%------------------------------------------------------------------------------ % 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 : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----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 *) %------------------------------------------------------------------------------