TSTP Solution File: SEU303+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SEU303+3 : 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 : n015.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 14:50:05 EDT 2022
% Result : Theorem 3.24s 3.44s
% Output : Proof 3.24s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SEU303+3 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.14 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 06:51:29 EDT 2022
% 0.14/0.35 % CPUTime :
% 3.24/3.44 % SZS status Theorem
% 3.24/3.44 (* PROOF-FOUND *)
% 3.24/3.44 (* BEGIN-PROOF *)
% 3.24/3.44 % SZS output start Proof
% 3.24/3.44 1. (relation T_0) (-. (relation T_0)) ### Axiom
% 3.24/3.44 2. (relation T_0) (-. (relation T_0)) ### Axiom
% 3.24/3.44 3. (function T_0) (-. (function T_0)) ### Axiom
% 3.24/3.44 4. (finite (relation_dom T_0)) (-. (finite (relation_dom T_0))) ### Axiom
% 3.24/3.44 5. (-. (finite (relation_image T_0 (relation_dom T_0)))) (finite (relation_image T_0 (relation_dom T_0))) ### Axiom
% 3.24/3.44 6. (((relation T_0) /\ (function T_0)) => ((finite (relation_dom T_0)) => (finite (relation_image T_0 (relation_dom T_0))))) (-. (finite (relation_image T_0 (relation_dom T_0)))) (finite (relation_dom T_0)) (function T_0) (relation T_0) ### DisjTree 2 3 4 5
% 3.24/3.44 7. (All B, (((relation B) /\ (function B)) => ((finite (relation_dom T_0)) => (finite (relation_image B (relation_dom T_0)))))) (relation T_0) (function T_0) (finite (relation_dom T_0)) (-. (finite (relation_image T_0 (relation_dom T_0)))) ### All 6
% 3.24/3.44 8. (All A, (All B, (((relation B) /\ (function B)) => ((finite A) => (finite (relation_image B A)))))) (-. (finite (relation_image T_0 (relation_dom T_0)))) (finite (relation_dom T_0)) (function T_0) (relation T_0) ### All 7
% 3.24/3.44 9. (-. (subset (relation_rng T_0) (relation_rng T_0))) ### Refl(subset)
% 3.24/3.44 10. ((relation_rng T_0) != (relation_rng T_0)) ### Refl(=)
% 3.24/3.44 11. ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) ((relation_rng T_0) != (relation_image T_0 (relation_dom T_0))) ### Sym(=)
% 3.24/3.44 12. ((powerset (relation_rng T_0)) != (powerset (relation_image T_0 (relation_dom T_0)))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) ### NotEqual 11
% 3.24/3.44 13. (-. (element (relation_rng T_0) (powerset (relation_image T_0 (relation_dom T_0))))) (element (relation_rng T_0) (powerset (relation_rng T_0))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) ### P-NotP 10 12
% 3.24/3.44 14. ((element (relation_rng T_0) (powerset (relation_rng T_0))) <=> (subset (relation_rng T_0) (relation_rng T_0))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) (-. (element (relation_rng T_0) (powerset (relation_image T_0 (relation_dom T_0))))) ### Equiv 9 13
% 3.24/3.44 15. (All B, ((element (relation_rng T_0) (powerset B)) <=> (subset (relation_rng T_0) B))) (-. (element (relation_rng T_0) (powerset (relation_image T_0 (relation_dom T_0))))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) ### All 14
% 3.24/3.44 16. (-. (finite (relation_rng T_0))) (finite (relation_rng T_0)) ### Axiom
% 3.24/3.44 17. ((element (relation_rng T_0) (powerset (relation_image T_0 (relation_dom T_0)))) => (finite (relation_rng T_0))) (-. (finite (relation_rng T_0))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) (All B, ((element (relation_rng T_0) (powerset B)) <=> (subset (relation_rng T_0) B))) ### Imply 15 16
% 3.24/3.44 18. (All B, ((element B (powerset (relation_image T_0 (relation_dom T_0)))) => (finite B))) (All B, ((element (relation_rng T_0) (powerset B)) <=> (subset (relation_rng T_0) B))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) (-. (finite (relation_rng T_0))) ### All 17
% 3.24/3.44 19. ((finite (relation_image T_0 (relation_dom T_0))) => (All B, ((element B (powerset (relation_image T_0 (relation_dom T_0)))) => (finite B)))) (-. (finite (relation_rng T_0))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) (All B, ((element (relation_rng T_0) (powerset B)) <=> (subset (relation_rng T_0) B))) (relation T_0) (function T_0) (finite (relation_dom T_0)) (All A, (All B, (((relation B) /\ (function B)) => ((finite A) => (finite (relation_image B A)))))) ### Imply 8 18
% 3.24/3.44 20. (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) (All A, (All B, (((relation B) /\ (function B)) => ((finite A) => (finite (relation_image B A)))))) (finite (relation_dom T_0)) (function T_0) (relation T_0) (All B, ((element (relation_rng T_0) (powerset B)) <=> (subset (relation_rng T_0) B))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) (-. (finite (relation_rng T_0))) ### All 19
% 3.24/3.44 21. (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (finite (relation_rng T_0))) ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0)) (relation T_0) (function T_0) (finite (relation_dom T_0)) (All A, (All B, (((relation B) /\ (function B)) => ((finite A) => (finite (relation_image B A)))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) ### All 20
% 3.24/3.44 22. ((relation T_0) => ((relation_image T_0 (relation_dom T_0)) = (relation_rng T_0))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) (All A, (All B, (((relation B) /\ (function B)) => ((finite A) => (finite (relation_image B A)))))) (finite (relation_dom T_0)) (function T_0) (-. (finite (relation_rng T_0))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (relation T_0) ### Imply 1 21
% 3.24/3.44 23. (All A, ((relation A) => ((relation_image A (relation_dom A)) = (relation_rng A)))) (relation T_0) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (-. (finite (relation_rng T_0))) (function T_0) (finite (relation_dom T_0)) (All A, (All B, (((relation B) /\ (function B)) => ((finite A) => (finite (relation_image B A)))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) ### All 22
% 3.24/3.44 24. (-. (((relation T_0) /\ (function T_0)) => ((finite (relation_dom T_0)) => (finite (relation_rng T_0))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) (All A, (All B, (((relation B) /\ (function B)) => ((finite A) => (finite (relation_image B A)))))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, ((relation A) => ((relation_image A (relation_dom A)) = (relation_rng A)))) ### ConjTree 23
% 3.24/3.44 25. (-. (All A, (((relation A) /\ (function A)) => ((finite (relation_dom A)) => (finite (relation_rng A)))))) (All A, ((relation A) => ((relation_image A (relation_dom A)) = (relation_rng A)))) (All A, (All B, ((element A (powerset B)) <=> (subset A B)))) (All A, (All B, (((relation B) /\ (function B)) => ((finite A) => (finite (relation_image B A)))))) (All A, ((finite A) => (All B, ((element B (powerset A)) => (finite B))))) ### NotAllEx 24
% 3.24/3.44 % SZS output end Proof
% 3.24/3.44 (* END-PROOF *)
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