%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : CAT003-1 : 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 46.62s 6.56s
% Output : CNFRefutation 46.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of clauses : 68 ( 31 unt; 0 nHn; 62 RR)
% Number of literals : 134 ( 13 equ; 68 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 107 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ab_equals_c,hypothesis,
product(a,b,c) ).
cnf(cancellation_for_product,hypothesis,
( X0 = X2
| ~ product(X2,c,X1)
| ~ product(X0,c,X1) ) ).
cnf(ha_equals_d,hypothesis,
product(h,a,d) ).
cnf(ga_equals_d,hypothesis,
product(g,a,d) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g ).
cnf(closure_of_composition,axiom,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ) ).
cnf(associative_property1,axiom,
( defined(X0,X1)
| ~ product(X0,X1,X2) ) ).
cnf(associative_property2,axiom,
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom2,axiom,
( product(X0,X5,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom4,axiom,
( defined(X4,X1)
| ~ defined(X3,X2)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom5,axiom,
( product(X5,X1,X4)
| ~ product(X3,X0,X5)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ) ).
cnf(category_theory_axiom6,axiom,
( defined(X0,X2)
| ~ 'identity$umap'(X1)
| ~ defined(X1,X2)
| ~ defined(X0,X1) ) ).
cnf(domain_is_an_identity_map,axiom,
'identity$umap'(domain(X0)) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X0,domain(X0)) ).
cnf(product_on_domain,axiom,
product(X0,domain(X0),X0) ).
cnf(identity1,axiom,
( product(X0,X1,X1)
| ~ 'identity$umap'(X0)
| ~ defined(X0,X1) ) ).
cnf(composition_is_well_defined,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
product(a,b,c),
inference(clausification,[status(esa)],[ab_equals_c]) ).
cnf(c1,plain,
( X0 = X2
| ~ product(X2,c,X1)
| ~ product(X0,c,X1) ),
inference(clausification,[status(esa)],[cancellation_for_product]) ).
cnf(c2,plain,
product(h,a,d),
inference(clausification,[status(esa)],[ha_equals_d]) ).
cnf(c3,plain,
product(g,a,d),
inference(clausification,[status(esa)],[ga_equals_d]) ).
cnf(c4,plain,
g != h,
inference(clausification,[status(esa)],[prove_h_equals_g]) ).
cnf(c5,plain,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[closure_of_composition]) ).
cnf(c6,plain,
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associative_property1]) ).
cnf(c7,plain,
( defined(X3,X1)
| ~ product(X2,X3,X0)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[associative_property2]) ).
cnf(c9,plain,
( product(X3,X2,X5)
| ~ product(X4,X1,X5)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[category_theory_axiom2]) ).
cnf(c11,plain,
( defined(X4,X3)
| ~ product(X0,X2,X4)
| ~ product(X2,X3,X1)
| ~ defined(X0,X1) ),
inference(clausification,[status(esa)],[category_theory_axiom4]) ).
cnf(c12,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[category_theory_axiom5]) ).
cnf(c13,plain,
( defined(X1,X2)
| ~ defined(X0,X2)
| ~ defined(X1,X0)
| ~ 'identity$umap'(X0) ),
inference(clausification,[status(esa)],[category_theory_axiom6]) ).
cnf(c14,plain,
'identity$umap'(domain(X0)),
inference(clausification,[status(esa)],[domain_is_an_identity_map]) ).
cnf(c16,plain,
defined(X0,domain(X0)),
inference(clausification,[status(esa)],[mapping_from_x_to_its_domain]) ).
cnf(c18,plain,
product(X0,domain(X0),X0),
inference(clausification,[status(esa)],[product_on_domain]) ).
cnf(c20,plain,
( product(X0,X1,X1)
| ~ defined(X0,X1)
| ~ 'identity$umap'(X0) ),
inference(clausification,[status(esa)],[identity1]) ).
cnf(c22,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[composition_is_well_defined]) ).
cnf(d0,plain,
( ~ defined(X0,c)
| defined(X1,b)
| ~ product(X0,a,X1) ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(d1,plain,
( ~ defined(g,c)
| defined(d,b) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( ~ 'identity$umap'(domain(X0))
| ~ defined(domain(X0),X1)
| defined(X0,X1) ),
inference(resolution,[status(thm)],[c13,c16]) ).
cnf(d3,plain,
( ~ defined(domain(X0),X1)
| defined(X0,X1) ),
inference(resolution,[status(thm)],[c14,d2]) ).
cnf(d4,plain,
defined(a,b),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(d5,plain,
product(a,b,compose(a,b)),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( ~ product(a,b,X0)
| X0 = compose(a,b) ),
inference(resolution,[status(thm)],[c22,d5]) ).
cnf(d7,plain,
c = compose(a,b),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
( ~ product(X2,b,X1)
| ~ product(X0,X2,a)
| product(X0,X1,c) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d9,plain,
( product(X0,compose(a,b),c)
| ~ product(X0,a,a) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( product(X0,c,c)
| ~ product(X0,a,a) ),
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
defined(g,a),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d12,plain,
( ~ defined(X0,X1)
| defined(domain(X0),X1) ),
inference(resolution,[status(thm)],[c18,c7]) ).
cnf(d13,plain,
defined(domain(g),a),
inference(resolution,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( ~ 'identity$umap'(domain(g))
| product(domain(g),a,a) ),
inference(resolution,[status(thm)],[d13,c20]) ).
cnf(d15,plain,
product(domain(g),a,a),
inference(resolution,[status(thm)],[c14,d14]) ).
cnf(d16,plain,
product(domain(g),c,c),
inference(resolution,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
defined(domain(g),c),
inference(resolution,[status(thm)],[d16,c6]) ).
cnf(d18,plain,
defined(g,c),
inference(resolution,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
defined(d,b),
inference(resolution,[status(thm)],[d18,d1]) ).
cnf(d20,plain,
product(d,b,compose(d,b)),
inference(resolution,[status(thm)],[d19,c5]) ).
cnf(d21,plain,
( ~ product(d,b,X0)
| X0 = compose(d,b) ),
inference(resolution,[status(thm)],[d20,c22]) ).
cnf(d22,plain,
product(g,c,compose(g,c)),
inference(resolution,[status(thm)],[d18,c5]) ).
cnf(d23,plain,
( ~ product(X2,X1,c)
| ~ product(g,X2,X0)
| product(X0,X1,compose(g,c)) ),
inference(resolution,[status(thm)],[d22,c12]) ).
cnf(d24,plain,
( ~ product(g,a,X0)
| product(X0,b,compose(g,c)) ),
inference(resolution,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
product(d,b,compose(g,c)),
inference(resolution,[status(thm)],[d24,c3]) ).
cnf(d26,plain,
compose(g,c) = compose(d,b),
inference(resolution,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
( ~ product(X0,c,compose(g,c))
| g = X0 ),
inference(resolution,[status(thm)],[d22,c1]) ).
cnf(d28,plain,
( ~ product(X0,c,compose(d,b))
| g = X0 ),
inference(demodulation,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( ~ product(X2,b,X1)
| ~ product(X0,X2,d)
| product(X0,X1,compose(d,b)) ),
inference(resolution,[status(thm)],[d20,c9]) ).
cnf(d30,plain,
( product(X0,c,compose(d,b))
| ~ product(X0,a,d) ),
inference(resolution,[status(thm)],[d29,c0]) ).
cnf(d31,plain,
product(h,c,compose(d,b)),
inference(resolution,[status(thm)],[d30,c2]) ).
cnf(d32,plain,
g = h,
inference(resolution,[status(thm)],[d31,d28]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[c4,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:49:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.62/6.56 % SZS status Unsatisfiable for theBenchmark.p
% 46.62/6.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------