TSTP Solution File: SWV273-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV273-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Thu Sep 29 15:10:46 EDT 2022
% Result : Unsatisfiable 0.64s 0.63s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV273-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 02:05:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.64/0.63 % SZS status Unsatisfiable
% 0.64/0.63 % SZS output start Proof
% 0.64/0.63 tff(c_lessequals_type, type, (
% 0.64/0.63 c_lessequals: ( $i * $i * $i ) > $o)).
% 0.64/0.63 tff(tc_set_type, type, (
% 0.64/0.63 tc_set: $i > $i)).
% 0.64/0.63 tff(tc_Message_Omsg_type, type, (
% 0.64/0.63 tc_Message_Omsg: $i)).
% 0.64/0.63 tff(c_Message_Oparts_type, type, (
% 0.64/0.63 c_Message_Oparts: $i > $i)).
% 0.64/0.63 tff(c_Message_Osynth_type, type, (
% 0.64/0.63 c_Message_Osynth: $i > $i)).
% 0.64/0.63 tff(v_H_type, type, (
% 0.64/0.63 v_H: $i)).
% 0.64/0.63 tff(c_union_type, type, (
% 0.64/0.63 c_union: ( $i * $i * $i ) > $i)).
% 0.64/0.63 tff(1,plain,
% 0.64/0.63 (^[T_a: $i, V_A: $i] : refl(c_lessequals(V_A, V_A, tc_set(T_a)) <=> c_lessequals(V_A, V_A, tc_set(T_a)))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(2,plain,
% 0.64/0.63 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[1])).
% 0.64/0.63 tff(3,plain,
% 0.64/0.63 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a)) <=> ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(4,axiom,(![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_Osubset__refl_0')).
% 0.64/0.63 tff(5,plain,
% 0.64/0.63 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.64/0.63 tff(6,plain,(
% 0.64/0.63 ![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.64/0.63 inference(skolemize,[status(sab)],[5])).
% 0.64/0.63 tff(7,plain,
% 0.64/0.63 (![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.64/0.63 tff(8,plain,
% 0.64/0.63 ((~![T_a: $i, V_A: $i] : c_lessequals(V_A, V_A, tc_set(T_a))) | c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(quant_inst,[status(thm)],[])).
% 0.64/0.63 tff(9,plain,
% 0.64/0.63 (c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.64/0.63 tff(10,plain,
% 0.64/0.63 (^[V_H: $i] : refl(c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)) <=> c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(11,plain,
% 0.64/0.63 (![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)) <=> ![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[10])).
% 0.64/0.63 tff(12,plain,
% 0.64/0.63 (![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)) <=> ![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(13,axiom,(![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Osynth__increasing_0')).
% 0.64/0.63 tff(14,plain,
% 0.64/0.63 (![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.64/0.63 tff(15,plain,(
% 0.64/0.63 ![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(skolemize,[status(sab)],[14])).
% 0.64/0.63 tff(16,plain,
% 0.64/0.63 (![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.64/0.63 tff(17,plain,
% 0.64/0.63 ((~![V_H: $i] : c_lessequals(V_H, c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(v_H, c_Message_Osynth(v_H), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(quant_inst,[status(thm)],[])).
% 0.64/0.63 tff(18,plain,
% 0.64/0.63 (c_lessequals(v_H, c_Message_Osynth(v_H), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.64/0.63 tff(19,assumption,(~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 0.64/0.63 tff(20,plain,
% 0.64/0.63 (^[V_H: $i, V_G: $i] : refl(((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(21,plain,
% 0.64/0.63 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[20])).
% 0.64/0.63 tff(22,plain,
% 0.64/0.63 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(23,axiom,(![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oparts__mono_0')).
% 0.64/0.63 tff(24,plain,
% 0.64/0.63 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.64/0.63 tff(25,plain,(
% 0.64/0.63 ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(skolemize,[status(sab)],[24])).
% 0.64/0.63 tff(26,plain,
% 0.64/0.63 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.64/0.63 tff(27,plain,
% 0.64/0.63 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H, c_Message_Osynth(v_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))) <=> ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H, c_Message_Osynth(v_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(28,plain,
% 0.64/0.63 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H, c_Message_Osynth(v_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(quant_inst,[status(thm)],[])).
% 0.64/0.63 tff(29,plain,
% 0.64/0.63 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H, c_Message_Osynth(v_H), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.64/0.63 tff(30,plain,
% 0.64/0.63 ($false),
% 0.64/0.63 inference(unit_resolution,[status(thm)],[29, 26, 19, 18])).
% 0.64/0.63 tff(31,plain,(c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.63 tff(32,plain,
% 0.64/0.63 (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : refl((c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(33,plain,
% 0.64/0.63 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[32])).
% 0.64/0.63 tff(34,plain,
% 0.64/0.63 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(35,plain,
% 0.64/0.63 (^[T_a: $i, V_B: $i, V_A: $i, V_C: $i] : trans(monotonicity(rewrite(((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) <=> ((~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))), ((((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) <=> (((~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))))), rewrite((((~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) <=> (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))), ((((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) <=> (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))))),
% 0.64/0.63 inference(bind,[status(th)],[])).
% 0.64/0.63 tff(36,plain,
% 0.64/0.63 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.64/0.63 inference(quant_intro,[status(thm)],[35])).
% 0.64/0.63 tff(37,axiom,(![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (((~c_lessequals(V_B, V_C, tc_set(T_a))) | (~c_lessequals(V_A, V_C, tc_set(T_a)))) | c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUn__subset__iff_2')).
% 0.64/0.63 tff(38,plain,
% 0.64/0.63 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.64/0.63 tff(39,plain,
% 0.64/0.63 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.64/0.63 tff(40,plain,(
% 0.64/0.63 ![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.64/0.63 inference(skolemize,[status(sab)],[39])).
% 0.64/0.63 tff(41,plain,
% 0.64/0.63 (![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))),
% 0.64/0.63 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.64/0.63 tff(42,plain,
% 0.64/0.63 ((~c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))),
% 0.64/0.63 inference(rewrite,[status(thm)],[])).
% 0.64/0.63 tff(43,axiom,(~c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.64/0.64 tff(44,plain,
% 0.64/0.64 (~c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.64/0.64 tff(45,plain,
% 0.64/0.64 (((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))))) <=> ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))))),
% 0.64/0.64 inference(rewrite,[status(thm)],[])).
% 0.64/0.64 tff(46,plain,
% 0.64/0.64 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | (c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))))),
% 0.64/0.64 inference(quant_inst,[status(thm)],[])).
% 0.64/0.64 tff(47,plain,
% 0.64/0.64 ((~![T_a: $i, V_B: $i, V_A: $i, V_C: $i] : (c_lessequals(c_union(V_A, V_B, T_a), V_C, tc_set(T_a)) | (~c_lessequals(V_A, V_C, tc_set(T_a))) | (~c_lessequals(V_B, V_C, tc_set(T_a))))) | c_lessequals(c_union(c_Message_Oparts(v_H), c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)) | (~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.64/0.64 tff(48,plain,
% 0.64/0.64 ((~c_lessequals(c_Message_Oparts(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[47, 44, 41])).
% 0.64/0.64 tff(49,plain,
% 0.64/0.64 (~c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[48, 31])).
% 0.64/0.64 tff(50,plain,
% 0.64/0.64 (^[V_H: $i, V_G: $i] : refl(((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))))),
% 0.64/0.64 inference(bind,[status(th)],[])).
% 0.64/0.64 tff(51,plain,
% 0.64/0.64 (![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(quant_intro,[status(thm)],[50])).
% 0.64/0.64 tff(52,plain,
% 0.64/0.64 (![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) <=> ![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(rewrite,[status(thm)],[])).
% 0.64/0.64 tff(53,axiom,(![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oparts__subset__iff_0')).
% 0.64/0.64 tff(54,plain,
% 0.64/0.64 (![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.64/0.64 tff(55,plain,(
% 0.64/0.64 ![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(skolemize,[status(sab)],[54])).
% 0.64/0.64 tff(56,plain,
% 0.64/0.64 (![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.64/0.64 tff(57,plain,
% 0.64/0.64 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))) <=> ((~![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(rewrite,[status(thm)],[])).
% 0.64/0.64 tff(58,plain,
% 0.64/0.64 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg)))),
% 0.64/0.64 inference(quant_inst,[status(thm)],[])).
% 0.64/0.64 tff(59,plain,
% 0.64/0.64 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))) | c_lessequals(V_G, c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Oparts(c_Message_Osynth(v_H)), tc_set(tc_Message_Omsg))),
% 0.64/0.64 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.64/0.64 tff(60,plain,
% 0.64/0.64 ($false),
% 0.64/0.64 inference(unit_resolution,[status(thm)],[59, 56, 49, 9])).
% 0.64/0.64 % SZS output end Proof
%------------------------------------------------------------------------------