TSTP Solution File: SWW955+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW955+1 : TPTP v8.1.0. Released v7.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 21:00:22 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW955+1 : TPTP v8.1.0. Released v7.4.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.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 : Mon Sep 5 00:15:23 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(pred_attacker_type, type, (
% 0.20/0.40 pred_attacker: $i > $o)).
% 0.20/0.40 tff(constr_dec_type, type, (
% 0.20/0.40 constr_dec: ( $i * $i ) > $i)).
% 0.20/0.40 tff(name_m_9_type, type, (
% 0.20/0.40 name_m_9: $i)).
% 0.20/0.40 tff(constr_enc_type, type, (
% 0.20/0.40 constr_enc: ( $i * $i ) > $i)).
% 0.20/0.40 tff(name_objective_type, type, (
% 0.20/0.40 name_objective: $i)).
% 0.20/0.40 tff(tuple_A_out_4_type, type, (
% 0.20/0.40 tuple_A_out_4: $i > $i)).
% 0.20/0.40 tff(tuple_A_in_2_type, type, (
% 0.20/0.40 tuple_A_in_2: $i > $i)).
% 0.20/0.40 tff(constr_comm_enc_type, type, (
% 0.20/0.40 constr_comm_enc: ( $i * $i ) > $i)).
% 0.20/0.40 tff(name_Ka_type, type, (
% 0.20/0.40 name_Ka: $i)).
% 0.20/0.40 tff(tuple_A_out_1_type, type, (
% 0.20/0.40 tuple_A_out_1: $i > $i)).
% 0.20/0.40 tff(tuple_A_out_3_type, type, (
% 0.20/0.40 tuple_A_out_3: $i > $i)).
% 0.20/0.40 tff(constr_comm_dec_type, type, (
% 0.20/0.40 constr_comm_dec: ( $i * $i ) > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[VAR_K_8: $i, VAR_M_7: $i] : refl((constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7) <=> (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7) <=> ![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7)),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7) <=> ![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax45')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,(
% 0.20/0.40 ![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7)),
% 0.20/0.40 inference(skolemize,[status(sab)],[5])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 ((~![VAR_K_8: $i, VAR_M_7: $i] : (constr_dec(constr_enc(VAR_M_7, VAR_K_8), VAR_K_8) = VAR_M_7)) | (constr_dec(constr_enc(name_objective, name_m_9), name_m_9) = name_objective)),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (constr_dec(constr_enc(name_objective, name_m_9), name_m_9) = name_objective),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) <=> pred_attacker(name_objective)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[9])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (pred_attacker(name_objective) <=> pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9))),
% 0.20/0.40 inference(symmetry,[status(thm)],[10])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((~pred_attacker(name_objective)) <=> (~pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[11])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 ((~pred_attacker(name_objective)) <=> (~pred_attacker(name_objective))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(14,axiom,(~pred_attacker(name_objective)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co0')).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (~pred_attacker(name_objective)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (~pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.20/0.40 tff(17,assumption,(~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))), introduced(assumption)).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (pred_attacker(tuple_A_out_1(constr_comm_enc(name_m_9, name_Ka))) <=> pred_attacker(tuple_A_out_1(constr_comm_enc(name_m_9, name_Ka)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(19,axiom,(pred_attacker(tuple_A_out_1(constr_comm_enc(name_m_9, name_Ka)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax77')).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (pred_attacker(tuple_A_out_1(constr_comm_enc(name_m_9, name_Ka)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (^[VAR_V_77: $i] : refl((pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77)))) <=> (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77)))) <=> ![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77)))) <=> ![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (^[VAR_V_77: $i] : rewrite((pred_attacker(tuple_A_out_1(VAR_V_77)) => pred_attacker(VAR_V_77)) <=> (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![VAR_V_77: $i] : (pred_attacker(tuple_A_out_1(VAR_V_77)) => pred_attacker(VAR_V_77)) <=> ![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.40 tff(26,axiom,(![VAR_V_77: $i] : (pred_attacker(tuple_A_out_1(VAR_V_77)) => pred_attacker(VAR_V_77))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax69')).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.40 tff(29,plain,(
% 0.20/0.40 ![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[28])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (((~![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))) | (pred_attacker(constr_comm_enc(name_m_9, name_Ka)) | (~pred_attacker(tuple_A_out_1(constr_comm_enc(name_m_9, name_Ka)))))) <=> ((~![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))) | pred_attacker(constr_comm_enc(name_m_9, name_Ka)) | (~pred_attacker(tuple_A_out_1(constr_comm_enc(name_m_9, name_Ka)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))) | (pred_attacker(constr_comm_enc(name_m_9, name_Ka)) | (~pred_attacker(tuple_A_out_1(constr_comm_enc(name_m_9, name_Ka)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ((~![VAR_V_77: $i] : (pred_attacker(VAR_V_77) | (~pred_attacker(tuple_A_out_1(VAR_V_77))))) | pred_attacker(constr_comm_enc(name_m_9, name_Ka)) | (~pred_attacker(tuple_A_out_1(constr_comm_enc(name_m_9, name_Ka))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (pred_attacker(constr_comm_enc(name_m_9, name_Ka))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (^[VAR_V_80X30: $i] : refl(((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30))) <=> ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30))) <=> ![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30))) <=> ![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (^[VAR_V_80X30: $i] : rewrite((pred_attacker(VAR_V_80X30) => pred_attacker(tuple_A_in_2(VAR_V_80X30))) <=> ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![VAR_V_80X30: $i] : (pred_attacker(VAR_V_80X30) => pred_attacker(tuple_A_in_2(VAR_V_80X30))) <=> ![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.40 tff(40,axiom,(![VAR_V_80X30: $i] : (pred_attacker(VAR_V_80X30) => pred_attacker(tuple_A_in_2(VAR_V_80X30)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax70')).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.40 tff(43,plain,(
% 0.20/0.40 ![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[42])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (((~![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))) | ((~pred_attacker(constr_comm_enc(name_m_9, name_Ka))) | pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka))))) <=> ((~![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))) | (~pred_attacker(constr_comm_enc(name_m_9, name_Ka))) | pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((~![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))) | ((~pred_attacker(constr_comm_enc(name_m_9, name_Ka))) | pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~![VAR_V_80X30: $i] : ((~pred_attacker(VAR_V_80X30)) | pred_attacker(tuple_A_in_2(VAR_V_80X30)))) | (~pred_attacker(constr_comm_enc(name_m_9, name_Ka))) | pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[47, 44, 34, 17])).
% 0.20/0.40 tff(49,plain,(pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (^[VAR_MSG1_142: $i] : refl(((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))) <=> ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))) <=> ![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))) <=> ![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (^[VAR_MSG1_142: $i] : rewrite((pred_attacker(tuple_A_in_2(VAR_MSG1_142)) => pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))) <=> ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![VAR_MSG1_142: $i] : (pred_attacker(tuple_A_in_2(VAR_MSG1_142)) => pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))) <=> ![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.40 tff(55,axiom,(![VAR_MSG1_142: $i] : (pred_attacker(tuple_A_in_2(VAR_MSG1_142)) => pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax79')).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.40 tff(58,plain,(
% 0.20/0.40 ![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[57])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (((~![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) | (pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))) | (~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))))) <=> ((~![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))) | (~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (((~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))) <=> (pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))) | (~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (((~![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) | ((~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) <=> ((~![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) | (pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))) | (~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (((~![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) | ((~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) <=> ((~![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))) | (~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ((~![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) | ((~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 ((~![VAR_MSG1_142: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_142))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))) | pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))) | (~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[65, 59, 49])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (^[VAR_V_65: $i] : refl((pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65)))) <=> (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65)))) <=> ![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65)))) <=> ![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (^[VAR_V_65: $i] : rewrite((pred_attacker(tuple_A_out_4(VAR_V_65)) => pred_attacker(VAR_V_65)) <=> (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (![VAR_V_65: $i] : (pred_attacker(tuple_A_out_4(VAR_V_65)) => pred_attacker(VAR_V_65)) <=> ![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.41 tff(72,axiom,(![VAR_V_65: $i] : (pred_attacker(tuple_A_out_4(VAR_V_65)) => pred_attacker(VAR_V_65))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax65')).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.41 tff(75,plain,(
% 0.20/0.41 ![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[74])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (((~![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))) | (pred_attacker(constr_enc(name_objective, name_m_9)) | (~pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))))) <=> ((~![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))) | pred_attacker(constr_enc(name_objective, name_m_9)) | (~pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 ((~![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))) | (pred_attacker(constr_enc(name_objective, name_m_9)) | (~pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~![VAR_V_65: $i] : (pred_attacker(VAR_V_65) | (~pred_attacker(tuple_A_out_4(VAR_V_65))))) | pred_attacker(constr_enc(name_objective, name_m_9)) | (~pred_attacker(tuple_A_out_4(constr_enc(name_objective, name_m_9))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (pred_attacker(constr_enc(name_objective, name_m_9))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[79, 76, 66])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (^[VAR_K_0X30: $i, VAR_M_0X30: $i] : refl((constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30) <=> (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30) <=> ![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30) <=> ![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(84,axiom,(![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax46')).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.41 tff(86,plain,(
% 0.20/0.41 ![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30)),
% 0.20/0.41 inference(skolemize,[status(sab)],[85])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 ((~![VAR_K_0X30: $i, VAR_M_0X30: $i] : (constr_comm_dec(constr_comm_enc(VAR_M_0X30, VAR_K_0X30), VAR_K_0X30) = VAR_M_0X30)) | (constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka) = name_m_9)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka) = name_m_9),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (name_m_9 = constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka)),
% 0.20/0.41 inference(symmetry,[status(thm)],[89])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (tuple_A_out_3(name_m_9) = tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[90])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (pred_attacker(tuple_A_out_3(name_m_9)) <=> pred_attacker(tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (pred_attacker(tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka))) <=> pred_attacker(tuple_A_out_3(name_m_9))),
% 0.20/0.41 inference(symmetry,[status(thm)],[92])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (^[VAR_MSG1_128: $i] : refl(((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka)))) <=> ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka)))) <=> ![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka)))) <=> ![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (^[VAR_MSG1_128: $i] : rewrite((pred_attacker(tuple_A_in_2(VAR_MSG1_128)) => pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka)))) <=> ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (![VAR_MSG1_128: $i] : (pred_attacker(tuple_A_in_2(VAR_MSG1_128)) => pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka)))) <=> ![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.41 tff(99,axiom,(![VAR_MSG1_128: $i] : (pred_attacker(tuple_A_in_2(VAR_MSG1_128)) => pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax78')).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.41 tff(102,plain,(
% 0.20/0.41 ![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[101])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (((~![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))) | ((~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka))))) <=> ((~![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))) | (~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 ((~![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))) | ((~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 ((~![VAR_MSG1_128: $i] : ((~pred_attacker(tuple_A_in_2(VAR_MSG1_128))) | pred_attacker(tuple_A_out_3(constr_comm_dec(VAR_MSG1_128, name_Ka))))) | (~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 ((~pred_attacker(tuple_A_in_2(constr_comm_enc(name_m_9, name_Ka)))) | pred_attacker(tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (pred_attacker(tuple_A_out_3(constr_comm_dec(constr_comm_enc(name_m_9, name_Ka), name_Ka)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[107, 49])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (pred_attacker(tuple_A_out_3(name_m_9))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[108, 93])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (^[VAR_V_71: $i] : refl((pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71)))) <=> (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71)))) <=> ![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71)))) <=> ![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (^[VAR_V_71: $i] : rewrite((pred_attacker(tuple_A_out_3(VAR_V_71)) => pred_attacker(VAR_V_71)) <=> (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (![VAR_V_71: $i] : (pred_attacker(tuple_A_out_3(VAR_V_71)) => pred_attacker(VAR_V_71)) <=> ![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.41 tff(115,axiom,(![VAR_V_71: $i] : (pred_attacker(tuple_A_out_3(VAR_V_71)) => pred_attacker(VAR_V_71))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax67')).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.41 tff(118,plain,(
% 0.20/0.41 ![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[117])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (((~![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))) | (pred_attacker(name_m_9) | (~pred_attacker(tuple_A_out_3(name_m_9))))) <=> ((~![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))) | pred_attacker(name_m_9) | (~pred_attacker(tuple_A_out_3(name_m_9))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 ((~![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))) | (pred_attacker(name_m_9) | (~pred_attacker(tuple_A_out_3(name_m_9))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(122,plain,
% 0.20/0.41 ((~![VAR_V_71: $i] : (pred_attacker(VAR_V_71) | (~pred_attacker(tuple_A_out_3(VAR_V_71))))) | pred_attacker(name_m_9) | (~pred_attacker(tuple_A_out_3(name_m_9)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (pred_attacker(name_m_9) | (~pred_attacker(tuple_A_out_3(name_m_9)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (pred_attacker(name_m_9)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[123, 109])).
% 0.20/0.41 tff(125,plain,
% 0.20/0.41 (^[VAR_V_33: $i, VAR_V_34: $i] : refl((pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33))) <=> (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33))) <=> ![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (^[VAR_V_33: $i, VAR_V_34: $i] : trans(monotonicity(trans(monotonicity(rewrite((pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)) <=> (~((~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33))))), ((~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34))) <=> (~(~((~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33))))))), rewrite((~(~((~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33))))) <=> ((~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))), ((~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34))) <=> ((~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33))))), ((pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)))) <=> (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | ((~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))))), rewrite((pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | ((~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) <=> (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))), ((pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)))) <=> (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)))) <=> ![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 (![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)))) <=> ![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (^[VAR_V_33: $i, VAR_V_34: $i] : rewrite(((pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)) => pred_attacker(constr_dec(VAR_V_33, VAR_V_34))) <=> (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 (![VAR_V_33: $i, VAR_V_34: $i] : ((pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)) => pred_attacker(constr_dec(VAR_V_33, VAR_V_34))) <=> ![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.41 tff(132,axiom,(![VAR_V_33: $i, VAR_V_34: $i] : ((pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34)) => pred_attacker(constr_dec(VAR_V_33, VAR_V_34)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ax50')).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 (![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 (![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.20/0.41 tff(135,plain,(
% 0.20/0.41 ![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~(pred_attacker(VAR_V_33) & pred_attacker(VAR_V_34))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[134])).
% 0.20/0.41 tff(136,plain,
% 0.20/0.41 (![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 (![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[136, 126])).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 (((~![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) | ((~pred_attacker(name_m_9)) | pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9))))) <=> ((~![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) | (~pred_attacker(name_m_9)) | pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 ((pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9)))) <=> ((~pred_attacker(name_m_9)) | pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 (((~![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) | (pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9))))) <=> ((~![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) | ((~pred_attacker(name_m_9)) | pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[139])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 (((~![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) | (pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9))))) <=> ((~![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) | (~pred_attacker(name_m_9)) | pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[140, 138])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 ((~![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) | (pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 ((~![VAR_V_33: $i, VAR_V_34: $i] : (pred_attacker(constr_dec(VAR_V_33, VAR_V_34)) | (~pred_attacker(VAR_V_34)) | (~pred_attacker(VAR_V_33)))) | (~pred_attacker(name_m_9)) | pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9)) | (~pred_attacker(constr_enc(name_objective, name_m_9)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (pred_attacker(constr_dec(constr_enc(name_objective, name_m_9), name_m_9))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[143, 137, 124, 80])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[144, 16])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------