TSTP Solution File: SWV245-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV245-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 15:10:32 EDT 2022
% Result : Unsatisfiable 0.13s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV245-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n008.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 01:56:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(c_in_type, type, (
% 0.13/0.41 c_in: ( $i * $i * $i ) > $o)).
% 0.13/0.41 tff(tc_Message_Omsg_type, type, (
% 0.13/0.41 tc_Message_Omsg: $i)).
% 0.13/0.41 tff(v_G_type, type, (
% 0.13/0.41 v_G: $i)).
% 0.13/0.41 tff(c_Message_Omsg_OMPair_type, type, (
% 0.13/0.41 c_Message_Omsg_OMPair: ( $i * $i ) > $i)).
% 0.13/0.41 tff(v_Y_type, type, (
% 0.13/0.41 v_Y: $i)).
% 0.13/0.41 tff(v_X_type, type, (
% 0.13/0.41 v_X: $i)).
% 0.13/0.41 tff(c_Message_Osynth_type, type, (
% 0.13/0.41 c_Message_Osynth: $i > $i)).
% 0.13/0.41 tff(c_union_type, type, (
% 0.13/0.41 c_union: ( $i * $i * $i ) > $i)).
% 0.13/0.41 tff(c_Message_Oanalz_type, type, (
% 0.13/0.41 c_Message_Oanalz: $i > $i)).
% 0.13/0.41 tff(v_H_type, type, (
% 0.13/0.41 v_H: $i)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(4,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnCI_0')).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.41 tff(6,plain,(
% 0.13/0.41 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.13/0.41 inference(skolemize,[status(sab)],[5])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 ((~c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)) <=> (~c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(9,axiom,(~c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_2')).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (~c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_B, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (~c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(18,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnCI_1')).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.41 tff(20,plain,(
% 0.19/0.41 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.19/0.41 inference(skolemize,[status(sab)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (~c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[24, 10, 21])).
% 0.19/0.41 tff(26,assumption,(c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), introduced(assumption)).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (^[V_Y: $i, V_H: $i, V_X: $i] : refl(((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(30,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__analz_1')).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.42 tff(32,plain,(
% 0.19/0.42 ![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.42 inference(skolemize,[status(sab)],[31])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 (((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~![V_Y: $i, V_H: $i, V_X: $i] : ((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Oanalz(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_in(v_X, c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[36, 33, 26, 25])).
% 0.19/0.42 tff(38,plain,(~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl((c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a)) <=> (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.42 tff(44,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, c_union(V_A, V_B, T_a), T_a)) | c_in(V_c, V_B, T_a)) | c_in(V_c, V_A, T_a))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Set_OUnE_0')).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.42 tff(47,plain,(
% 0.19/0.42 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[46])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg) <=> c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(50,axiom,(c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (c_in(V_c, V_B, T_a) | c_in(V_c, V_A, T_a) | (~c_in(V_c, c_union(V_A, V_B, T_a), T_a)))) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), c_Message_Osynth(v_G), tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[54, 51, 48])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[55, 38])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (^[V_Y: $i, V_H: $i, V_X: $i] : refl((c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> ![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg))) <=> ![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (^[V_Y: $i, V_H: $i, V_X: $i] : rewrite((((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg)) <=> (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (![V_Y: $i, V_H: $i, V_X: $i] : (((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg)) <=> ![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.43 tff(62,axiom,(![V_Y: $i, V_H: $i, V_X: $i] : (((~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_OMPair__synth_1')).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.43 tff(65,plain,(
% 0.19/0.43 ![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[64])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (((~![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg)))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 ((c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg))) <=> (c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (((~![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg)))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (((~![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg)))) <=> ((~![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 ((~![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))) | (c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 ((~![V_Y: $i, V_H: $i, V_X: $i] : (c_in(c_Message_Omsg_OMPair(V_X, V_Y), V_H, tc_Message_Omsg) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(V_X, V_Y), c_Message_Osynth(V_H), tc_Message_Omsg)))) | c_in(v_X, c_Message_Osynth(v_G), tc_Message_Omsg) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Osynth(v_G), tc_Message_Omsg))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[72, 66, 56, 14])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg)) <=> ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(77,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cls_Message_Oanalz_OInj_0')).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.43 tff(79,plain,(
% 0.19/0.43 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.43 inference(skolemize,[status(sab)],[78])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))) <=> ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(82,plain,
% 0.19/0.44 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(83,plain,
% 0.19/0.44 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Oanalz(V_H), tc_Message_Omsg))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_Message_Oanalz(c_union(v_G, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[83, 80, 38])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | ((~c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_in(V_c, V_A, T_a)) | c_in(V_c, c_union(V_A, V_B, T_a), T_a))) | (~c_in(c_Message_Omsg_OMPair(v_X, v_Y), v_G, tc_Message_Omsg)) | c_in(c_Message_Omsg_OMPair(v_X, v_Y), c_union(v_G, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[87, 21, 84, 73])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------