d5]) ).
cnf(d7,plain,
product(i(i(X0)),one) = product(eta(X0),X0),
inference(superposition,[status(thm)],[d6,c12]) ).
cnf(d8,plain,
i(i(X0)) = product(eta(X0),X0),
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
difference(product(eta(X0),X0),product(i(i(X0)),X1)) = quotient(quotient(product(X1,product(eta(X0),X0)),X0),eta(X0)),
inference(superposition,[status(thm)],[c12,c7]) ).
cnf(d10,plain,
difference(i(i(X0)),product(i(i(X0)),X1)) = quotient(quotient(product(X1,product(eta(X0),X0)),X0),eta(X0)),
inference(demodulation,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
X1 = quotient(quotient(product(X1,product(eta(X0),X0)),X0),eta(X0)),
inference(demodulation,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
X1 = quotient(quotient(product(X1,i(i(X0))),X0),eta(X0)),
inference(demodulation,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
quotient(X0,i(i(X1))) = quotient(quotient(X0,X1),eta(X1)),
inference(superposition,[status(thm)],[c5,d12]) ).
cnf(d14,plain,
difference(X0,product(X1,X2)) = quotient(product(difference(X0,X1),product(X2,X0)),X0),
inference(superposition,[status(thm)],[c2,c6]) ).
cnf(d15,plain,
difference(product(X2,X0),product(X2,X1)) = quotient(quotient(product(difference(X0,X1),product(X2,X0)),X0),X2),
inference(superposition,[status(thm)],[c2,c7]) ).
cnf(d16,plain,
difference(product(X2,X0),product(X2,X1)) = quotient(difference(X0,product(X1,X2)),X2),
inference(demodulation,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
difference(product(eta(X0),X1),product(eta(X0),product(X1,X2))) = X2,
inference(superposition,[status(thm)],[c15,c3]) ).
cnf(d18,plain,
quotient(difference(X1,product(product(X1,X2),eta(X0))),eta(X0)) = X2,
inference(demodulation,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
quotient(quotient(product(X1,product(eta(X2),X0)),X0),eta(X2)) = X1,
inference(demodulation,[status(thm)],[d18,c6]) ).
cnf(d20,plain,
product(X0,i(X0)) = one,
inference(superposition,[status(thm)],[c8,c2]) ).
cnf(d21,plain,
difference(X0,product(one,X1)) = quotient(product(i(X0),product(X1,X0)),X0),
inference(superposition,[status(thm)],[d20,c6]) ).
cnf(d22,plain,
difference(X1,X0) = quotient(product(i(X1),product(X0,X1)),X1),
inference(demodulation,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
quotient(difference(X0,eta(X1)),eta(X1)) = i(X0),
inference(superposition,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
eta(X0) = product(X0,j(X0)),
inference(demodulation,[status(thm)],[c10,c11]) ).
cnf(d25,plain,
product(X0,quotient(product(X1,product(X2,X0)),X0)) = product(product(X0,X1),X2),
inference(superposition,[status(thm)],[c6,c2]) ).
cnf(d26,plain,
product(X1,quotient(one,X1)) = product(product(X1,j(product(X0,X1))),X0),
inference(superposition,[status(thm)],[d0,d25]) ).
cnf(d27,plain,
product(X0,j(X0)) = product(product(X0,j(product(X1,X0))),X1),
inference(demodulation,[status(thm)],[d26,c9]) ).
cnf(d28,plain,
eta(X0) = product(product(X0,j(product(X1,X0))),X1),
inference(demodulation,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
difference(product(X0,j(product(X1,X0))),eta(X0)) = X1,
inference(superposition,[status(thm)],[d28,c3]) ).
cnf(d30,plain,
difference(product(X1,j(X0)),eta(X1)) = quotient(X0,X1),
inference(superposition,[status(thm)],[c5,d29]) ).
cnf(d31,plain,
quotient(quotient(X1,X0),eta(X0)) = i(product(X0,j(X1))),
inference(superposition,[status(thm)],[d30,d23]) ).
cnf(d32,plain,
quotient(X0,i(i(X1))) = i(product(X1,j(X0))),
inference(demodulation,[status(thm)],[d31,d13]) ).
cnf(d33,plain,
product(X0,j(X1)) = j(quotient(X1,i(i(X0)))),
inference(superposition,[status(thm)],[d32,d4]) ).
cnf(d34,plain,
difference(X0,one) = i(X0),
inference(superposition,[status(thm)],[d20,c3]) ).
cnf(d35,plain,
difference(quotient(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c5,c3]) ).
cnf(d36,plain,
X0 = i(quotient(one,X0)),
inference(superposition,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
X0 = i(j(X0)),
inference(demodulation,[status(thm)],[d36,c9]) ).
cnf(d38,plain,
product(j(X0),j(X1)) = j(quotient(X1,i(X0))),
inference(superposition,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
product(j(j(X0)),j(X1)) = j(quotient(X1,X0)),
inference(superposition,[status(thm)],[d37,d38]) ).
cnf(d40,plain,
j(quotient(product(x1,x0),x0)) != j(x1),
inference(demodulation,[status(thm)],[c20,d39]) ).
cnf(d41,plain,
j(x1) != j(x1),
inference(demodulation,[status(thm)],[d40,c4]) ).
cnf(d42,plain,
difference(t(X0,X1),product(X0,X1)) = X0,
inference(superposition,[status(thm)],[c18,d35]) ).
cnf(d43,plain,
t(X0,X0) = X0,
inference(superposition,[status(thm)],[c18,c4]) ).
cnf(d44,plain,
difference(X0,product(X0,X0)) = X0,
inference(superposition,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d44,c3]) ).
cnf(d46,plain,
$false,
inference(resolution,[status(thm)],[d45,d41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP767-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 15:45:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.35/24.59 % SZS status Unsatisfiable for theBenchmark.p
% 52.35/24.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------