TSTP Solution File: SET146+3 by SuperZenon---0.0.1
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- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n013.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 05:39:52 EDT 2022
% Result : Theorem 2.19s 2.38s
% Output : Proof 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET146+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 00:43:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.19/2.38 % SZS status Theorem
% 2.19/2.38 (* PROOF-FOUND *)
% 2.19/2.38 (* BEGIN-PROOF *)
% 2.19/2.38 % SZS output start Proof
% 2.19/2.38 1. (T_0 != T_0) ### Refl(=)
% 2.19/2.38 2. ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) ((intersection T_1 (empty_set)) != (intersection (empty_set) T_1)) ### Sym(=)
% 2.19/2.38 3. (-. (member T_0 (intersection (empty_set) T_1))) (member T_0 (intersection T_1 (empty_set))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) ### P-NotP 1 2
% 2.19/2.38 4. (-. (member T_0 (empty_set))) (member T_0 (empty_set)) ### Axiom
% 2.19/2.38 5. ((member T_0 (empty_set)) /\ (member T_0 T_1)) (-. (member T_0 (empty_set))) ### And 4
% 2.19/2.38 6. ((member T_0 (intersection (empty_set) T_1)) <=> ((member T_0 (empty_set)) /\ (member T_0 T_1))) (-. (member T_0 (empty_set))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (member T_0 (intersection T_1 (empty_set))) ### Equiv 3 5
% 2.19/2.38 7. (All D, ((member D (intersection (empty_set) T_1)) <=> ((member D (empty_set)) /\ (member D T_1)))) (member T_0 (intersection T_1 (empty_set))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (-. (member T_0 (empty_set))) ### All 6
% 2.19/2.38 8. (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) (-. (member T_0 (empty_set))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (member T_0 (intersection T_1 (empty_set))) ### All 7
% 2.19/2.38 9. (member T_0 (empty_set)) (-. (member T_0 (empty_set))) ### Axiom
% 2.19/2.38 10. (All B, (-. (member B (empty_set)))) (member T_0 (empty_set)) ### All 9
% 2.19/2.38 11. (-. ((member T_0 (empty_set)) <=> (member T_0 (intersection T_1 (empty_set))))) (All B, (-. (member B (empty_set)))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ### NotEquiv 8 10
% 2.19/2.38 12. (-. (All D, ((member D (empty_set)) <=> (member D (intersection T_1 (empty_set)))))) (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All B, (-. (member B (empty_set)))) ### NotAllEx 11
% 2.19/2.38 13. ((intersection T_1 (empty_set)) != (empty_set)) ((empty_set) = (intersection T_1 (empty_set))) ### Sym(=)
% 2.19/2.38 14. (((empty_set) = (intersection T_1 (empty_set))) <=> (All D, ((member D (empty_set)) <=> (member D (intersection T_1 (empty_set)))))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (-. (member B (empty_set)))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ### Equiv 12 13
% 2.19/2.38 15. (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) (All C, (All D, ((member D (intersection (empty_set) C)) <=> ((member D (empty_set)) /\ (member D C))))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All B, (-. (member B (empty_set)))) ((intersection T_1 (empty_set)) != (empty_set)) ### All 14
% 2.19/2.38 16. (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (-. (member B (empty_set)))) ((intersection (empty_set) T_1) = (intersection T_1 (empty_set))) (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) ### All 15
% 2.19/2.38 17. (All C, ((intersection (empty_set) C) = (intersection C (empty_set)))) (All C, (((empty_set) = C) <=> (All D, ((member D (empty_set)) <=> (member D C))))) (All B, (-. (member B (empty_set)))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ### All 16
% 2.19/2.38 18. (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (-. (member B (empty_set)))) (All C, ((intersection (empty_set) C) = (intersection C (empty_set)))) ### All 17
% 2.19/2.38 19. (All B, (All C, ((intersection B C) = (intersection C B)))) (All B, (-. (member B (empty_set)))) ((intersection T_1 (empty_set)) != (empty_set)) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) ### All 18
% 2.19/2.38 20. (-. (All B, ((intersection B (empty_set)) = (empty_set)))) (All B, (All C, ((B = C) <=> (All D, ((member D B) <=> (member D C)))))) (All B, (All C, (All D, ((member D (intersection B C)) <=> ((member D B) /\ (member D C)))))) (All B, (-. (member B (empty_set)))) (All B, (All C, ((intersection B C) = (intersection C B)))) ### NotAllEx 19
% 2.19/2.38 % SZS output end Proof
% 2.19/2.38 (* END-PROOF *)
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