%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 19.69s 12.92s
% Output : CNFRefutation 19.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of clauses : 88 ( 46 unt; 0 nHn; 69 RR)
% Number of literals : 164 ( 163 equ; 79 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 : 84 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(endomorphism,hypothesis,
( X0 = X2
| compose(compose(a,b),X2) != X1
| codomain(compose(a,b)) != domain(X2)
| compose(compose(a,b),X0) != X1
| codomain(compose(a,b)) != domain(X0) ) ).
cnf(codomain_of_a_equals_domain_of_b,hypothesis,
codomain(a) = domain(b) ).
cnf(codomain_of_b_equals_domain_of_h,hypothesis,
codomain(b) = domain(h) ).
cnf(codomain_of_b_equals_domain_of_g,hypothesis,
codomain(b) = domain(g) ).
cnf(bh_equals_bg,hypothesis,
compose(b,h) = compose(b,g) ).
cnf(prove_g_equals_h,negated_conjecture,
g != h ).
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_composition,axiom,
compose(X0,codomain(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
| codomain(compose(a,b)) != domain(X0)
| compose(compose(a,b),X2) != X1
| codomain(compose(a,b)) != domain(X2)
| compose(compose(a,b),X0) != X1 ),
inference(clausification,[status(esa)],[endomorphism]) ).
cnf(c1,plain,
codomain(a) = domain(b),
inference(clausification,[status(esa)],[codomain_of_a_equals_domain_of_b]) ).
cnf(c2,plain,
codomain(b) = domain(h),
inference(clausification,[status(esa)],[codomain_of_b_equals_domain_of_h]) ).
cnf(c3,plain,
codomain(b) = domain(g),
inference(clausification,[status(esa)],[codomain_of_b_equals_domain_of_g]) ).
cnf(c4,plain,
compose(b,h) = compose(b,g),
inference(clausification,[status(esa)],[bh_equals_bg]) ).
cnf(c5,plain,
g != h,
inference(clausification,[status(esa)],[prove_g_equals_h]) ).
cnf(c6,plain,
codomain(domain(X0)) = domain(X0),
inference(clausification,[status(esa)],[codomain_of_domain_is_domain]) ).
cnf(c7,plain,
domain(codomain(X0)) = codomain(X0),
inference(clausification,[status(esa)],[domain_of_codomain_is_codomain]) ).
cnf(c8,plain,
compose(domain(X0),X0) = X0,
inference(clausification,[status(esa)],[domain_composition]) ).
cnf(c9,plain,
compose(X0,codomain(X0)) = X0,
inference(clausification,[status(esa)],[codomain_composition]) ).
cnf(c10,plain,
( domain(compose(X0,X1)) = domain(X0)
| codomain(X0) != domain(X1) ),
inference(clausification,[status(esa)],[codomain_domain1]) ).
cnf(c11,plain,
( codomain(compose(X0,X1)) = codomain(X1)
| codomain(X0) != domain(X1) ),
inference(clausification,[status(esa)],[codomain_domain2]) ).
cnf(c12,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)],[c1,c11]) ).
cnf(d1,plain,
codomain(compose(a,b)) = codomain(b),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
( codomain(compose(a,b)) != domain(X0)
| codomain(b) != domain(X1)
| compose(compose(a,b),X0) != X2
| compose(compose(a,b),X1) != X2
| X0 = X1 ),
inference(demodulation,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
( codomain(b) != domain(X0)
| codomain(b) != domain(X1)
| compose(compose(a,b),X0) != X2
| compose(compose(a,b),X1) != X2
| X0 = X1 ),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( codomain(b) != domain(X1)
| compose(X0,compose(b,X1)) = compose(compose(X0,b),X1)
| codomain(X0) != codomain(a) ),
inference(superposition,[status(thm)],[c1,c12]) ).
cnf(d5,plain,
( codomain(X0) != codomain(a)
| compose(X0,compose(b,h)) = compose(compose(X0,b),h)
| codomain(b) != codomain(b) ),
inference(superposition,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
( codomain(compose(domain(X0),X1)) = codomain(X1)
| domain(X0) != domain(X1) ),
inference(superposition,[status(thm)],[c6,c11]) ).
cnf(d7,plain,
codomain(compose(domain(X0),X0)) = codomain(X0),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
codomain(X0) = codomain(X0),
inference(demodulation,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
( codomain(X0) != codomain(a)
| compose(X0,compose(b,h)) = compose(compose(X0,b),h) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
compose(a,compose(b,h)) = compose(compose(a,b),h),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( codomain(b) != domain(h)
| codomain(b) != domain(X1)
| compose(compose(a,b),X1) != X0
| h = X1
| compose(a,compose(b,h)) != X0 ),
inference(superposition,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
( h = X0
| codomain(b) != codomain(b)
| codomain(b) != domain(X0)
| compose(a,compose(b,h)) != X1
| compose(compose(a,b),X0) != X1 ),
inference(demodulation,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
( h = X0
| codomain(b) != domain(X0)
| compose(a,compose(b,h)) != X1
| compose(compose(a,b),X0) != X1 ),
inference(resolution,[status(thm)],[d8,d12]) ).
cnf(d14,plain,
( h = X0
| codomain(b) != domain(X0)
| compose(compose(a,b),X0) != compose(a,compose(b,h)) ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
( codomain(X0) != codomain(a)
| compose(X0,compose(b,g)) = compose(compose(X0,b),g)
| codomain(b) != codomain(b) ),
inference(superposition,[status(thm)],[c3,d4]) ).
cnf(d16,plain,
( codomain(b) != codomain(b)
| codomain(X0) != codomain(a)
| compose(X0,compose(b,h)) = compose(compose(X0,b),g) ),
inference(demodulation,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
( codomain(X0) != codomain(a)
| compose(X0,compose(b,h)) = compose(compose(X0,b),g) ),
inference(resolution,[status(thm)],[d8,d16]) ).
cnf(d18,plain,
compose(a,compose(b,h)) = compose(compose(a,b),g),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( h = g
| codomain(b) != domain(g)
| compose(a,compose(b,h)) != compose(a,compose(b,h)) ),
inference(superposition,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
( h = g
| codomain(b) != codomain(b)
| compose(a,compose(b,h)) != compose(a,compose(b,h)) ),
inference(demodulation,[status(thm)],[d19,c3]) ).
cnf(d21,plain,
( h = g
| compose(a,compose(b,h)) != compose(a,compose(b,h)) ),
inference(resolution,[status(thm)],[d8,d20]) ).
cnf(d22,plain,
compose(compose(a,b),codomain(b)) = compose(a,b),
inference(superposition,[status(thm)],[d1,c9]) ).
cnf(d23,plain,
domain(domain(X0)) = codomain(domain(X0)),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d24,plain,
domain(domain(X0)) = domain(X0),
inference(demodulation,[status(thm)],[d23,c6]) ).
cnf(d25,plain,
( codomain(domain(X0)) != domain(X2)
| compose(X1,compose(domain(X0),X2)) = compose(compose(X1,domain(X0)),X2)
| codomain(X1) != domain(X0) ),
inference(superposition,[status(thm)],[d24,c12]) ).
cnf(d26,plain,
( domain(X0) != domain(X2)
| codomain(X1) != domain(X0)
| compose(X1,compose(domain(X0),X2)) = compose(compose(X1,domain(X0)),X2) ),
inference(demodulation,[status(thm)],[d25,c6]) ).
cnf(d27,plain,
( codomain(X0) != domain(X1)
| compose(X0,compose(domain(X1),X1)) = compose(compose(X0,domain(X1)),X1) ),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
( codomain(X1) != domain(X0)
| compose(X1,X0) = compose(compose(X1,domain(X0)),X0) ),
inference(demodulation,[status(thm)],[d27,c8]) ).
cnf(d29,plain,
( domain(compose(domain(X0),X1)) = domain(domain(X0))
| domain(X0) != domain(X1) ),
inference(superposition,[status(thm)],[c6,c10]) ).
cnf(d30,plain,
( domain(compose(domain(X0),X1)) = domain(X0)
| domain(X0) != domain(X1) ),
inference(demodulation,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
domain(compose(domain(X0),X0)) = domain(X0),
inference(equality_resolution,[status(thm)],[d30]) ).
cnf(d32,plain,
domain(X0) = domain(X0),
inference(demodulation,[status(thm)],[d31,c8]) ).
cnf(d33,plain,
domain(h) = codomain(b),
inference(superposition,[status(thm)],[c2,d32]) ).
cnf(d34,plain,
( compose(X0,h) = compose(compose(X0,domain(h)),h)
| codomain(X0) != codomain(b) ),
inference(superposition,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
( codomain(X0) != codomain(b)
| compose(X0,h) = compose(compose(X0,codomain(b)),h) ),
inference(demodulation,[status(thm)],[d34,c2]) ).
cnf(d36,plain,
codomain(b) = codomain(compose(a,b)),
inference(superposition,[status(thm)],[d1,d8]) ).
cnf(d37,plain,
( compose(compose(a,b),h) = compose(compose(compose(a,b),codomain(b)),h)
| codomain(b) != codomain(b) ),
inference(superposition,[status(thm)],[d36,d35]) ).
cnf(d38,plain,
( codomain(b) != codomain(b)
| compose(a,compose(b,h)) = compose(compose(compose(a,b),codomain(b)),h) ),
inference(demodulation,[status(thm)],[d37,d10]) ).
cnf(d39,plain,
( codomain(b) != codomain(b)
| compose(a,compose(b,h)) = compose(compose(a,b),h) ),
inference(demodulation,[status(thm)],[d38,d22]) ).
cnf(d40,plain,
( codomain(b) != codomain(b)
| compose(a,compose(b,h)) = compose(a,compose(b,h)) ),
inference(demodulation,[status(thm)],[d39,d10]) ).
cnf(d41,plain,
compose(a,compose(b,h)) = compose(a,compose(b,h)),
inference(resolution,[status(thm)],[d8,d40]) ).
cnf(d42,plain,
h = g,
inference(resolution,[status(thm)],[d41,d21]) ).
cnf(d43,plain,
h != h,
inference(demodulation,[status(thm)],[c5,d42]) ).
cnf(d44,plain,
compose(codomain(b),h) = h,
inference(superposition,[status(thm)],[c2,c8]) ).
cnf(d45,plain,
codomain(codomain(b)) = domain(h),
inference(superposition,[status(thm)],[c2,c6]) ).
cnf(d46,plain,
codomain(codomain(b)) = codomain(b),
inference(demodulation,[status(thm)],[d45,c2]) ).
cnf(d47,plain,
( codomain(X0) != domain(X1)
| compose(codomain(b),compose(X0,X1)) = compose(compose(codomain(b),X0),X1)
| codomain(b) != domain(X0) ),
inference(superposition,[status(thm)],[d46,c12]) ).
cnf(d48,plain,
( codomain(h) != domain(X0)
| compose(codomain(b),compose(h,X0)) = compose(compose(codomain(b),h),X0)
| codomain(b) != codomain(b) ),
inference(superposition,[status(thm)],[c2,d47]) ).
cnf(d49,plain,
( codomain(h) != domain(X0)
| codomain(b) != codomain(b)
| compose(codomain(b),compose(h,X0)) = compose(h,X0) ),
inference(demodulation,[status(thm)],[d48,d44]) ).
cnf(d50,plain,
( codomain(h) != domain(X0)
| compose(codomain(b),compose(h,X0)) = compose(h,X0) ),
inference(resolution,[status(thm)],[d8,d49]) ).
cnf(d51,plain,
compose(codomain(X0),codomain(X0)) = codomain(X0),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d52,plain,
compose(domain(X0),domain(X0)) = domain(X0),
inference(superposition,[status(thm)],[c6,c9]) ).
cnf(d53,plain,
compose(codomain(X0),domain(codomain(X0))) = domain(codomain(X0)),
inference(superposition,[status(thm)],[c7,d52]) ).
cnf(d54,plain,
compose(codomain(X0),codomain(X0)) = domain(codomain(X0)),
inference(demodulation,[status(thm)],[d53,c7]) ).
cnf(d55,plain,
codomain(X0) = domain(codomain(X0)),
inference(demodulation,[status(thm)],[d54,d51]) ).
cnf(d56,plain,
( compose(codomain(b),compose(h,codomain(X0))) = compose(h,codomain(X0))
| codomain(h) != codomain(X0) ),
inference(superposition,[status(thm)],[d55,d50]) ).
cnf(d57,plain,
compose(codomain(b),compose(h,codomain(h))) = compose(h,codomain(h)),
inference(equality_resolution,[status(thm)],[d56]) ).
cnf(d58,plain,
compose(codomain(b),h) = compose(h,codomain(h)),
inference(demodulation,[status(thm)],[d57,c9]) ).
cnf(d59,plain,
h = compose(h,codomain(h)),
inference(demodulation,[status(thm)],[d58,d44]) ).
cnf(d60,plain,
h = h,
inference(demodulation,[status(thm)],[d59,c9]) ).
cnf(d61,plain,
$false,
inference(resolution,[status(thm)],[d60,d43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/10.38 % Computer : n010.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.38 % DateTime : Sat Sep 26 22:48:46 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.69/12.92 % SZS status Unsatisfiable for theBenchmark.p
% 19.69/12.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------