TSTP Solution File: SYN982-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN982-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Fri Sep 30 00:01:29 EDT 2022
% Result : Unsatisfiable 9.05s 6.08s
% Output : Proof 9.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN982-1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 09:58:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 9.05/6.08 % SZS status Unsatisfiable
% 9.05/6.08 % SZS output start Proof
% 9.05/6.08 tff(ssIm_type, type, (
% 9.05/6.08 ssIm: $i > $o)).
% 9.05/6.08 tff(pair_type, type, (
% 9.05/6.08 pair: ( $i * $i ) > $i)).
% 9.05/6.08 tff(encr_type, type, (
% 9.05/6.08 encr: ( $i * $i ) > $i)).
% 9.05/6.08 tff(na_type, type, (
% 9.05/6.08 na: $i)).
% 9.05/6.08 tff(nb_type, type, (
% 9.05/6.08 nb: $i > $i)).
% 9.05/6.08 tff(bt_type, type, (
% 9.05/6.08 bt: $i)).
% 9.05/6.08 tff(triple_type, type, (
% 9.05/6.08 triple: ( $i * $i * $i ) > $i)).
% 9.05/6.08 tff(tb_type, type, (
% 9.05/6.08 tb: $i > $i)).
% 9.05/6.08 tff(a_type, type, (
% 9.05/6.08 a: $i)).
% 9.05/6.08 tff(ssIk_type, type, (
% 9.05/6.08 ssIk: $i > $o)).
% 9.05/6.08 tff(key_type, type, (
% 9.05/6.08 key: ( $i * $i ) > $i)).
% 9.05/6.08 tff(ssM_type, type, (
% 9.05/6.08 ssM: $i > $o)).
% 9.05/6.08 tff(sent_type, type, (
% 9.05/6.08 sent: ( $i * $i * $i ) > $i)).
% 9.05/6.08 tff(b_type, type, (
% 9.05/6.08 b: $i)).
% 9.05/6.08 tff(ssP_type, type, (
% 9.05/6.08 ssP: $i > $o)).
% 9.05/6.08 tff(t_type, type, (
% 9.05/6.08 t: $i)).
% 9.05/6.08 tff(ssBf_type, type, (
% 9.05/6.08 ssBf: $i > $o)).
% 9.05/6.08 tff(ssBk_type, type, (
% 9.05/6.08 ssBk: $i > $o)).
% 9.05/6.08 tff(ssSb_type, type, (
% 9.05/6.08 ssSb: $i > $o)).
% 9.05/6.08 tff(1,assumption,(~ssIk(key(na, a))), introduced(assumption)).
% 9.05/6.08 tff(2,plain,
% 9.05/6.08 (^[W: $i, V: $i, U: $i] : refl((ssIm(W) | (~ssM(sent(U, V, W)))) <=> (ssIm(W) | (~ssM(sent(U, V, W)))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(3,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W)))) <=> ![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[2])).
% 9.05/6.08 tff(4,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W)))) <=> ![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(5,plain,
% 9.05/6.08 (^[W: $i, V: $i, U: $i] : rewrite(((~ssM(sent(U, V, W))) | ssIm(W)) <=> (ssIm(W) | (~ssM(sent(U, V, W)))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(6,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : ((~ssM(sent(U, V, W))) | ssIm(W)) <=> ![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[5])).
% 9.05/6.08 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((~ssM(sent(U, V, W))) | ssIm(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause20')).
% 9.05/6.08 tff(8,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[7, 6])).
% 9.05/6.08 tff(9,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[8, 4])).
% 9.05/6.08 tff(10,plain,(
% 9.05/6.08 ![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))),
% 9.05/6.08 inference(skolemize,[status(sab)],[9])).
% 9.05/6.08 tff(11,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[10, 3])).
% 9.05/6.08 tff(12,plain,
% 9.05/6.08 (ssM(sent(a, b, pair(a, na))) <=> ssM(sent(a, b, pair(a, na)))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(13,axiom,(ssM(sent(a, b, pair(a, na)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause16')).
% 9.05/6.08 tff(14,plain,
% 9.05/6.08 (ssM(sent(a, b, pair(a, na)))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[13, 12])).
% 9.05/6.08 tff(15,plain,
% 9.05/6.08 (((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))) | (ssIm(pair(a, na)) | (~ssM(sent(a, b, pair(a, na)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))) | ssIm(pair(a, na)) | (~ssM(sent(a, b, pair(a, na)))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(16,plain,
% 9.05/6.08 ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))) | (ssIm(pair(a, na)) | (~ssM(sent(a, b, pair(a, na)))))),
% 9.05/6.08 inference(quant_inst,[status(thm)],[])).
% 9.05/6.08 tff(17,plain,
% 9.05/6.08 ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))) | ssIm(pair(a, na)) | (~ssM(sent(a, b, pair(a, na))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[16, 15])).
% 9.05/6.08 tff(18,plain,
% 9.05/6.08 (ssIm(pair(a, na))),
% 9.05/6.08 inference(unit_resolution,[status(thm)],[17, 14, 11])).
% 9.05/6.08 tff(19,plain,
% 9.05/6.08 (^[V: $i, U: $i] : refl((ssIm(V) | (~ssIm(pair(U, V)))) <=> (ssIm(V) | (~ssIm(pair(U, V)))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(20,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V)))) <=> ![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[19])).
% 9.05/6.08 tff(21,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V)))) <=> ![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(22,plain,
% 9.05/6.08 (^[V: $i, U: $i] : rewrite(((~ssIm(pair(U, V))) | ssIm(V)) <=> (ssIm(V) | (~ssIm(pair(U, V)))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(23,plain,
% 9.05/6.08 (![V: $i, U: $i] : ((~ssIm(pair(U, V))) | ssIm(V)) <=> ![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[22])).
% 9.05/6.08 tff(24,axiom,(![V: $i, U: $i] : ((~ssIm(pair(U, V))) | ssIm(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause14')).
% 9.05/6.08 tff(25,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[24, 23])).
% 9.05/6.08 tff(26,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[25, 21])).
% 9.05/6.08 tff(27,plain,(
% 9.05/6.08 ![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))),
% 9.05/6.08 inference(skolemize,[status(sab)],[26])).
% 9.05/6.08 tff(28,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[27, 20])).
% 9.05/6.08 tff(29,plain,
% 9.05/6.08 (((~![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))) | (ssIm(na) | (~ssIm(pair(a, na))))) <=> ((~![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))) | ssIm(na) | (~ssIm(pair(a, na))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(30,plain,
% 9.05/6.08 ((~![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))) | (ssIm(na) | (~ssIm(pair(a, na))))),
% 9.05/6.08 inference(quant_inst,[status(thm)],[])).
% 9.05/6.08 tff(31,plain,
% 9.05/6.08 ((~![V: $i, U: $i] : (ssIm(V) | (~ssIm(pair(U, V))))) | ssIm(na) | (~ssIm(pair(a, na)))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[30, 29])).
% 9.05/6.08 tff(32,plain,
% 9.05/6.08 (ssIm(na) | (~ssIm(pair(a, na)))),
% 9.05/6.08 inference(unit_resolution,[status(thm)],[31, 28])).
% 9.05/6.08 tff(33,plain,
% 9.05/6.08 (ssIm(na)),
% 9.05/6.08 inference(unit_resolution,[status(thm)],[32, 18])).
% 9.05/6.08 tff(34,plain,
% 9.05/6.08 (^[V: $i, U: $i] : refl((ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U))) <=> (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(35,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U))) <=> ![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[34])).
% 9.05/6.08 tff(36,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U))) <=> ![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(37,plain,
% 9.05/6.08 (^[V: $i, U: $i] : rewrite((((~ssIm(U)) | (~ssP(V))) | ssIk(key(U, V))) <=> (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(38,plain,
% 9.05/6.08 (![V: $i, U: $i] : (((~ssIm(U)) | (~ssP(V))) | ssIk(key(U, V))) <=> ![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[37])).
% 9.05/6.08 tff(39,axiom,(![V: $i, U: $i] : (((~ssIm(U)) | (~ssP(V))) | ssIk(key(U, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause25')).
% 9.05/6.08 tff(40,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[39, 38])).
% 9.05/6.08 tff(41,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[40, 36])).
% 9.05/6.08 tff(42,plain,(
% 9.05/6.08 ![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))),
% 9.05/6.08 inference(skolemize,[status(sab)],[41])).
% 9.05/6.08 tff(43,plain,
% 9.05/6.08 (![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[42, 35])).
% 9.05/6.08 tff(44,plain,
% 9.05/6.08 (ssP(a) <=> ssP(a)),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(45,axiom,(ssP(a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 9.05/6.08 tff(46,plain,
% 9.05/6.08 (ssP(a)),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[45, 44])).
% 9.05/6.08 tff(47,plain,
% 9.05/6.08 (((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | ((~ssIm(na)) | (~ssP(a)) | ssIk(key(na, a)))) <=> ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (~ssIm(na)) | (~ssP(a)) | ssIk(key(na, a)))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(48,plain,
% 9.05/6.08 ((ssIk(key(na, a)) | (~ssP(a)) | (~ssIm(na))) <=> ((~ssIm(na)) | (~ssP(a)) | ssIk(key(na, a)))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(49,plain,
% 9.05/6.08 (((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (ssIk(key(na, a)) | (~ssP(a)) | (~ssIm(na)))) <=> ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | ((~ssIm(na)) | (~ssP(a)) | ssIk(key(na, a))))),
% 9.05/6.08 inference(monotonicity,[status(thm)],[48])).
% 9.05/6.08 tff(50,plain,
% 9.05/6.08 (((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (ssIk(key(na, a)) | (~ssP(a)) | (~ssIm(na)))) <=> ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (~ssIm(na)) | (~ssP(a)) | ssIk(key(na, a)))),
% 9.05/6.08 inference(transitivity,[status(thm)],[49, 47])).
% 9.05/6.08 tff(51,plain,
% 9.05/6.08 ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (ssIk(key(na, a)) | (~ssP(a)) | (~ssIm(na)))),
% 9.05/6.08 inference(quant_inst,[status(thm)],[])).
% 9.05/6.08 tff(52,plain,
% 9.05/6.08 ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (~ssIm(na)) | (~ssP(a)) | ssIk(key(na, a))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[51, 50])).
% 9.05/6.08 tff(53,plain,
% 9.05/6.08 ($false),
% 9.05/6.08 inference(unit_resolution,[status(thm)],[52, 46, 43, 33, 1])).
% 9.05/6.08 tff(54,plain,(ssIk(key(na, a))), inference(lemma,lemma(discharge,[]))).
% 9.05/6.08 tff(55,plain,
% 9.05/6.08 (^[V: $i, U: $i] : refl(((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))) <=> ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(56,plain,
% 9.05/6.08 (![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))) <=> ![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[55])).
% 9.05/6.08 tff(57,plain,
% 9.05/6.08 (![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))) <=> ![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(58,plain,
% 9.05/6.08 (^[V: $i, U: $i] : trans(monotonicity(rewrite(((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) <=> ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))))), ((((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))) <=> (((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V))))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))))), rewrite((((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V))))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))) <=> ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))), ((((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))) <=> ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(59,plain,
% 9.05/6.08 (![V: $i, U: $i] : (((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt))))) <=> ![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[58])).
% 9.05/6.08 tff(60,axiom,(![V: $i, U: $i] : (((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 9.05/6.08 tff(61,plain,
% 9.05/6.08 (![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[60, 59])).
% 9.05/6.08 tff(62,plain,
% 9.05/6.08 (![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[61, 57])).
% 9.05/6.08 tff(63,plain,(
% 9.05/6.08 ![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))),
% 9.05/6.08 inference(skolemize,[status(sab)],[62])).
% 9.05/6.08 tff(64,plain,
% 9.05/6.08 (![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[63, 56])).
% 9.05/6.08 tff(65,plain,
% 9.05/6.08 (ssBf(na) <=> ssBf(na)),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(66,axiom,(ssBf(na)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 9.05/6.08 tff(67,plain,
% 9.05/6.08 (ssBf(na)),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[66, 65])).
% 9.05/6.08 tff(68,plain,
% 9.05/6.08 (((~![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))) | ((~ssBf(na)) | (~ssM(sent(a, b, pair(a, na)))) | ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))) <=> ((~![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))) | (~ssBf(na)) | (~ssM(sent(a, b, pair(a, na)))) | ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(69,plain,
% 9.05/6.08 ((~![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))) | ((~ssBf(na)) | (~ssM(sent(a, b, pair(a, na)))) | ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))),
% 9.05/6.08 inference(quant_inst,[status(thm)],[])).
% 9.05/6.08 tff(70,plain,
% 9.05/6.08 ((~![V: $i, U: $i] : ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))) | ssM(sent(b, t, triple(b, nb(V), encr(triple(U, V, tb(V)), bt)))))) | (~ssBf(na)) | (~ssM(sent(a, b, pair(a, na)))) | ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[69, 68])).
% 9.05/6.08 tff(71,plain,
% 9.05/6.08 (ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt))))),
% 9.05/6.08 inference(unit_resolution,[status(thm)],[70, 67, 14, 64])).
% 9.05/6.08 tff(72,plain,
% 9.05/6.08 (((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))) | (ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt))) | (~ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))) | ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt))) | (~ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt))))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(73,plain,
% 9.05/6.08 ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))) | (ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt))) | (~ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt))))))),
% 9.05/6.08 inference(quant_inst,[status(thm)],[])).
% 9.05/6.08 tff(74,plain,
% 9.05/6.08 ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssM(sent(U, V, W))))) | ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt))) | (~ssM(sent(b, t, triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[73, 72])).
% 9.05/6.08 tff(75,plain,
% 9.05/6.08 (ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))),
% 9.05/6.08 inference(unit_resolution,[status(thm)],[74, 11, 71])).
% 9.05/6.08 tff(76,plain,
% 9.05/6.08 (^[W: $i, V: $i, U: $i] : refl((ssIm(V) | (~ssIm(triple(U, V, W)))) <=> (ssIm(V) | (~ssIm(triple(U, V, W)))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(77,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W)))) <=> ![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[76])).
% 9.05/6.08 tff(78,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W)))) <=> ![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(79,plain,
% 9.05/6.08 (^[W: $i, V: $i, U: $i] : rewrite(((~ssIm(triple(U, V, W))) | ssIm(V)) <=> (ssIm(V) | (~ssIm(triple(U, V, W)))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(80,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : ((~ssIm(triple(U, V, W))) | ssIm(V)) <=> ![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[79])).
% 9.05/6.08 tff(81,axiom,(![W: $i, V: $i, U: $i] : ((~ssIm(triple(U, V, W))) | ssIm(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause18')).
% 9.05/6.08 tff(82,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[81, 80])).
% 9.05/6.08 tff(83,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[82, 78])).
% 9.05/6.08 tff(84,plain,(
% 9.05/6.08 ![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))),
% 9.05/6.08 inference(skolemize,[status(sab)],[83])).
% 9.05/6.08 tff(85,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[84, 77])).
% 9.05/6.08 tff(86,plain,
% 9.05/6.08 (((~![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))) | (ssIm(nb(na)) | (~ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))) | ssIm(nb(na)) | (~ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(87,plain,
% 9.05/6.08 ((~![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))) | (ssIm(nb(na)) | (~ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))),
% 9.05/6.08 inference(quant_inst,[status(thm)],[])).
% 9.05/6.08 tff(88,plain,
% 9.05/6.08 ((~![W: $i, V: $i, U: $i] : (ssIm(V) | (~ssIm(triple(U, V, W))))) | ssIm(nb(na)) | (~ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[87, 86])).
% 9.05/6.08 tff(89,plain,
% 9.05/6.08 (ssIm(nb(na))),
% 9.05/6.08 inference(unit_resolution,[status(thm)],[88, 85, 75])).
% 9.05/6.08 tff(90,plain,
% 9.05/6.08 (^[W: $i, V: $i, U: $i] : refl(((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W)))) <=> ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W)))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(91,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W)))) <=> ![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[90])).
% 9.05/6.08 tff(92,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W)))) <=> ![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))),
% 9.05/6.08 inference(rewrite,[status(thm)],[])).
% 9.05/6.08 tff(93,plain,
% 9.05/6.08 (^[W: $i, V: $i, U: $i] : trans(monotonicity(rewrite((((~ssIm(U)) | (~ssIk(key(V, W)))) | (~ssP(W))) <=> ((~ssIm(U)) | (~ssP(W)) | (~ssIk(key(V, W))))), (((((~ssIm(U)) | (~ssIk(key(V, W)))) | (~ssP(W))) | ssIm(encr(U, V))) <=> (((~ssIm(U)) | (~ssP(W)) | (~ssIk(key(V, W)))) | ssIm(encr(U, V))))), rewrite((((~ssIm(U)) | (~ssP(W)) | (~ssIk(key(V, W)))) | ssIm(encr(U, V))) <=> ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))), (((((~ssIm(U)) | (~ssIk(key(V, W)))) | (~ssP(W))) | ssIm(encr(U, V))) <=> ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))))),
% 9.05/6.08 inference(bind,[status(th)],[])).
% 9.05/6.08 tff(94,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : ((((~ssIm(U)) | (~ssIk(key(V, W)))) | (~ssP(W))) | ssIm(encr(U, V))) <=> ![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))),
% 9.05/6.08 inference(quant_intro,[status(thm)],[93])).
% 9.05/6.08 tff(95,axiom,(![W: $i, V: $i, U: $i] : ((((~ssIm(U)) | (~ssIk(key(V, W)))) | (~ssP(W))) | ssIm(encr(U, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause29')).
% 9.05/6.08 tff(96,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[95, 94])).
% 9.05/6.08 tff(97,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[96, 92])).
% 9.05/6.08 tff(98,plain,(
% 9.05/6.08 ![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))),
% 9.05/6.08 inference(skolemize,[status(sab)],[97])).
% 9.05/6.08 tff(99,plain,
% 9.05/6.08 (![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))),
% 9.05/6.08 inference(modus_ponens,[status(thm)],[98, 91])).
% 9.05/6.08 tff(100,plain,
% 9.05/6.08 (((~![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))) | ((~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIm(nb(na))) | (~ssIk(key(na, a))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))) | (~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIm(nb(na))) | (~ssIk(key(na, a))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(101,plain,
% 9.05/6.09 (((~ssIm(nb(na))) | (~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIk(key(na, a)))) <=> ((~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIm(nb(na))) | (~ssIk(key(na, a))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(102,plain,
% 9.05/6.09 (((~![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))) | ((~ssIm(nb(na))) | (~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIk(key(na, a))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))) | ((~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIm(nb(na))) | (~ssIk(key(na, a)))))),
% 9.05/6.09 inference(monotonicity,[status(thm)],[101])).
% 9.05/6.09 tff(103,plain,
% 9.05/6.09 (((~![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))) | ((~ssIm(nb(na))) | (~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIk(key(na, a))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))) | (~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIm(nb(na))) | (~ssIk(key(na, a))))),
% 9.05/6.09 inference(transitivity,[status(thm)],[102, 100])).
% 9.05/6.09 tff(104,plain,
% 9.05/6.09 ((~![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))) | ((~ssIm(nb(na))) | (~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIk(key(na, a))))),
% 9.05/6.09 inference(quant_inst,[status(thm)],[])).
% 9.05/6.09 tff(105,plain,
% 9.05/6.09 ((~![W: $i, V: $i, U: $i] : ((~ssIm(U)) | (~ssP(W)) | ssIm(encr(U, V)) | (~ssIk(key(V, W))))) | (~ssP(a)) | ssIm(encr(nb(na), na)) | (~ssIm(nb(na))) | (~ssIk(key(na, a)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[104, 103])).
% 9.05/6.09 tff(106,plain,
% 9.05/6.09 (ssIm(encr(nb(na), na)) | (~ssIk(key(na, a)))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[105, 46, 99, 89])).
% 9.05/6.09 tff(107,plain,
% 9.05/6.09 (ssIm(encr(nb(na), na))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[106, 54])).
% 9.05/6.09 tff(108,plain,
% 9.05/6.09 (^[W: $i, V: $i, U: $i] : refl((ssIm(W) | (~ssIm(triple(U, V, W)))) <=> (ssIm(W) | (~ssIm(triple(U, V, W)))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(109,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W)))) <=> ![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[108])).
% 9.05/6.09 tff(110,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W)))) <=> ![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(111,plain,
% 9.05/6.09 (^[W: $i, V: $i, U: $i] : rewrite(((~ssIm(triple(U, V, W))) | ssIm(W)) <=> (ssIm(W) | (~ssIm(triple(U, V, W)))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(112,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : ((~ssIm(triple(U, V, W))) | ssIm(W)) <=> ![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[111])).
% 9.05/6.09 tff(113,axiom,(![W: $i, V: $i, U: $i] : ((~ssIm(triple(U, V, W))) | ssIm(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause17')).
% 9.05/6.09 tff(114,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[113, 112])).
% 9.05/6.09 tff(115,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[114, 110])).
% 9.05/6.09 tff(116,plain,(
% 9.05/6.09 ![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))),
% 9.05/6.09 inference(skolemize,[status(sab)],[115])).
% 9.05/6.09 tff(117,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[116, 109])).
% 9.05/6.09 tff(118,plain,
% 9.05/6.09 (((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))) | (ssIm(encr(triple(a, na, tb(na)), bt)) | (~ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))) <=> ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))) | ssIm(encr(triple(a, na, tb(na)), bt)) | (~ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(119,plain,
% 9.05/6.09 ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))) | (ssIm(encr(triple(a, na, tb(na)), bt)) | (~ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt)))))),
% 9.05/6.09 inference(quant_inst,[status(thm)],[])).
% 9.05/6.09 tff(120,plain,
% 9.05/6.09 ((~![W: $i, V: $i, U: $i] : (ssIm(W) | (~ssIm(triple(U, V, W))))) | ssIm(encr(triple(a, na, tb(na)), bt)) | (~ssIm(triple(b, nb(na), encr(triple(a, na, tb(na)), bt))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[119, 118])).
% 9.05/6.09 tff(121,plain,
% 9.05/6.09 (ssIm(encr(triple(a, na, tb(na)), bt))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[120, 117, 75])).
% 9.05/6.09 tff(122,plain,
% 9.05/6.09 (^[V: $i, U: $i] : refl((ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V))) <=> (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(123,plain,
% 9.05/6.09 (![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V))) <=> ![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[122])).
% 9.05/6.09 tff(124,plain,
% 9.05/6.09 (![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V))) <=> ![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(125,plain,
% 9.05/6.09 (^[V: $i, U: $i] : rewrite((((~ssIm(U)) | (~ssIm(V))) | ssIm(pair(U, V))) <=> (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(126,plain,
% 9.05/6.09 (![V: $i, U: $i] : (((~ssIm(U)) | (~ssIm(V))) | ssIm(pair(U, V))) <=> ![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[125])).
% 9.05/6.09 tff(127,axiom,(![V: $i, U: $i] : (((~ssIm(U)) | (~ssIm(V))) | ssIm(pair(U, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause26')).
% 9.05/6.09 tff(128,plain,
% 9.05/6.09 (![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[127, 126])).
% 9.05/6.09 tff(129,plain,
% 9.05/6.09 (![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[128, 124])).
% 9.05/6.09 tff(130,plain,(
% 9.05/6.09 ![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))),
% 9.05/6.09 inference(skolemize,[status(sab)],[129])).
% 9.05/6.09 tff(131,plain,
% 9.05/6.09 (![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[130, 123])).
% 9.05/6.09 tff(132,plain,
% 9.05/6.09 (((~![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))) | (ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))) | (~ssIm(encr(triple(a, na, tb(na)), bt))) | (~ssIm(encr(nb(na), na))))) <=> ((~![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))) | ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))) | (~ssIm(encr(triple(a, na, tb(na)), bt))) | (~ssIm(encr(nb(na), na))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(133,plain,
% 9.05/6.09 ((~![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))) | (ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))) | (~ssIm(encr(triple(a, na, tb(na)), bt))) | (~ssIm(encr(nb(na), na))))),
% 9.05/6.09 inference(quant_inst,[status(thm)],[])).
% 9.05/6.09 tff(134,plain,
% 9.05/6.09 ((~![V: $i, U: $i] : (ssIm(pair(U, V)) | (~ssIm(U)) | (~ssIm(V)))) | ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))) | (~ssIm(encr(triple(a, na, tb(na)), bt))) | (~ssIm(encr(nb(na), na)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[133, 132])).
% 9.05/6.09 tff(135,plain,
% 9.05/6.09 (ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))) | (~ssIm(encr(nb(na), na)))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[134, 131, 121])).
% 9.05/6.09 tff(136,plain,
% 9.05/6.09 (ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[135, 107])).
% 9.05/6.09 tff(137,plain,
% 9.05/6.09 (ssP(b) <=> ssP(b)),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(138,axiom,(ssP(b)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 9.05/6.09 tff(139,plain,
% 9.05/6.09 (ssP(b)),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[138, 137])).
% 9.05/6.09 tff(140,plain,
% 9.05/6.09 (((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | ((~ssIm(na)) | (~ssP(b)) | ssIk(key(na, b)))) <=> ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (~ssIm(na)) | (~ssP(b)) | ssIk(key(na, b)))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(141,plain,
% 9.05/6.09 ((ssIk(key(na, b)) | (~ssP(b)) | (~ssIm(na))) <=> ((~ssIm(na)) | (~ssP(b)) | ssIk(key(na, b)))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(142,plain,
% 9.05/6.09 (((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (ssIk(key(na, b)) | (~ssP(b)) | (~ssIm(na)))) <=> ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | ((~ssIm(na)) | (~ssP(b)) | ssIk(key(na, b))))),
% 9.05/6.09 inference(monotonicity,[status(thm)],[141])).
% 9.05/6.09 tff(143,plain,
% 9.05/6.09 (((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (ssIk(key(na, b)) | (~ssP(b)) | (~ssIm(na)))) <=> ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (~ssIm(na)) | (~ssP(b)) | ssIk(key(na, b)))),
% 9.05/6.09 inference(transitivity,[status(thm)],[142, 140])).
% 9.05/6.09 tff(144,plain,
% 9.05/6.09 ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (ssIk(key(na, b)) | (~ssP(b)) | (~ssIm(na)))),
% 9.05/6.09 inference(quant_inst,[status(thm)],[])).
% 9.05/6.09 tff(145,plain,
% 9.05/6.09 ((~![V: $i, U: $i] : (ssIk(key(U, V)) | (~ssP(V)) | (~ssIm(U)))) | (~ssIm(na)) | (~ssP(b)) | ssIk(key(na, b))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[144, 143])).
% 9.05/6.09 tff(146,plain,
% 9.05/6.09 (ssIk(key(na, b))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[145, 139, 43, 33])).
% 9.05/6.09 tff(147,plain,
% 9.05/6.09 (^[U: $i] : refl(((~ssIk(key(U, b))) | (~ssBk(key(U, a)))) <=> ((~ssIk(key(U, b))) | (~ssBk(key(U, a)))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(148,plain,
% 9.05/6.09 (![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a)))) <=> ![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[147])).
% 9.05/6.09 tff(149,plain,
% 9.05/6.09 (![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a)))) <=> ![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(150,axiom,(![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 9.05/6.09 tff(151,plain,
% 9.05/6.09 (![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[150, 149])).
% 9.05/6.09 tff(152,plain,(
% 9.05/6.09 ![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))),
% 9.05/6.09 inference(skolemize,[status(sab)],[151])).
% 9.05/6.09 tff(153,plain,
% 9.05/6.09 (![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[152, 148])).
% 9.05/6.09 tff(154,plain,
% 9.05/6.09 (((~![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))) | ((~ssIk(key(na, b))) | (~ssBk(key(na, a))))) <=> ((~![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))) | (~ssIk(key(na, b))) | (~ssBk(key(na, a))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(155,plain,
% 9.05/6.09 ((~![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))) | ((~ssIk(key(na, b))) | (~ssBk(key(na, a))))),
% 9.05/6.09 inference(quant_inst,[status(thm)],[])).
% 9.05/6.09 tff(156,plain,
% 9.05/6.09 ((~![U: $i] : ((~ssIk(key(U, b))) | (~ssBk(key(U, a))))) | (~ssIk(key(na, b))) | (~ssBk(key(na, a)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[155, 154])).
% 9.05/6.09 tff(157,plain,
% 9.05/6.09 ((~ssIk(key(na, b))) | (~ssBk(key(na, a)))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[156, 153])).
% 9.05/6.09 tff(158,plain,
% 9.05/6.09 (~ssBk(key(na, a))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[157, 146])).
% 9.05/6.09 tff(159,plain,
% 9.05/6.09 (^[V: $i, U: $i] : refl(((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V))))) <=> ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V))))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(160,plain,
% 9.05/6.09 (![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V))))) <=> ![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[159])).
% 9.05/6.09 tff(161,plain,
% 9.05/6.09 (![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V))))) <=> ![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(162,plain,
% 9.05/6.09 (^[V: $i, U: $i] : trans(monotonicity(rewrite(((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) <=> ((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V)))))), ((((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) | ssSb(pair(U, V))) <=> (((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V))))) | ssSb(pair(U, V))))), rewrite((((~ssBf(V)) | (~ssM(sent(U, b, pair(U, V))))) | ssSb(pair(U, V))) <=> ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))), ((((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) | ssSb(pair(U, V))) <=> ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(163,plain,
% 9.05/6.09 (![V: $i, U: $i] : (((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) | ssSb(pair(U, V))) <=> ![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[162])).
% 9.05/6.09 tff(164,axiom,(![V: $i, U: $i] : (((~ssM(sent(U, b, pair(U, V)))) | (~ssBf(V))) | ssSb(pair(U, V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 9.05/6.09 tff(165,plain,
% 9.05/6.09 (![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[164, 163])).
% 9.05/6.09 tff(166,plain,
% 9.05/6.09 (![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[165, 161])).
% 9.05/6.09 tff(167,plain,(
% 9.05/6.09 ![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))),
% 9.05/6.09 inference(skolemize,[status(sab)],[166])).
% 9.05/6.09 tff(168,plain,
% 9.05/6.09 (![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[167, 160])).
% 9.05/6.09 tff(169,plain,
% 9.05/6.09 (((~![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))) | ((~ssBf(na)) | ssSb(pair(a, na)) | (~ssM(sent(a, b, pair(a, na)))))) <=> ((~![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))) | (~ssBf(na)) | ssSb(pair(a, na)) | (~ssM(sent(a, b, pair(a, na)))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(170,plain,
% 9.05/6.09 ((~![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))) | ((~ssBf(na)) | ssSb(pair(a, na)) | (~ssM(sent(a, b, pair(a, na)))))),
% 9.05/6.09 inference(quant_inst,[status(thm)],[])).
% 9.05/6.09 tff(171,plain,
% 9.05/6.09 ((~![V: $i, U: $i] : ((~ssBf(V)) | ssSb(pair(U, V)) | (~ssM(sent(U, b, pair(U, V)))))) | (~ssBf(na)) | ssSb(pair(a, na)) | (~ssM(sent(a, b, pair(a, na))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[170, 169])).
% 9.05/6.09 tff(172,plain,
% 9.05/6.09 (ssSb(pair(a, na))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[171, 67, 14, 168])).
% 9.05/6.09 tff(173,plain,
% 9.05/6.09 (^[W: $i, V: $i, U: $i] : refl((ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V)))))) <=> (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V)))))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(174,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V)))))) <=> ![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[173])).
% 9.05/6.09 tff(175,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V)))))) <=> ![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(176,plain,
% 9.05/6.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(rewrite(((~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))) | (~ssSb(pair(U, W)))) <=> ((~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))), ((((~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))) | (~ssSb(pair(U, W)))) | ssBk(key(V, U))) <=> (((~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V)))))) | ssBk(key(V, U))))), rewrite((((~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V)))))) | ssBk(key(V, U))) <=> (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))), ((((~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))) | (~ssSb(pair(U, W)))) | ssBk(key(V, U))) <=> (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(177,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (((~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))) | (~ssSb(pair(U, W)))) | ssBk(key(V, U))) <=> ![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[176])).
% 9.05/6.09 tff(178,axiom,(![W: $i, V: $i, U: $i] : (((~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))) | (~ssSb(pair(U, W)))) | ssBk(key(V, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 9.05/6.09 tff(179,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[178, 177])).
% 9.05/6.09 tff(180,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[179, 175])).
% 9.05/6.09 tff(181,plain,(
% 9.05/6.09 ![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))),
% 9.05/6.09 inference(skolemize,[status(sab)],[180])).
% 9.05/6.09 tff(182,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[181, 174])).
% 9.05/6.09 tff(183,plain,
% 9.05/6.09 (((~![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))) | (ssBk(key(na, a)) | (~ssSb(pair(a, na))) | (~ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))))))) <=> ((~![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))) | ssBk(key(na, a)) | (~ssSb(pair(a, na))) | (~ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(184,plain,
% 9.05/6.09 ((~![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))) | (ssBk(key(na, a)) | (~ssSb(pair(a, na))) | (~ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))))))),
% 9.05/6.09 inference(quant_inst,[status(thm)],[])).
% 9.05/6.09 tff(185,plain,
% 9.05/6.09 ((~![W: $i, V: $i, U: $i] : (ssBk(key(V, U)) | (~ssSb(pair(U, W))) | (~ssM(sent(U, b, pair(encr(triple(U, V, tb(W)), bt), encr(nb(W), V))))))) | ssBk(key(na, a)) | (~ssSb(pair(a, na))) | (~ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[184, 183])).
% 9.05/6.09 tff(186,plain,
% 9.05/6.09 (ssBk(key(na, a)) | (~ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[185, 182, 172])).
% 9.05/6.09 tff(187,plain,
% 9.05/6.09 (~ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))))),
% 9.05/6.09 inference(unit_resolution,[status(thm)],[186, 158])).
% 9.05/6.09 tff(188,plain,
% 9.05/6.09 (^[W: $i, V: $i, U: $i] : refl(((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W))) <=> ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(189,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[188])).
% 9.05/6.09 tff(190,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W))) <=> ![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(191,plain,
% 9.05/6.09 (^[W: $i, V: $i, U: $i] : trans(monotonicity(rewrite((((~ssIm(U)) | (~ssP(V))) | (~ssP(W))) <=> ((~ssP(V)) | (~ssIm(U)) | (~ssP(W)))), (((((~ssIm(U)) | (~ssP(V))) | (~ssP(W))) | ssM(sent(V, W, U))) <=> (((~ssP(V)) | (~ssIm(U)) | (~ssP(W))) | ssM(sent(V, W, U))))), rewrite((((~ssP(V)) | (~ssIm(U)) | (~ssP(W))) | ssM(sent(V, W, U))) <=> ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))), (((((~ssIm(U)) | (~ssP(V))) | (~ssP(W))) | ssM(sent(V, W, U))) <=> ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))))),
% 9.05/6.09 inference(bind,[status(th)],[])).
% 9.05/6.09 tff(192,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : ((((~ssIm(U)) | (~ssP(V))) | (~ssP(W))) | ssM(sent(V, W, U))) <=> ![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))),
% 9.05/6.09 inference(quant_intro,[status(thm)],[191])).
% 9.05/6.09 tff(193,axiom,(![W: $i, V: $i, U: $i] : ((((~ssIm(U)) | (~ssP(V))) | (~ssP(W))) | ssM(sent(V, W, U)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 9.05/6.09 tff(194,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[193, 192])).
% 9.05/6.09 tff(195,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[194, 190])).
% 9.05/6.09 tff(196,plain,(
% 9.05/6.09 ![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))),
% 9.05/6.09 inference(skolemize,[status(sab)],[195])).
% 9.05/6.09 tff(197,plain,
% 9.05/6.09 (![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))),
% 9.05/6.09 inference(modus_ponens,[status(thm)],[196, 189])).
% 9.05/6.09 tff(198,plain,
% 9.05/6.09 (((~![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))) | ((~ssP(b)) | (~ssP(a)) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))) | (~ssP(b)) | (~ssP(a)) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(199,plain,
% 9.05/6.09 (((~ssP(a)) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssP(b))) <=> ((~ssP(b)) | (~ssP(a)) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))))),
% 9.05/6.09 inference(rewrite,[status(thm)],[])).
% 9.05/6.09 tff(200,plain,
% 9.05/6.09 (((~![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))) | ((~ssP(a)) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssP(b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))) | ((~ssP(b)) | (~ssP(a)) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))))))),
% 9.05/6.09 inference(monotonicity,[status(thm)],[199])).
% 9.05/6.09 tff(201,plain,
% 9.05/6.09 (((~![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))) | ((~ssP(a)) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssP(b)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))) | (~ssP(b)) | (~ssP(a)) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))))),
% 9.05/6.09 inference(transitivity,[status(thm)],[200, 198])).
% 9.05/6.09 tff(202,plain,
% 9.05/6.09 ((~![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))) | ((~ssP(a)) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssP(b)))),
% 9.05/6.09 inference(quant_inst,[status(thm)],[])).
% 9.05/6.09 tff(203,plain,
% 9.05/6.09 ((~![W: $i, V: $i, U: $i] : ((~ssP(V)) | (~ssIm(U)) | ssM(sent(V, W, U)) | (~ssP(W)))) | (~ssP(b)) | (~ssP(a)) | ssM(sent(a, b, pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na)))) | (~ssIm(pair(encr(triple(a, na, tb(na)), bt), encr(nb(na), na))))),
% 9.05/6.10 inference(modus_ponens,[status(thm)],[202, 201])).
% 9.05/6.10 tff(204,plain,
% 9.05/6.10 ($false),
% 9.05/6.10 inference(unit_resolution,[status(thm)],[203, 139, 46, 197, 187, 136])).
% 9.05/6.10 % SZS output end Proof
%------------------------------------------------------------------------------