%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT004-2 : 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 : n020.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 06:55:32 AM UTC 2026
% Result : Unsatisfiable 19.67s 5.17s
% Output : CNFRefutation 19.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of clauses : 74 ( 41 unt; 0 nHn; 62 RR)
% Number of literals : 141 ( 140 equ; 72 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(epimorphism1,hypothesis,
( X0 = X2
| compose(a,X2) != X1
| codomain(a) != domain(X2)
| compose(a,X0) != X1
| codomain(a) != domain(X0) ) ).
cnf(epimorphism2,hypothesis,
( X0 = X2
| compose(b,X2) != X1
| codomain(b) != domain(X2)
| compose(b,X0) != X1
| codomain(b) != domain(X0) ) ).
cnf(codomain_of_a_equals_domain_of_b,hypothesis,
codomain(a) = domain(b) ).
cnf(codomain_of_ab_equals_domain_of_h,hypothesis,
codomain(compose(a,b)) = domain(h) ).
cnf(codomain_of_ab_equals_domain_of_g,hypothesis,
codomain(compose(a,b)) = domain(g) ).
cnf(ab_h_equals_ab_g,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g ).
cnf(codomain_of_domain_is_domain,axiom,
codomain(domain(X0)) = domain(X0) ).
cnf(domain_of_codomain_is_codomain,axiom,
domain(codomain(X0)) = codomain(X0) ).
cnf(domain_composition,axiom,
compose(domain(X0),X0) = X0 ).
cnf(codomain_domain1,axiom,
( domain(compose(X0,X1)) = domain(X0)
| codomain(X0) != domain(X1) ) ).
cnf(codomain_domain2,axiom,
( codomain(compose(X0,X1)) = codomain(X1)
| codomain(X0) != domain(X1) ) ).
cnf(star_property,axiom,
( compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2)
| codomain(X1) != domain(X2)
| codomain(X0) != domain(X1) ) ).
cnf(c0,plain,
( X0 = X2
| compose(a,X2) != X1
| codomain(a) != domain(X2)
| compose(a,X0) != X1
| codomain(a) != domain(X0) ),
inference(clausification,[status(esa)],[epimorphism1]) ).
cnf(c1,plain,
( compose(b,X0) != X2
| X1 = X0
| compose(b,X1) != X2
| codomain(b) != domain(X1)
| codomain(b) != domain(X0) ),
inference(clausification,[status(esa)],[epimorphism2]) ).
cnf(c2,plain,
codomain(a) = domain(b),
inference(clausification,[status(esa)],[codomain_of_a_equals_domain_of_b]) ).
cnf(c3,plain,
codomain(compose(a,b)) = domain(h),
inference(clausification,[status(esa)],[codomain_of_ab_equals_domain_of_h]) ).
cnf(c4,plain,
codomain(compose(a,b)) = domain(g),
inference(clausification,[status(esa)],[codomain_of_ab_equals_domain_of_g]) ).
cnf(c5,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(clausification,[status(esa)],[ab_h_equals_ab_g]) ).
cnf(c6,plain,
h != g,
inference(clausification,[status(esa)],[prove_h_equals_g]) ).
cnf(c7,plain,
codomain(domain(X0)) = domain(X0),
inference(clausification,[status(esa)],[codomain_of_domain_is_domain]) ).
cnf(c8,plain,
domain(codomain(X0)) = codomain(X0),
inference(clausification,[status(esa)],[domain_of_codomain_is_codomain]) ).
cnf(c9,plain,
compose(domain(X0),X0) = X0,
inference(clausification,[status(esa)],[domain_composition]) ).
cnf(c11,plain,
( domain(compose(X0,X1)) = domain(X0)
| codomain(X0) != domain(X1) ),
inference(clausification,[status(esa)],[codomain_domain1]) ).
cnf(c12,plain,
( codomain(compose(X0,X1)) = codomain(X1)
| codomain(X0) != domain(X1) ),
inference(clausification,[status(esa)],[codomain_domain2]) ).
cnf(c13,plain,
( compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2)
| codomain(X1) != domain(X2)
| codomain(X0) != domain(X1) ),
inference(clausification,[status(esa)],[star_property]) ).
cnf(d0,plain,
( codomain(compose(X0,b)) = codomain(b)
| codomain(X0) != codomain(a) ),
inference(superposition,[status(thm)],[c2,c12]) ).
cnf(d1,plain,
codomain(compose(a,b)) = codomain(b),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
domain(domain(X0)) = codomain(domain(X0)),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d3,plain,
domain(domain(X0)) = domain(X0),
inference(demodulation,[status(thm)],[d2,c7]) ).
cnf(d4,plain,
domain(domain(h)) = codomain(compose(a,b)),
inference(superposition,[status(thm)],[c3,c8]) ).
cnf(d5,plain,
domain(h) = codomain(compose(a,b)),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
domain(h) = codomain(b),
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( domain(compose(X0,h)) = domain(X0)
| codomain(X0) != codomain(b) ),
inference(superposition,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
domain(compose(b,h)) = domain(b),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
domain(compose(b,h)) = codomain(a),
inference(demodulation,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
( codomain(b) != domain(X1)
| compose(X0,compose(b,X1)) = compose(compose(X0,b),X1)
| codomain(X0) != codomain(a) ),
inference(superposition,[status(thm)],[c2,c13]) ).
cnf(d11,plain,
codomain(b) = domain(h),
inference(demodulation,[status(thm)],[c3,d1]) ).
cnf(d12,plain,
( codomain(X0) != codomain(a)
| compose(X0,compose(b,h)) = compose(compose(X0,b),h)
| codomain(b) != codomain(b) ),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( codomain(compose(domain(X0),X1)) = codomain(X1)
| domain(X0) != domain(X1) ),
inference(superposition,[status(thm)],[c7,c12]) ).
cnf(d14,plain,
codomain(compose(domain(X0),X0)) = codomain(X0),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
codomain(X0) = codomain(X0),
inference(demodulation,[status(thm)],[d14,c9]) ).
cnf(d16,plain,
( codomain(X0) != codomain(a)
| compose(X0,compose(b,h)) = compose(compose(X0,b),h) ),
inference(resolution,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
compose(a,compose(b,h)) = compose(compose(a,b),g),
inference(demodulation,[status(thm)],[c5,d17]) ).
cnf(d19,plain,
domain(h) = domain(g),
inference(demodulation,[status(thm)],[c4,c3]) ).
cnf(d20,plain,
codomain(b) = domain(g),
inference(demodulation,[status(thm)],[d19,d6]) ).
cnf(d21,plain,
( codomain(X0) != codomain(a)
| compose(X0,compose(b,g)) = compose(compose(X0,b),g)
| codomain(b) != codomain(b) ),
inference(superposition,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
( codomain(X0) != codomain(a)
| compose(X0,compose(b,g)) = compose(compose(X0,b),g) ),
inference(resolution,[status(thm)],[d15,d21]) ).
cnf(d23,plain,
compose(a,compose(b,g)) = compose(compose(a,b),g),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
compose(a,compose(b,g)) = compose(a,compose(b,h)),
inference(demodulation,[status(thm)],[d23,d18]) ).
cnf(d25,plain,
( domain(compose(X0,g)) = domain(X0)
| codomain(X0) != domain(h) ),
inference(superposition,[status(thm)],[d19,c11]) ).
cnf(d26,plain,
( domain(compose(X0,g)) = domain(X0)
| codomain(X0) != codomain(b) ),
inference(demodulation,[status(thm)],[d25,d6]) ).
cnf(d27,plain,
domain(compose(b,g)) = domain(b),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
domain(compose(b,g)) = codomain(a),
inference(demodulation,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
( codomain(a) != domain(X0)
| compose(a,compose(b,g)) != X1
| compose(a,X0) != X1
| X0 = compose(b,g)
| codomain(a) != codomain(a) ),
inference(superposition,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
( codomain(a) != domain(X0)
| codomain(a) != codomain(a)
| compose(a,compose(b,h)) != X1
| compose(a,X0) != X1
| X0 = compose(b,g) ),
inference(demodulation,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
( codomain(a) != domain(X0)
| compose(a,compose(b,h)) != X1
| compose(a,X0) != X1
| X0 = compose(b,g) ),
inference(resolution,[status(thm)],[d15,d30]) ).
cnf(d32,plain,
( codomain(a) != domain(X0)
| compose(a,X0) != compose(a,compose(b,h))
| X0 = compose(b,g) ),
inference(equality_resolution,[status(thm)],[d31]) ).
cnf(d33,plain,
( codomain(a) != domain(compose(b,h))
| compose(b,h) = compose(b,g) ),
inference(equality_resolution,[status(thm)],[d32]) ).
cnf(d34,plain,
( codomain(a) != codomain(a)
| compose(b,h) = compose(b,g) ),
inference(demodulation,[status(thm)],[d33,d9]) ).
cnf(d35,plain,
compose(b,h) = compose(b,g),
inference(resolution,[status(thm)],[d15,d34]) ).
cnf(d36,plain,
( codomain(b) != domain(X0)
| compose(b,h) != X1
| compose(b,X0) != X1
| h = X0
| codomain(b) != codomain(b) ),
inference(superposition,[status(thm)],[d6,c1]) ).
cnf(d37,plain,
( h = X0
| codomain(b) != domain(X0)
| compose(b,h) != X1
| compose(b,X0) != X1 ),
inference(resolution,[status(thm)],[d15,d36]) ).
cnf(d38,plain,
( domain(compose(domain(X0),X1)) = domain(domain(X0))
| domain(X0) != domain(X1) ),
inference(superposition,[status(thm)],[c7,c11]) ).
cnf(d39,plain,
( domain(compose(domain(X0),X1)) = domain(X0)
| domain(X0) != domain(X1) ),
inference(demodulation,[status(thm)],[d38,d3]) ).
cnf(d40,plain,
domain(compose(domain(X0),X0)) = domain(X0),
inference(equality_resolution,[status(thm)],[d39]) ).
cnf(d41,plain,
domain(X0) = domain(X0),
inference(demodulation,[status(thm)],[d40,c9]) ).
cnf(d42,plain,
domain(g) = codomain(b),
inference(superposition,[status(thm)],[d20,d41]) ).
cnf(d43,plain,
( h = g
| compose(b,h) != X0
| compose(b,g) != X0
| codomain(b) != codomain(b) ),
inference(superposition,[status(thm)],[d42,d37]) ).
cnf(d44,plain,
( codomain(b) != codomain(b)
| compose(b,g) != X0
| compose(b,h) != X0 ),
inference(resolution,[status(thm)],[c6,d43]) ).
cnf(d45,plain,
( compose(b,g) != X0
| compose(b,h) != X0 ),
inference(resolution,[status(thm)],[d15,d44]) ).
cnf(d46,plain,
compose(b,h) != compose(b,g),
inference(equality_resolution,[status(thm)],[d45]) ).
cnf(d47,plain,
$false,
inference(resolution,[status(thm)],[d46,d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n020.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 22:49:20 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.67/5.17 % SZS status Unsatisfiable for theBenchmark.p
% 19.67/5.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------