%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:22:12 AM UTC 2026
% Result : Unsatisfiable 136.68s 30.45s
% Output : CNFRefutation 136.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of clauses : 71 ( 71 unt; 0 nHn; 23 RR)
% Number of literals : 71 ( 70 equ; 2 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 : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 132 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(left_identity,axiom,
product(identity,X0,X0) = true ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) = true ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) = true ).
cnf(total_function2,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,equalish(X3,X2),true),true) = true ).
cnf(associativity1,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true ).
cnf(associativity2,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true) = true ).
cnf(product_substitution3,axiom,
ifeq(equalish(X0,X1),true,ifeq(product(X2,X3,X0),true,product(X2,X3,X1),true),true) = true ).
cnf(a_equals_b,hypothesis,
equalish(a,b) = true ).
cnf(prove_inverse_substitution,negated_conjecture,
equalish(inverse(a),inverse(b)) != true ).
cnf(c0,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
product(identity,X0,X0) = true,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c2,plain,
product(inverse(X0),X0,identity) = true,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c3,plain,
product(X0,X1,multiply(X0,X1)) = true,
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c4,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,equalish(X3,X2),true),true) = true,
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c5,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true,
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c6,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true) = true,
inference(clausification,[status(esa)],[associativity2]) ).
cnf(c7,plain,
ifeq(equalish(X0,X1),true,ifeq(product(X2,X3,X0),true,product(X2,X3,X1),true),true) = true,
inference(clausification,[status(esa)],[product_substitution3]) ).
cnf(c8,plain,
equalish(a,b) = true,
inference(clausification,[status(esa)],[a_equals_b]) ).
cnf(c9,plain,
equalish(inverse(a),inverse(b)) != true,
inference(clausification,[status(esa)],[prove_inverse_substitution]) ).
cnf(d0,plain,
ifeq(true,true,ifeq(product(identity,X0,X1),true,equalish(X1,X0),true),true) = true,
inference(superposition,[status(thm)],[c1,c4]) ).
cnf(d1,plain,
ifeq(product(identity,X0,X1),true,equalish(X1,X0),true) = true,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(true,true,ifeq(product(X1,identity,X2),true,ifeq(product(X1,inverse(X0),X3),true,product(X3,X0,X2),true),true),true) = true,
inference(superposition,[status(thm)],[c2,c6]) ).
cnf(d3,plain,
ifeq(product(X0,identity,X1),true,ifeq(product(X0,inverse(X2),X3),true,product(X3,X2,X1),true),true) = true,
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq(product(inverse(inverse(X0)),identity,X1),true,ifeq(true,true,product(identity,X0,X1),true),true) = true,
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d5,plain,
ifeq(product(inverse(inverse(X0)),identity,X1),true,product(identity,X0,X1),true) = true,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq(true,true,ifeq(product(X1,X0,X2),true,ifeq(product(X3,X1,identity),true,product(X3,X2,X0),true),true),true) = true,
inference(superposition,[status(thm)],[c1,c5]) ).
cnf(d7,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,identity),true,product(X3,X2,X1),true),true) = true,
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
ifeq(product(X0,X1,X2),true,ifeq(true,true,product(inverse(X0),X2,X1),true),true) = true,
inference(superposition,[status(thm)],[c2,d7]) ).
cnf(d9,plain,
ifeq(product(X0,X2,X1),true,product(inverse(X0),X1,X2),true) = true,
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq(equalish(multiply(X0,X1),X2),true,ifeq(true,true,product(X0,X1,X2),true),true) = true,
inference(superposition,[status(thm)],[c3,c7]) ).
cnf(d11,plain,
ifeq(equalish(multiply(X0,X1),X2),true,product(X0,X1,X2),true) = true,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq(true,true,ifeq(product(X2,X1,X3),true,ifeq(product(X4,X2,X0),true,product(X4,X3,multiply(X0,X1)),true),true),true) = true,
inference(superposition,[status(thm)],[c3,c5]) ).
cnf(d13,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,X4),true,product(X3,X2,multiply(X4,X1)),true),true) = true,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
ifeq(equalish(X0,X1),true,ifeq(true,true,product(identity,X0,X1),true),true) = true,
inference(superposition,[status(thm)],[c1,c7]) ).
cnf(d15,plain,
ifeq(equalish(X0,X1),true,product(identity,X0,X1),true) = true,
inference(demodulation,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
ifeq(true,true,product(identity,a,b),true) = true,
inference(superposition,[status(thm)],[c8,d15]) ).
cnf(d17,plain,
product(identity,a,b) = true,
inference(demodulation,[status(thm)],[d16,c0]) ).
cnf(d18,plain,
ifeq(product(a,X0,X1),true,ifeq(true,true,product(identity,X1,multiply(b,X0)),true),true) = true,
inference(superposition,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
ifeq(product(a,X1,X0),true,product(identity,X0,multiply(b,X1)),true) = true,
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
ifeq(true,true,ifeq(product(inverse(X0),X0,X1),true,equalish(X1,identity),true),true) = true,
inference(superposition,[status(thm)],[c2,c4]) ).
cnf(d21,plain,
ifeq(product(inverse(X0),X0,X1),true,equalish(X1,identity),true) = true,
inference(demodulation,[status(thm)],[d20,c0]) ).
cnf(d22,plain,
ifeq(true,true,ifeq(product(X1,identity,X2),true,product(X1,X0,multiply(X2,X0)),true),true) = true,
inference(superposition,[status(thm)],[c1,d13]) ).
cnf(d23,plain,
ifeq(product(X0,identity,X1),true,product(X0,X2,multiply(X1,X2)),true) = true,
inference(demodulation,[status(thm)],[d22,c0]) ).
cnf(d24,plain,
ifeq(true,true,ifeq(product(X1,inverse(X0),identity),true,product(X1,identity,X0),true),true) = true,
inference(superposition,[status(thm)],[c2,d7]) ).
cnf(d25,plain,
ifeq(product(X0,inverse(X1),identity),true,product(X0,identity,X1),true) = true,
inference(demodulation,[status(thm)],[d24,c0]) ).
cnf(d26,plain,
ifeq(true,true,product(inverse(inverse(X0)),identity,X0),true) = true,
inference(superposition,[status(thm)],[c2,d25]) ).
cnf(d27,plain,
product(inverse(inverse(X0)),identity,X0) = true,
inference(demodulation,[status(thm)],[d26,c0]) ).
cnf(d28,plain,
ifeq(true,true,product(inverse(inverse(X0)),X1,multiply(X0,X1)),true) = true,
inference(superposition,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
product(inverse(inverse(X0)),X1,multiply(X0,X1)) = true,
inference(demodulation,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
ifeq(true,true,equalish(multiply(X0,inverse(X0)),identity),true) = true,
inference(superposition,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
equalish(multiply(X0,inverse(X0)),identity) = true,
inference(demodulation,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
ifeq(true,true,product(X0,inverse(X0),identity),true) = true,
inference(superposition,[status(thm)],[d31,d11]) ).
cnf(d33,plain,
product(X0,inverse(X0),identity) = true,
inference(demodulation,[status(thm)],[d32,c0]) ).
cnf(d34,plain,
ifeq(true,true,product(identity,identity,multiply(b,inverse(a))),true) = true,
inference(superposition,[status(thm)],[d33,d19]) ).
cnf(d35,plain,
product(identity,identity,multiply(b,inverse(a))) = true,
inference(demodulation,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
ifeq(true,true,equalish(multiply(b,inverse(a)),identity),true) = true,
inference(superposition,[status(thm)],[d35,d1]) ).
cnf(d37,plain,
equalish(multiply(b,inverse(a)),identity) = true,
inference(demodulation,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
ifeq(true,true,product(b,inverse(a),identity),true) = true,
inference(superposition,[status(thm)],[d37,d11]) ).
cnf(d39,plain,
product(b,inverse(a),identity) = true,
inference(demodulation,[status(thm)],[d38,c0]) ).
cnf(d40,plain,
ifeq(true,true,product(inverse(b),identity,inverse(a)),true) = true,
inference(superposition,[status(thm)],[d39,d9]) ).
cnf(d41,plain,
product(inverse(b),identity,inverse(a)) = true,
inference(demodulation,[status(thm)],[d40,c0]) ).
cnf(d42,plain,
ifeq(true,true,product(inverse(inverse(b)),inverse(a),identity),true) = true,
inference(superposition,[status(thm)],[d41,d9]) ).
cnf(d43,plain,
product(inverse(inverse(b)),inverse(a),identity) = true,
inference(demodulation,[status(thm)],[d42,c0]) ).
cnf(d44,plain,
ifeq(true,true,product(inverse(inverse(inverse(b))),identity,inverse(a)),true) = true,
inference(superposition,[status(thm)],[d43,d9]) ).
cnf(d45,plain,
product(inverse(inverse(inverse(b))),identity,inverse(a)) = true,
inference(demodulation,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
ifeq(true,true,product(identity,inverse(b),inverse(a)),true) = true,
inference(superposition,[status(thm)],[d45,d5]) ).
cnf(d47,plain,
product(identity,inverse(b),inverse(a)) = true,
inference(demodulation,[status(thm)],[d46,c0]) ).
cnf(d48,plain,
ifeq(true,true,equalish(inverse(a),inverse(b)),true) = true,
inference(superposition,[status(thm)],[d47,d1]) ).
cnf(d49,plain,
equalish(inverse(a),inverse(b)) = true,
inference(demodulation,[status(thm)],[d48,c0]) ).
cnf(d50,plain,
$false,
inference(resolution,[status(thm)],[c9,d49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 14:24:29 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 136.68/30.45 % SZS status Unsatisfiable for theBenchmark.p
% 136.68/30.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------