TSTP Solution File: PUZ133_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ133_2 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : PUZ133_2 : TPTP v8.1.0. Released v5.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.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 19:07:35 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.
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(q_type, type, (
% 0.21/0.41 q: $int > $int)).
% 0.21/0.41 tff(tptp_fun_I_1_type, type, (
% 0.21/0.41 tptp_fun_I_1: $int)).
% 0.21/0.41 tff(tptp_fun_J_0_type, type, (
% 0.21/0.41 tptp_fun_J_0: $int)).
% 0.21/0.41 tff(p_type, type, (
% 0.21/0.41 p: $int > $int)).
% 0.21/0.41 tff(perm_type, type, (
% 0.21/0.41 perm: $int > $int)).
% 0.21/0.41 tff(queens_p_type, type, (
% 0.21/0.41 queens_p: $o)).
% 0.21/0.41 tff(queens_q_type, type, (
% 0.21/0.41 queens_q: $o)).
% 0.21/0.41 tff(n_type, type, (
% 0.21/0.41 n: $int)).
% 0.21/0.41 tff(1,assumption,($sum(q(J!0), $product(-1, q(I!1))) = 0), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 ((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) | $lesseq($sum(q(J!0), $product(-1, q(I!1))), 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 ($lesseq($sum(q(J!0), $product(-1, q(I!1))), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 ((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) | $greatereq($sum(q(J!0), $product(-1, q(I!1))), 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 ($greatereq($sum(q(J!0), $product(-1, q(I!1))), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.21/0.41 tff(6,assumption,($greatereq($sum(q(J!0), $product(-1, q(I!1))), 0)), introduced(assumption)).
% 0.21/0.41 tff(7,assumption,(~$greatereq($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))), 0)), introduced(assumption)).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (^[I: $int] : refl(($sum(p(perm(I)), $product(-1, q(I))) = 0) <=> ($sum(p(perm(I)), $product(-1, q(I))) = 0))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0) <=> ![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (^[I: $int] : trans(monotonicity(rewrite($sum(q(I), $product(-1, p(perm(I)))) = $sum($product(-1, p(perm(I))), q(I))), (($sum(q(I), $product(-1, p(perm(I)))) = 0) <=> ($sum($product(-1, p(perm(I))), q(I)) = 0))), rewrite(($sum($product(-1, p(perm(I))), q(I)) = 0) <=> ($sum(p(perm(I)), $product(-1, q(I))) = 0)), (($sum(q(I), $product(-1, p(perm(I)))) = 0) <=> ($sum(p(perm(I)), $product(-1, q(I))) = 0)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (![I: $int] : ($sum(q(I), $product(-1, p(perm(I)))) = 0) <=> ![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (^[I: $int] : rewrite((q(I) = p(perm(I))) <=> ($sum(q(I), $product(-1, p(perm(I)))) = 0))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (![I: $int] : (q(I) = p(perm(I))) <=> ![I: $int] : ($sum(q(I), $product(-1, p(perm(I)))) = 0)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (![I: $int] : (q(I) = p(perm(I))) <=> ![I: $int] : (q(I) = p(perm(I)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 ((~((queens_p & ![I: $int] : (q(I) = p(perm(I)))) => queens_q)) <=> (~(queens_q | (~(queens_p & ![I: $int] : (q(I) = p(perm(I)))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(16,axiom,(~((queens_p & ![I: $int] : (q(I) = p(perm(I)))) => queens_q)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','queens_sym')).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (~(queens_q | (~(queens_p & ![I: $int] : (q(I) = p(perm(I))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (queens_p & ![I: $int] : (q(I) = p(perm(I)))),
% 0.21/0.41 inference(or_elim,[status(thm)],[17])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (![I: $int] : (q(I) = p(perm(I)))),
% 0.21/0.41 inference(and_elim,[status(thm)],[18])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (![I: $int] : (q(I) = p(perm(I)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (![I: $int] : ($sum(q(I), $product(-1, p(perm(I)))) = 0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.21/0.41 tff(23,plain,(
% 0.21/0.41 ![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)),
% 0.21/0.41 inference(skolemize,[status(sab)],[22])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 9])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0)) <=> ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (($sum($product(-1, q(J!0)), p(perm(J!0))) = 0) <=> ($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 ($sum(p(perm(J!0)), $product(-1, q(J!0))) = $sum($product(-1, q(J!0)), p(perm(J!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (($sum(p(perm(J!0)), $product(-1, q(J!0))) = 0) <=> ($sum($product(-1, q(J!0)), p(perm(J!0))) = 0)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (($sum(p(perm(J!0)), $product(-1, q(J!0))) = 0) <=> ($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0)),
% 0.21/0.41 inference(transitivity,[status(thm)],[28, 26])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(p(perm(J!0)), $product(-1, q(J!0))) = 0)) <=> ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(p(perm(J!0)), $product(-1, q(J!0))) = 0)) <=> ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0))),
% 0.21/0.41 inference(transitivity,[status(thm)],[30, 25])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(p(perm(J!0)), $product(-1, q(J!0))) = 0)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[33, 24])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((~($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0)) | $lesseq($sum(q(J!0), $product(-1, p(perm(J!0)))), 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 ($lesseq($sum(q(J!0), $product(-1, p(perm(J!0)))), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0)) <=> ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (($sum($product(-1, q(I!1)), p(perm(I!1))) = 0) <=> ($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ($sum(p(perm(I!1)), $product(-1, q(I!1))) = $sum($product(-1, q(I!1)), p(perm(I!1)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (($sum(p(perm(I!1)), $product(-1, q(I!1))) = 0) <=> ($sum($product(-1, q(I!1)), p(perm(I!1))) = 0)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (($sum(p(perm(I!1)), $product(-1, q(I!1))) = 0) <=> ($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0)),
% 0.21/0.41 inference(transitivity,[status(thm)],[40, 38])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(p(perm(I!1)), $product(-1, q(I!1))) = 0)) <=> ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(p(perm(I!1)), $product(-1, q(I!1))) = 0)) <=> ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0))),
% 0.21/0.41 inference(transitivity,[status(thm)],[42, 37])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(p(perm(I!1)), $product(-1, q(I!1))) = 0)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 ((~![I: $int] : ($sum(p(perm(I)), $product(-1, q(I))) = 0)) | ($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 ($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[45, 24])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 ((~($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0)) | $greatereq($sum(q(I!1), $product(-1, p(perm(I!1)))), 0)),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 ($greatereq($sum(q(I!1), $product(-1, p(perm(I!1)))), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(theory_lemma,[status(thm)],[48, 36, 7, 6])).
% 0.21/0.41 tff(50,plain,($greatereq($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))), 0) | (~$greatereq($sum(q(J!0), $product(-1, q(I!1))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 ($greatereq($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))), 0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[50, 5])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (^[I: $int] : refl(((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0))))) <=> ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0))))) <=> ![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (^[I: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0)) <=> (~((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0))))), ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) <=> (~(~((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0))))))), rewrite((~(~((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0))))) <=> ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)))), ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) <=> ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0))))), rewrite(($greatereq(perm(I), 1) & $greatereq($sum(n, $product(-1, perm(I))), 0)) <=> (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0))))), (((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) | ($greatereq(perm(I), 1) & $greatereq($sum(n, $product(-1, perm(I))), 0))) <=> (((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0))) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0))))))), rewrite((((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0))) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0))))) <=> ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))), (((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) | ($greatereq(perm(I), 1) & $greatereq($sum(n, $product(-1, perm(I))), 0))) <=> ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (![I: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) | ($greatereq(perm(I), 1) & $greatereq($sum(n, $product(-1, perm(I))), 0))) <=> ![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (^[I: $int] : rewrite(((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0))) | ($greatereq(perm(I), 1) & $lesseq($sum(perm(I), $product(-1, n)), 0))) <=> ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) | ($greatereq(perm(I), 1) & $greatereq($sum(n, $product(-1, perm(I))), 0))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (![I: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0))) | ($greatereq(perm(I), 1) & $lesseq($sum(perm(I), $product(-1, n)), 0))) <=> ![I: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) | ($greatereq(perm(I), 1) & $greatereq($sum(n, $product(-1, perm(I))), 0)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (^[I: $int] : rewrite(((~($lesseq(1, I) & $lesseq(I, n))) | ($lesseq(1, perm(I)) & $lesseq(perm(I), n))) <=> ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0))) | ($greatereq(perm(I), 1) & $lesseq($sum(perm(I), $product(-1, n)), 0))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![I: $int] : ((~($lesseq(1, I) & $lesseq(I, n))) | ($lesseq(1, perm(I)) & $lesseq(perm(I), n))) <=> ![I: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0))) | ($greatereq(perm(I), 1) & $lesseq($sum(perm(I), $product(-1, n)), 0)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![I: $int] : ((~($lesseq(1, I) & $lesseq(I, n))) | ($lesseq(1, perm(I)) & $lesseq(perm(I), n))) <=> ![I: $int] : ((~($lesseq(1, I) & $lesseq(I, n))) | ($lesseq(1, perm(I)) & $lesseq(perm(I), n)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (^[I: $int] : rewrite((($lesseq(1, I) & $lesseq(I, n)) => ($lesseq(1, perm(I)) & $lesseq(perm(I), n))) <=> ((~($lesseq(1, I) & $lesseq(I, n))) | ($lesseq(1, perm(I)) & $lesseq(perm(I), n))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![I: $int] : (($lesseq(1, I) & $lesseq(I, n)) => ($lesseq(1, perm(I)) & $lesseq(perm(I), n))) <=> ![I: $int] : ((~($lesseq(1, I) & $lesseq(I, n))) | ($lesseq(1, perm(I)) & $lesseq(perm(I), n)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.41 tff(63,axiom,(![I: $int] : (($lesseq(1, I) & $lesseq(I, n)) => ($lesseq(1, perm(I)) & $lesseq(perm(I), n)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permutation_range')).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (![I: $int] : ((~($lesseq(1, I) & $lesseq(I, n))) | ($lesseq(1, perm(I)) & $lesseq(perm(I), n)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![I: $int] : ((~($lesseq(1, I) & $lesseq(I, n))) | ($lesseq(1, perm(I)) & $lesseq(perm(I), n)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![I: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0))) | ($greatereq(perm(I), 1) & $lesseq($sum(perm(I), $product(-1, n)), 0)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[65, 59])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (![I: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) | ($greatereq(perm(I), 1) & $greatereq($sum(n, $product(-1, perm(I))), 0)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 57])).
% 0.21/0.41 tff(68,plain,(
% 0.21/0.41 ![I: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0))) | ($greatereq(perm(I), 1) & $greatereq($sum(n, $product(-1, perm(I))), 0)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[67])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[68, 55])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[69, 53])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 ((~((~($greatereq(I!1, 1) & $greatereq($sum(n, $product(-1, I!1)), 0) & $lesseq($sum(I!1, $product(-1, J!0)), -1) & $greatereq($sum(n, $product(-1, J!0)), 0) & ($lesseq($sum(I!1, $product(-1, J!0)), -1) <=> $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)))) | ((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) & (~($sum(I!1, $sum($product(-1, J!0), $sum($product(-1, q(J!0)), q(I!1)))) = 0)) & (~($sum(I!1, $sum($product(-1, J!0), $sum(q(J!0), $product(-1, q(I!1))))) = 0))))) <=> (~((~($greatereq(I!1, 1) & $greatereq($sum(n, $product(-1, I!1)), 0) & $greatereq($sum(J!0, $product(-1, I!1)), 1) & $greatereq($sum(n, $product(-1, J!0)), 0) & ($greatereq($sum(J!0, $product(-1, I!1)), 1) <=> $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)))) | ((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 ((~![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(J), $product(-1, q(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, q(J)), q(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(q(J), $product(-1, q(I))))) = 0))))) <=> (~![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(J), $product(-1, q(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, q(J)), q(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(q(J), $product(-1, q(I))))) = 0)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 ((~![I: $int, J: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $lesseq($sum(J, $product(-1, n)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(I), $product(-1, q(J))) = 0)) & (~($sum(q(I), $sum(I, $sum($product(-1, q(J)), $product(-1, J)))) = 0)) & (~($sum(q(I), $sum($product(-1, I), $sum($product(-1, q(J)), J))) = 0))))) <=> (~![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(J), $product(-1, q(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, q(J)), q(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(q(J), $product(-1, q(I))))) = 0)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 ((~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))) <=> (~![I: $int, J: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $lesseq($sum(J, $product(-1, n)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(I), $product(-1, q(J))) = 0)) & (~($sum(q(I), $sum(I, $sum($product(-1, q(J)), $product(-1, J)))) = 0)) & (~($sum(q(I), $sum($product(-1, I), $sum($product(-1, q(J)), J))) = 0)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))) <=> (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (($false | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))) <=> (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (~queens_q),
% 0.21/0.41 inference(or_elim,[status(thm)],[17])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (queens_q <=> $false),
% 0.21/0.41 inference(iff_false,[status(thm)],[77])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 ((queens_q | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))) <=> ($false | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[78, 75])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ((queens_q | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))) <=> (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[79, 76])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 ((queens_q | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))) <=> (queens_q | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 ((![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))) => queens_q) <=> (queens_q | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 (^[I: $int, J: $int] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite($lesseq($sum(1, I), J) <=> $lesseq(I, $sum(-1, J))), ((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) <=> (($lesseq(1, I) & $lesseq(I, n)) & $lesseq(I, $sum(-1, J))))), rewrite((($lesseq(1, I) & $lesseq(I, n)) & $lesseq(I, $sum(-1, J))) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)))), ((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J))))), (((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) <=> (($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J))) & $lesseq(J, n)))), rewrite((($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J))) & $lesseq(J, n)) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))), (((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n)))), rewrite(($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I))) <=> ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I))))), ((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) & ($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I)))) <=> (($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n)) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I))))))), rewrite((($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n)) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I))))) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))), ((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) & ($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I)))) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I))))))), trans(monotonicity(rewrite((~($difference(q(I), I) = $difference(q(J), J))) <=> (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))), ((((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($difference(q(I), I) = $difference(q(J), J)))) <=> (((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))), rewrite((((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))) <=> ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))), ((((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($difference(q(I), I) = $difference(q(J), J)))) <=> ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))), (((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) & ($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($difference(q(I), I) = $difference(q(J), J))))) <=> (($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I))))) => ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))), rewrite((($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I))))) => ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))) <=> ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))), (((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) & ($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($difference(q(I), I) = $difference(q(J), J))))) <=> ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (![I: $int, J: $int] : ((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) & ($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($difference(q(I), I) = $difference(q(J), J))))) <=> ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ((![I: $int, J: $int] : ((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) & ($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($difference(q(I), I) = $difference(q(J), J))))) => queens_q) <=> (![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))) => queens_q)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ((![I: $int, J: $int] : ((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) & ($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($difference(q(I), I) = $difference(q(J), J))))) => queens_q) <=> (queens_q | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[85, 82])).
% 0.21/0.42 tff(87,axiom,(![I: $int, J: $int] : ((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) & ($lesseq($sum(1, I), J) <=> $lesseq($sum(1, perm(J)), perm(I)))) => (((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J)))) & (~($difference(q(I), I) = $difference(q(J), J))))) => queens_q), file('/export/starexec/sandbox/benchmark/theBenchmark.p','queens_q')).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (queens_q | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (queens_q | (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[89, 80])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[90, 75])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[91, 75])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (~![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n) & ($lesseq(I, $sum(-1, J)) <=> $lesseq(perm(J), $sum(-1, perm(I)))))) | ((~(q(I) = q(J))) & (~($sum(q(I), I) = $sum(q(J), J))) & (~($sum(q(I), $product(-1, I)) = $sum(q(J), $product(-1, J))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[92, 75])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (~![I: $int, J: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $lesseq($sum(J, $product(-1, n)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(I), $product(-1, q(J))) = 0)) & (~($sum(q(I), $sum(I, $sum($product(-1, q(J)), $product(-1, J)))) = 0)) & (~($sum(q(I), $sum($product(-1, I), $sum($product(-1, q(J)), J))) = 0))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[93, 74])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (~![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(J), $product(-1, q(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, q(J)), q(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(q(J), $product(-1, q(I))))) = 0))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[94, 73])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (~![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(J), $product(-1, q(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, q(J)), q(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(q(J), $product(-1, q(I))))) = 0))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[95, 72])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (~![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0) & ($lesseq($sum(I, $product(-1, J)), -1) <=> $lesseq($sum(perm(J), $product(-1, perm(I))), -1)))) | ((~($sum(q(J), $product(-1, q(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, q(J)), q(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(q(J), $product(-1, q(I))))) = 0))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[96, 72])).
% 0.21/0.42 tff(98,plain,(
% 0.21/0.42 ~((~($greatereq(I!1, 1) & $greatereq($sum(n, $product(-1, I!1)), 0) & $lesseq($sum(I!1, $product(-1, J!0)), -1) & $greatereq($sum(n, $product(-1, J!0)), 0) & ($lesseq($sum(I!1, $product(-1, J!0)), -1) <=> $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)))) | ((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) & (~($sum(I!1, $sum($product(-1, J!0), $sum($product(-1, q(J!0)), q(I!1)))) = 0)) & (~($sum(I!1, $sum($product(-1, J!0), $sum(q(J!0), $product(-1, q(I!1))))) = 0))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[97])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (~((~($greatereq(I!1, 1) & $greatereq($sum(n, $product(-1, I!1)), 0) & $greatereq($sum(J!0, $product(-1, I!1)), 1) & $greatereq($sum(n, $product(-1, J!0)), 0) & ($greatereq($sum(J!0, $product(-1, I!1)), 1) <=> $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)))) | ((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[98, 71])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ($greatereq(I!1, 1) & $greatereq($sum(n, $product(-1, I!1)), 0) & $greatereq($sum(J!0, $product(-1, I!1)), 1) & $greatereq($sum(n, $product(-1, J!0)), 0) & ($greatereq($sum(J!0, $product(-1, I!1)), 1) <=> $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1))),
% 0.21/0.42 inference(or_elim,[status(thm)],[99])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ($greatereq($sum(n, $product(-1, I!1)), 0)),
% 0.21/0.42 inference(and_elim,[status(thm)],[100])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 ($greatereq(I!1, 1)),
% 0.21/0.42 inference(and_elim,[status(thm)],[100])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (((~![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))) | ((~$greatereq($sum(n, $product(-1, I!1)), 0)) | (~$greatereq(I!1, 1)) | (~((~$greatereq(perm(I!1), 1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)))))) <=> ((~![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))) | (~$greatereq($sum(n, $product(-1, I!1)), 0)) | (~$greatereq(I!1, 1)) | (~((~$greatereq(perm(I!1), 1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 ((~![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))) | ((~$greatereq($sum(n, $product(-1, I!1)), 0)) | (~$greatereq(I!1, 1)) | (~((~$greatereq(perm(I!1), 1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 ((~![I: $int] : ((~$greatereq($sum(n, $product(-1, I)), 0)) | (~$greatereq(I, 1)) | (~((~$greatereq(perm(I), 1)) | (~$greatereq($sum(n, $product(-1, perm(I))), 0)))))) | (~$greatereq($sum(n, $product(-1, I!1)), 0)) | (~$greatereq(I!1, 1)) | (~((~$greatereq(perm(I!1), 1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (~((~$greatereq(perm(I!1), 1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[105, 102, 101, 70])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (((~$greatereq(perm(I!1), 1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0))) | $greatereq($sum(n, $product(-1, perm(I!1))), 0)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 ($greatereq($sum(n, $product(-1, perm(I!1))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (^[I: $int] : refl(($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1) <=> ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1) <=> ![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)),
% 0.21/0.42 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (^[I: $int] : trans(monotonicity(rewrite($sum(perm(I), $sum($product(-1, n), I)) = $sum($product(-1, n), $sum(perm(I), I))), (($sum(perm(I), $sum($product(-1, n), I)) = 1) <=> ($sum($product(-1, n), $sum(perm(I), I)) = 1))), rewrite(($sum($product(-1, n), $sum(perm(I), I)) = 1) <=> ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)), (($sum(perm(I), $sum($product(-1, n), I)) = 1) <=> ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![I: $int] : ($sum(perm(I), $sum($product(-1, n), I)) = 1) <=> ![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)),
% 0.21/0.42 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (^[I: $int] : rewrite((perm(I) = $sum(1, $sum(n, $product(-1, I)))) <=> ($sum(perm(I), $sum($product(-1, n), I)) = 1))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 (![I: $int] : (perm(I) = $sum(1, $sum(n, $product(-1, I)))) <=> ![I: $int] : ($sum(perm(I), $sum($product(-1, n), I)) = 1)),
% 0.21/0.42 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (![I: $int] : (perm(I) = $sum(1, $sum(n, $product(-1, I)))) <=> ![I: $int] : (perm(I) = $sum(1, $sum(n, $product(-1, I))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (^[I: $int] : rewrite((perm(I) = $difference($sum(1, n), I)) <=> (perm(I) = $sum(1, $sum(n, $product(-1, I)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (![I: $int] : (perm(I) = $difference($sum(1, n), I)) <=> ![I: $int] : (perm(I) = $sum(1, $sum(n, $product(-1, I))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.42 tff(118,axiom,(![I: $int] : (perm(I) = $difference($sum(1, n), I))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permutation')).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (![I: $int] : (perm(I) = $sum(1, $sum(n, $product(-1, I))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (![I: $int] : (perm(I) = $sum(1, $sum(n, $product(-1, I))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (![I: $int] : ($sum(perm(I), $sum($product(-1, n), I)) = 1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[120, 114])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[121, 112])).
% 0.21/0.42 tff(123,plain,(
% 0.21/0.42 ![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)),
% 0.21/0.42 inference(skolemize,[status(sab)],[122])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[123, 110])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (((~![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)) | ($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1)) <=> ((~![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)) | ($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (($sum(n, $sum($product(-1, perm(J!0)), $product(-1, J!0))) = -1) <=> ($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(127,plain,
% 0.21/0.42 (((~![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)) | ($sum(n, $sum($product(-1, perm(J!0)), $product(-1, J!0))) = -1)) <=> ((~![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)) | ($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (((~![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)) | ($sum(n, $sum($product(-1, perm(J!0)), $product(-1, J!0))) = -1)) <=> ((~![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)) | ($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1))),
% 0.21/0.42 inference(transitivity,[status(thm)],[127, 125])).
% 0.21/0.42 tff(129,plain,
% 0.21/0.42 ((~![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)) | ($sum(n, $sum($product(-1, perm(J!0)), $product(-1, J!0))) = -1)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(130,plain,
% 0.21/0.42 ((~![I: $int] : ($sum(n, $sum($product(-1, perm(I)), $product(-1, I))) = -1)) | ($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 ($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[130, 124])).
% 0.21/0.42 tff(132,plain,
% 0.21/0.42 ((~($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1)) | $greatereq($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))), -1)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 ($greatereq($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))), -1)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 ($greatereq($sum(J!0, $product(-1, I!1)), 1)),
% 0.21/0.42 inference(and_elim,[status(thm)],[100])).
% 0.21/0.42 tff(135,plain,
% 0.21/0.42 ($greatereq($sum(n, $product(-1, perm(J!0))), 0) | (~$greatereq(I!1, 1)) | (~$greatereq($sum(J!0, $product(-1, I!1)), 1)) | (~$greatereq($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))), -1))),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 ($greatereq($sum(n, $product(-1, perm(J!0))), 0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[135, 134, 133, 102])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 ($greatereq($sum(n, $product(-1, J!0)), 0)),
% 0.21/0.42 inference(and_elim,[status(thm)],[100])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 ((~($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))) = -1)) | $lesseq($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))), -1)),
% 0.21/0.42 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 ($lesseq($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))), -1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[138, 131])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 ($greatereq(perm(J!0), 1) | (~$lesseq($sum(n, $sum($product(-1, J!0), $product(-1, perm(J!0)))), -1)) | (~$greatereq($sum(n, $product(-1, J!0)), 0))),
% 0.21/0.43 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 ($greatereq(perm(J!0), 1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[140, 139, 137])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 ($greatereq($sum(J!0, $product(-1, I!1)), 1) <=> $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)),
% 0.21/0.43 inference(and_elim,[status(thm)],[100])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 ((~$greatereq($sum(J!0, $product(-1, I!1)), 1)) | $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1) | (~($greatereq($sum(J!0, $product(-1, I!1)), 1) <=> $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 ((~$greatereq($sum(J!0, $product(-1, I!1)), 1)) | $lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 ($lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[144, 134])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 (^[I: $int, J: $int] : refl(((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0)))) <=> ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0)))) <=> ![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[146])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (^[I: $int, J: $int] : trans(monotonicity(trans(monotonicity(rewrite(($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0)) <=> (~((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0))))), ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) <=> (~(~((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0))))))), rewrite((~(~((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0))))) <=> ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)))), ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) <=> ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0))))), rewrite(((~($sum(p(J), $product(-1, p(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0))) <=> (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0)))), (((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) | ((~($sum(p(J), $product(-1, p(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0)))) <=> (((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0))) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0)))))), rewrite((((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0))) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0)))) <=> ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))), (((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) | ((~($sum(p(J), $product(-1, p(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0)))) <=> ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) | ((~($sum(p(J), $product(-1, p(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0)))) <=> ![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[148])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 (^[I: $int, J: $int] : rewrite(((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $lesseq($sum(J, $product(-1, n)), 0))) | ((~($sum(p(I), $product(-1, p(J))) = 0)) & (~($sum(p(I), $sum(I, $sum($product(-1, p(J)), $product(-1, J)))) = 0)) & (~($sum(p(I), $sum($product(-1, I), $sum($product(-1, p(J)), J))) = 0)))) <=> ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) | ((~($sum(p(J), $product(-1, p(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(151,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $lesseq($sum(J, $product(-1, n)), 0))) | ((~($sum(p(I), $product(-1, p(J))) = 0)) & (~($sum(p(I), $sum(I, $sum($product(-1, p(J)), $product(-1, J)))) = 0)) & (~($sum(p(I), $sum($product(-1, I), $sum($product(-1, p(J)), J))) = 0)))) <=> ![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) | ((~($sum(p(J), $product(-1, p(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.43 tff(152,plain,
% 0.21/0.43 (^[I: $int, J: $int] : rewrite(((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))) <=> ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $lesseq($sum(J, $product(-1, n)), 0))) | ((~($sum(p(I), $product(-1, p(J))) = 0)) & (~($sum(p(I), $sum(I, $sum($product(-1, p(J)), $product(-1, J)))) = 0)) & (~($sum(p(I), $sum($product(-1, I), $sum($product(-1, p(J)), J))) = 0)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(153,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))) <=> ![I: $int, J: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $lesseq($sum(J, $product(-1, n)), 0))) | ((~($sum(p(I), $product(-1, p(J))) = 0)) & (~($sum(p(I), $sum(I, $sum($product(-1, p(J)), $product(-1, J)))) = 0)) & (~($sum(p(I), $sum($product(-1, I), $sum($product(-1, p(J)), J))) = 0))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.43 tff(154,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))) <=> ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(155,plain,
% 0.21/0.43 (($false | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))) <=> ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(156,plain,
% 0.21/0.43 ((~$true) <=> $false),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(157,plain,
% 0.21/0.43 (queens_p),
% 0.21/0.43 inference(and_elim,[status(thm)],[18])).
% 0.21/0.43 tff(158,plain,
% 0.21/0.43 (queens_p <=> $true),
% 0.21/0.43 inference(iff_true,[status(thm)],[157])).
% 0.21/0.43 tff(159,plain,
% 0.21/0.43 ((~queens_p) <=> (~$true)),
% 0.21/0.43 inference(monotonicity,[status(thm)],[158])).
% 0.21/0.43 tff(160,plain,
% 0.21/0.43 ((~queens_p) <=> $false),
% 0.21/0.43 inference(transitivity,[status(thm)],[159, 156])).
% 0.21/0.43 tff(161,plain,
% 0.21/0.43 (((~queens_p) | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))) <=> ($false | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[160])).
% 0.21/0.43 tff(162,plain,
% 0.21/0.43 (((~queens_p) | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))) <=> ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[161, 155])).
% 0.21/0.43 tff(163,plain,
% 0.21/0.43 (((~queens_p) | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))) <=> ((~queens_p) | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 ((queens_p => ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))) <=> ((~queens_p) | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 (^[I: $int, J: $int] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite($lesseq($sum(1, I), J) <=> $lesseq(I, $sum(-1, J))), ((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) <=> (($lesseq(1, I) & $lesseq(I, n)) & $lesseq(I, $sum(-1, J))))), rewrite((($lesseq(1, I) & $lesseq(I, n)) & $lesseq(I, $sum(-1, J))) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)))), ((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J))))), (((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) <=> (($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J))) & $lesseq(J, n)))), rewrite((($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J))) & $lesseq(J, n)) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))), (((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) <=> ($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n)))), trans(monotonicity(rewrite((~($difference(p(I), I) = $difference(p(J), J))) <=> (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))), ((((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($difference(p(I), I) = $difference(p(J), J)))) <=> (((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))), rewrite((((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))) <=> ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))), ((((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($difference(p(I), I) = $difference(p(J), J)))) <=> ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))), ((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) => (((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($difference(p(I), I) = $difference(p(J), J))))) <=> (($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n)) => ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))))), rewrite((($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n)) => ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))) <=> ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))), ((((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) => (((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($difference(p(I), I) = $difference(p(J), J))))) <=> ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 (![I: $int, J: $int] : (((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) => (((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($difference(p(I), I) = $difference(p(J), J))))) <=> ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[165])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 ((queens_p => ![I: $int, J: $int] : (((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) => (((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($difference(p(I), I) = $difference(p(J), J)))))) <=> (queens_p => ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[166])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 ((queens_p => ![I: $int, J: $int] : (((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) => (((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($difference(p(I), I) = $difference(p(J), J)))))) <=> ((~queens_p) | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J)))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[167, 164])).
% 0.21/0.43 tff(169,axiom,(queens_p => ![I: $int, J: $int] : (((($lesseq(1, I) & $lesseq(I, n)) & $lesseq($sum(1, I), J)) & $lesseq(J, n)) => (((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J)))) & (~($difference(p(I), I) = $difference(p(J), J)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','queens_p')).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 ((~queens_p) | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 ((~queens_p) | ![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.21/0.43 tff(172,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[171, 162])).
% 0.21/0.43 tff(173,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~($lesseq(1, I) & $lesseq(I, n) & $lesseq(I, $sum(-1, J)) & $lesseq(J, n))) | ((~(p(I) = p(J))) & (~($sum(p(I), I) = $sum(p(J), J))) & (~($sum(p(I), $product(-1, I)) = $sum(p(J), $product(-1, J))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[172, 154])).
% 0.21/0.43 tff(174,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~($greatereq(I, 1) & $lesseq($sum(I, $product(-1, n)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $lesseq($sum(J, $product(-1, n)), 0))) | ((~($sum(p(I), $product(-1, p(J))) = 0)) & (~($sum(p(I), $sum(I, $sum($product(-1, p(J)), $product(-1, J)))) = 0)) & (~($sum(p(I), $sum($product(-1, I), $sum($product(-1, p(J)), J))) = 0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[173, 153])).
% 0.21/0.43 tff(175,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) | ((~($sum(p(J), $product(-1, p(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[174, 151])).
% 0.21/0.43 tff(176,plain,(
% 0.21/0.43 ![I: $int, J: $int] : ((~($greatereq(I, 1) & $greatereq($sum(n, $product(-1, I)), 0) & $lesseq($sum(I, $product(-1, J)), -1) & $greatereq($sum(n, $product(-1, J)), 0))) | ((~($sum(p(J), $product(-1, p(I))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0)) & (~($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[175])).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[176, 149])).
% 0.21/0.43 tff(178,plain,
% 0.21/0.43 (![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[177, 147])).
% 0.21/0.43 tff(179,plain,
% 0.21/0.43 (((~![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))) | ((~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0))))) <=> ((~![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(180,plain,
% 0.21/0.43 (((~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0)))) <=> ((~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(181,plain,
% 0.21/0.44 ((~(($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(I!1))), p(perm(J!0))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(I!1)), $product(-1, p(perm(J!0)))))) = 0) | ($sum(p(perm(I!1)), $product(-1, p(perm(J!0)))) = 0))) <=> (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(182,plain,
% 0.21/0.44 (((~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(I!1))), p(perm(J!0))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(I!1)), $product(-1, p(perm(J!0)))))) = 0) | ($sum(p(perm(I!1)), $product(-1, p(perm(J!0)))) = 0)))) <=> ((~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[181])).
% 0.21/0.44 tff(183,plain,
% 0.21/0.44 (((~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(I!1))), p(perm(J!0))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(I!1)), $product(-1, p(perm(J!0)))))) = 0) | ($sum(p(perm(I!1)), $product(-1, p(perm(J!0)))) = 0)))) <=> ((~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[182, 180])).
% 0.21/0.44 tff(184,plain,
% 0.21/0.44 (((~![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))) | ((~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(I!1))), p(perm(J!0))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(I!1)), $product(-1, p(perm(J!0)))))) = 0) | ($sum(p(perm(I!1)), $product(-1, p(perm(J!0)))) = 0))))) <=> ((~![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))) | ((~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0)))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[183])).
% 0.21/0.44 tff(185,plain,
% 0.21/0.44 (((~![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))) | ((~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(I!1))), p(perm(J!0))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(I!1)), $product(-1, p(perm(J!0)))))) = 0) | ($sum(p(perm(I!1)), $product(-1, p(perm(J!0)))) = 0))))) <=> ((~![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[184, 179])).
% 0.21/0.44 tff(186,plain,
% 0.21/0.44 ((~![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))) | ((~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(I!1))), p(perm(J!0))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(I!1)), $product(-1, p(perm(J!0)))))) = 0) | ($sum(p(perm(I!1)), $product(-1, p(perm(J!0)))) = 0))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(187,plain,
% 0.21/0.44 ((~![I: $int, J: $int] : ((~$greatereq(I, 1)) | (~$greatereq($sum(n, $product(-1, I)), 0)) | (~$lesseq($sum(I, $product(-1, J)), -1)) | (~$greatereq($sum(n, $product(-1, J)), 0)) | (~(($sum(I, $sum($product(-1, J), $sum($product(-1, p(J)), p(I)))) = 0) | ($sum(I, $sum($product(-1, J), $sum(p(J), $product(-1, p(I))))) = 0) | ($sum(p(J), $product(-1, p(I))) = 0))))) | (~$lesseq($sum(perm(J!0), $product(-1, perm(I!1))), -1)) | (~$greatereq(perm(J!0), 1)) | (~$greatereq($sum(n, $product(-1, perm(J!0))), 0)) | (~$greatereq($sum(n, $product(-1, perm(I!1))), 0)) | (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.21/0.44 tff(188,plain,
% 0.21/0.44 (~(($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[187, 178, 145, 141, 136, 108])).
% 0.21/0.44 tff(189,plain,
% 0.21/0.44 ((($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0)) | (~($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(190,plain,
% 0.21/0.44 (~($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.21/0.44 tff(191,plain,
% 0.21/0.44 (($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | (~$lesseq($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))), 0)) | (~$greatereq($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))), 0))),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(192,plain,
% 0.21/0.44 ((~$lesseq($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))), 0)) | (~$greatereq($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))), 0))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.21/0.44 tff(193,plain,
% 0.21/0.44 (~$lesseq($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))), 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[192, 51])).
% 0.21/0.44 tff(194,plain,
% 0.21/0.44 ((~($sum(q(J!0), $product(-1, p(perm(J!0)))) = 0)) | $greatereq($sum(q(J!0), $product(-1, p(perm(J!0)))), 0)),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(195,plain,
% 0.21/0.44 ($greatereq($sum(q(J!0), $product(-1, p(perm(J!0)))), 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[194, 34])).
% 0.21/0.44 tff(196,plain,
% 0.21/0.44 ((~($sum(q(I!1), $product(-1, p(perm(I!1)))) = 0)) | $lesseq($sum(q(I!1), $product(-1, p(perm(I!1)))), 0)),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.44 tff(197,plain,
% 0.21/0.44 ($lesseq($sum(q(I!1), $product(-1, p(perm(I!1)))), 0)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[196, 46])).
% 0.21/0.44 tff(198,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(theory_lemma,[status(thm)],[197, 195, 193, 3])).
% 0.21/0.44 tff(199,plain,(~($sum(q(J!0), $product(-1, q(I!1))) = 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(200,plain,
% 0.21/0.44 (^[J: $int, I: $int] : refl(($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0) <=> ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(201,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0) <=> ![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[200])).
% 0.21/0.44 tff(202,plain,
% 0.21/0.44 (^[J: $int, I: $int] : rewrite(($sum(I, $sum($product(-1, J), $sum($product(-1, perm(J)), perm(I)))) = 0) <=> ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(203,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(I, $sum($product(-1, J), $sum($product(-1, perm(J)), perm(I)))) = 0) <=> ![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[202])).
% 0.21/0.44 tff(204,plain,
% 0.21/0.44 (^[J: $int, I: $int] : rewrite(($sum(I, $product(-1, J)) = $sum(perm(J), $product(-1, perm(I)))) <=> ($sum(I, $sum($product(-1, J), $sum($product(-1, perm(J)), perm(I)))) = 0))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(205,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(I, $product(-1, J)) = $sum(perm(J), $product(-1, perm(I)))) <=> ![J: $int, I: $int] : ($sum(I, $sum($product(-1, J), $sum($product(-1, perm(J)), perm(I)))) = 0)),
% 0.21/0.44 inference(quant_intro,[status(thm)],[204])).
% 0.21/0.44 tff(206,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(I, $product(-1, J)) = $sum(perm(J), $product(-1, perm(I)))) <=> ![J: $int, I: $int] : ($sum(I, $product(-1, J)) = $sum(perm(J), $product(-1, perm(I))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(207,plain,
% 0.21/0.44 (^[J: $int, I: $int] : rewrite(($difference(I, J) = $difference(perm(J), perm(I))) <=> ($sum(I, $product(-1, J)) = $sum(perm(J), $product(-1, perm(I)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(208,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($difference(I, J) = $difference(perm(J), perm(I))) <=> ![J: $int, I: $int] : ($sum(I, $product(-1, J)) = $sum(perm(J), $product(-1, perm(I))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[207])).
% 0.21/0.44 tff(209,axiom,(![J: $int, I: $int] : ($difference(I, J) = $difference(perm(J), perm(I)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','permutation_another_one')).
% 0.21/0.44 tff(210,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(I, $product(-1, J)) = $sum(perm(J), $product(-1, perm(I))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.21/0.44 tff(211,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(I, $product(-1, J)) = $sum(perm(J), $product(-1, perm(I))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.21/0.44 tff(212,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(I, $sum($product(-1, J), $sum($product(-1, perm(J)), perm(I)))) = 0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[211, 205])).
% 0.21/0.44 tff(213,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[212, 203])).
% 0.21/0.44 tff(214,plain,(
% 0.21/0.44 ![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)),
% 0.21/0.44 inference(skolemize,[status(sab)],[213])).
% 0.21/0.44 tff(215,plain,
% 0.21/0.44 (![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[214, 201])).
% 0.21/0.44 tff(216,plain,
% 0.21/0.44 (((~![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)) | ($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0)) <=> ((~![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)) | ($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(217,plain,
% 0.21/0.44 (($sum(perm(J!0), $sum($product(-1, I!1), $sum(J!0, $product(-1, perm(I!1))))) = 0) <=> ($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(218,plain,
% 0.21/0.44 (((~![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)) | ($sum(perm(J!0), $sum($product(-1, I!1), $sum(J!0, $product(-1, perm(I!1))))) = 0)) <=> ((~![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)) | ($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[217])).
% 0.21/0.44 tff(219,plain,
% 0.21/0.44 (((~![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)) | ($sum(perm(J!0), $sum($product(-1, I!1), $sum(J!0, $product(-1, perm(I!1))))) = 0)) <=> ((~![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)) | ($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0))),
% 0.21/0.44 inference(transitivity,[status(thm)],[218, 216])).
% 0.21/0.44 tff(220,plain,
% 0.21/0.44 ((~![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)) | ($sum(perm(J!0), $sum($product(-1, I!1), $sum(J!0, $product(-1, perm(I!1))))) = 0)),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(221,plain,
% 0.21/0.44 ((~![J: $int, I: $int] : ($sum(perm(I), $sum($product(-1, J), $sum(I, $product(-1, perm(J))))) = 0)) | ($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.21/0.44 tff(222,plain,
% 0.21/0.44 ($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[221, 215])).
% 0.21/0.45 tff(223,plain,
% 0.21/0.45 ((~($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0)) | $greatereq($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))), 0)),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(224,plain,
% 0.21/0.45 ($greatereq($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.21/0.45 tff(225,assumption,($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0), introduced(assumption)).
% 0.21/0.45 tff(226,plain,
% 0.21/0.45 ((~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)) | $greatereq($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))), 0)),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(227,plain,
% 0.21/0.45 ($greatereq($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.21/0.45 tff(228,plain,
% 0.21/0.45 ((~($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))) = 0)) | $lesseq($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))), 0)),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(229,plain,
% 0.21/0.45 ($lesseq($sum(J!0, $sum($product(-1, I!1), $sum(perm(J!0), $product(-1, perm(I!1))))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[228, 222])).
% 0.21/0.45 tff(230,assumption,(~$lesseq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))), 0)), introduced(assumption)).
% 0.21/0.45 tff(231,assumption,($greatereq($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))), 0)), introduced(assumption)).
% 0.21/0.45 tff(232,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[231, 230, 48, 36, 229])).
% 0.21/0.45 tff(233,plain,($lesseq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))), 0) | (~$greatereq($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))), 0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(234,plain,
% 0.21/0.45 ($lesseq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[233, 227])).
% 0.21/0.45 tff(235,plain,
% 0.21/0.45 ((($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0)) | (~($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(236,plain,
% 0.21/0.45 (~($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[235, 188])).
% 0.21/0.45 tff(237,plain,
% 0.21/0.45 (($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0) | (~$lesseq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))), 0)) | (~$greatereq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))), 0))),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(238,plain,
% 0.21/0.45 ((~$lesseq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))), 0)) | (~$greatereq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))), 0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.21/0.45 tff(239,plain,
% 0.21/0.45 (~$greatereq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[238, 234])).
% 0.21/0.45 tff(240,plain,
% 0.21/0.45 ((~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)) | $lesseq($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))), 0)),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(241,plain,
% 0.21/0.45 ($lesseq($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[240, 225])).
% 0.21/0.45 tff(242,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[241, 239, 197, 195, 224])).
% 0.21/0.45 tff(243,plain,(~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(244,plain,
% 0.21/0.45 ((~(~(($sum(q(J!0), $product(-1, q(I!1))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)))) <=> (($sum(q(J!0), $product(-1, q(I!1))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(245,plain,
% 0.21/0.45 (((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0))) <=> (~(($sum(q(J!0), $product(-1, q(I!1))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(246,plain,
% 0.21/0.45 ((~((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)))) <=> (~(~(($sum(q(J!0), $product(-1, q(I!1))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[245])).
% 0.21/0.45 tff(247,plain,
% 0.21/0.45 ((~((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)))) <=> (($sum(q(J!0), $product(-1, q(I!1))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0))),
% 0.21/0.45 inference(transitivity,[status(thm)],[246, 244])).
% 0.21/0.45 tff(248,plain,
% 0.21/0.45 (~((~($sum(q(J!0), $product(-1, q(I!1))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0)) & (~($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)))),
% 0.21/0.45 inference(or_elim,[status(thm)],[99])).
% 0.21/0.45 tff(249,plain,
% 0.21/0.45 (($sum(q(J!0), $product(-1, q(I!1))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum(q(J!0), $product(-1, q(I!1))))) = 0) | ($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.21/0.45 tff(250,plain,
% 0.21/0.45 ($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[249, 243, 199])).
% 0.21/0.45 tff(251,plain,
% 0.21/0.45 ((~($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)) | $greatereq($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))), 0)),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(252,plain,
% 0.21/0.45 ($greatereq($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.21/0.45 tff(253,plain,
% 0.21/0.45 ((~($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))) = 0)) | $lesseq($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))), 0)),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(254,plain,
% 0.21/0.45 ($lesseq($sum(J!0, $sum($product(-1, I!1), $sum($product(-1, q(J!0)), q(I!1)))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[253, 250])).
% 0.21/0.45 tff(255,assumption,(~$greatereq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))), 0)), introduced(assumption)).
% 0.21/0.45 tff(256,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[224, 255, 48, 36, 254])).
% 0.21/0.45 tff(257,plain,($greatereq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))), 0)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(258,plain,
% 0.21/0.45 ((($sum(p(perm(J!0)), $product(-1, p(perm(I!1)))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | ($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum($product(-1, p(perm(J!0))), p(perm(I!1))))) = 0)) | (~($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(259,plain,
% 0.21/0.45 (~($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[258, 188])).
% 0.21/0.45 tff(260,plain,
% 0.21/0.45 (($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))) = 0) | (~$lesseq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))), 0)) | (~$greatereq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))), 0))),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[])).
% 0.21/0.45 tff(261,plain,
% 0.21/0.45 ((~$lesseq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))), 0)) | (~$greatereq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))), 0))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.21/0.45 tff(262,plain,
% 0.21/0.45 (~$lesseq($sum(perm(J!0), $sum($product(-1, perm(I!1)), $sum(p(perm(J!0)), $product(-1, p(perm(I!1)))))), 0)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[261, 257])).
% 0.21/0.45 tff(263,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(theory_lemma,[status(thm)],[229, 262, 197, 195, 252])).
% 0.21/0.45 % SZS output end Proof
%------------------------------------------------------------------------------