TSTP Solution File: SWV275-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV275-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 15:10:47 EDT 2022
% Result : Unsatisfiable 26.36s 16.66s
% Output : Proof 26.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SWV275-1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n015.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 : Sun Sep 4 02:17:26 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 26.36/16.66 % SZS status Unsatisfiable
% 26.36/16.66 % SZS output start Proof
% 26.36/16.66 tff(c_in_type, type, (
% 26.36/16.66 c_in: ( $i * $i * $i ) > $o)).
% 26.36/16.66 tff(tc_Message_Omsg_type, type, (
% 26.36/16.66 tc_Message_Omsg: $i)).
% 26.36/16.66 tff(c_insert_type, type, (
% 26.36/16.66 c_insert: ( $i * $i * $i ) > $i)).
% 26.36/16.66 tff(v_H_type, type, (
% 26.36/16.66 v_H: $i)).
% 26.36/16.66 tff(v_X_type, type, (
% 26.36/16.66 v_X: $i)).
% 26.36/16.66 tff(c_Main_OsubsetI__1_type, type, (
% 26.36/16.66 c_Main_OsubsetI__1: ( $i * $i * $i ) > $i)).
% 26.36/16.66 tff(c_Message_Osynth_type, type, (
% 26.36/16.66 c_Message_Osynth: $i > $i)).
% 26.36/16.66 tff(c_lessequals_type, type, (
% 26.36/16.66 c_lessequals: ( $i * $i * $i ) > $o)).
% 26.36/16.66 tff(tc_set_type, type, (
% 26.36/16.66 tc_set: $i > $i)).
% 26.36/16.66 tff(1,assumption,(~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 26.36/16.66 tff(2,assumption,(~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), introduced(assumption)).
% 26.36/16.66 tff(3,plain,
% 26.36/16.66 (^[T_a: $i, V_B: $i, V_A: $i] : refl((c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 26.36/16.66 inference(bind,[status(th)],[])).
% 26.36/16.66 tff(4,plain,
% 26.36/16.66 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.66 inference(quant_intro,[status(thm)],[3])).
% 26.36/16.66 tff(5,plain,
% 26.36/16.66 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.66 inference(rewrite,[status(thm)],[])).
% 26.36/16.66 tff(6,axiom,(![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax','cls_Set_OsubsetI_0')).
% 26.36/16.66 tff(7,plain,
% 26.36/16.66 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.66 inference(modus_ponens,[status(thm)],[6, 5])).
% 26.36/16.66 tff(8,plain,(
% 26.36/16.66 ![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.66 inference(skolemize,[status(sab)],[7])).
% 26.36/16.66 tff(9,plain,
% 26.36/16.66 (![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.66 inference(modus_ponens,[status(thm)],[8, 4])).
% 26.36/16.66 tff(10,plain,
% 26.36/16.66 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 26.36/16.66 inference(rewrite,[status(thm)],[])).
% 26.36/16.66 tff(11,plain,
% 26.36/16.66 ((c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) <=> (c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 26.36/16.66 inference(rewrite,[status(thm)],[])).
% 26.36/16.66 tff(12,plain,
% 26.36/16.66 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)))),
% 26.36/16.67 inference(monotonicity,[status(thm)],[11])).
% 26.36/16.67 tff(13,plain,
% 26.36/16.67 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg))),
% 26.36/16.67 inference(transitivity,[status(thm)],[12, 10])).
% 26.36/16.67 tff(14,plain,
% 26.36/16.67 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 26.36/16.67 inference(quant_inst,[status(thm)],[])).
% 26.36/16.67 tff(15,plain,
% 26.36/16.67 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)),
% 26.36/16.67 inference(modus_ponens,[status(thm)],[14, 13])).
% 26.36/16.67 tff(16,plain,
% 26.36/16.67 (c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)),
% 26.36/16.67 inference(unit_resolution,[status(thm)],[15, 9, 2])).
% 26.36/16.67 tff(17,plain,
% 26.36/16.67 (^[T_a: $i, V_B: $i, V_A: $i] : refl(((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))))),
% 26.36/16.67 inference(bind,[status(th)],[])).
% 26.36/16.67 tff(18,plain,
% 26.36/16.67 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.67 inference(quant_intro,[status(thm)],[17])).
% 26.36/16.67 tff(19,plain,
% 26.36/16.67 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a))) <=> ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.67 inference(rewrite,[status(thm)],[])).
% 26.36/16.67 tff(20,axiom,(![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))), file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax','cls_Set_OsubsetI_1')).
% 26.36/16.67 tff(21,plain,
% 26.36/16.67 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.67 inference(modus_ponens,[status(thm)],[20, 19])).
% 26.36/16.67 tff(22,plain,(
% 26.36/16.67 ![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.67 inference(skolemize,[status(sab)],[21])).
% 26.36/16.67 tff(23,plain,
% 26.36/16.67 (![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))),
% 26.36/16.67 inference(modus_ponens,[status(thm)],[22, 18])).
% 26.36/16.67 tff(24,plain,
% 26.36/16.67 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 26.36/16.67 inference(rewrite,[status(thm)],[])).
% 26.36/16.67 tff(25,plain,
% 26.36/16.67 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg)))),
% 26.36/16.67 inference(quant_inst,[status(thm)],[])).
% 26.36/16.67 tff(26,plain,
% 26.36/16.67 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))),
% 26.36/16.67 inference(modus_ponens,[status(thm)],[25, 24])).
% 26.36/16.67 tff(27,plain,
% 26.36/16.67 (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 26.36/16.67 inference(unit_resolution,[status(thm)],[26, 23, 2])).
% 26.36/16.67 tff(28,plain,
% 26.36/16.67 (^[V_b: $i, V_a: $i, T_a: $i, V_B: $i] : refl(((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)))),
% 26.36/16.67 inference(bind,[status(th)],[])).
% 26.36/16.67 tff(29,plain,
% 26.36/16.67 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 26.36/16.67 inference(quant_intro,[status(thm)],[28])).
% 26.36/16.67 tff(30,plain,
% 26.36/16.67 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 26.36/16.67 inference(rewrite,[status(thm)],[])).
% 26.36/16.67 tff(31,axiom,(![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))), file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax','cls_Set_OinsertCI_0')).
% 26.36/16.67 tff(32,plain,
% 26.36/16.67 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 26.36/16.67 inference(modus_ponens,[status(thm)],[31, 30])).
% 26.36/16.67 tff(33,plain,(
% 26.36/16.67 ![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 26.36/16.67 inference(skolemize,[status(sab)],[32])).
% 26.36/16.67 tff(34,plain,
% 26.36/16.67 (![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))),
% 26.36/16.67 inference(modus_ponens,[status(thm)],[33, 29])).
% 26.36/16.67 tff(35,plain,
% 26.36/16.67 (((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 26.36/16.67 inference(rewrite,[status(thm)],[])).
% 26.36/16.67 tff(36,plain,
% 26.36/16.67 ((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | ((~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg))),
% 26.48/16.67 inference(quant_inst,[status(thm)],[])).
% 26.48/16.67 tff(37,plain,
% 26.48/16.67 ((~![V_b: $i, V_a: $i, T_a: $i, V_B: $i] : ((~c_in(V_a, V_B, T_a)) | c_in(V_a, c_insert(V_b, V_B, T_a), T_a))) | (~c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), v_H, tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 26.48/16.67 inference(modus_ponens,[status(thm)],[36, 35])).
% 26.48/16.67 tff(38,plain,
% 26.48/16.67 ($false),
% 26.48/16.67 inference(unit_resolution,[status(thm)],[37, 34, 27, 16])).
% 26.48/16.67 tff(39,plain,(c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 26.48/16.67 tff(40,plain,
% 26.48/16.67 (^[V_H: $i, V_G: $i] : refl(((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))) <=> ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg))))),
% 26.48/16.67 inference(bind,[status(th)],[])).
% 26.48/16.67 tff(41,plain,
% 26.48/16.67 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), 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_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(quant_intro,[status(thm)],[40])).
% 26.48/16.67 tff(42,plain,
% 26.48/16.67 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), 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_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(rewrite,[status(thm)],[])).
% 26.48/16.67 tff(43,axiom,(![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Message_Osynth__mono_0')).
% 26.48/16.67 tff(44,plain,
% 26.48/16.67 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(modus_ponens,[status(thm)],[43, 42])).
% 26.48/16.67 tff(45,plain,(
% 26.48/16.67 ![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(skolemize,[status(sab)],[44])).
% 26.48/16.67 tff(46,plain,
% 26.48/16.67 (![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(modus_ponens,[status(thm)],[45, 41])).
% 26.48/16.67 tff(47,plain,
% 26.48/16.67 (((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), 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_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(rewrite,[status(thm)],[])).
% 26.48/16.67 tff(48,plain,
% 26.48/16.67 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))) | ((~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(quant_inst,[status(thm)],[])).
% 26.48/16.67 tff(49,plain,
% 26.48/16.67 ((~![V_H: $i, V_G: $i] : ((~c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(V_G), c_Message_Osynth(V_H), tc_set(tc_Message_Omsg)))) | (~c_lessequals(v_H, c_insert(v_X, v_H, tc_Message_Omsg), tc_set(tc_Message_Omsg))) | c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 26.48/16.67 inference(modus_ponens,[status(thm)],[48, 47])).
% 26.48/16.67 tff(50,plain,
% 26.48/16.67 ($false),
% 26.48/16.67 inference(unit_resolution,[status(thm)],[49, 46, 39, 1])).
% 26.48/16.67 tff(51,plain,(c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), inference(lemma,lemma(discharge,[]))).
% 26.48/16.67 tff(52,assumption,(c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)), introduced(assumption)).
% 26.48/16.67 tff(53,plain,
% 26.48/16.67 ((~c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (~c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(rewrite,[status(thm)],[])).
% 26.48/16.67 tff(54,axiom,(~c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 26.48/16.67 tff(55,plain,
% 26.48/16.67 (~c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 26.48/16.67 inference(modus_ponens,[status(thm)],[54, 53])).
% 26.48/16.67 tff(56,plain,
% 26.48/16.67 (((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(rewrite,[status(thm)],[])).
% 26.48/16.67 tff(57,plain,
% 26.48/16.67 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 26.48/16.67 inference(quant_inst,[status(thm)],[])).
% 26.48/16.67 tff(58,plain,
% 26.48/16.67 ((~![T_a: $i, V_B: $i, V_A: $i] : ((~c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_B, T_a)) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))),
% 26.48/16.67 inference(modus_ponens,[status(thm)],[57, 56])).
% 26.48/16.67 tff(59,plain,
% 26.48/16.68 (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 26.48/16.68 inference(unit_resolution,[status(thm)],[58, 23, 55])).
% 26.48/16.68 tff(60,plain,
% 26.48/16.68 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : refl(((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a))) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a))))),
% 26.48/16.68 inference(bind,[status(th)],[])).
% 26.48/16.68 tff(61,plain,
% 26.48/16.68 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(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_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 26.48/16.68 inference(quant_intro,[status(thm)],[60])).
% 26.48/16.68 tff(62,plain,
% 26.48/16.68 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(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_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 26.48/16.68 inference(rewrite,[status(thm)],[])).
% 26.48/16.68 tff(63,plain,
% 26.48/16.68 (^[V_c: $i, T_a: $i, V_B: $i, V_A: $i] : rewrite((((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a))))),
% 26.48/16.68 inference(bind,[status(th)],[])).
% 26.48/16.68 tff(64,plain,
% 26.48/16.68 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a)) <=> ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 26.48/16.68 inference(quant_intro,[status(thm)],[63])).
% 26.48/16.68 tff(65,axiom,(![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : (((~c_in(V_c, V_A, T_a)) | (~c_lessequals(V_A, V_B, tc_set(T_a)))) | c_in(V_c, V_B, T_a))), file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax','cls_Set_OsubsetD_0')).
% 26.48/16.68 tff(66,plain,
% 26.48/16.68 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 26.48/16.68 inference(modus_ponens,[status(thm)],[65, 64])).
% 26.48/16.68 tff(67,plain,
% 26.48/16.68 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 26.48/16.68 inference(modus_ponens,[status(thm)],[66, 62])).
% 26.48/16.68 tff(68,plain,(
% 26.48/16.68 ![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 26.48/16.68 inference(skolemize,[status(sab)],[67])).
% 26.48/16.68 tff(69,plain,
% 26.48/16.68 (![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))),
% 26.48/16.68 inference(modus_ponens,[status(thm)],[68, 61])).
% 26.48/16.68 tff(70,plain,
% 26.48/16.68 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))),
% 26.48/16.68 inference(rewrite,[status(thm)],[])).
% 26.48/16.68 tff(71,plain,
% 26.48/16.68 (((~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg))) <=> (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))),
% 26.48/16.68 inference(rewrite,[status(thm)],[])).
% 26.48/16.68 tff(72,plain,
% 26.48/16.68 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | ((~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg))))),
% 26.48/16.68 inference(monotonicity,[status(thm)],[71])).
% 26.48/16.68 tff(73,plain,
% 26.48/16.68 (((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | ((~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))) <=> ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))),
% 26.48/16.68 inference(transitivity,[status(thm)],[72, 70])).
% 26.48/16.68 tff(74,plain,
% 26.48/16.68 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | ((~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))),
% 26.48/16.68 inference(quant_inst,[status(thm)],[])).
% 26.48/16.68 tff(75,plain,
% 26.48/16.68 ((~![V_c: $i, T_a: $i, V_B: $i, V_A: $i] : ((~c_lessequals(V_A, V_B, tc_set(T_a))) | c_in(V_c, V_B, T_a) | (~c_in(V_c, V_A, T_a)))) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) | (~c_lessequals(c_Message_Osynth(v_H), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg))),
% 26.48/16.68 inference(modus_ponens,[status(thm)],[74, 73])).
% 26.48/16.68 tff(76,plain,
% 26.48/16.68 ($false),
% 26.48/16.68 inference(unit_resolution,[status(thm)],[75, 69, 59, 52, 51])).
% 26.48/16.68 tff(77,plain,(~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)), inference(lemma,lemma(discharge,[]))).
% 26.48/16.68 tff(78,plain,
% 26.48/16.68 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))),
% 26.48/16.68 inference(rewrite,[status(thm)],[])).
% 26.48/16.68 tff(79,plain,
% 26.48/16.68 ((c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg))) <=> (c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))),
% 26.48/16.68 inference(rewrite,[status(thm)],[])).
% 26.48/16.68 tff(80,plain,
% 26.48/16.68 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)))),
% 26.48/16.69 inference(monotonicity,[status(thm)],[79])).
% 26.48/16.69 tff(81,plain,
% 26.48/16.69 (((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))) <=> ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))),
% 26.48/16.69 inference(transitivity,[status(thm)],[80, 78])).
% 26.48/16.69 tff(82,plain,
% 26.48/16.69 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)))),
% 26.48/16.69 inference(quant_inst,[status(thm)],[])).
% 26.48/16.69 tff(83,plain,
% 26.48/16.69 ((~![T_a: $i, V_B: $i, V_A: $i] : (c_in(c_Main_OsubsetI__1(V_A, V_B, T_a), V_A, T_a) | c_lessequals(V_A, V_B, tc_set(T_a)))) | c_lessequals(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_set(tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)),
% 26.48/16.69 inference(modus_ponens,[status(thm)],[82, 81])).
% 26.48/16.69 tff(84,plain,
% 26.48/16.69 (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)),
% 26.48/16.69 inference(unit_resolution,[status(thm)],[83, 9, 55])).
% 26.48/16.69 tff(85,plain,
% 26.48/16.69 (^[V_b: $i, V_a: $i, T_a: $i, V_A: $i] : refl((c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))))),
% 26.48/16.69 inference(bind,[status(th)],[])).
% 26.48/16.69 tff(86,plain,
% 26.48/16.69 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 26.48/16.69 inference(quant_intro,[status(thm)],[85])).
% 26.48/16.69 tff(87,plain,
% 26.48/16.69 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 26.48/16.69 inference(rewrite,[status(thm)],[])).
% 26.48/16.69 tff(88,plain,
% 26.48/16.69 (^[V_b: $i, V_a: $i, T_a: $i, V_A: $i] : rewrite((((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b)) <=> (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a))))),
% 26.48/16.69 inference(bind,[status(th)],[])).
% 26.48/16.69 tff(89,plain,
% 26.48/16.69 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b)) <=> ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 26.48/16.69 inference(quant_intro,[status(thm)],[88])).
% 26.48/16.69 tff(90,axiom,(![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (((~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)) | c_in(V_a, V_A, T_a)) | (V_a = V_b))), file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax','cls_Set_OinsertE_0')).
% 26.48/16.69 tff(91,plain,
% 26.48/16.69 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 26.48/16.69 inference(modus_ponens,[status(thm)],[90, 89])).
% 26.48/16.69 tff(92,plain,
% 26.48/16.69 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 26.48/16.69 inference(modus_ponens,[status(thm)],[91, 87])).
% 26.48/16.69 tff(93,plain,(
% 26.48/16.69 ![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 26.48/16.69 inference(skolemize,[status(sab)],[92])).
% 26.48/16.69 tff(94,plain,
% 26.48/16.69 (![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))),
% 26.48/16.69 inference(modus_ponens,[status(thm)],[93, 86])).
% 26.48/16.69 tff(95,plain,
% 26.48/16.69 (((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg))) <=> ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg))),
% 26.48/16.69 inference(rewrite,[status(thm)],[])).
% 26.48/16.69 tff(96,plain,
% 26.48/16.69 ((c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg))) <=> ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg))),
% 26.48/16.69 inference(rewrite,[status(thm)],[])).
% 26.48/16.69 tff(97,plain,
% 26.48/16.69 (((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)))),
% 26.48/16.69 inference(monotonicity,[status(thm)],[96])).
% 26.48/16.69 tff(98,plain,
% 26.48/16.69 (((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)))) <=> ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg))),
% 26.48/16.69 inference(transitivity,[status(thm)],[97, 95])).
% 26.48/16.69 tff(99,plain,
% 26.48/16.69 ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)))),
% 26.48/16.69 inference(quant_inst,[status(thm)],[])).
% 26.48/16.69 tff(100,plain,
% 26.48/16.69 ((~![V_b: $i, V_a: $i, T_a: $i, V_A: $i] : (c_in(V_a, V_A, T_a) | (V_a = V_b) | (~c_in(V_a, c_insert(V_b, V_A, T_a), T_a)))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), tc_Message_Omsg)) | (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)),
% 26.48/16.69 inference(modus_ponens,[status(thm)],[99, 98])).
% 26.48/16.69 tff(101,plain,
% 26.48/16.69 ((c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(v_H), tc_Message_Omsg)),
% 26.48/16.69 inference(unit_resolution,[status(thm)],[100, 94, 84])).
% 26.48/16.69 tff(102,plain,
% 26.48/16.69 (c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg) = v_X),
% 26.48/16.69 inference(unit_resolution,[status(thm)],[101, 77])).
% 26.48/16.69 tff(103,plain,
% 26.48/16.69 (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg) <=> c_in(v_X, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 26.48/16.69 inference(monotonicity,[status(thm)],[102])).
% 26.48/16.69 tff(104,plain,
% 26.48/16.69 (c_in(v_X, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg) <=> c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 26.48/16.69 inference(symmetry,[status(thm)],[103])).
% 26.48/16.69 tff(105,plain,
% 26.48/16.69 (^[V_x: $i, T_a: $i, V_B: $i] : refl(c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> c_in(V_x, c_insert(V_x, V_B, T_a), T_a))),
% 26.48/16.69 inference(bind,[status(th)],[])).
% 26.48/16.69 tff(106,plain,
% 26.48/16.69 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 26.48/16.69 inference(quant_intro,[status(thm)],[105])).
% 26.48/16.69 tff(107,plain,
% 26.48/16.69 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a) <=> ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 26.48/16.69 inference(rewrite,[status(thm)],[])).
% 26.48/16.69 tff(108,axiom,(![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)), file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax','cls_Set_OinsertCI_1')).
% 26.48/16.69 tff(109,plain,
% 26.48/16.69 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 26.48/16.69 inference(modus_ponens,[status(thm)],[108, 107])).
% 26.48/16.69 tff(110,plain,(
% 26.48/16.69 ![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 26.48/16.69 inference(skolemize,[status(sab)],[109])).
% 26.48/16.69 tff(111,plain,
% 26.48/16.69 (![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)),
% 26.48/16.69 inference(modus_ponens,[status(thm)],[110, 106])).
% 26.48/16.69 tff(112,plain,
% 26.48/16.69 ((~![V_x: $i, T_a: $i, V_B: $i] : c_in(V_x, c_insert(V_x, V_B, T_a), T_a)) | c_in(v_X, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 26.48/16.69 inference(quant_inst,[status(thm)],[])).
% 26.48/16.69 tff(113,plain,
% 26.48/16.69 (c_in(v_X, c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 26.48/16.69 inference(unit_resolution,[status(thm)],[112, 111])).
% 26.48/16.69 tff(114,plain,
% 26.48/16.69 (c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 26.48/16.69 inference(modus_ponens,[status(thm)],[113, 104])).
% 26.48/16.69 tff(115,plain,
% 26.48/16.69 (^[V_H: $i, V_X: $i] : refl(((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)) <=> ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg)))),
% 26.48/16.70 inference(bind,[status(th)],[])).
% 26.48/16.70 tff(116,plain,
% 26.48/16.70 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(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_Osynth(V_H), tc_Message_Omsg))),
% 26.48/16.70 inference(quant_intro,[status(thm)],[115])).
% 26.48/16.70 tff(117,plain,
% 26.48/16.70 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(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_Osynth(V_H), tc_Message_Omsg))),
% 26.48/16.70 inference(rewrite,[status(thm)],[])).
% 26.48/16.70 tff(118,axiom,(![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))), file('/export/starexec/sandbox/benchmark/Axioms/SWV004-0.ax','cls_Message_Osynth_OInj_0')).
% 26.48/16.70 tff(119,plain,
% 26.48/16.70 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 26.48/16.70 inference(modus_ponens,[status(thm)],[118, 117])).
% 26.48/16.70 tff(120,plain,(
% 26.48/16.70 ![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 26.48/16.70 inference(skolemize,[status(sab)],[119])).
% 26.48/16.70 tff(121,plain,
% 26.48/16.70 (![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))),
% 26.48/16.70 inference(modus_ponens,[status(thm)],[120, 116])).
% 26.48/16.70 tff(122,plain,
% 26.48/16.70 (((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, 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_Osynth(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 26.48/16.70 inference(rewrite,[status(thm)],[])).
% 26.48/16.70 tff(123,plain,
% 26.48/16.70 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | ((~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg))),
% 26.48/16.70 inference(quant_inst,[status(thm)],[])).
% 26.48/16.70 tff(124,plain,
% 26.48/16.70 ((~![V_H: $i, V_X: $i] : ((~c_in(V_X, V_H, tc_Message_Omsg)) | c_in(V_X, c_Message_Osynth(V_H), tc_Message_Omsg))) | (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)) | c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg)),
% 26.48/16.70 inference(modus_ponens,[status(thm)],[123, 122])).
% 26.48/16.70 tff(125,plain,
% 26.48/16.70 (~c_in(c_Main_OsubsetI__1(c_insert(v_X, c_Message_Osynth(v_H), tc_Message_Omsg), c_Message_Osynth(c_insert(v_X, v_H, tc_Message_Omsg)), tc_Message_Omsg), c_insert(v_X, v_H, tc_Message_Omsg), tc_Message_Omsg)),
% 26.53/16.74 inference(unit_resolution,[status(thm)],[124, 121, 59])).
% 26.53/16.74 tff(126,plain,
% 26.53/16.74 ($false),
% 26.53/16.74 inference(unit_resolution,[status(thm)],[125, 114])).
% 26.53/16.74 % SZS output end Proof
%------------------------------------------------------------------------------