TSTP Solution File: SET041-3 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET041-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Mar 25 14:30:52 EDT 2024
% Result : Unsatisfiable 12.17s 12.36s
% Output : Proof 12.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET041-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Mar 20 21:53:58 EDT 2024
% 0.12/0.33 % CPUTime :
% 12.17/12.36 % SZS status Unsatisfiable for theBenchmark
% 12.17/12.36 % SZS output start Proof for theBenchmark
% 12.17/12.36
% 12.17/12.36 % Problem matrix:
% 12.17/12.36 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 12.17/12.36 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 12.17/12.36 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 12.17/12.36 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f1(__eqx_0, __eqx_1) = f1(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( non_ordered_pair(__eqx_0, __eqx_1) = non_ordered_pair(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( singleton_set(__eqx_0) = singleton_set(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( ordered_pair(__eqx_0, __eqx_1) = ordered_pair(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( f2(__eqx_0) = f2(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( f3(__eqx_0) = f3(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( first(__eqx_0) = first(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f4(__eqx_0, __eqx_1) = f4(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f5(__eqx_0, __eqx_1) = f5(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( second(__eqx_0) = second(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f6(__eqx_0, __eqx_1) = f6(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f7(__eqx_0, __eqx_1) = f7(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( intersection(__eqx_0, __eqx_1) = intersection(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( complement(__eqx_0) = complement(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( union(__eqx_0, __eqx_1) = union(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( domain_of(__eqx_0) = domain_of(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f8(__eqx_0, __eqx_1) = f8(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( cross_product(__eqx_0, __eqx_1) = cross_product(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( converse(__eqx_0) = converse(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( rotate_right(__eqx_0) = rotate_right(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f9(__eqx_0, __eqx_1) = f9(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f10(__eqx_0, __eqx_1) = f10(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f11(__eqx_0, __eqx_1) = f11(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( flip_range_of(__eqx_0) = flip_range_of(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f12(__eqx_0, __eqx_1) = f12(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f13(__eqx_0, __eqx_1) = f13(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f14(__eqx_0, __eqx_1) = f14(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( successor(__eqx_0) = successor(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ( sigma(__eqx_0) = sigma(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-32, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f16(__eqx_0, __eqx_1) = f16(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-33, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f17(__eqx_0, __eqx_1) = f17(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-34, plain, ( ( __eqx_0 != __eqy_0) | ( powerset(__eqx_0) = powerset(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-35, plain, ( ( __eqx_0 != __eqy_0) | ( f18(__eqx_0) = f18(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-36, plain, ( ( __eqx_0 != __eqy_0) | ( f19(__eqx_0) = f19(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-37, plain, ( ( __eqx_0 != __eqy_0) | ( f20(__eqx_0) = f20(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-38, plain, ( ( __eqx_0 != __eqy_0) | ( f21(__eqx_0) = f21(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-39, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( image(__eqx_0, __eqx_1) = image(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-40, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( f22(__eqx_0, __eqx_1, __eqx_2) = f22(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.17/12.36 cnf(matrix-41, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f23(__eqx_0, __eqx_1) = f23(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-42, plain, ( ( __eqx_0 != __eqy_0) | ( f24(__eqx_0) = f24(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-43, plain, ( ( __eqx_0 != __eqy_0) | ( f26(__eqx_0) = f26(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-44, plain, ( ( __eqx_0 != __eqy_0) | ( range_of(__eqx_0) = range_of(__eqy_0)) )).
% 12.17/12.36 cnf(matrix-45, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( f27(__eqx_0, __eqx_1) = f27(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-46, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( restrict(__eqx_0, __eqx_1) = restrict(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-47, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( apply(__eqx_0, __eqx_1) = apply(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-48, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( f28(__eqx_0, __eqx_1, __eqx_2) = f28(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.17/12.36 cnf(matrix-49, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( apply_to_two_arguments(__eqx_0, __eqx_1, __eqx_2) = apply_to_two_arguments(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.17/12.36 cnf(matrix-50, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( compose(__eqx_0, __eqx_1) = compose(__eqy_0, __eqy_1)) )).
% 12.17/12.36 cnf(matrix-51, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( f29(__eqx_0, __eqx_1, __eqx_2) = f29(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.17/12.36 cnf(matrix-52, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( f30(__eqx_0, __eqx_1, __eqx_2) = f30(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.17/12.36 cnf(matrix-53, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( f31(__eqx_0, __eqx_1, __eqx_2) = f31(__eqy_0, __eqy_1, __eqy_2)) )).
% 12.17/12.36 cnf(matrix-54, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( f32(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) = f32(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4)) )).
% 12.17/12.36 cnf(matrix-55, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ( f33(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) = f33(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4)) )).
% 12.17/12.36 cnf(matrix-56, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 12.17/12.36 cnf(matrix-57, plain, ( ( __eqx_0 != __eqy_0) | ~little_set(__eqx_0) | little_set(__eqy_0) )).
% 12.17/12.36 cnf(matrix-58, plain, ( ( __eqx_0 != __eqy_0) | ~ordered_pair_predicate(__eqx_0) | ordered_pair_predicate(__eqy_0) )).
% 12.17/12.36 cnf(matrix-59, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 12.17/12.36 cnf(matrix-60, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~proper_subset(__eqx_0, __eqx_1) | proper_subset(__eqy_0, __eqy_1) )).
% 12.17/12.36 cnf(matrix-61, plain, ( ( __eqx_0 != __eqy_0) | ~relation(__eqx_0) | relation(__eqy_0) )).
% 12.17/12.36 cnf(matrix-62, plain, ( ( __eqx_0 != __eqy_0) | ~single_valued_set(__eqx_0) | single_valued_set(__eqy_0) )).
% 12.17/12.36 cnf(matrix-63, plain, ( ( __eqx_0 != __eqy_0) | ~function(__eqx_0) | function(__eqy_0) )).
% 12.17/12.36 cnf(matrix-64, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~disjoint(__eqx_0, __eqx_1) | disjoint(__eqy_0, __eqy_1) )).
% 12.17/12.36 cnf(matrix-65, plain, ( ( __eqx_0 != __eqy_0) | ~one_to_one_function(__eqx_0) | one_to_one_function(__eqy_0) )).
% 12.17/12.36 cnf(matrix-66, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~maps(__eqx_0, __eqx_1, __eqx_2) | maps(__eqy_0, __eqy_1, __eqy_2) )).
% 12.17/12.36 cnf(matrix-67, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~closed(__eqx_0, __eqx_1) | closed(__eqy_0, __eqy_1) )).
% 12.17/12.36 cnf(matrix-68, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( __eqx_4 != __eqy_4) | ~homomorphism(__eqx_0, __eqx_1, __eqx_2, __eqx_3, __eqx_4) | homomorphism(__eqy_0, __eqy_1, __eqy_2, __eqy_3, __eqy_4) )).
% 12.17/12.36 cnf(matrix-69, plain, ( ~member(X, Y) | little_set(X) )).
% 12.17/12.36 cnf(matrix-70, plain, ( little_set(f1(X, Y)) | ( X = Y) )).
% 12.17/12.36 cnf(matrix-71, plain, ( member(f1(X, Y), X) | member(f1(X, Y), Y) | ( X = Y) )).
% 12.17/12.36 cnf(matrix-72, plain, ( ~member(f1(X, Y), X) | ~member(f1(X, Y), Y) | ( X = Y) )).
% 12.17/12.36 cnf(matrix-73, plain, ( ~member(U, non_ordered_pair(X, Y)) | ( U = X) | ( U = Y) )).
% 12.17/12.36 cnf(matrix-74, plain, ( member(U, non_ordered_pair(X, Y)) | ~little_set(U) | ( U != X) )).
% 12.17/12.36 cnf(matrix-75, plain, ( member(U, non_ordered_pair(X, Y)) | ~little_set(U) | ( U != Y) )).
% 12.17/12.36 cnf(matrix-76, plain, ( little_set(non_ordered_pair(X, Y)) )).
% 12.17/12.36 cnf(matrix-77, plain, ( ( singleton_set(X) = non_ordered_pair(X, X)) )).
% 12.17/12.36 cnf(matrix-78, plain, ( ( ordered_pair(X, Y) = non_ordered_pair(singleton_set(X), non_ordered_pair(X, Y))) )).
% 12.17/12.36 cnf(matrix-79, plain, ( ~ordered_pair_predicate(X) | little_set(f2(X)) )).
% 12.17/12.36 cnf(matrix-80, plain, ( ~ordered_pair_predicate(X) | little_set(f3(X)) )).
% 12.17/12.36 cnf(matrix-81, plain, ( ~ordered_pair_predicate(X) | ( X = ordered_pair(f2(X), f3(X))) )).
% 12.17/12.36 cnf(matrix-82, plain, ( ordered_pair_predicate(X) | ~little_set(Y) | ~little_set(Z) | ( X != ordered_pair(Y, Z)) )).
% 12.17/12.36 cnf(matrix-83, plain, ( ~member(Z, first(X)) | little_set(f4(Z, X)) )).
% 12.17/12.36 cnf(matrix-84, plain, ( ~member(Z, first(X)) | little_set(f5(Z, X)) )).
% 12.17/12.36 cnf(matrix-85, plain, ( ~member(Z, first(X)) | ( X = ordered_pair(f4(Z, X), f5(Z, X))) )).
% 12.17/12.36 cnf(matrix-86, plain, ( ~member(Z, first(X)) | member(Z, f4(Z, X)) )).
% 12.17/12.36 cnf(matrix-87, plain, ( member(Z, first(X)) | ~little_set(U) | ~little_set(V) | ( X != ordered_pair(U, V)) | ~member(Z, U) )).
% 12.17/12.36 cnf(matrix-88, plain, ( ~member(Z, second(X)) | little_set(f6(Z, X)) )).
% 12.17/12.36 cnf(matrix-89, plain, ( ~member(Z, second(X)) | little_set(f7(Z, X)) )).
% 12.17/12.36 cnf(matrix-90, plain, ( ~member(Z, second(X)) | ( X = ordered_pair(f6(Z, X), f7(Z, X))) )).
% 12.17/12.36 cnf(matrix-91, plain, ( ~member(Z, second(X)) | member(Z, f7(Z, X)) )).
% 12.17/12.36 cnf(matrix-92, plain, ( member(Z, second(X)) | ~little_set(U) | ~little_set(V) | ( X != ordered_pair(U, V)) | ~member(Z, V) )).
% 12.17/12.36 cnf(matrix-93, plain, ( ~member(Z, estin) | ordered_pair_predicate(Z) )).
% 12.17/12.36 cnf(matrix-94, plain, ( ~member(Z, estin) | member(first(Z), second(Z)) )).
% 12.17/12.36 cnf(matrix-95, plain, ( member(Z, estin) | ~little_set(Z) | ~ordered_pair_predicate(Z) | ~member(first(Z), second(Z)) )).
% 12.17/12.36 cnf(matrix-96, plain, ( ~member(Z, intersection(X, Y)) | member(Z, X) )).
% 12.17/12.36 cnf(matrix-97, plain, ( ~member(Z, intersection(X, Y)) | member(Z, Y) )).
% 12.17/12.36 cnf(matrix-98, plain, ( member(Z, intersection(X, Y)) | ~member(Z, X) | ~member(Z, Y) )).
% 12.17/12.36 cnf(matrix-99, plain, ( ~member(Z, complement(X)) | ~member(Z, X) )).
% 12.17/12.36 cnf(matrix-100, plain, ( member(Z, complement(X)) | ~little_set(Z) | member(Z, X) )).
% 12.17/12.36 cnf(matrix-101, plain, ( ( union(X, Y) = complement(intersection(complement(X), complement(Y)))) )).
% 12.17/12.36 cnf(matrix-102, plain, ( ~member(Z, domain_of(X)) | ordered_pair_predicate(f8(Z, X)) )).
% 12.17/12.36 cnf(matrix-103, plain, ( ~member(Z, domain_of(X)) | member(f8(Z, X), X) )).
% 12.17/12.36 cnf(matrix-104, plain, ( ~member(Z, domain_of(X)) | ( Z = first(f8(Z, X))) )).
% 12.17/12.36 cnf(matrix-105, plain, ( member(Z, domain_of(X)) | ~little_set(Z) | ~ordered_pair_predicate(Xp) | ~member(Xp, X) | ( Z != first(Xp)) )).
% 12.17/12.36 cnf(matrix-106, plain, ( ~member(Z, cross_product(X, Y)) | ordered_pair_predicate(Z) )).
% 12.17/12.36 cnf(matrix-107, plain, ( ~member(Z, cross_product(X, Y)) | member(first(Z), X) )).
% 12.17/12.36 cnf(matrix-108, plain, ( ~member(Z, cross_product(X, Y)) | member(second(Z), Y) )).
% 12.17/12.36 cnf(matrix-109, plain, ( member(Z, cross_product(X, Y)) | ~little_set(Z) | ~ordered_pair_predicate(Z) | ~member(first(Z), X) | ~member(second(Z), Y) )).
% 12.17/12.36 cnf(matrix-110, plain, ( ~member(Z, converse(X)) | ordered_pair_predicate(Z) )).
% 12.17/12.36 cnf(matrix-111, plain, ( ~member(Z, converse(X)) | member(ordered_pair(second(Z), first(Z)), X) )).
% 12.17/12.36 cnf(matrix-112, plain, ( member(Z, converse(X)) | ~little_set(Z) | ~ordered_pair_predicate(Z) | ~member(ordered_pair(second(Z), first(Z)), X) )).
% 12.17/12.36 cnf(matrix-113, plain, ( ~member(Z, rotate_right(X)) | little_set(f9(Z, X)) )).
% 12.17/12.36 cnf(matrix-114, plain, ( ~member(Z, rotate_right(X)) | little_set(f10(Z, X)) )).
% 12.17/12.36 cnf(matrix-115, plain, ( ~member(Z, rotate_right(X)) | little_set(f11(Z, X)) )).
% 12.17/12.36 cnf(matrix-116, plain, ( ~member(Z, rotate_right(X)) | ( Z = ordered_pair(f9(Z, X), ordered_pair(f10(Z, X), f11(Z, X)))) )).
% 12.17/12.36 cnf(matrix-117, plain, ( ~member(Z, rotate_right(X)) | member(ordered_pair(f10(Z, X), ordered_pair(f11(Z, X), f9(Z, X))), X) )).
% 12.17/12.36 cnf(matrix-118, plain, ( member(Z, rotate_right(X)) | ~little_set(Z) | ~little_set(U) | ~little_set(V) | ~little_set(W) | ( Z != ordered_pair(U, ordered_pair(V, W))) | ~member(ordered_pair(V, ordered_pair(W, U)), X) )).
% 12.17/12.36 cnf(matrix-119, plain, ( ~member(Z, flip_range_of(X)) | little_set(f12(Z, X)) )).
% 12.17/12.36 cnf(matrix-120, plain, ( ~member(Z, flip_range_of(X)) | little_set(f13(Z, X)) )).
% 12.17/12.36 cnf(matrix-121, plain, ( ~member(Z, flip_range_of(X)) | little_set(f14(Z, X)) )).
% 12.17/12.36 cnf(matrix-122, plain, ( ~member(Z, flip_range_of(X)) | ( Z = ordered_pair(f12(Z, X), ordered_pair(f13(Z, X), f14(Z, X)))) )).
% 12.17/12.36 cnf(matrix-123, plain, ( ~member(Z, flip_range_of(X)) | member(ordered_pair(f12(Z, X), ordered_pair(f14(Z, X), f13(Z, X))), X) )).
% 12.17/12.36 cnf(matrix-124, plain, ( member(Z, flip_range_of(X)) | ~little_set(Z) | ~little_set(U) | ~little_set(V) | ~little_set(W) | ( Z != ordered_pair(U, ordered_pair(V, W))) | ~member(ordered_pair(U, ordered_pair(W, V)), X) )).
% 12.17/12.36 cnf(matrix-125, plain, ( ( successor(X) = union(X, singleton_set(X))) )).
% 12.17/12.36 cnf(matrix-126, plain, ( ~member(Z, empty_set) )).
% 12.17/12.36 cnf(matrix-127, plain, ( member(Z, universal_set) | ~little_set(Z) )).
% 12.17/12.36 cnf(matrix-128, plain, ( little_set(infinity) )).
% 12.17/12.36 cnf(matrix-129, plain, ( member(empty_set, infinity) )).
% 12.17/12.36 cnf(matrix-130, plain, ( ~member(X, infinity) | member(successor(X), infinity) )).
% 12.17/12.36 cnf(matrix-131, plain, ( ~member(Z, sigma(X)) | member(f16(Z, X), X) )).
% 12.17/12.36 cnf(matrix-132, plain, ( ~member(Z, sigma(X)) | member(Z, f16(Z, X)) )).
% 12.17/12.36 cnf(matrix-133, plain, ( member(Z, sigma(X)) | ~member(Y, X) | ~member(Z, Y) )).
% 12.17/12.36 cnf(matrix-134, plain, ( ~little_set(U) | little_set(sigma(U)) )).
% 12.17/12.36 cnf(matrix-135, plain, ( ~subset(X, Y) | ~member(U, X) | member(U, Y) )).
% 12.17/12.36 cnf(matrix-136, plain, ( subset(X, Y) | member(f17(X, Y), X) )).
% 12.17/12.36 cnf(matrix-137, plain, ( subset(X, Y) | ~member(f17(X, Y), Y) )).
% 12.17/12.36 cnf(matrix-138, plain, ( ~proper_subset(X, Y) | subset(X, Y) )).
% 12.17/12.36 cnf(matrix-139, plain, ( ~proper_subset(X, Y) | ( X != Y) )).
% 12.17/12.36 cnf(matrix-140, plain, ( proper_subset(X, Y) | ~subset(X, Y) | ( X = Y) )).
% 12.17/12.36 cnf(matrix-141, plain, ( ~member(Z, powerset(X)) | subset(Z, X) )).
% 12.17/12.36 cnf(matrix-142, plain, ( member(Z, powerset(X)) | ~little_set(Z) | ~subset(Z, X) )).
% 12.17/12.36 cnf(matrix-143, plain, ( ~little_set(U) | little_set(powerset(U)) )).
% 12.17/12.36 cnf(matrix-144, plain, ( ~relation(Z) | ~member(X, Z) | ordered_pair_predicate(X) )).
% 12.17/12.36 cnf(matrix-145, plain, ( relation(Z) | member(f18(Z), Z) )).
% 12.17/12.36 cnf(matrix-146, plain, ( relation(Z) | ~ordered_pair_predicate(f18(Z)) )).
% 12.17/12.36 cnf(matrix-147, plain, ( ~single_valued_set(X) | ~little_set(U) | ~little_set(V) | ~little_set(W) | ~member(ordered_pair(U, V), X) | ~member(ordered_pair(U, W), X) | ( V = W) )).
% 12.17/12.36 cnf(matrix-148, plain, ( single_valued_set(X) | little_set(f19(X)) )).
% 12.17/12.36 cnf(matrix-149, plain, ( single_valued_set(X) | little_set(f20(X)) )).
% 12.17/12.36 cnf(matrix-150, plain, ( single_valued_set(X) | little_set(f21(X)) )).
% 12.17/12.36 cnf(matrix-151, plain, ( single_valued_set(X) | member(ordered_pair(f19(X), f20(X)), X) )).
% 12.17/12.36 cnf(matrix-152, plain, ( single_valued_set(X) | member(ordered_pair(f19(X), f21(X)), X) )).
% 12.17/12.36 cnf(matrix-153, plain, ( single_valued_set(X) | ( f20(X) != f21(X)) )).
% 12.17/12.36 cnf(matrix-154, plain, ( ~function(Xf) | relation(Xf) )).
% 12.17/12.36 cnf(matrix-155, plain, ( ~function(Xf) | single_valued_set(Xf) )).
% 12.17/12.36 cnf(matrix-156, plain, ( function(Xf) | ~relation(Xf) | ~single_valued_set(Xf) )).
% 12.17/12.36 cnf(matrix-157, plain, ( ~member(Z, image(X, Xf)) | ordered_pair_predicate(f22(Z, X, Xf)) )).
% 12.17/12.36 cnf(matrix-158, plain, ( ~member(Z, image(X, Xf)) | member(f22(Z, X, Xf), Xf) )).
% 12.17/12.36 cnf(matrix-159, plain, ( ~member(Z, image(X, Xf)) | member(first(f22(Z, X, Xf)), X) )).
% 12.17/12.36 cnf(matrix-160, plain, ( ~member(Z, image(X, Xf)) | ( second(f22(Z, X, Xf)) = Z) )).
% 12.17/12.36 cnf(matrix-161, plain, ( member(Z, image(X, Xf)) | ~little_set(Z) | ~ordered_pair_predicate(Y) | ~member(Y, Xf) | ~member(first(Y), X) | ( second(Y) != Z) )).
% 12.17/12.36 cnf(matrix-162, plain, ( ~little_set(X) | ~function(Xf) | little_set(image(X, Xf)) )).
% 12.17/12.36 cnf(matrix-163, plain, ( ~disjoint(X, Y) | ~member(U, X) | ~member(U, Y) )).
% 12.17/12.36 cnf(matrix-164, plain, ( disjoint(X, Y) | member(f23(X, Y), X) )).
% 12.17/12.36 cnf(matrix-165, plain, ( disjoint(X, Y) | member(f23(X, Y), Y) )).
% 12.17/12.36 cnf(matrix-166, plain, ( ( X = empty_set) | member(f24(X), X) )).
% 12.17/12.36 cnf(matrix-167, plain, ( ( X = empty_set) | disjoint(f24(X), X) )).
% 12.17/12.36 cnf(matrix-168, plain, ( function(f25) )).
% 12.17/12.36 cnf(matrix-169, plain, ( ~little_set(X) | ( X = empty_set) | member(f26(X), X) )).
% 12.17/12.36 cnf(matrix-170, plain, ( ~little_set(X) | ( X = empty_set) | member(ordered_pair(X, f26(X)), f25) )).
% 12.17/12.36 cnf(matrix-171, plain, ( ~member(Z, range_of(X)) | ordered_pair_predicate(f27(Z, X)) )).
% 12.17/12.36 cnf(matrix-172, plain, ( ~member(Z, range_of(X)) | member(f27(Z, X), X) )).
% 12.17/12.36 cnf(matrix-173, plain, ( ~member(Z, range_of(X)) | ( Z = second(f27(Z, X))) )).
% 12.17/12.36 cnf(matrix-174, plain, ( member(Z, range_of(X)) | ~little_set(Z) | ~ordered_pair_predicate(Xp) | ~member(Xp, X) | ( Z != second(Xp)) )).
% 12.17/12.36 cnf(matrix-175, plain, ( ~member(Z, identity_relation) | ordered_pair_predicate(Z) )).
% 12.17/12.36 cnf(matrix-176, plain, ( ~member(Z, identity_relation) | ( first(Z) = second(Z)) )).
% 12.17/12.36 cnf(matrix-177, plain, ( member(Z, identity_relation) | ~little_set(Z) | ~ordered_pair_predicate(Z) | ( first(Z) != second(Z)) )).
% 12.17/12.36 cnf(matrix-178, plain, ( ( restrict(X, Y) = intersection(X, cross_product(Y, universal_set))) )).
% 12.17/12.36 cnf(matrix-179, plain, ( ~one_to_one_function(Xf) | function(Xf) )).
% 12.17/12.36 cnf(matrix-180, plain, ( ~one_to_one_function(Xf) | function(converse(Xf)) )).
% 12.17/12.36 cnf(matrix-181, plain, ( one_to_one_function(Xf) | ~function(Xf) | ~function(converse(Xf)) )).
% 12.17/12.36 cnf(matrix-182, plain, ( ~member(Z, apply(Xf, Y)) | ordered_pair_predicate(f28(Z, Xf, Y)) )).
% 12.17/12.36 cnf(matrix-183, plain, ( ~member(Z, apply(Xf, Y)) | member(f28(Z, Xf, Y), Xf) )).
% 12.17/12.36 cnf(matrix-184, plain, ( ~member(Z, apply(Xf, Y)) | ( first(f28(Z, Xf, Y)) = Y) )).
% 12.17/12.36 cnf(matrix-185, plain, ( ~member(Z, apply(Xf, Y)) | member(Z, second(f28(Z, Xf, Y))) )).
% 12.17/12.36 cnf(matrix-186, plain, ( member(Z, apply(Xf, Y)) | ~ordered_pair_predicate(W) | ~member(W, Xf) | ( first(W) != Y) | ~member(Z, second(W)) )).
% 12.17/12.36 cnf(matrix-187, plain, ( ( apply_to_two_arguments(Xf, X, Y) = apply(Xf, ordered_pair(X, Y))) )).
% 12.17/12.36 cnf(matrix-188, plain, ( ~maps(Xf, X, Y) | function(Xf) )).
% 12.17/12.36 cnf(matrix-189, plain, ( ~maps(Xf, X, Y) | ( domain_of(Xf) = X) )).
% 12.17/12.36 cnf(matrix-190, plain, ( ~maps(Xf, X, Y) | subset(range_of(Xf), Y) )).
% 12.17/12.36 cnf(matrix-191, plain, ( maps(Xf, X, Y) | ~function(Xf) | ( domain_of(Xf) != X) | ~subset(range_of(Xf), Y) )).
% 12.17/12.36 cnf(matrix-192, plain, ( ~closed(Xs, Xf) | little_set(Xs) )).
% 12.17/12.36 cnf(matrix-193, plain, ( ~closed(Xs, Xf) | little_set(Xf) )).
% 12.17/12.36 cnf(matrix-194, plain, ( ~closed(Xs, Xf) | maps(Xf, cross_product(Xs, Xs), Xs) )).
% 12.17/12.36 cnf(matrix-195, plain, ( closed(Xs, Xf) | ~little_set(Xs) | ~little_set(Xf) | ~maps(Xf, cross_product(Xs, Xs), Xs) )).
% 12.17/12.36 cnf(matrix-196, plain, ( ~member(Z, compose(Xf, Xg)) | little_set(f29(Z, Xf, Xg)) )).
% 12.17/12.36 cnf(matrix-197, plain, ( ~member(Z, compose(Xf, Xg)) | little_set(f30(Z, Xf, Xg)) )).
% 12.17/12.36 cnf(matrix-198, plain, ( ~member(Z, compose(Xf, Xg)) | little_set(f31(Z, Xf, Xg)) )).
% 12.17/12.36 cnf(matrix-199, plain, ( ~member(Z, compose(Xf, Xg)) | ( Z = ordered_pair(f29(Z, Xf, Xg), f30(Z, Xf, Xg))) )).
% 12.17/12.36 cnf(matrix-200, plain, ( ~member(Z, compose(Xf, Xg)) | member(ordered_pair(f29(Z, Xf, Xg), f31(Z, Xf, Xg)), Xf) )).
% 12.17/12.36 cnf(matrix-201, plain, ( ~member(Z, compose(Xf, Xg)) | member(ordered_pair(f31(Z, Xf, Xg), f30(Z, Xf, Xg)), Xg) )).
% 12.17/12.36 cnf(matrix-202, plain, ( member(Z, compose(Xf, Xg)) | ~little_set(Z) | ~little_set(X) | ~little_set(Y) | ~little_set(W) | ( Z != ordered_pair(X, Y)) | ~member(ordered_pair(X, W), Xf) | ~member(ordered_pair(W, Y), Xg) )).
% 12.17/12.36 cnf(matrix-203, plain, ( ~homomorphism(Xh, Xs1, Xf1, Xs2, Xf2) | closed(Xs1, Xf1) )).
% 12.17/12.36 cnf(matrix-204, plain, ( ~homomorphism(Xh, Xs1, Xf1, Xs2, Xf2) | closed(Xs2, Xf2) )).
% 12.17/12.36 cnf(matrix-205, plain, ( ~homomorphism(Xh, Xs1, Xf1, Xs2, Xf2) | maps(Xh, Xs1, Xs2) )).
% 12.17/12.36 cnf(matrix-206, plain, ( ~homomorphism(Xh, Xs1, Xf1, Xs2, Xf2) | ~member(X, Xs1) | ~member(Y, Xs1) | ( apply(Xh, apply_to_two_arguments(Xf1, X, Y)) = apply_to_two_arguments(Xf2, apply(Xh, X), apply(Xh, Y))) )).
% 12.17/12.36 cnf(matrix-207, plain, ( homomorphism(Xh, Xs1, Xf1, Xs2, Xf2) | ~closed(Xs1, Xf1) | ~closed(Xs2, Xf2) | ~maps(Xh, Xs1, Xs2) | member(f32(Xh, Xs1, Xf1, Xs2, Xf2), Xs1) )).
% 12.17/12.36 cnf(matrix-208, plain, ( homomorphism(Xh, Xs1, Xf1, Xs2, Xf2) | ~closed(Xs1, Xf1) | ~closed(Xs2, Xf2) | ~maps(Xh, Xs1, Xs2) | member(f33(Xh, Xs1, Xf1, Xs2, Xf2), Xs1) )).
% 12.17/12.36 cnf(matrix-209, plain, ( homomorphism(Xh, Xs1, Xf1, Xs2, Xf2) | ~closed(Xs1, Xf1) | ~closed(Xs2, Xf2) | ~maps(Xh, Xs1, Xs2) | ( apply(Xh, apply_to_two_arguments(Xf1, f32(Xh, Xs1, Xf1, Xs2, Xf2), f33(Xh, Xs1, Xf1, Xs2, Xf2))) != apply_to_two_arguments(Xf2, apply(Xh, f32(Xh, Xs1, Xf1, Xs2, Xf2)), apply(Xh, f33(Xh, Xs1, Xf1, Xs2, Xf2)))) )).
% 12.17/12.36 cnf(matrix-210, plain, ( ~little_set(X) | ~little_set(U) | ( ordered_pair(X, Y) != ordered_pair(U, V)) | ( X = U) )).
% 12.17/12.36 cnf(matrix-211, plain, ( ~little_set(X) | ~little_set(Y) | ( non_ordered_pair(Z, X) != non_ordered_pair(Z, Y)) | ( X = Y) )).
% 12.17/12.36 cnf(matrix-212, plain, ( ~little_set(X) | ~little_set(Y) | ~little_set(U) | ~little_set(V) | ( ordered_pair(X, Y) != ordered_pair(U, V)) | ( Y = V) )).
% 12.17/12.36 cnf(matrix-213, plain, ( ~subset(X, Y) | ~subset(Y, X) | ( X = Y) )).
% 12.17/12.36 cnf(matrix-214, plain, ( ~little_set(X) | ~little_set(Y) | ( first(ordered_pair(X, Y)) = X) )).
% 12.17/12.36 cnf(matrix-215, plain, ( ~little_set(X) | ~little_set(Y) | ( second(ordered_pair(X, Y)) = Y) )).
% 12.17/12.36 cnf(matrix-216, plain, ( ~ordered_pair_predicate(X) | little_set(first(X)) )).
% 12.17/12.36 cnf(matrix-217, plain, ( ~ordered_pair_predicate(X) | little_set(second(X)) )).
% 12.17/12.36 cnf(matrix-218, plain, ( ~little_set(X) | member(X, singleton_set(X)) )).
% 12.17/12.36 cnf(matrix-219, plain, ( little_set(ordered_pair(X, Y)) )).
% 12.17/12.36 cnf(matrix-220, plain, ( ~ordered_pair_predicate(X) | little_set(X) )).
% 12.17/12.36 cnf(matrix-221, plain, ( ~subset(X, Y) | ~subset(Y, Z) | subset(X, Z) )).
% 12.17/12.36 cnf(matrix-222, plain, ( subset(apply(Xf, Y), sigma(image(singleton_set(Y), Xf))) )).
% 12.17/12.36 cnf(matrix-223, plain, ( subset(image(singleton_set(Y), Xf), apply(Xf, Y)) )).
% 12.17/12.36 cnf(matrix-224, plain, ( ~function(Y) | little_set(apply(Y, X)) )).
% 12.17/12.36 cnf(matrix-225, plain, ( relation(compose(Y, X)) )).
% 12.17/12.36 cnf(matrix-226, plain, ( subset(range_of(compose(Y, X)), range_of(Y)) )).
% 12.17/12.36 cnf(matrix-227, plain, ( ~subset(range_of(X), domain_of(Y)) | ( domain_of(X) = domain_of(compose(Y, X))) )).
% 12.17/12.36 cnf(matrix-228, plain, ( ~function(X) | ~function(Y) | function(compose(Y, X)) )).
% 12.17/12.36 cnf(matrix-229, plain, ( ~maps(Xf, U, V) | ~maps(Xg, V, W) | maps(compose(Xg, Xf), U, W) )).
% 12.17/12.36 cnf(matrix-230, plain, ( ~little_set(X) | ~little_set(Y) | ~function(Xf) | ~member(ordered_pair(X, Y), Xf) | ( apply(Xf, X) = Y) )).
% 12.17/12.36 cnf(matrix-231, plain, ( ~function(Xf) | ~member(X, domain_of(Xf)) | ( apply(Xf, X) != Y) | member(ordered_pair(X, Y), Xf) )).
% 12.17/12.36 cnf(matrix-232, plain, ( ~maps(Xf, Xd, Xr) | ~member(X, Xd) | member(apply(Xf, X), Xr) )).
% 12.17/12.36 cnf(matrix-233, plain, ( ~function(Xf) | ~member(X, domain_of(Xf)) | subset(apply(Xg, apply(Xf, X)), apply(compose(Xg, Xf), X)) )).
% 12.17/12.36 cnf(matrix-234, plain, ( ~function(Xf) | subset(apply(compose(Xg, Xf), X), apply(Xg, apply(Xf, X))) )).
% 12.17/12.36 cnf(matrix-235, plain, ( function(a_function) )).
% 12.17/12.36 cnf(matrix-236, plain, ( member(a, domain_of(a_function)) )).
% 12.17/12.36 cnf(matrix-237, plain, ( ( apply(another_function, apply(a_function, a)) != apply(compose(another_function, a_function), a)) )).
% 12.17/12.36
% 12.17/12.36 % Proof stack:
% 12.17/12.36 cnf(proof-stack, plain,
% 12.17/12.36 proof_stack(
% 12.17/12.36 start(237),
% 12.17/12.36 left_branch(0, 213, 2, 2),
% 12.17/12.36 left_branch(0, 233, 2, 3),
% 12.17/12.36 left_branch(0, 235, 0, 4),
% 12.17/12.36 right_branch(4),
% 12.17/12.36 left_branch(0, 236, 0, 5),
% 12.17/12.36 right_branch(5),
% 12.17/12.36 right_branch(3),
% 12.17/12.36 left_branch(0, 234, 1, 4),
% 12.17/12.36 left_branch(0, 235, 0, 5),
% 12.17/12.36 right_branch(5),
% 12.17/12.36 right_branch(4),
% 12.17/12.36 right_branch(2)
% 12.17/12.36 )).
% 12.17/12.36 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------