TSTP Solution File: SEU234+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU234+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 : Tue Sep 20 07:28:22 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU234+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n011.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 : Sat Sep 3 10:48:13 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(tptp_fun_C_1_type, type, (
% 0.21/0.42 tptp_fun_C_1: $i > $i)).
% 0.21/0.42 tff(tptp_fun_A_16_type, type, (
% 0.21/0.42 tptp_fun_A_16: $i)).
% 0.21/0.42 tff(in_type, type, (
% 0.21/0.42 in: ( $i * $i ) > $o)).
% 0.21/0.42 tff(ordinal_type, type, (
% 0.21/0.42 ordinal: $i > $o)).
% 0.21/0.42 tff(subset_type, type, (
% 0.21/0.42 subset: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_B_2_type, type, (
% 0.21/0.42 tptp_fun_B_2: $i > $i)).
% 0.21/0.42 tff(epsilon_connected_type, type, (
% 0.21/0.42 epsilon_connected: $i > $o)).
% 0.21/0.42 tff(epsilon_transitive_type, type, (
% 0.21/0.42 epsilon_transitive: $i > $o)).
% 0.21/0.42 tff(tptp_fun_B_0_type, type, (
% 0.21/0.42 tptp_fun_B_0: $i > $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (^[A: $i] : refl((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (^[A: $i] : rewrite((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))), rewrite((epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))) <=> (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))), ((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> (((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A)))) & (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))), rewrite((((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A)))) & (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))), ((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (^[A: $i] : rewrite((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (~(~(in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))))) <=> (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (~(~(in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A)))))))) <=> ![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (^[A: $i] : rewrite((epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.43 tff(13,axiom,(![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_ordinal1')).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.43 tff(16,plain,(
% 0.21/0.43 ![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (~(~(in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[15])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16)))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 ((~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!16)) | (~in(C, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | (~in(tptp_fun_C_1(A!16), A!16)))))))) <=> (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!16)) | (~in(C, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | (~in(tptp_fun_C_1(A!16), A!16))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16)))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[21])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!16)) | (~in(C, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | (~in(tptp_fun_C_1(A!16), A!16))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16)))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[22, 20])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!16)) | (~in(C, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (~in(tptp_fun_B_2(A!16), A!16)) | (~in(tptp_fun_C_1(A!16), A!16))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (~((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16)))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (((~((~epsilon_connected(A!16)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A!16)) | (~in(B, A!16))))) | (~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))))))) | (epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.21/0.43 tff(29,assumption,((~((~epsilon_transitive(A!16)) | ![B: $i] : ((~in(B, A!16)) | subset(B, A!16)))) | (~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))))), introduced(assumption)).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[33, 31])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[38])).
% 0.21/0.44 tff(40,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.21/0.44 tff(43,plain,(
% 0.21/0.44 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[42])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(A!16)) | ![B: $i] : ((~in(B, A!16)) | subset(B, A!16)))) | (~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[46, 45, 29])).
% 0.21/0.44 tff(48,plain,(~((~((~epsilon_transitive(A!16)) | ![B: $i] : ((~in(B, A!16)) | subset(B, A!16)))) | (~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (((~((~epsilon_transitive(A!16)) | ![B: $i] : ((~in(B, A!16)) | subset(B, A!16)))) | (~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))))) | (epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.21/0.44 tff(51,assumption,(~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))), introduced(assumption)).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)) | (~subset(tptp_fun_B_0(A!16), A!16))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (~subset(tptp_fun_B_0(A!16), A!16)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16))) | subset(tptp_fun_B_0(A!16), A!16)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 ((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)) | in(tptp_fun_B_0(A!16), A!16)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (in(tptp_fun_B_0(A!16), A!16)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[56, 51])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (^[B: $i] : refl(((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16))))) <=> ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16))))) <=> ![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (^[B: $i] : rewrite(((~in(B, A!16)) | (ordinal(B) & subset(B, A!16))) <=> ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16))) <=> ![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (((~ordinal(A!16)) & ![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16)))) <=> ((~ordinal(A!16)) & ![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 ((~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))) <=> (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 ((~![A: $i] : (![B: $i] : (in(B, A) => (ordinal(B) & subset(B, A))) => ordinal(A))) <=> (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(65,axiom,(~![A: $i] : (![B: $i] : (in(B, A) => (ordinal(B) & subset(B, A))) => ordinal(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t31_ordinal1')).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[66, 63])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[68, 63])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[69, 63])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (~![A: $i] : (ordinal(A) | (~![B: $i] : ((~in(B, A)) | (ordinal(B) & subset(B, A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[71, 63])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 ((~ordinal(A!16)) & ![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 (![B: $i] : ((~in(B, A!16)) | (ordinal(B) & subset(B, A!16)))),
% 0.21/0.44 inference(and_elim,[status(thm)],[73])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[74, 61])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 (![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[75, 59])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_B_0(A!16), A!16)) | (~((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16)))))) <=> ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_B_0(A!16), A!16)) | (~((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_B_0(A!16), A!16)) | (~((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_B_0(A!16), A!16)) | (~((~ordinal(tptp_fun_B_0(A!16))) | (~subset(tptp_fun_B_0(A!16), A!16))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[79, 76, 57, 55])).
% 0.21/0.44 tff(81,plain,((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 ((~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))))) | epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 ((~(epsilon_transitive(A!16) | (~((~in(tptp_fun_B_0(A!16), A!16)) | subset(tptp_fun_B_0(A!16), A!16))))) | epsilon_transitive(A!16)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 (epsilon_transitive(A!16)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[83, 50])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (^[A: $i] : refl((ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.44 tff(87,plain,
% 0.21/0.44 (^[A: $i] : rewrite((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(90,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_ordinal1')).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.21/0.44 tff(92,plain,(
% 0.21/0.44 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[91])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 ((~![A: $i] : (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (ordinal(A!16) <=> (~((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (ordinal(A!16) <=> (~((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (~ordinal(A!16)),
% 0.21/0.44 inference(and_elim,[status(thm)],[73])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 ((~(ordinal(A!16) <=> (~((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16)))))) | ordinal(A!16) | ((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 ((~(ordinal(A!16) <=> (~((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16)))))) | ((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 ((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 ((~((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16)))) | (~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 ((~epsilon_transitive(A!16)) | (~epsilon_connected(A!16))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (~epsilon_connected(A!16)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[102, 84])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 ((~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16)))))) | epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 ((~(epsilon_connected(A!16) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16)))))) | (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (~(in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[105, 28])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 ((in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))) | in(tptp_fun_C_1(A!16), A!16)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (in(tptp_fun_C_1(A!16), A!16)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 (((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_C_1(A!16), A!16)) | (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16)))))) <=> ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_C_1(A!16), A!16)) | (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_C_1(A!16), A!16)) | (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_C_1(A!16), A!16)) | (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (~((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[111, 76, 108])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (((~ordinal(tptp_fun_C_1(A!16))) | (~subset(tptp_fun_C_1(A!16), A!16))) | ordinal(tptp_fun_C_1(A!16))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (ordinal(tptp_fun_C_1(A!16))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[115])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))) <=> (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> (ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), rewrite((ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), (![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.45 tff(125,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_ordinal1')).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.21/0.45 tff(128,plain,(
% 0.21/0.45 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[127])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : (in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : (in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[132])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : (in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[133, 131])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : (in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B) | (~ordinal(B))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(A!16))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.45 tff(137,plain,
% 0.21/0.45 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[136, 130, 114])).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 ((in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))) | in(tptp_fun_B_2(A!16), A!16)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 (in(tptp_fun_B_2(A!16), A!16)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[138, 106])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 (((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_B_2(A!16), A!16)) | (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16)))))) <=> ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_B_2(A!16), A!16)) | (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | ((~in(tptp_fun_B_2(A!16), A!16)) | (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 ((~![B: $i] : ((~in(B, A!16)) | (~((~ordinal(B)) | (~subset(B, A!16)))))) | (~in(tptp_fun_B_2(A!16), A!16)) | (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.45 tff(143,plain,
% 0.21/0.45 (~((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[142, 76, 139])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (((~ordinal(tptp_fun_B_2(A!16))) | (~subset(tptp_fun_B_2(A!16), A!16))) | ordinal(tptp_fun_B_2(A!16))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 (ordinal(tptp_fun_B_2(A!16))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[144, 143])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 ((tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) <=> (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16))),
% 0.21/0.45 inference(commutativity,[status(thm)],[])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 ((tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) <=> (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16))),
% 0.21/0.45 inference(symmetry,[status(thm)],[146])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 ((~(tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16))) <=> (~(tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[147])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 ((in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))) | (~(tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (~(tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[149, 106])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 (~(tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[150, 148])).
% 0.21/0.45 tff(152,plain,
% 0.21/0.45 ((in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))) | (~in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (~in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[152, 106])).
% 0.21/0.45 tff(154,plain,
% 0.21/0.45 ((in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_B_2(A!16) = tptp_fun_C_1(A!16)) | (~in(tptp_fun_C_1(A!16), A!16)) | (~in(tptp_fun_B_2(A!16), A!16))) | (~in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 (~in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[154, 106])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | (in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(157,plain,
% 0.21/0.45 (((~ordinal(tptp_fun_B_2(A!16))) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16))) <=> (in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | ((~ordinal(tptp_fun_B_2(A!16))) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | (in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[157])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | ((~ordinal(tptp_fun_B_2(A!16))) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[158, 156])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | ((~ordinal(tptp_fun_B_2(A!16))) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(A!16)) | in(tptp_fun_C_1(A!16), B) | (tptp_fun_C_1(A!16) = B))) | in(tptp_fun_C_1(A!16), tptp_fun_B_2(A!16)) | in(tptp_fun_B_2(A!16), tptp_fun_C_1(A!16)) | (tptp_fun_C_1(A!16) = tptp_fun_B_2(A!16)) | (~ordinal(tptp_fun_B_2(A!16)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[161, 155, 153, 151, 145, 137])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------