TSTP Solution File: PUZ133+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ133+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Sun Sep 18 14:11:33 EDT 2022
% Result : Theorem 1.06s 0.93s
% Output : Proof 1.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : PUZ133+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 19:01:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.06/0.93 % SZS status Theorem
% 1.06/0.93 % SZS output start Proof
% 1.06/0.93 tff(plus_type, type, (
% 1.06/0.93 plus: ( $i * $i ) > $i)).
% 1.06/0.93 tff(tptp_fun_I_1_type, type, (
% 1.06/0.93 tptp_fun_I_1: $i)).
% 1.06/0.93 tff(p_type, type, (
% 1.06/0.93 p: $i > $i)).
% 1.06/0.93 tff(perm_type, type, (
% 1.06/0.93 perm: $i > $i)).
% 1.06/0.93 tff(tptp_fun_J_0_type, type, (
% 1.06/0.93 tptp_fun_J_0: $i)).
% 1.06/0.93 tff(q_type, type, (
% 1.06/0.93 q: $i > $i)).
% 1.06/0.93 tff(queens_p_type, type, (
% 1.06/0.93 queens_p: $o)).
% 1.06/0.93 tff(queens_q_type, type, (
% 1.06/0.93 queens_q: $o)).
% 1.06/0.93 tff(minus_type, type, (
% 1.06/0.93 minus: ( $i * $i ) > $i)).
% 1.06/0.93 tff(le_type, type, (
% 1.06/0.93 le: ( $i * $i ) > $o)).
% 1.06/0.93 tff(s_type, type, (
% 1.06/0.93 s: $i > $i)).
% 1.06/0.93 tff(n0_type, type, (
% 1.06/0.93 n0: $i)).
% 1.06/0.93 tff(n_type, type, (
% 1.06/0.93 n: $i)).
% 1.06/0.93 tff(1,plain,
% 1.06/0.93 (^[I: $i] : refl((q(I) = p(perm(I))) <=> (q(I) = p(perm(I))))),
% 1.06/0.93 inference(bind,[status(th)],[])).
% 1.06/0.93 tff(2,plain,
% 1.06/0.93 (![I: $i] : (q(I) = p(perm(I))) <=> ![I: $i] : (q(I) = p(perm(I)))),
% 1.06/0.93 inference(quant_intro,[status(thm)],[1])).
% 1.06/0.93 tff(3,plain,
% 1.06/0.93 (![I: $i] : (q(I) = p(perm(I))) <=> ![I: $i] : (q(I) = p(perm(I)))),
% 1.06/0.93 inference(rewrite,[status(thm)],[])).
% 1.06/0.93 tff(4,plain,
% 1.06/0.93 ((~((queens_p & ![I: $i] : (q(I) = p(perm(I)))) => queens_q)) <=> (~(queens_q | (~(queens_p & ![I: $i] : (q(I) = p(perm(I)))))))),
% 1.06/0.93 inference(rewrite,[status(thm)],[])).
% 1.06/0.93 tff(5,axiom,(~((queens_p & ![I: $i] : (q(I) = p(perm(I)))) => queens_q)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','queens_sym')).
% 1.06/0.93 tff(6,plain,
% 1.06/0.93 (~(queens_q | (~(queens_p & ![I: $i] : (q(I) = p(perm(I))))))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.06/0.93 tff(7,plain,
% 1.06/0.93 (queens_p & ![I: $i] : (q(I) = p(perm(I)))),
% 1.06/0.93 inference(or_elim,[status(thm)],[6])).
% 1.06/0.93 tff(8,plain,
% 1.06/0.93 (![I: $i] : (q(I) = p(perm(I)))),
% 1.06/0.93 inference(and_elim,[status(thm)],[7])).
% 1.06/0.93 tff(9,plain,
% 1.06/0.93 (![I: $i] : (q(I) = p(perm(I)))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[8, 3])).
% 1.06/0.93 tff(10,plain,(
% 1.06/0.93 ![I: $i] : (q(I) = p(perm(I)))),
% 1.06/0.93 inference(skolemize,[status(sab)],[9])).
% 1.06/0.93 tff(11,plain,
% 1.06/0.93 (![I: $i] : (q(I) = p(perm(I)))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[10, 2])).
% 1.06/0.93 tff(12,plain,
% 1.06/0.93 ((~![I: $i] : (q(I) = p(perm(I)))) | (q(I!1) = p(perm(I!1)))),
% 1.06/0.93 inference(quant_inst,[status(thm)],[])).
% 1.06/0.93 tff(13,plain,
% 1.06/0.93 (q(I!1) = p(perm(I!1))),
% 1.06/0.93 inference(unit_resolution,[status(thm)],[12, 11])).
% 1.06/0.93 tff(14,plain,
% 1.06/0.93 (p(perm(I!1)) = q(I!1)),
% 1.06/0.93 inference(symmetry,[status(thm)],[13])).
% 1.06/0.93 tff(15,plain,
% 1.06/0.93 (plus(p(perm(I!1)), I!1) = plus(q(I!1), I!1)),
% 1.06/0.93 inference(monotonicity,[status(thm)],[14])).
% 1.06/0.93 tff(16,plain,
% 1.06/0.93 (plus(q(I!1), I!1) = plus(p(perm(I!1)), I!1)),
% 1.06/0.93 inference(symmetry,[status(thm)],[15])).
% 1.06/0.93 tff(17,plain,
% 1.06/0.93 ((p(perm(I!1)) = p(perm(J!0))) <=> (p(perm(J!0)) = p(perm(I!1)))),
% 1.06/0.93 inference(commutativity,[status(thm)],[])).
% 1.06/0.93 tff(18,plain,
% 1.06/0.93 ((~![I: $i] : (q(I) = p(perm(I)))) | (q(J!0) = p(perm(J!0)))),
% 1.06/0.93 inference(quant_inst,[status(thm)],[])).
% 1.06/0.93 tff(19,plain,
% 1.06/0.93 (q(J!0) = p(perm(J!0))),
% 1.06/0.93 inference(unit_resolution,[status(thm)],[18, 11])).
% 1.06/0.93 tff(20,plain,
% 1.06/0.93 ((q(I!1) = q(J!0)) <=> (p(perm(I!1)) = p(perm(J!0)))),
% 1.06/0.93 inference(monotonicity,[status(thm)],[13, 19])).
% 1.06/0.93 tff(21,plain,
% 1.06/0.93 ((q(I!1) = q(J!0)) <=> (p(perm(J!0)) = p(perm(I!1)))),
% 1.06/0.93 inference(transitivity,[status(thm)],[20, 17])).
% 1.06/0.93 tff(22,plain,
% 1.06/0.93 ((p(perm(J!0)) = p(perm(I!1))) <=> (q(I!1) = q(J!0))),
% 1.06/0.93 inference(symmetry,[status(thm)],[21])).
% 1.06/0.93 tff(23,plain,
% 1.06/0.93 ((~(p(perm(J!0)) = p(perm(I!1)))) <=> (~(q(I!1) = q(J!0)))),
% 1.06/0.93 inference(monotonicity,[status(thm)],[22])).
% 1.06/0.93 tff(24,plain,
% 1.06/0.93 (^[X: $i] : refl(le(X, s(X)) <=> le(X, s(X)))),
% 1.06/0.93 inference(bind,[status(th)],[])).
% 1.06/0.93 tff(25,plain,
% 1.06/0.93 (![X: $i] : le(X, s(X)) <=> ![X: $i] : le(X, s(X))),
% 1.06/0.93 inference(quant_intro,[status(thm)],[24])).
% 1.06/0.93 tff(26,plain,
% 1.06/0.93 (![X: $i] : le(X, s(X)) <=> ![X: $i] : le(X, s(X))),
% 1.06/0.93 inference(rewrite,[status(thm)],[])).
% 1.06/0.93 tff(27,axiom,(![X: $i] : le(X, s(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','succ_le')).
% 1.06/0.93 tff(28,plain,
% 1.06/0.93 (![X: $i] : le(X, s(X))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.06/0.93 tff(29,plain,(
% 1.06/0.93 ![X: $i] : le(X, s(X))),
% 1.06/0.93 inference(skolemize,[status(sab)],[28])).
% 1.06/0.93 tff(30,plain,
% 1.06/0.93 (![X: $i] : le(X, s(X))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.06/0.93 tff(31,plain,
% 1.06/0.93 ((~![X: $i] : le(X, s(X))) | le(I!1, s(I!1))),
% 1.06/0.93 inference(quant_inst,[status(thm)],[])).
% 1.06/0.93 tff(32,plain,
% 1.06/0.93 (le(I!1, s(I!1))),
% 1.06/0.93 inference(unit_resolution,[status(thm)],[31, 30])).
% 1.06/0.93 tff(33,plain,
% 1.06/0.93 (![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))),
% 1.06/0.93 inference(rewrite,[status(thm)],[])).
% 1.06/0.93 tff(34,plain,
% 1.06/0.93 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((le(X, Y) & le(Y, Z)) <=> (~((~le(X, Y)) | (~le(Y, Z))))), ((~(le(X, Y) & le(Y, Z))) <=> (~(~((~le(X, Y)) | (~le(Y, Z))))))), rewrite((~(~((~le(X, Y)) | (~le(Y, Z))))) <=> ((~le(X, Y)) | (~le(Y, Z)))), ((~(le(X, Y) & le(Y, Z))) <=> ((~le(X, Y)) | (~le(Y, Z))))), (((~(le(X, Y) & le(Y, Z))) | le(X, Z)) <=> (((~le(X, Y)) | (~le(Y, Z))) | le(X, Z)))), rewrite((((~le(X, Y)) | (~le(Y, Z))) | le(X, Z)) <=> (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))), (((~(le(X, Y) & le(Y, Z))) | le(X, Z)) <=> (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))))),
% 1.06/0.93 inference(bind,[status(th)],[])).
% 1.06/0.93 tff(35,plain,
% 1.06/0.93 (![X: $i, Y: $i, Z: $i] : ((~(le(X, Y) & le(Y, Z))) | le(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))),
% 1.06/0.93 inference(quant_intro,[status(thm)],[34])).
% 1.06/0.93 tff(36,plain,
% 1.06/0.93 (![X: $i, Y: $i, Z: $i] : ((~(le(X, Y) & le(Y, Z))) | le(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(le(X, Y) & le(Y, Z))) | le(X, Z))),
% 1.06/0.93 inference(rewrite,[status(thm)],[])).
% 1.06/0.93 tff(37,plain,
% 1.06/0.93 (^[X: $i, Y: $i, Z: $i] : rewrite(((le(X, Y) & le(Y, Z)) => le(X, Z)) <=> ((~(le(X, Y) & le(Y, Z))) | le(X, Z)))),
% 1.06/0.93 inference(bind,[status(th)],[])).
% 1.06/0.93 tff(38,plain,
% 1.06/0.93 (![X: $i, Y: $i, Z: $i] : ((le(X, Y) & le(Y, Z)) => le(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(le(X, Y) & le(Y, Z))) | le(X, Z))),
% 1.06/0.93 inference(quant_intro,[status(thm)],[37])).
% 1.06/0.93 tff(39,axiom,(![X: $i, Y: $i, Z: $i] : ((le(X, Y) & le(Y, Z)) => le(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','le_trans')).
% 1.06/0.93 tff(40,plain,
% 1.06/0.93 (![X: $i, Y: $i, Z: $i] : ((~(le(X, Y) & le(Y, Z))) | le(X, Z))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.06/0.93 tff(41,plain,
% 1.06/0.93 (![X: $i, Y: $i, Z: $i] : ((~(le(X, Y) & le(Y, Z))) | le(X, Z))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.06/0.93 tff(42,plain,(
% 1.06/0.93 ![X: $i, Y: $i, Z: $i] : ((~(le(X, Y) & le(Y, Z))) | le(X, Z))),
% 1.06/0.93 inference(skolemize,[status(sab)],[41])).
% 1.06/0.93 tff(43,plain,
% 1.06/0.93 (![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[42, 35])).
% 1.06/0.93 tff(44,plain,
% 1.06/0.93 (![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))),
% 1.06/0.93 inference(modus_ponens,[status(thm)],[43, 33])).
% 1.06/0.93 tff(45,plain,
% 1.06/0.93 ((~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))) <=> (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.06/0.93 inference(rewrite,[status(thm)],[])).
% 1.06/0.93 tff(46,plain,
% 1.06/0.93 (($false | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))) <=> (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.06/0.93 inference(rewrite,[status(thm)],[])).
% 1.06/0.93 tff(47,plain,
% 1.06/0.93 (~queens_q),
% 1.06/0.93 inference(or_elim,[status(thm)],[6])).
% 1.06/0.93 tff(48,plain,
% 1.06/0.93 (queens_q <=> $false),
% 1.06/0.93 inference(iff_false,[status(thm)],[47])).
% 1.06/0.93 tff(49,plain,
% 1.06/0.93 ((queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))) <=> ($false | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.11/0.93 inference(monotonicity,[status(thm)],[48, 45])).
% 1.11/0.93 tff(50,plain,
% 1.11/0.93 ((queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))) <=> (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.11/0.93 inference(transitivity,[status(thm)],[49, 46])).
% 1.11/0.93 tff(51,plain,
% 1.11/0.93 ((queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))) <=> (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.11/0.93 inference(monotonicity,[status(thm)],[45])).
% 1.11/0.93 tff(52,plain,
% 1.11/0.93 ((![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q) <=> (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.11/0.93 inference(rewrite,[status(thm)],[])).
% 1.11/0.93 tff(53,plain,
% 1.11/0.93 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((le(s(n0), I) & le(I, n)) & le(s(I), J)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J))), ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) <=> ((le(s(n0), I) & le(I, n) & le(s(I), J)) & le(J, n)))), rewrite(((le(s(n0), I) & le(I, n) & le(s(I), J)) & le(J, n)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))), ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)))), (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) <=> ((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))))), rewrite(((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))), (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))))), rewrite((((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J)))) <=> ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))), ((((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) <=> ((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))), rewrite(((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))) <=> ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))), ((((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) <=> ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.11/0.93 inference(bind,[status(th)],[])).
% 1.11/0.93 tff(54,plain,
% 1.11/0.93 (![I: $i, J: $i] : (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) <=> ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.11/0.93 inference(quant_intro,[status(thm)],[53])).
% 1.11/0.93 tff(55,plain,
% 1.11/0.93 ((![I: $i, J: $i] : (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q) <=> (![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q)),
% 1.11/0.93 inference(monotonicity,[status(thm)],[54])).
% 1.11/0.93 tff(56,plain,
% 1.11/0.93 ((![I: $i, J: $i] : (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q) <=> (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))))),
% 1.11/0.93 inference(transitivity,[status(thm)],[55, 52])).
% 1.11/0.93 tff(57,axiom,(![I: $i, J: $i] : (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) & (le(s(I), J) <=> le(s(perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J)))) & (~(minus(q(I), I) = minus(q(J), J))))) => queens_q), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','queens_q')).
% 1.11/0.93 tff(58,plain,
% 1.11/0.93 (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.11/0.93 tff(59,plain,
% 1.11/0.93 (queens_q | (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J))))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[58, 51])).
% 1.11/0.93 tff(60,plain,
% 1.11/0.93 (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[59, 50])).
% 1.11/0.93 tff(61,plain,
% 1.11/0.93 (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[60, 45])).
% 1.11/0.93 tff(62,plain,
% 1.11/0.93 (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[61, 45])).
% 1.11/0.93 tff(63,plain,
% 1.11/0.93 (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[62, 45])).
% 1.11/0.93 tff(64,plain,
% 1.11/0.93 (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[63, 45])).
% 1.11/0.93 tff(65,plain,
% 1.11/0.93 (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[64, 45])).
% 1.11/0.93 tff(66,plain,
% 1.11/0.93 (~![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n) & (le(s(I), J) <=> le(s(perm(J)), perm(I))))) | ((~(q(I) = q(J))) & (~(plus(q(I), I) = plus(q(J), J))) & (~(minus(q(I), I) = minus(q(J), J)))))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[65, 45])).
% 1.11/0.93 tff(67,plain,(
% 1.11/0.93 ~((~(le(s(n0), I!1) & le(I!1, n) & le(s(I!1), J!0) & le(J!0, n) & (le(s(I!1), J!0) <=> le(s(perm(J!0)), perm(I!1))))) | ((~(q(I!1) = q(J!0))) & (~(plus(q(I!1), I!1) = plus(q(J!0), J!0))) & (~(minus(q(I!1), I!1) = minus(q(J!0), J!0)))))),
% 1.11/0.93 inference(skolemize,[status(sab)],[66])).
% 1.11/0.93 tff(68,plain,
% 1.11/0.93 (le(s(n0), I!1) & le(I!1, n) & le(s(I!1), J!0) & le(J!0, n) & (le(s(I!1), J!0) <=> le(s(perm(J!0)), perm(I!1)))),
% 1.11/0.93 inference(or_elim,[status(thm)],[67])).
% 1.11/0.93 tff(69,plain,
% 1.11/0.93 (le(s(n0), I!1)),
% 1.11/0.93 inference(and_elim,[status(thm)],[68])).
% 1.11/0.93 tff(70,plain,
% 1.11/0.93 (((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | ((~le(s(n0), I!1)) | le(s(n0), s(I!1)) | (~le(I!1, s(I!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (~le(s(n0), I!1)) | le(s(n0), s(I!1)) | (~le(I!1, s(I!1))))),
% 1.11/0.93 inference(rewrite,[status(thm)],[])).
% 1.11/0.93 tff(71,plain,
% 1.11/0.93 ((le(s(n0), s(I!1)) | (~le(s(n0), I!1)) | (~le(I!1, s(I!1)))) <=> ((~le(s(n0), I!1)) | le(s(n0), s(I!1)) | (~le(I!1, s(I!1))))),
% 1.11/0.93 inference(rewrite,[status(thm)],[])).
% 1.11/0.93 tff(72,plain,
% 1.11/0.93 (((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (le(s(n0), s(I!1)) | (~le(s(n0), I!1)) | (~le(I!1, s(I!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | ((~le(s(n0), I!1)) | le(s(n0), s(I!1)) | (~le(I!1, s(I!1)))))),
% 1.11/0.93 inference(monotonicity,[status(thm)],[71])).
% 1.11/0.93 tff(73,plain,
% 1.11/0.93 (((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (le(s(n0), s(I!1)) | (~le(s(n0), I!1)) | (~le(I!1, s(I!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (~le(s(n0), I!1)) | le(s(n0), s(I!1)) | (~le(I!1, s(I!1))))),
% 1.11/0.93 inference(transitivity,[status(thm)],[72, 70])).
% 1.11/0.93 tff(74,plain,
% 1.11/0.93 ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (le(s(n0), s(I!1)) | (~le(s(n0), I!1)) | (~le(I!1, s(I!1))))),
% 1.11/0.93 inference(quant_inst,[status(thm)],[])).
% 1.11/0.93 tff(75,plain,
% 1.11/0.93 ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (~le(s(n0), I!1)) | le(s(n0), s(I!1)) | (~le(I!1, s(I!1)))),
% 1.11/0.93 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.11/0.93 tff(76,plain,
% 1.11/0.93 (le(s(n0), s(I!1))),
% 1.11/0.93 inference(unit_resolution,[status(thm)],[75, 69, 44, 32])).
% 1.11/0.93 tff(77,plain,
% 1.11/0.93 (le(s(I!1), J!0)),
% 1.11/0.93 inference(and_elim,[status(thm)],[68])).
% 1.11/0.93 tff(78,plain,
% 1.11/0.93 (((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | ((~le(s(I!1), J!0)) | le(s(n0), J!0) | (~le(s(n0), s(I!1))))) <=> ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (~le(s(I!1), J!0)) | le(s(n0), J!0) | (~le(s(n0), s(I!1))))),
% 1.11/0.93 inference(rewrite,[status(thm)],[])).
% 1.11/0.93 tff(79,plain,
% 1.11/0.93 ((le(s(n0), J!0) | (~le(s(n0), s(I!1))) | (~le(s(I!1), J!0))) <=> ((~le(s(I!1), J!0)) | le(s(n0), J!0) | (~le(s(n0), s(I!1))))),
% 1.11/0.93 inference(rewrite,[status(thm)],[])).
% 1.11/0.93 tff(80,plain,
% 1.11/0.93 (((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (le(s(n0), J!0) | (~le(s(n0), s(I!1))) | (~le(s(I!1), J!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | ((~le(s(I!1), J!0)) | le(s(n0), J!0) | (~le(s(n0), s(I!1)))))),
% 1.11/0.93 inference(monotonicity,[status(thm)],[79])).
% 1.11/0.93 tff(81,plain,
% 1.11/0.93 (((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (le(s(n0), J!0) | (~le(s(n0), s(I!1))) | (~le(s(I!1), J!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (~le(s(I!1), J!0)) | le(s(n0), J!0) | (~le(s(n0), s(I!1))))),
% 1.11/0.94 inference(transitivity,[status(thm)],[80, 78])).
% 1.11/0.94 tff(82,plain,
% 1.11/0.94 ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (le(s(n0), J!0) | (~le(s(n0), s(I!1))) | (~le(s(I!1), J!0)))),
% 1.11/0.94 inference(quant_inst,[status(thm)],[])).
% 1.11/0.94 tff(83,plain,
% 1.11/0.94 ((~![X: $i, Y: $i, Z: $i] : (le(X, Z) | (~le(X, Y)) | (~le(Y, Z)))) | (~le(s(I!1), J!0)) | le(s(n0), J!0) | (~le(s(n0), s(I!1)))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.11/0.94 tff(84,plain,
% 1.11/0.94 (le(s(n0), J!0)),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[83, 77, 44, 76])).
% 1.11/0.94 tff(85,plain,
% 1.11/0.94 (^[I: $i] : refl(((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n))))) <=> ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n))))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(86,plain,
% 1.11/0.94 (![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n))))) <=> ![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[85])).
% 1.11/0.94 tff(87,plain,
% 1.11/0.94 (^[I: $i] : trans(monotonicity(trans(monotonicity(rewrite((le(s(n0), I) & le(I, n)) <=> (~((~le(I, n)) | (~le(s(n0), I))))), ((~(le(s(n0), I) & le(I, n))) <=> (~(~((~le(I, n)) | (~le(s(n0), I))))))), rewrite((~(~((~le(I, n)) | (~le(s(n0), I))))) <=> ((~le(I, n)) | (~le(s(n0), I)))), ((~(le(s(n0), I) & le(I, n))) <=> ((~le(I, n)) | (~le(s(n0), I))))), rewrite((le(s(n0), perm(I)) & le(perm(I), n)) <=> (~((~le(s(n0), perm(I))) | (~le(perm(I), n))))), (((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n))) <=> (((~le(I, n)) | (~le(s(n0), I))) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n))))))), rewrite((((~le(I, n)) | (~le(s(n0), I))) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n))))) <=> ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))), (((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n))) <=> ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(88,plain,
% 1.11/0.94 (![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n))) <=> ![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[87])).
% 1.11/0.94 tff(89,plain,
% 1.11/0.94 (![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n))) <=> ![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n)))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(90,plain,
% 1.11/0.94 (^[I: $i] : rewrite(((le(s(n0), I) & le(I, n)) => (le(s(n0), perm(I)) & le(perm(I), n))) <=> ((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(91,plain,
% 1.11/0.94 (![I: $i] : ((le(s(n0), I) & le(I, n)) => (le(s(n0), perm(I)) & le(perm(I), n))) <=> ![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n)))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[90])).
% 1.11/0.94 tff(92,axiom,(![I: $i] : ((le(s(n0), I) & le(I, n)) => (le(s(n0), perm(I)) & le(perm(I), n)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permutation_range')).
% 1.11/0.94 tff(93,plain,
% 1.11/0.94 (![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n)))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.11/0.94 tff(94,plain,
% 1.11/0.94 (![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n)))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[93, 89])).
% 1.11/0.94 tff(95,plain,(
% 1.11/0.94 ![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (le(s(n0), perm(I)) & le(perm(I), n)))),
% 1.11/0.94 inference(skolemize,[status(sab)],[94])).
% 1.11/0.94 tff(96,plain,
% 1.11/0.94 (![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[95, 88])).
% 1.11/0.94 tff(97,plain,
% 1.11/0.94 (![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[96, 86])).
% 1.11/0.94 tff(98,plain,
% 1.11/0.94 (le(J!0, n)),
% 1.11/0.94 inference(and_elim,[status(thm)],[68])).
% 1.11/0.94 tff(99,plain,
% 1.11/0.94 (((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | ((~le(J!0, n)) | (~le(s(n0), J!0)) | (~((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)))))) <=> ((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | (~le(J!0, n)) | (~le(s(n0), J!0)) | (~((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(100,plain,
% 1.11/0.94 ((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | ((~le(J!0, n)) | (~le(s(n0), J!0)) | (~((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)))))),
% 1.11/0.94 inference(quant_inst,[status(thm)],[])).
% 1.11/0.94 tff(101,plain,
% 1.11/0.94 ((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | (~le(J!0, n)) | (~le(s(n0), J!0)) | (~((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[100, 99])).
% 1.11/0.94 tff(102,plain,
% 1.11/0.94 ((~le(s(n0), J!0)) | (~((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n))))),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[101, 98, 97])).
% 1.11/0.94 tff(103,plain,
% 1.11/0.94 (~((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)))),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[102, 84])).
% 1.11/0.94 tff(104,plain,
% 1.11/0.94 (((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n))) | le(s(n0), perm(J!0))),
% 1.11/0.94 inference(tautology,[status(thm)],[])).
% 1.11/0.94 tff(105,plain,
% 1.11/0.94 (le(s(n0), perm(J!0))),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[104, 103])).
% 1.11/0.94 tff(106,plain,
% 1.11/0.94 (le(I!1, n)),
% 1.11/0.94 inference(and_elim,[status(thm)],[68])).
% 1.11/0.94 tff(107,plain,
% 1.11/0.94 (((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | ((~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(perm(I!1), n)) | (~le(s(n0), perm(I!1))))))) <=> ((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | (~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(perm(I!1), n)) | (~le(s(n0), perm(I!1))))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(108,plain,
% 1.11/0.94 (((~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(s(n0), perm(I!1))) | (~le(perm(I!1), n))))) <=> ((~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(perm(I!1), n)) | (~le(s(n0), perm(I!1))))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(109,plain,
% 1.11/0.94 (((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | ((~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(s(n0), perm(I!1))) | (~le(perm(I!1), n)))))) <=> ((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | ((~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(perm(I!1), n)) | (~le(s(n0), perm(I!1)))))))),
% 1.11/0.94 inference(monotonicity,[status(thm)],[108])).
% 1.11/0.94 tff(110,plain,
% 1.11/0.94 (((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | ((~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(s(n0), perm(I!1))) | (~le(perm(I!1), n)))))) <=> ((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | (~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(perm(I!1), n)) | (~le(s(n0), perm(I!1))))))),
% 1.11/0.94 inference(transitivity,[status(thm)],[109, 107])).
% 1.11/0.94 tff(111,plain,
% 1.11/0.94 ((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | ((~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(s(n0), perm(I!1))) | (~le(perm(I!1), n)))))),
% 1.11/0.94 inference(quant_inst,[status(thm)],[])).
% 1.11/0.94 tff(112,plain,
% 1.11/0.94 ((~![I: $i] : ((~le(I, n)) | (~le(s(n0), I)) | (~((~le(s(n0), perm(I))) | (~le(perm(I), n)))))) | (~le(I!1, n)) | (~le(s(n0), I!1)) | (~((~le(perm(I!1), n)) | (~le(s(n0), perm(I!1)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.11/0.94 tff(113,plain,
% 1.11/0.94 (~((~le(perm(I!1), n)) | (~le(s(n0), perm(I!1))))),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[112, 69, 106, 97])).
% 1.11/0.94 tff(114,plain,
% 1.11/0.94 (((~le(perm(I!1), n)) | (~le(s(n0), perm(I!1)))) | le(perm(I!1), n)),
% 1.11/0.94 inference(tautology,[status(thm)],[])).
% 1.11/0.94 tff(115,plain,
% 1.11/0.94 (le(perm(I!1), n)),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[114, 113])).
% 1.11/0.94 tff(116,plain,
% 1.11/0.94 (((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n))) | le(perm(J!0), n)),
% 1.11/0.94 inference(tautology,[status(thm)],[])).
% 1.11/0.94 tff(117,plain,
% 1.11/0.94 (le(perm(J!0), n)),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[116, 103])).
% 1.11/0.94 tff(118,plain,
% 1.11/0.94 (le(s(I!1), J!0) <=> le(s(perm(J!0)), perm(I!1))),
% 1.11/0.94 inference(and_elim,[status(thm)],[68])).
% 1.11/0.94 tff(119,plain,
% 1.11/0.94 ((~le(s(I!1), J!0)) | le(s(perm(J!0)), perm(I!1)) | (~(le(s(I!1), J!0) <=> le(s(perm(J!0)), perm(I!1))))),
% 1.11/0.94 inference(tautology,[status(thm)],[])).
% 1.11/0.94 tff(120,plain,
% 1.11/0.94 ((~le(s(I!1), J!0)) | le(s(perm(J!0)), perm(I!1))),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[119, 118])).
% 1.11/0.94 tff(121,plain,
% 1.11/0.94 (le(s(perm(J!0)), perm(I!1))),
% 1.11/0.94 inference(unit_resolution,[status(thm)],[120, 77])).
% 1.11/0.94 tff(122,plain,
% 1.11/0.94 (^[I: $i, J: $i] : refl(((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J))))) <=> ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J))))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(123,plain,
% 1.11/0.94 (![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J))))) <=> ![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[122])).
% 1.11/0.94 tff(124,plain,
% 1.11/0.94 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)) <=> (~((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n))))), ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) <=> (~(~((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n))))))), rewrite((~(~((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n))))) <=> ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)))), ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) <=> ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n))))), rewrite(((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))) <=> (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J))))), (((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))) <=> (((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n))) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J))))))), rewrite((((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n))) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J))))) <=> ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))), (((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))) <=> ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(125,plain,
% 1.11/0.94 (![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))) <=> ![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[124])).
% 1.11/0.94 tff(126,plain,
% 1.11/0.94 (![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))) <=> ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(127,plain,
% 1.11/0.94 (($false | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))) <=> ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(128,plain,
% 1.11/0.94 ((~$true) <=> $false),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(129,plain,
% 1.11/0.94 (queens_p),
% 1.11/0.94 inference(and_elim,[status(thm)],[7])).
% 1.11/0.94 tff(130,plain,
% 1.11/0.94 (queens_p <=> $true),
% 1.11/0.94 inference(iff_true,[status(thm)],[129])).
% 1.11/0.94 tff(131,plain,
% 1.11/0.94 ((~queens_p) <=> (~$true)),
% 1.11/0.94 inference(monotonicity,[status(thm)],[130])).
% 1.11/0.94 tff(132,plain,
% 1.11/0.94 ((~queens_p) <=> $false),
% 1.11/0.94 inference(transitivity,[status(thm)],[131, 128])).
% 1.11/0.94 tff(133,plain,
% 1.11/0.94 (((~queens_p) | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))) <=> ($false | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))))),
% 1.11/0.94 inference(monotonicity,[status(thm)],[132])).
% 1.11/0.94 tff(134,plain,
% 1.11/0.94 (((~queens_p) | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))) <=> ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(transitivity,[status(thm)],[133, 127])).
% 1.11/0.94 tff(135,plain,
% 1.11/0.94 (((~queens_p) | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))) <=> ((~queens_p) | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(136,plain,
% 1.11/0.94 ((queens_p => ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))) <=> ((~queens_p) | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(137,plain,
% 1.11/0.94 (^[I: $i, J: $i] : trans(monotonicity(trans(monotonicity(rewrite(((le(s(n0), I) & le(I, n)) & le(s(I), J)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J))), ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) <=> ((le(s(n0), I) & le(I, n) & le(s(I), J)) & le(J, n)))), rewrite(((le(s(n0), I) & le(I, n) & le(s(I), J)) & le(J, n)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))), ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) <=> (le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)))), rewrite((((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J)))) & (~(minus(p(I), I) = minus(p(J), J)))) <=> ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))), (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) => (((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J)))) & (~(minus(p(I), I) = minus(p(J), J))))) <=> ((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)) => ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))))), rewrite(((le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n)) => ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))) <=> ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))), (((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) => (((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J)))) & (~(minus(p(I), I) = minus(p(J), J))))) <=> ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(138,plain,
% 1.11/0.94 (![I: $i, J: $i] : ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) => (((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J)))) & (~(minus(p(I), I) = minus(p(J), J))))) <=> ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[137])).
% 1.11/0.94 tff(139,plain,
% 1.11/0.94 ((queens_p => ![I: $i, J: $i] : ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) => (((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J)))) & (~(minus(p(I), I) = minus(p(J), J)))))) <=> (queens_p => ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))))),
% 1.11/0.94 inference(monotonicity,[status(thm)],[138])).
% 1.11/0.94 tff(140,plain,
% 1.11/0.94 ((queens_p => ![I: $i, J: $i] : ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) => (((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J)))) & (~(minus(p(I), I) = minus(p(J), J)))))) <=> ((~queens_p) | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J))))))),
% 1.11/0.94 inference(transitivity,[status(thm)],[139, 136])).
% 1.11/0.94 tff(141,axiom,(queens_p => ![I: $i, J: $i] : ((((le(s(n0), I) & le(I, n)) & le(s(I), J)) & le(J, n)) => (((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J)))) & (~(minus(p(I), I) = minus(p(J), J)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','queens_p')).
% 1.11/0.94 tff(142,plain,
% 1.11/0.94 ((~queens_p) | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.11/0.94 tff(143,plain,
% 1.11/0.94 ((~queens_p) | ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[142, 135])).
% 1.11/0.94 tff(144,plain,
% 1.11/0.94 (![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[143, 134])).
% 1.11/0.94 tff(145,plain,
% 1.11/0.94 (![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[144, 126])).
% 1.11/0.94 tff(146,plain,(
% 1.11/0.94 ![I: $i, J: $i] : ((~(le(s(n0), I) & le(I, n) & le(s(I), J) & le(J, n))) | ((~(p(I) = p(J))) & (~(plus(p(I), I) = plus(p(J), J))) & (~(minus(p(I), I) = minus(p(J), J)))))),
% 1.11/0.94 inference(skolemize,[status(sab)],[145])).
% 1.11/0.94 tff(147,plain,
% 1.11/0.94 (![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[146, 125])).
% 1.11/0.94 tff(148,plain,
% 1.11/0.94 (![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[147, 123])).
% 1.11/0.94 tff(149,plain,
% 1.11/0.94 (((~![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))) | ((~le(s(perm(J!0)), perm(I!1))) | (~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))) <=> ((~![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))) | (~le(s(perm(J!0)), perm(I!1))) | (~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(150,plain,
% 1.11/0.94 (((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(s(perm(J!0)), perm(I!1))) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))))) <=> ((~le(s(perm(J!0)), perm(I!1))) | (~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(151,plain,
% 1.11/0.94 ((~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))) <=> (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(152,plain,
% 1.11/0.94 (((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(s(perm(J!0)), perm(I!1))) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))))) <=> ((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(s(perm(J!0)), perm(I!1))) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))),
% 1.11/0.94 inference(monotonicity,[status(thm)],[151])).
% 1.11/0.94 tff(153,plain,
% 1.11/0.94 (((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(s(perm(J!0)), perm(I!1))) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))))) <=> ((~le(s(perm(J!0)), perm(I!1))) | (~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))),
% 1.11/0.94 inference(transitivity,[status(thm)],[152, 150])).
% 1.11/0.94 tff(154,plain,
% 1.11/0.94 (((~![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))) | ((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(s(perm(J!0)), perm(I!1))) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))) <=> ((~![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))) | ((~le(s(perm(J!0)), perm(I!1))) | (~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))))))),
% 1.11/0.94 inference(monotonicity,[status(thm)],[153])).
% 1.11/0.94 tff(155,plain,
% 1.11/0.94 (((~![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))) | ((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(s(perm(J!0)), perm(I!1))) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))) <=> ((~![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))) | (~le(s(perm(J!0)), perm(I!1))) | (~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))),
% 1.11/0.95 inference(transitivity,[status(thm)],[154, 149])).
% 1.11/0.95 tff(156,plain,
% 1.11/0.95 ((~![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))) | ((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(s(perm(J!0)), perm(I!1))) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(157,plain,
% 1.11/0.95 ((~![I: $i, J: $i] : ((~le(s(n0), I)) | (~le(I, n)) | (~le(s(I), J)) | (~le(J, n)) | (~((minus(p(I), I) = minus(p(J), J)) | (plus(p(I), I) = plus(p(J), J)) | (p(I) = p(J)))))) | (~le(s(perm(J!0)), perm(I!1))) | (~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.11/0.95 tff(158,plain,
% 1.11/0.95 ((~le(s(n0), perm(J!0))) | (~le(perm(J!0), n)) | (~le(perm(I!1), n)) | (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[157, 148, 121])).
% 1.11/0.95 tff(159,plain,
% 1.11/0.95 (~((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1))))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[158, 117, 115, 105])).
% 1.11/0.95 tff(160,plain,
% 1.11/0.95 (((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))) | (~(p(perm(J!0)) = p(perm(I!1))))),
% 1.11/0.95 inference(tautology,[status(thm)],[])).
% 1.11/0.95 tff(161,plain,
% 1.11/0.95 (~(p(perm(J!0)) = p(perm(I!1)))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[160, 159])).
% 1.11/0.95 tff(162,plain,
% 1.11/0.95 (~(q(I!1) = q(J!0))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[161, 23])).
% 1.11/0.95 tff(163,plain,
% 1.11/0.95 (p(perm(J!0)) = q(J!0)),
% 1.11/0.95 inference(symmetry,[status(thm)],[19])).
% 1.11/0.95 tff(164,plain,
% 1.11/0.95 (minus(p(perm(J!0)), J!0) = minus(q(J!0), J!0)),
% 1.11/0.95 inference(monotonicity,[status(thm)],[163])).
% 1.11/0.95 tff(165,plain,
% 1.11/0.95 (minus(p(perm(I!1)), I!1) = minus(q(I!1), I!1)),
% 1.11/0.95 inference(monotonicity,[status(thm)],[14])).
% 1.11/0.95 tff(166,plain,
% 1.11/0.95 ((minus(p(perm(I!1)), I!1) = minus(p(perm(J!0)), J!0)) <=> (minus(q(I!1), I!1) = minus(q(J!0), J!0))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[165, 164])).
% 1.11/0.95 tff(167,plain,
% 1.11/0.95 ((~(minus(p(perm(I!1)), I!1) = minus(p(perm(J!0)), J!0))) <=> (~(minus(q(I!1), I!1) = minus(q(J!0), J!0)))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[166])).
% 1.11/0.95 tff(168,plain,
% 1.11/0.95 (^[I: $i, J: $i, K: $i, L: $i] : refl(((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L))) <=> ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(169,plain,
% 1.11/0.95 (![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L))) <=> ![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[168])).
% 1.11/0.95 tff(170,plain,
% 1.11/0.95 (![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L))) <=> ![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(171,axiom,(![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','minus1')).
% 1.11/0.95 tff(172,plain,
% 1.11/0.95 (![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.11/0.95 tff(173,plain,(
% 1.11/0.95 ![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[172])).
% 1.11/0.95 tff(174,plain,
% 1.11/0.95 (![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[173, 169])).
% 1.11/0.95 tff(175,plain,
% 1.11/0.95 ((~![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L)))) | ((minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0)) <=> (minus(p(perm(I!1)), I!1) = minus(p(perm(J!0)), J!0)))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(176,plain,
% 1.11/0.95 ((minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0)) <=> (minus(p(perm(I!1)), I!1) = minus(p(perm(J!0)), J!0))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[175, 174])).
% 1.11/0.95 tff(177,plain,
% 1.11/0.95 ((minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0)) <=> (minus(I!1, J!0) = minus(p(perm(I!1)), p(perm(J!0))))),
% 1.11/0.95 inference(commutativity,[status(thm)],[])).
% 1.11/0.95 tff(178,plain,
% 1.11/0.95 ((minus(I!1, J!0) = minus(p(perm(I!1)), p(perm(J!0)))) <=> (minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0))),
% 1.11/0.95 inference(symmetry,[status(thm)],[177])).
% 1.11/0.95 tff(179,plain,
% 1.11/0.95 (^[J: $i, I: $i] : refl((minus(I, J) = minus(perm(J), perm(I))) <=> (minus(I, J) = minus(perm(J), perm(I))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(180,plain,
% 1.11/0.95 (![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I))) <=> ![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[179])).
% 1.11/0.95 tff(181,plain,
% 1.11/0.95 (![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I))) <=> ![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(182,axiom,(![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permutation_another_one')).
% 1.11/0.95 tff(183,plain,
% 1.11/0.95 (![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.11/0.95 tff(184,plain,(
% 1.11/0.95 ![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[183])).
% 1.11/0.95 tff(185,plain,
% 1.11/0.95 (![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[184, 180])).
% 1.11/0.95 tff(186,plain,
% 1.11/0.95 ((~![J: $i, I: $i] : (minus(I, J) = minus(perm(J), perm(I)))) | (minus(I!1, J!0) = minus(perm(J!0), perm(I!1)))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(187,plain,
% 1.11/0.95 (minus(I!1, J!0) = minus(perm(J!0), perm(I!1))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[186, 185])).
% 1.11/0.95 tff(188,plain,
% 1.11/0.95 (minus(perm(J!0), perm(I!1)) = minus(I!1, J!0)),
% 1.11/0.95 inference(symmetry,[status(thm)],[187])).
% 1.11/0.95 tff(189,plain,
% 1.11/0.95 (^[I: $i] : refl(((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I))) <=> ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(190,plain,
% 1.11/0.95 (![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I))) <=> ![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[189])).
% 1.11/0.95 tff(191,plain,
% 1.11/0.95 (^[I: $i] : trans(monotonicity(trans(monotonicity(rewrite((le(s(n0), I) & le(I, n)) <=> (~((~le(I, n)) | (~le(s(n0), I))))), ((~(le(s(n0), I) & le(I, n))) <=> (~(~((~le(I, n)) | (~le(s(n0), I))))))), rewrite((~(~((~le(I, n)) | (~le(s(n0), I))))) <=> ((~le(I, n)) | (~le(s(n0), I)))), ((~(le(s(n0), I) & le(I, n))) <=> ((~le(I, n)) | (~le(s(n0), I))))), (((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I))) <=> (((~le(I, n)) | (~le(s(n0), I))) | (perm(I) = minus(s(n), I))))), rewrite((((~le(I, n)) | (~le(s(n0), I))) | (perm(I) = minus(s(n), I))) <=> ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))), (((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I))) <=> ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(192,plain,
% 1.11/0.95 (![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I))) <=> ![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[191])).
% 1.11/0.95 tff(193,plain,
% 1.11/0.95 (![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I))) <=> ![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(194,plain,
% 1.11/0.95 (^[I: $i] : rewrite(((le(s(n0), I) & le(I, n)) => (perm(I) = minus(s(n), I))) <=> ((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(195,plain,
% 1.11/0.95 (![I: $i] : ((le(s(n0), I) & le(I, n)) => (perm(I) = minus(s(n), I))) <=> ![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[194])).
% 1.11/0.95 tff(196,axiom,(![I: $i] : ((le(s(n0), I) & le(I, n)) => (perm(I) = minus(s(n), I)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','permutation')).
% 1.11/0.95 tff(197,plain,
% 1.11/0.95 (![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[196, 195])).
% 1.11/0.95 tff(198,plain,
% 1.11/0.95 (![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[197, 193])).
% 1.11/0.95 tff(199,plain,(
% 1.11/0.95 ![I: $i] : ((~(le(s(n0), I) & le(I, n))) | (perm(I) = minus(s(n), I)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[198])).
% 1.11/0.95 tff(200,plain,
% 1.11/0.95 (![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[199, 192])).
% 1.11/0.95 tff(201,plain,
% 1.11/0.95 (![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[200, 190])).
% 1.11/0.95 tff(202,plain,
% 1.11/0.95 (((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((~le(s(n0), I!1)) | (~le(I!1, n)) | (perm(I!1) = minus(s(n), I!1)))) <=> ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | (~le(s(n0), I!1)) | (~le(I!1, n)) | (perm(I!1) = minus(s(n), I!1)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(203,plain,
% 1.11/0.95 (((perm(I!1) = minus(s(n), I!1)) | (~le(I!1, n)) | (~le(s(n0), I!1))) <=> ((~le(s(n0), I!1)) | (~le(I!1, n)) | (perm(I!1) = minus(s(n), I!1)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(204,plain,
% 1.11/0.95 (((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((perm(I!1) = minus(s(n), I!1)) | (~le(I!1, n)) | (~le(s(n0), I!1)))) <=> ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((~le(s(n0), I!1)) | (~le(I!1, n)) | (perm(I!1) = minus(s(n), I!1))))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[203])).
% 1.11/0.95 tff(205,plain,
% 1.11/0.95 (((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((perm(I!1) = minus(s(n), I!1)) | (~le(I!1, n)) | (~le(s(n0), I!1)))) <=> ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | (~le(s(n0), I!1)) | (~le(I!1, n)) | (perm(I!1) = minus(s(n), I!1)))),
% 1.11/0.95 inference(transitivity,[status(thm)],[204, 202])).
% 1.11/0.95 tff(206,plain,
% 1.11/0.95 ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((perm(I!1) = minus(s(n), I!1)) | (~le(I!1, n)) | (~le(s(n0), I!1)))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(207,plain,
% 1.11/0.95 ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | (~le(s(n0), I!1)) | (~le(I!1, n)) | (perm(I!1) = minus(s(n), I!1))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[206, 205])).
% 1.11/0.95 tff(208,plain,
% 1.11/0.95 (perm(I!1) = minus(s(n), I!1)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[207, 201, 69, 106])).
% 1.11/0.95 tff(209,plain,
% 1.11/0.95 (minus(s(n), I!1) = perm(I!1)),
% 1.11/0.95 inference(symmetry,[status(thm)],[208])).
% 1.11/0.95 tff(210,plain,
% 1.11/0.95 (((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((~le(J!0, n)) | (perm(J!0) = minus(s(n), J!0)) | (~le(s(n0), J!0)))) <=> ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | (~le(J!0, n)) | (perm(J!0) = minus(s(n), J!0)) | (~le(s(n0), J!0)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(211,plain,
% 1.11/0.95 (((perm(J!0) = minus(s(n), J!0)) | (~le(J!0, n)) | (~le(s(n0), J!0))) <=> ((~le(J!0, n)) | (perm(J!0) = minus(s(n), J!0)) | (~le(s(n0), J!0)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(212,plain,
% 1.11/0.95 (((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((perm(J!0) = minus(s(n), J!0)) | (~le(J!0, n)) | (~le(s(n0), J!0)))) <=> ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((~le(J!0, n)) | (perm(J!0) = minus(s(n), J!0)) | (~le(s(n0), J!0))))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[211])).
% 1.11/0.95 tff(213,plain,
% 1.11/0.95 (((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((perm(J!0) = minus(s(n), J!0)) | (~le(J!0, n)) | (~le(s(n0), J!0)))) <=> ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | (~le(J!0, n)) | (perm(J!0) = minus(s(n), J!0)) | (~le(s(n0), J!0)))),
% 1.11/0.95 inference(transitivity,[status(thm)],[212, 210])).
% 1.11/0.95 tff(214,plain,
% 1.11/0.95 ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | ((perm(J!0) = minus(s(n), J!0)) | (~le(J!0, n)) | (~le(s(n0), J!0)))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(215,plain,
% 1.11/0.95 ((~![I: $i] : ((perm(I) = minus(s(n), I)) | (~le(I, n)) | (~le(s(n0), I)))) | (~le(J!0, n)) | (perm(J!0) = minus(s(n), J!0)) | (~le(s(n0), J!0))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.11/0.95 tff(216,plain,
% 1.11/0.95 ((perm(J!0) = minus(s(n), J!0)) | (~le(s(n0), J!0))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[215, 201, 98])).
% 1.11/0.95 tff(217,plain,
% 1.11/0.95 (perm(J!0) = minus(s(n), J!0)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[216, 84])).
% 1.11/0.95 tff(218,plain,
% 1.11/0.95 (minus(s(n), J!0) = perm(J!0)),
% 1.11/0.95 inference(symmetry,[status(thm)],[217])).
% 1.11/0.95 tff(219,plain,
% 1.11/0.95 (minus(minus(s(n), J!0), minus(s(n), I!1)) = minus(perm(J!0), perm(I!1))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[218, 209])).
% 1.11/0.95 tff(220,plain,
% 1.11/0.95 (minus(minus(s(n), J!0), minus(s(n), I!1)) = minus(I!1, J!0)),
% 1.11/0.95 inference(transitivity,[status(thm)],[219, 188])).
% 1.11/0.95 tff(221,plain,
% 1.11/0.95 ((minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1))) <=> (minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[220])).
% 1.11/0.95 tff(222,plain,
% 1.11/0.95 ((minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1))) <=> (minus(I!1, J!0) = minus(p(perm(I!1)), p(perm(J!0))))),
% 1.11/0.95 inference(transitivity,[status(thm)],[221, 177])).
% 1.11/0.95 tff(223,plain,
% 1.11/0.95 ((minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1))) <=> (minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0))),
% 1.11/0.95 inference(transitivity,[status(thm)],[222, 178])).
% 1.11/0.95 tff(224,plain,
% 1.11/0.95 ((~(minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1)))) <=> (~(minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0)))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[223])).
% 1.11/0.95 tff(225,plain,
% 1.11/0.95 (^[I: $i, J: $i, K: $i, L: $i] : refl(((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J))) <=> ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(226,plain,
% 1.11/0.95 (![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J))) <=> ![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[225])).
% 1.11/0.95 tff(227,plain,
% 1.11/0.95 (![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J))) <=> ![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(228,axiom,(![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','plus1')).
% 1.11/0.95 tff(229,plain,
% 1.11/0.95 (![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[228, 227])).
% 1.11/0.95 tff(230,plain,(
% 1.11/0.95 ![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[229])).
% 1.11/0.95 tff(231,plain,
% 1.11/0.95 (![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[230, 226])).
% 1.11/0.95 tff(232,plain,
% 1.11/0.95 ((~![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J)))) | ((plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(J!0)), minus(s(n), J!0))) <=> (minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1))))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(233,plain,
% 1.11/0.95 ((plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(J!0)), minus(s(n), J!0))) <=> (minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1)))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[232, 231])).
% 1.11/0.95 tff(234,plain,
% 1.11/0.95 ((plus(p(perm(J!0)), minus(s(n), J!0)) = plus(p(perm(I!1)), minus(s(n), I!1))) <=> (plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(J!0)), minus(s(n), J!0)))),
% 1.11/0.95 inference(commutativity,[status(thm)],[])).
% 1.11/0.95 tff(235,plain,
% 1.11/0.95 (plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(I!1)), perm(I!1))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[209])).
% 1.11/0.95 tff(236,plain,
% 1.11/0.95 (plus(p(perm(I!1)), perm(I!1)) = plus(p(perm(I!1)), minus(s(n), I!1))),
% 1.11/0.95 inference(symmetry,[status(thm)],[235])).
% 1.11/0.95 tff(237,plain,
% 1.11/0.95 (plus(p(perm(J!0)), minus(s(n), J!0)) = plus(p(perm(J!0)), perm(J!0))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[218])).
% 1.11/0.95 tff(238,plain,
% 1.11/0.95 (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(J!0)), minus(s(n), J!0))),
% 1.11/0.95 inference(symmetry,[status(thm)],[237])).
% 1.11/0.95 tff(239,plain,
% 1.11/0.95 ((plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) <=> (plus(p(perm(J!0)), minus(s(n), J!0)) = plus(p(perm(I!1)), minus(s(n), I!1)))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[238, 236])).
% 1.11/0.95 tff(240,plain,
% 1.11/0.95 ((plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) <=> (plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(J!0)), minus(s(n), J!0)))),
% 1.11/0.95 inference(transitivity,[status(thm)],[239, 234])).
% 1.11/0.95 tff(241,plain,
% 1.11/0.95 ((~(plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1)))) <=> (~(plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(J!0)), minus(s(n), J!0))))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[240])).
% 1.11/0.95 tff(242,plain,
% 1.11/0.95 (((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))) | (~(plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))))),
% 1.11/0.95 inference(tautology,[status(thm)],[])).
% 1.11/0.95 tff(243,plain,
% 1.11/0.95 (~(plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1)))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[242, 159])).
% 1.11/0.95 tff(244,plain,
% 1.11/0.95 (~(plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(J!0)), minus(s(n), J!0)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[243, 241])).
% 1.11/0.95 tff(245,plain,
% 1.11/0.95 ((~((plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(J!0)), minus(s(n), J!0))) <=> (minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1))))) | (plus(p(perm(I!1)), minus(s(n), I!1)) = plus(p(perm(J!0)), minus(s(n), J!0))) | (~(minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1))))),
% 1.11/0.95 inference(tautology,[status(thm)],[])).
% 1.11/0.95 tff(246,plain,
% 1.11/0.95 (~(minus(p(perm(I!1)), p(perm(J!0))) = minus(minus(s(n), J!0), minus(s(n), I!1)))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[245, 244, 233])).
% 1.11/0.95 tff(247,plain,
% 1.11/0.95 (~(minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[246, 224])).
% 1.11/0.95 tff(248,plain,
% 1.11/0.95 ((~((minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0)) <=> (minus(p(perm(I!1)), I!1) = minus(p(perm(J!0)), J!0)))) | (minus(p(perm(I!1)), p(perm(J!0))) = minus(I!1, J!0)) | (~(minus(p(perm(I!1)), I!1) = minus(p(perm(J!0)), J!0)))),
% 1.11/0.95 inference(tautology,[status(thm)],[])).
% 1.11/0.95 tff(249,plain,
% 1.11/0.95 (~(minus(p(perm(I!1)), I!1) = minus(p(perm(J!0)), J!0))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[248, 247, 176])).
% 1.11/0.95 tff(250,plain,
% 1.11/0.95 (~(minus(q(I!1), I!1) = minus(q(J!0), J!0))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[249, 167])).
% 1.11/0.95 tff(251,plain,
% 1.11/0.95 ((~(~((q(I!1) = q(J!0)) | (plus(q(I!1), I!1) = plus(q(J!0), J!0)) | (minus(q(I!1), I!1) = minus(q(J!0), J!0))))) <=> ((q(I!1) = q(J!0)) | (plus(q(I!1), I!1) = plus(q(J!0), J!0)) | (minus(q(I!1), I!1) = minus(q(J!0), J!0)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(252,plain,
% 1.11/0.95 (((~(q(I!1) = q(J!0))) & (~(plus(q(I!1), I!1) = plus(q(J!0), J!0))) & (~(minus(q(I!1), I!1) = minus(q(J!0), J!0)))) <=> (~((q(I!1) = q(J!0)) | (plus(q(I!1), I!1) = plus(q(J!0), J!0)) | (minus(q(I!1), I!1) = minus(q(J!0), J!0))))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(253,plain,
% 1.11/0.95 ((~((~(q(I!1) = q(J!0))) & (~(plus(q(I!1), I!1) = plus(q(J!0), J!0))) & (~(minus(q(I!1), I!1) = minus(q(J!0), J!0))))) <=> (~(~((q(I!1) = q(J!0)) | (plus(q(I!1), I!1) = plus(q(J!0), J!0)) | (minus(q(I!1), I!1) = minus(q(J!0), J!0)))))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[252])).
% 1.11/0.95 tff(254,plain,
% 1.11/0.95 ((~((~(q(I!1) = q(J!0))) & (~(plus(q(I!1), I!1) = plus(q(J!0), J!0))) & (~(minus(q(I!1), I!1) = minus(q(J!0), J!0))))) <=> ((q(I!1) = q(J!0)) | (plus(q(I!1), I!1) = plus(q(J!0), J!0)) | (minus(q(I!1), I!1) = minus(q(J!0), J!0)))),
% 1.11/0.95 inference(transitivity,[status(thm)],[253, 251])).
% 1.11/0.95 tff(255,plain,
% 1.11/0.95 (~((~(q(I!1) = q(J!0))) & (~(plus(q(I!1), I!1) = plus(q(J!0), J!0))) & (~(minus(q(I!1), I!1) = minus(q(J!0), J!0))))),
% 1.11/0.95 inference(or_elim,[status(thm)],[67])).
% 1.11/0.95 tff(256,plain,
% 1.11/0.95 ((q(I!1) = q(J!0)) | (plus(q(I!1), I!1) = plus(q(J!0), J!0)) | (minus(q(I!1), I!1) = minus(q(J!0), J!0))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.11/0.95 tff(257,plain,
% 1.11/0.95 (plus(q(I!1), I!1) = plus(q(J!0), J!0)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[256, 250, 162])).
% 1.11/0.95 tff(258,plain,
% 1.11/0.95 (plus(q(J!0), J!0) = plus(q(I!1), I!1)),
% 1.11/0.95 inference(symmetry,[status(thm)],[257])).
% 1.11/0.95 tff(259,plain,
% 1.11/0.95 (plus(p(perm(J!0)), J!0) = plus(q(J!0), J!0)),
% 1.11/0.95 inference(monotonicity,[status(thm)],[163])).
% 1.11/0.95 tff(260,plain,
% 1.11/0.95 (plus(p(perm(J!0)), J!0) = plus(p(perm(I!1)), I!1)),
% 1.11/0.95 inference(transitivity,[status(thm)],[259, 258, 16])).
% 1.11/0.95 tff(261,plain,
% 1.11/0.95 ((~![I: $i, J: $i, K: $i, L: $i] : ((plus(I, J) = plus(K, L)) <=> (minus(I, K) = minus(L, J)))) | ((plus(p(perm(J!0)), J!0) = plus(p(perm(I!1)), I!1)) <=> (minus(p(perm(J!0)), p(perm(I!1))) = minus(I!1, J!0)))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(262,plain,
% 1.11/0.95 ((plus(p(perm(J!0)), J!0) = plus(p(perm(I!1)), I!1)) <=> (minus(p(perm(J!0)), p(perm(I!1))) = minus(I!1, J!0))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[261, 231])).
% 1.11/0.95 tff(263,plain,
% 1.11/0.95 ((minus(p(perm(J!0)), p(perm(I!1))) = minus(minus(s(n), J!0), minus(s(n), I!1))) <=> (minus(p(perm(J!0)), p(perm(I!1))) = minus(I!1, J!0))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[220])).
% 1.11/0.95 tff(264,plain,
% 1.11/0.95 ((~(minus(p(perm(J!0)), p(perm(I!1))) = minus(minus(s(n), J!0), minus(s(n), I!1)))) <=> (~(minus(p(perm(J!0)), p(perm(I!1))) = minus(I!1, J!0)))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[263])).
% 1.11/0.95 tff(265,plain,
% 1.11/0.95 ((~![I: $i, J: $i, K: $i, L: $i] : ((minus(I, J) = minus(K, L)) <=> (minus(I, K) = minus(J, L)))) | ((minus(p(perm(J!0)), minus(s(n), J!0)) = minus(p(perm(I!1)), minus(s(n), I!1))) <=> (minus(p(perm(J!0)), p(perm(I!1))) = minus(minus(s(n), J!0), minus(s(n), I!1))))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(266,plain,
% 1.11/0.95 ((minus(p(perm(J!0)), minus(s(n), J!0)) = minus(p(perm(I!1)), minus(s(n), I!1))) <=> (minus(p(perm(J!0)), p(perm(I!1))) = minus(minus(s(n), J!0), minus(s(n), I!1)))),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[265, 174])).
% 1.11/0.95 tff(267,plain,
% 1.11/0.95 (minus(p(perm(I!1)), minus(s(n), I!1)) = minus(p(perm(I!1)), perm(I!1))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[209])).
% 1.11/0.95 tff(268,plain,
% 1.11/0.95 (minus(p(perm(I!1)), perm(I!1)) = minus(p(perm(I!1)), minus(s(n), I!1))),
% 1.11/0.96 inference(symmetry,[status(thm)],[267])).
% 1.11/0.96 tff(269,plain,
% 1.11/0.96 (minus(p(perm(J!0)), minus(s(n), J!0)) = minus(p(perm(J!0)), perm(J!0))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[218])).
% 1.11/0.96 tff(270,plain,
% 1.11/0.96 (minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(J!0)), minus(s(n), J!0))),
% 1.11/0.96 inference(symmetry,[status(thm)],[269])).
% 1.11/0.96 tff(271,plain,
% 1.11/0.96 ((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) <=> (minus(p(perm(J!0)), minus(s(n), J!0)) = minus(p(perm(I!1)), minus(s(n), I!1)))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[270, 268])).
% 1.11/0.96 tff(272,plain,
% 1.11/0.96 ((~(minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1)))) <=> (~(minus(p(perm(J!0)), minus(s(n), J!0)) = minus(p(perm(I!1)), minus(s(n), I!1))))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[271])).
% 1.11/0.96 tff(273,plain,
% 1.11/0.96 (((minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))) | (plus(p(perm(J!0)), perm(J!0)) = plus(p(perm(I!1)), perm(I!1))) | (p(perm(J!0)) = p(perm(I!1)))) | (~(minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1))))),
% 1.11/0.96 inference(tautology,[status(thm)],[])).
% 1.11/0.96 tff(274,plain,
% 1.11/0.96 (~(minus(p(perm(J!0)), perm(J!0)) = minus(p(perm(I!1)), perm(I!1)))),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[273, 159])).
% 1.11/0.96 tff(275,plain,
% 1.11/0.96 (~(minus(p(perm(J!0)), minus(s(n), J!0)) = minus(p(perm(I!1)), minus(s(n), I!1)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[274, 272])).
% 1.11/0.96 tff(276,plain,
% 1.11/0.96 ((~((minus(p(perm(J!0)), minus(s(n), J!0)) = minus(p(perm(I!1)), minus(s(n), I!1))) <=> (minus(p(perm(J!0)), p(perm(I!1))) = minus(minus(s(n), J!0), minus(s(n), I!1))))) | (minus(p(perm(J!0)), minus(s(n), J!0)) = minus(p(perm(I!1)), minus(s(n), I!1))) | (~(minus(p(perm(J!0)), p(perm(I!1))) = minus(minus(s(n), J!0), minus(s(n), I!1))))),
% 1.11/0.96 inference(tautology,[status(thm)],[])).
% 1.11/0.96 tff(277,plain,
% 1.11/0.96 (~(minus(p(perm(J!0)), p(perm(I!1))) = minus(minus(s(n), J!0), minus(s(n), I!1)))),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[276, 275, 266])).
% 1.11/0.96 tff(278,plain,
% 1.11/0.96 (~(minus(p(perm(J!0)), p(perm(I!1))) = minus(I!1, J!0))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[277, 264])).
% 1.11/0.96 tff(279,plain,
% 1.11/0.96 ((~((plus(p(perm(J!0)), J!0) = plus(p(perm(I!1)), I!1)) <=> (minus(p(perm(J!0)), p(perm(I!1))) = minus(I!1, J!0)))) | (~(plus(p(perm(J!0)), J!0) = plus(p(perm(I!1)), I!1))) | (minus(p(perm(J!0)), p(perm(I!1))) = minus(I!1, J!0))),
% 1.11/0.96 inference(tautology,[status(thm)],[])).
% 1.11/0.96 tff(280,plain,
% 1.11/0.96 ((~((plus(p(perm(J!0)), J!0) = plus(p(perm(I!1)), I!1)) <=> (minus(p(perm(J!0)), p(perm(I!1))) = minus(I!1, J!0)))) | (~(plus(p(perm(J!0)), J!0) = plus(p(perm(I!1)), I!1)))),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[279, 278])).
% 1.11/0.96 tff(281,plain,
% 1.11/0.96 (~(plus(p(perm(J!0)), J!0) = plus(p(perm(I!1)), I!1))),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[280, 262])).
% 1.11/0.96 tff(282,plain,
% 1.11/0.96 ($false),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[281, 260])).
% 1.11/0.96 % SZS output end Proof
%------------------------------------------------------------------------------