TSTP Solution File: SEU062+1 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n019.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 : 600s
% DateTime : Tue Jul 19 14:48:10 EDT 2022
% Result : Theorem 2.58s 2.74s
% Output : Proof 2.58s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 01:32:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.58/2.74 % SZS status Theorem
% 2.58/2.74 (* PROOF-FOUND *)
% 2.58/2.74 (* BEGIN-PROOF *)
% 2.58/2.74 % SZS output start Proof
% 2.58/2.74 1. (relation T_0) (-. (relation T_0)) ### Axiom
% 2.58/2.74 2. (in T_1 T_2) (-. (in T_1 T_2)) ### Axiom
% 2.58/2.74 3. ((relation_inverse_image T_0 (singleton T_1)) = (empty_set)) ((relation_inverse_image T_0 (singleton T_1)) != (empty_set)) ### Axiom
% 2.58/2.74 4. (-. ((in T_1 T_2) /\ ((relation_inverse_image T_0 (singleton T_1)) = (empty_set)))) ((relation_inverse_image T_0 (singleton T_1)) = (empty_set)) (in T_1 T_2) ### NotAnd 2 3
% 2.58/2.74 5. (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) (in T_1 T_2) ((relation_inverse_image T_0 (singleton T_1)) = (empty_set)) ### All 4
% 2.58/2.74 6. (-. ((relation_inverse_image T_0 (singleton T_1)) != (empty_set))) (in T_1 T_2) (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) ### NotNot 5
% 2.58/2.74 7. (-. (in T_1 (relation_rng T_0))) (in T_1 (relation_rng T_0)) ### Axiom
% 2.58/2.74 8. ((in T_1 (relation_rng T_0)) <=> ((relation_inverse_image T_0 (singleton T_1)) != (empty_set))) (-. (in T_1 (relation_rng T_0))) (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) (in T_1 T_2) ### Equiv 6 7
% 2.58/2.74 9. ((relation T_0) => ((in T_1 (relation_rng T_0)) <=> ((relation_inverse_image T_0 (singleton T_1)) != (empty_set)))) (in T_1 T_2) (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) (-. (in T_1 (relation_rng T_0))) (relation T_0) ### Imply 1 8
% 2.58/2.74 10. (All B, ((relation B) => ((in T_1 (relation_rng B)) <=> ((relation_inverse_image B (singleton T_1)) != (empty_set))))) (relation T_0) (-. (in T_1 (relation_rng T_0))) (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) (in T_1 T_2) ### All 9
% 2.58/2.74 11. (All A, (All B, ((relation B) => ((in A (relation_rng B)) <=> ((relation_inverse_image B (singleton A)) != (empty_set)))))) (in T_1 T_2) (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) (-. (in T_1 (relation_rng T_0))) (relation T_0) ### All 10
% 2.58/2.74 12. (-. ((in T_1 T_2) => (in T_1 (relation_rng T_0)))) (relation T_0) (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) (All A, (All B, ((relation B) => ((in A (relation_rng B)) <=> ((relation_inverse_image B (singleton A)) != (empty_set)))))) ### NotImply 11
% 2.58/2.74 13. (-. (All C, ((in C T_2) => (in C (relation_rng T_0))))) (All A, (All B, ((relation B) => ((in A (relation_rng B)) <=> ((relation_inverse_image B (singleton A)) != (empty_set)))))) (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) (relation T_0) ### NotAllEx 12
% 2.58/2.74 14. (-. (subset T_2 (relation_rng T_0))) (relation T_0) (All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) (All A, (All B, ((relation B) => ((in A (relation_rng B)) <=> ((relation_inverse_image B (singleton A)) != (empty_set)))))) ### Definition-Pseudo(subset) 13
% 2.58/2.74 15. (-. ((relation T_0) => ((All C, (-. ((in C T_2) /\ ((relation_inverse_image T_0 (singleton C)) = (empty_set))))) => (subset T_2 (relation_rng T_0))))) (All A, (All B, ((relation B) => ((in A (relation_rng B)) <=> ((relation_inverse_image B (singleton A)) != (empty_set)))))) ### ConjTree 14
% 2.58/2.74 16. (-. (All B, ((relation B) => ((All C, (-. ((in C T_2) /\ ((relation_inverse_image B (singleton C)) = (empty_set))))) => (subset T_2 (relation_rng B)))))) (All A, (All B, ((relation B) => ((in A (relation_rng B)) <=> ((relation_inverse_image B (singleton A)) != (empty_set)))))) ### NotAllEx 15
% 2.58/2.74 17. (-. (All A, (All B, ((relation B) => ((All C, (-. ((in C A) /\ ((relation_inverse_image B (singleton C)) = (empty_set))))) => (subset A (relation_rng B))))))) (All A, (All B, ((relation B) => ((in A (relation_rng B)) <=> ((relation_inverse_image B (singleton A)) != (empty_set)))))) ### NotAllEx 16
% 2.58/2.74 % SZS output end Proof
% 2.58/2.74 (* END-PROOF *)
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