%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU341+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : 300s
% DateTime : Sat Jun 21 05:27:39 AM UTC 2025
% Result : Theorem 0.22s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEU341+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 06:49:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 tff(in_type, type, (
% 0.22/0.42 in: ( $i * $i ) > $o)).
% 0.22/0.42 tff(interior_type, type, (
% 0.22/0.42 interior: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_B_8_type, type, (
% 0.22/0.42 tptp_fun_B_8: $i)).
% 0.22/0.42 tff(tptp_fun_A_7_type, type, (
% 0.22/0.42 tptp_fun_A_7: $i)).
% 0.22/0.42 tff(tptp_fun_C_9_type, type, (
% 0.22/0.42 tptp_fun_C_9: $i)).
% 0.22/0.42 tff(open_subset_type, type, (
% 0.22/0.42 open_subset: ( $i * $i ) > $o)).
% 0.22/0.42 tff(tptp_fun_B_5_type, type, (
% 0.22/0.42 tptp_fun_B_5: $i > $i)).
% 0.22/0.42 tff(the_carrier_type, type, (
% 0.22/0.42 the_carrier: $i > $i)).
% 0.22/0.42 tff(element_type, type, (
% 0.22/0.42 element: ( $i * $i ) > $o)).
% 0.22/0.42 tff(powerset_type, type, (
% 0.22/0.42 powerset: $i > $i)).
% 0.22/0.42 tff(top_str_type, type, (
% 0.22/0.42 top_str: $i > $o)).
% 0.22/0.42 tff(point_neighbourhood_type, type, (
% 0.22/0.42 point_neighbourhood: ( $i * $i * $i ) > $o)).
% 0.22/0.42 tff(topological_space_type, type, (
% 0.22/0.42 topological_space: $i > $o)).
% 0.22/0.42 tff(empty_carrier_type, type, (
% 0.22/0.42 empty_carrier: $i > $o)).
% 0.22/0.42 tff(empty_type, type, (
% 0.22/0.42 empty: $i > $o)).
% 0.22/0.42 tff(1,plain,
% 0.22/0.42 ((((~empty_carrier(A!7)) & topological_space(A!7) & top_str(A!7)) & (element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7))))))) <=> ((~empty_carrier(A!7)) & topological_space(A!7) & top_str(A!7) & element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(2,plain,
% 0.22/0.42 ((~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7))))) <=> (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(3,plain,
% 0.22/0.42 ((element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7)))))) <=> (element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[2])).
% 0.22/0.42 tff(4,plain,
% 0.22/0.42 ((((~empty_carrier(A!7)) & topological_space(A!7) & top_str(A!7)) & (element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7))))))) <=> (((~empty_carrier(A!7)) & topological_space(A!7) & top_str(A!7)) & (element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7)))))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.22/0.42 tff(5,plain,
% 0.22/0.42 ((((~empty_carrier(A!7)) & topological_space(A!7) & top_str(A!7)) & (element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7))))))) <=> ((~empty_carrier(A!7)) & topological_space(A!7) & top_str(A!7) & element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7))))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[4, 1])).
% 0.22/0.42 tff(6,plain,
% 0.22/0.42 ((~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(7,plain,
% 0.22/0.42 ((~![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(8,axiom,(~![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_connsp_2')).
% 0.22/0.43 tff(9,plain,
% 0.22/0.43 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.43 tff(10,plain,
% 0.22/0.43 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.22/0.43 tff(11,plain,
% 0.22/0.43 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.22/0.43 tff(12,plain,
% 0.22/0.43 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.22/0.43 tff(13,plain,
% 0.22/0.43 ((~empty_carrier(A!7)) & topological_space(A!7) & top_str(A!7) & element(B!8, powerset(the_carrier(A!7))) & (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.22/0.43 tff(14,plain,
% 0.22/0.43 (top_str(A!7)),
% 0.22/0.43 inference(and_elim,[status(thm)],[13])).
% 0.22/0.43 tff(15,plain,
% 0.22/0.43 (topological_space(A!7)),
% 0.22/0.43 inference(and_elim,[status(thm)],[13])).
% 0.22/0.43 tff(16,plain,
% 0.22/0.43 (^[A: $i] : refl(((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(17,plain,
% 0.22/0.43 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.43 tff(18,plain,
% 0.22/0.43 (^[A: $i] : rewrite(((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(19,plain,
% 0.22/0.43 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.43 tff(20,plain,
% 0.22/0.43 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[19, 17])).
% 0.22/0.43 tff(21,plain,
% 0.22/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((topological_space(A) & top_str(A)) <=> (~((~top_str(A)) | (~topological_space(A))))), ((~(topological_space(A) & top_str(A))) <=> (~(~((~top_str(A)) | (~topological_space(A))))))), rewrite((~(~((~top_str(A)) | (~topological_space(A))))) <=> ((~top_str(A)) | (~topological_space(A)))), ((~(topological_space(A) & top_str(A))) <=> ((~top_str(A)) | (~topological_space(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))) <=> ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))), (![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))) <=> ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))) <=> (((~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))))), rewrite((((~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A))))))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(22,plain,
% 0.22/0.43 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.22/0.43 tff(23,plain,
% 0.22/0.43 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(24,plain,
% 0.22/0.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A))) <=> (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))), ((element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))) <=> (element(D, powerset(the_carrier(B))) => (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))), rewrite((element(D, powerset(the_carrier(B))) => (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))) <=> ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))), ((element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))) <=> ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))), (![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))) <=> ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))), ((element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A))))) <=> (element(C, powerset(the_carrier(A))) => ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))), rewrite((element(C, powerset(the_carrier(A))) => ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))) <=> ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))), ((element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A))))) <=> ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A))))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))), ((top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))))) <=> (top_str(B) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))), rewrite((top_str(B) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))) <=> ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))), ((top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))))) <=> ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))))), (![B: $i] : (top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))))) <=> ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))), (((topological_space(A) & top_str(A)) => ![B: $i] : (top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A))))))) <=> ((topological_space(A) & top_str(A)) => ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))))), rewrite(((topological_space(A) & top_str(A)) => ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))), (((topological_space(A) & top_str(A)) => ![B: $i] : (top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A))))))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(25,plain,
% 0.22/0.43 (![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A))))))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.22/0.43 tff(26,axiom,(![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t55_tops_1')).
% 0.22/0.43 tff(27,plain,
% 0.22/0.43 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.43 tff(28,plain,
% 0.22/0.43 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.22/0.43 tff(29,plain,(
% 0.22/0.43 ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(skolemize,[status(sab)],[28])).
% 0.22/0.43 tff(30,plain,
% 0.22/0.43 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.22/0.43 tff(31,plain,
% 0.22/0.43 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.22/0.43 tff(32,plain,
% 0.22/0.43 (((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))) | ((~top_str(A!7)) | (~topological_space(A!7)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))))) <=> ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))) | (~top_str(A!7)) | (~topological_space(A!7)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(33,plain,
% 0.22/0.43 ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))) | ((~top_str(A!7)) | (~topological_space(A!7)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(34,plain,
% 0.22/0.43 ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A, C) = C)) | open_subset(C, A)))))))))) | (~top_str(A!7)) | (~topological_space(A!7)) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.22/0.43 tff(35,plain,
% 0.22/0.43 (![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[34, 31, 15, 14])).
% 0.22/0.43 tff(36,plain,
% 0.22/0.43 (((~![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))) | ((~top_str(A!7)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))) <=> ((~![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))) | (~top_str(A!7)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(37,plain,
% 0.22/0.43 ((~![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))) | ((~top_str(A!7)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(38,plain,
% 0.22/0.43 ((~![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (~((~((~open_subset(D, B)) | (interior(B, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7))))))))) | (~top_str(A!7)) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.22/0.44 tff(39,plain,
% 0.22/0.44 (![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[38, 14, 35])).
% 0.22/0.44 tff(40,plain,
% 0.22/0.44 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(41,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.44 tff(42,plain,
% 0.22/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(43,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.44 tff(44,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(45,plain,
% 0.22/0.44 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(46,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.44 tff(47,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 0.22/0.44 tff(48,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.44 tff(49,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.22/0.44 tff(50,plain,(
% 0.22/0.44 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[49])).
% 0.22/0.44 tff(51,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.22/0.44 tff(52,plain,
% 0.22/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.22/0.44 tff(53,plain,
% 0.22/0.44 (~(point_neighbourhood(B!8, A!7, C!9) | (~(open_subset(B!8, A!7) & in(C!9, B!8))) | (~element(C!9, the_carrier(A!7))))),
% 0.22/0.44 inference(and_elim,[status(thm)],[13])).
% 0.22/0.44 tff(54,plain,
% 0.22/0.44 (open_subset(B!8, A!7) & in(C!9, B!8)),
% 0.22/0.44 inference(or_elim,[status(thm)],[53])).
% 0.22/0.44 tff(55,plain,
% 0.22/0.44 (in(C!9, B!8)),
% 0.22/0.44 inference(and_elim,[status(thm)],[54])).
% 0.22/0.44 tff(56,plain,
% 0.22/0.44 (element(B!8, powerset(the_carrier(A!7)))),
% 0.22/0.44 inference(and_elim,[status(thm)],[13])).
% 0.22/0.44 tff(57,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (~in(C!9, B!8)) | (~empty(the_carrier(A!7))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~in(C!9, B!8)) | (~empty(the_carrier(A!7))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(58,plain,
% 0.22/0.44 (((~empty(the_carrier(A!7))) | (~in(C!9, B!8)) | (~element(B!8, powerset(the_carrier(A!7))))) <=> ((~element(B!8, powerset(the_carrier(A!7)))) | (~in(C!9, B!8)) | (~empty(the_carrier(A!7))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(59,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_carrier(A!7))) | (~in(C!9, B!8)) | (~element(B!8, powerset(the_carrier(A!7)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (~in(C!9, B!8)) | (~empty(the_carrier(A!7)))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[58])).
% 0.22/0.44 tff(60,plain,
% 0.22/0.44 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_carrier(A!7))) | (~in(C!9, B!8)) | (~element(B!8, powerset(the_carrier(A!7)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~in(C!9, B!8)) | (~empty(the_carrier(A!7))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[59, 57])).
% 0.22/0.44 tff(61,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_carrier(A!7))) | (~in(C!9, B!8)) | (~element(B!8, powerset(the_carrier(A!7)))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(62,plain,
% 0.22/0.44 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~in(C!9, B!8)) | (~empty(the_carrier(A!7)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.22/0.44 tff(63,plain,
% 0.22/0.44 (~empty(the_carrier(A!7))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[62, 56, 55, 52])).
% 0.22/0.44 tff(64,plain,
% 0.22/0.44 (^[A: $i] : refl((empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A)))))) <=> (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(65,plain,
% 0.22/0.44 (![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A)))))) <=> ![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[64])).
% 0.22/0.44 tff(66,plain,
% 0.22/0.44 (^[A: $i] : rewrite((empty(A) | (element(tptp_fun_B_5(A), powerset(A)) & (~empty(tptp_fun_B_5(A))))) <=> (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A)))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(67,plain,
% 0.22/0.44 (![A: $i] : (empty(A) | (element(tptp_fun_B_5(A), powerset(A)) & (~empty(tptp_fun_B_5(A))))) <=> ![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A))))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.22/0.44 tff(68,plain,
% 0.22/0.44 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> ![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(69,plain,
% 0.22/0.44 (^[A: $i] : rewrite(((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(70,plain,
% 0.22/0.44 (![A: $i] : ((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B)))) <=> ![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.22/0.44 tff(71,axiom,(![A: $i] : ((~empty(A)) => ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc1_subset_1')).
% 0.22/0.44 tff(72,plain,
% 0.22/0.44 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.22/0.44 tff(73,plain,
% 0.22/0.44 (![A: $i] : (empty(A) | ?[B: $i] : (element(B, powerset(A)) & (~empty(B))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.22/0.44 tff(74,plain,(
% 0.22/0.44 ![A: $i] : (empty(A) | (element(tptp_fun_B_5(A), powerset(A)) & (~empty(tptp_fun_B_5(A)))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[73])).
% 0.22/0.44 tff(75,plain,
% 0.22/0.44 (![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.22/0.44 tff(76,plain,
% 0.22/0.44 (![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.22/0.44 tff(77,plain,
% 0.22/0.44 (((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A))))))) | (empty(the_carrier(A!7)) | (~(empty(tptp_fun_B_5(the_carrier(A!7))) | (~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))))))) <=> ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A))))))) | empty(the_carrier(A!7)) | (~(empty(tptp_fun_B_5(the_carrier(A!7))) | (~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(78,plain,
% 0.22/0.44 ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A))))))) | (empty(the_carrier(A!7)) | (~(empty(tptp_fun_B_5(the_carrier(A!7))) | (~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(79,plain,
% 0.22/0.44 ((~![A: $i] : (empty(A) | (~(empty(tptp_fun_B_5(A)) | (~element(tptp_fun_B_5(A), powerset(A))))))) | empty(the_carrier(A!7)) | (~(empty(tptp_fun_B_5(the_carrier(A!7))) | (~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7))))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.22/0.44 tff(80,plain,
% 0.22/0.44 (~(empty(tptp_fun_B_5(the_carrier(A!7))) | (~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[79, 76, 63])).
% 0.22/0.44 tff(81,plain,
% 0.22/0.44 ((empty(tptp_fun_B_5(the_carrier(A!7))) | (~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7))))) | element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(82,plain,
% 0.22/0.44 (element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.22/0.44 tff(83,plain,
% 0.22/0.44 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))) | ((~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7)))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))) | (~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7)))))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(84,plain,
% 0.22/0.44 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))) | ((~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7)))))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(85,plain,
% 0.22/0.45 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, C) = C)) | open_subset(C, A!7)))))))) | (~element(tptp_fun_B_5(the_carrier(A!7)), powerset(the_carrier(A!7)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.22/0.45 tff(86,plain,
% 0.22/0.45 (![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[85, 82, 39])).
% 0.22/0.45 tff(87,plain,
% 0.22/0.45 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (~((~((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~((~((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(88,plain,
% 0.22/0.45 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (~((~((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(89,plain,
% 0.22/0.45 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!7)))) | (~((~((~open_subset(D, A!7)) | (interior(A!7, D) = D))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~((~((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.22/0.45 tff(90,plain,
% 0.22/0.45 (~((~((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[89, 56, 86])).
% 0.22/0.45 tff(91,plain,
% 0.22/0.45 (((~((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))) | (~((~(interior(A!7, tptp_fun_B_5(the_carrier(A!7))) = tptp_fun_B_5(the_carrier(A!7)))) | open_subset(tptp_fun_B_5(the_carrier(A!7)), A!7)))) | ((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(92,plain,
% 0.22/0.45 ((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.22/0.45 tff(93,plain,
% 0.22/0.45 (open_subset(B!8, A!7)),
% 0.22/0.45 inference(and_elim,[status(thm)],[54])).
% 0.22/0.45 tff(94,plain,
% 0.22/0.45 ((~((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))) | (~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(95,plain,
% 0.22/0.45 ((~((~open_subset(B!8, A!7)) | (interior(A!7, B!8) = B!8))) | (interior(A!7, B!8) = B!8)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.22/0.45 tff(96,plain,
% 0.22/0.45 (interior(A!7, B!8) = B!8),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[95, 92])).
% 0.22/0.45 tff(97,plain,
% 0.22/0.45 (in(C!9, interior(A!7, B!8)) <=> in(C!9, B!8)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[96])).
% 0.22/0.45 tff(98,plain,
% 0.22/0.45 (in(C!9, B!8) <=> in(C!9, interior(A!7, B!8))),
% 0.22/0.45 inference(symmetry,[status(thm)],[97])).
% 0.22/0.45 tff(99,plain,
% 0.22/0.45 (in(C!9, interior(A!7, B!8))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[55, 98])).
% 0.22/0.45 tff(100,plain,
% 0.22/0.45 (~empty_carrier(A!7)),
% 0.22/0.45 inference(and_elim,[status(thm)],[13])).
% 0.22/0.45 tff(101,plain,
% 0.22/0.45 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(102,plain,
% 0.22/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[101])).
% 0.22/0.45 tff(103,plain,
% 0.22/0.45 (^[A: $i] : refl((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(104,plain,
% 0.22/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[103])).
% 0.22/0.45 tff(105,plain,
% 0.22/0.45 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(106,plain,
% 0.22/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[105])).
% 0.22/0.45 tff(107,plain,
% 0.22/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A)))),
% 0.22/0.45 inference(transitivity,[status(thm)],[106, 104])).
% 0.22/0.45 tff(108,plain,
% 0.22/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A)) <=> (~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), rewrite(((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A)))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(109,plain,
% 0.22/0.45 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[108])).
% 0.22/0.45 tff(110,plain,
% 0.22/0.45 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(111,plain,
% 0.22/0.45 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))) <=> ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(112,plain,
% 0.23/0.45 (![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[111])).
% 0.23/0.45 tff(113,axiom,(![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_connsp_2')).
% 0.23/0.45 tff(114,plain,
% 0.23/0.45 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.23/0.45 tff(115,plain,
% 0.23/0.45 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.23/0.45 tff(116,plain,(
% 0.23/0.45 ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[115])).
% 0.23/0.45 tff(117,plain,
% 0.23/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.23/0.45 tff(118,plain,
% 0.23/0.45 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~top_str(A)) | (~topological_space(A)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[117, 107])).
% 0.23/0.45 tff(119,plain,
% 0.23/0.45 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[118, 102])).
% 0.23/0.45 tff(120,plain,
% 0.23/0.45 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | (empty_carrier(A!7) | (~top_str(A!7)) | (~topological_space(A!7)) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | empty_carrier(A!7) | (~top_str(A!7)) | (~topological_space(A!7)) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C))))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(121,plain,
% 0.23/0.45 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | (empty_carrier(A!7) | (~top_str(A!7)) | (~topological_space(A!7)) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C))))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(122,plain,
% 0.23/0.45 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | empty_carrier(A!7) | (~top_str(A!7)) | (~topological_space(A!7)) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C)))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.23/0.45 tff(123,plain,
% 0.23/0.45 (![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C)))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[122, 119, 100, 15, 14])).
% 0.23/0.45 tff(124,plain,
% 0.23/0.45 (element(C!9, the_carrier(A!7))),
% 0.23/0.45 inference(or_elim,[status(thm)],[53])).
% 0.23/0.45 tff(125,plain,
% 0.23/0.45 (((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C)))))) | ((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C)))))) | (~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C)))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(126,plain,
% 0.23/0.46 ((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C)))))) | ((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C)))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(127,plain,
% 0.23/0.46 ((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, B) <=> in(B, interior(A!7, C)))))) | (~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.23/0.46 tff(128,plain,
% 0.23/0.46 (![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C))))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[127, 124, 123])).
% 0.23/0.46 tff(129,plain,
% 0.23/0.46 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (point_neighbourhood(B!8, A!7, C!9) <=> in(C!9, interior(A!7, B!8))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (point_neighbourhood(B!8, A!7, C!9) <=> in(C!9, interior(A!7, B!8))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(130,plain,
% 0.23/0.46 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (point_neighbourhood(B!8, A!7, C!9) <=> in(C!9, interior(A!7, B!8))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(131,plain,
% 0.23/0.46 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!7)))) | (point_neighbourhood(C, A!7, C!9) <=> in(C!9, interior(A!7, C))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (point_neighbourhood(B!8, A!7, C!9) <=> in(C!9, interior(A!7, B!8)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.23/0.46 tff(132,plain,
% 0.23/0.46 (point_neighbourhood(B!8, A!7, C!9) <=> in(C!9, interior(A!7, B!8))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[131, 56, 128])).
% 0.23/0.46 tff(133,plain,
% 0.23/0.46 (~point_neighbourhood(B!8, A!7, C!9)),
% 0.23/0.46 inference(or_elim,[status(thm)],[53])).
% 0.23/0.46 tff(134,plain,
% 0.23/0.46 ((~(point_neighbourhood(B!8, A!7, C!9) <=> in(C!9, interior(A!7, B!8)))) | point_neighbourhood(B!8, A!7, C!9) | (~in(C!9, interior(A!7, B!8)))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(135,plain,
% 0.23/0.46 ((~(point_neighbourhood(B!8, A!7, C!9) <=> in(C!9, interior(A!7, B!8)))) | (~in(C!9, interior(A!7, B!8)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.23/0.46 tff(136,plain,
% 0.23/0.46 (~in(C!9, interior(A!7, B!8))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.23/0.46 tff(137,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[136, 99])).
% 0.23/0.46 % SZS output end Proof
% 0.23/0.46 % E exiting
%------------------------------------------------------------------------------