TSTP Solution File: GEO464+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO464+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:36:42 EDT 2022
% Result : Theorem 86.66s 57.17s
% Output : Proof 87.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO464+1 : TPTP v8.1.0. Released v7.0.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 31 09:17:06 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 86.66/57.17 % SZS status Theorem
% 86.66/57.17 % SZS output start Proof
% 86.66/57.17 tff(p_type, type, (
% 86.66/57.17 p: $i > $o)).
% 86.66/57.17 tff(s_type, type, (
% 86.66/57.17 s: ( $i * $i ) > $i)).
% 86.66/57.17 tff(i_type, type, (
% 86.66/57.17 i: ( $i * $i ) > $i)).
% 86.66/57.17 tff(tptp_fun_S0_3500_type, type, (
% 86.66/57.17 tptp_fun_S0_3500: $i)).
% 86.66/57.17 tff(fun_type, type, (
% 86.66/57.17 fun: ( $i * $i ) > $i)).
% 86.66/57.17 tff(bool_type, type, (
% 86.66/57.17 bool: $i)).
% 86.66/57.17 tff(cart_type, type, (
% 86.66/57.17 cart: ( $i * $i ) > $i)).
% 86.66/57.17 tff(tptp_fun_Q122108_3503_type, type, (
% 86.66/57.17 tptp_fun_Q122108_3503: $i)).
% 86.66/57.17 tff(real_type, type, (
% 86.66/57.17 real: $i)).
% 86.66/57.17 tff(span_type, type, (
% 86.66/57.17 span: $i)).
% 86.66/57.17 tff(subspace_type, type, (
% 86.66/57.17 subspace: $i)).
% 86.66/57.17 tff(tptp_fun_X_3502_type, type, (
% 86.66/57.17 tptp_fun_X_3502: $i)).
% 86.66/57.17 tff(tptp_fun_C0_3501_type, type, (
% 86.66/57.17 tptp_fun_C0_3501: $i)).
% 86.66/57.17 tff(r__type, type, (
% 86.66/57.17 r_: $i)).
% 86.66/57.17 tff(in_type, type, (
% 86.66/57.17 in: $i)).
% 86.66/57.17 tff(1,plain,
% 86.66/57.17 (^[Q122015: $i, S0: $i] : refl(p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0)))))) <=> p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0)))))))),
% 86.66/57.17 inference(bind,[status(th)],[])).
% 86.66/57.17 tff(2,plain,
% 86.66/57.17 (![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0)))))) <=> ![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0))))))),
% 86.66/57.17 inference(quant_intro,[status(thm)],[1])).
% 86.66/57.17 tff(3,plain,
% 86.66/57.17 (![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0)))))) <=> ![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0))))))),
% 86.66/57.17 inference(rewrite,[status(thm)],[])).
% 86.66/57.17 tff(4,axiom,(![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSUBSPACEu_SPAN')).
% 86.66/57.17 tff(5,plain,
% 86.66/57.17 (![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0))))))),
% 86.66/57.17 inference(modus_ponens,[status(thm)],[4, 3])).
% 86.66/57.17 tff(6,plain,(
% 86.66/57.17 ![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0))))))),
% 86.66/57.17 inference(skolemize,[status(sab)],[5])).
% 86.66/57.17 tff(7,plain,
% 86.66/57.17 (![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0))))))),
% 86.66/57.17 inference(modus_ponens,[status(thm)],[6, 2])).
% 86.66/57.17 tff(8,plain,
% 86.66/57.17 ((~![Q122015: $i, S0: $i] : p(s(bool, i(s(fun(fun(cart(real, Q122015), bool), bool), subspace), s(fun(cart(real, Q122015), bool), i(s(fun(fun(cart(real, Q122015), bool), fun(cart(real, Q122015), bool)), span), s(fun(cart(real, Q122015), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))),
% 86.66/57.17 inference(quant_inst,[status(thm)],[])).
% 86.66/57.17 tff(9,plain,
% 86.66/57.17 (p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))),
% 86.66/57.17 inference(unit_resolution,[status(thm)],[8, 7])).
% 86.66/57.17 tff(10,plain,
% 86.66/57.17 ((~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))) <=> (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))))),
% 86.66/57.17 inference(rewrite,[status(thm)],[])).
% 86.66/57.17 tff(11,plain,
% 86.66/57.17 ((~![Q122108: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))) => p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))) <=> (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))))),
% 86.66/57.17 inference(rewrite,[status(thm)],[])).
% 86.66/57.17 tff(12,axiom,(~![Q122108: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))) => p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSPANu_CLAUSESu_conjunct3')).
% 86.66/57.17 tff(13,plain,
% 86.66/57.17 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.17 inference(modus_ponens,[status(thm)],[12, 11])).
% 86.66/57.17 tff(14,plain,
% 86.66/57.17 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.17 inference(modus_ponens,[status(thm)],[13, 10])).
% 86.66/57.17 tff(15,plain,
% 86.66/57.17 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.17 inference(modus_ponens,[status(thm)],[14, 10])).
% 86.66/57.17 tff(16,plain,
% 86.66/57.17 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[15, 10])).
% 86.66/57.18 tff(17,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[16, 10])).
% 86.66/57.18 tff(18,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[17, 10])).
% 86.66/57.18 tff(19,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[18, 10])).
% 86.66/57.18 tff(20,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[19, 10])).
% 86.66/57.18 tff(21,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[20, 10])).
% 86.66/57.18 tff(22,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[21, 10])).
% 86.66/57.18 tff(23,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[22, 10])).
% 86.66/57.18 tff(24,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[23, 10])).
% 86.66/57.18 tff(25,plain,
% 86.66/57.18 (~![Q122108: $i, X: $i, C0: $i, S0: $i] : ((~p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), X))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108), bool), bool), i(s(fun(cart(real, Q122108), fun(fun(cart(real, Q122108), bool), bool)), in), s(cart(real, Q122108), i(s(fun(cart(real, Q122108), cart(real, Q122108)), i(s(fun(real, fun(cart(real, Q122108), cart(real, Q122108))), r_), s(real, C0))), s(cart(real, Q122108), X))))), s(fun(cart(real, Q122108), bool), i(s(fun(fun(cart(real, Q122108), bool), fun(cart(real, Q122108), bool)), span), s(fun(cart(real, Q122108), bool), S0)))))))),
% 86.66/57.18 inference(modus_ponens,[status(thm)],[24, 10])).
% 86.66/57.18 tff(26,plain,(
% 86.66/57.18 ~((~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))))),
% 86.66/57.18 inference(skolemize,[status(sab)],[25])).
% 86.66/57.18 tff(27,plain,
% 86.66/57.18 (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))),
% 86.66/57.18 inference(or_elim,[status(thm)],[26])).
% 86.66/57.18 tff(28,plain,
% 86.66/57.18 (p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))),
% 86.66/57.18 inference(or_elim,[status(thm)],[26])).
% 86.66/57.18 tff(29,plain,
% 86.66/57.18 (^[Q121516: $i, X: $i, C0: $i, S0: $i] : refl((p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) <=> (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))))),
% 86.66/57.18 inference(bind,[status(th)],[])).
% 86.66/57.18 tff(30,plain,
% 86.66/57.18 (![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) <=> ![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))),
% 86.66/57.18 inference(quant_intro,[status(thm)],[29])).
% 86.66/57.18 tff(31,plain,
% 86.66/57.18 (^[Q121516: $i, X: $i, C0: $i, S0: $i] : trans(monotonicity(trans(monotonicity(rewrite((p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))) <=> (~((~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))))), ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) <=> (~(~((~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))))))), rewrite((~(~((~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))))) <=> ((~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))), ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) <=> ((~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))))), (((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))) <=> (((~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))))), rewrite((((~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))) <=> (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))), (((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))) <=> (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))))),
% 86.66/57.19 inference(bind,[status(th)],[])).
% 86.66/57.19 tff(32,plain,
% 86.66/57.19 (![Q121516: $i, X: $i, C0: $i, S0: $i] : ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))) <=> ![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))),
% 86.66/57.19 inference(quant_intro,[status(thm)],[31])).
% 86.66/57.19 tff(33,plain,
% 86.66/57.19 (![Q121516: $i, X: $i, C0: $i, S0: $i] : ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))) <=> ![Q121516: $i, X: $i, C0: $i, S0: $i] : ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))))),
% 86.66/57.19 inference(rewrite,[status(thm)],[])).
% 86.66/57.19 tff(34,plain,
% 86.66/57.19 (^[Q121516: $i, X: $i, C0: $i, S0: $i] : rewrite(((p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))) => p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))) <=> ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))))),
% 86.66/57.19 inference(bind,[status(th)],[])).
% 86.66/57.19 tff(35,plain,
% 86.66/57.19 (![Q121516: $i, X: $i, C0: $i, S0: $i] : ((p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))) => p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0))))) <=> ![Q121516: $i, X: $i, C0: $i, S0: $i] : ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))))),
% 86.66/57.19 inference(quant_intro,[status(thm)],[34])).
% 86.66/57.19 tff(36,axiom,(![Q121516: $i, X: $i, C0: $i, S0: $i] : ((p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))) => p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','aSUBSPACEu_MUL')).
% 86.66/57.19 tff(37,plain,
% 86.66/57.19 (![Q121516: $i, X: $i, C0: $i, S0: $i] : ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))))),
% 86.66/57.19 inference(modus_ponens,[status(thm)],[36, 35])).
% 86.66/57.19 tff(38,plain,
% 86.66/57.19 (![Q121516: $i, X: $i, C0: $i, S0: $i] : ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))))),
% 86.66/57.19 inference(modus_ponens,[status(thm)],[37, 33])).
% 86.66/57.19 tff(39,plain,(
% 86.66/57.19 ![Q121516: $i, X: $i, C0: $i, S0: $i] : ((~(p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0)))) & p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0)))))) | p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))))),
% 86.66/57.19 inference(skolemize,[status(sab)],[38])).
% 86.66/57.19 tff(40,plain,
% 86.66/57.19 (![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))),
% 86.66/57.19 inference(modus_ponens,[status(thm)],[39, 32])).
% 86.66/57.19 tff(41,plain,
% 86.66/57.19 (![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))),
% 86.66/57.19 inference(modus_ponens,[status(thm)],[40, 30])).
% 86.66/57.19 tff(42,plain,
% 86.66/57.19 (((~![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))) | ((~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))))) <=> ((~![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))))),
% 86.66/57.19 inference(rewrite,[status(thm)],[])).
% 86.66/57.19 tff(43,plain,
% 86.66/57.19 ((p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))))) <=> ((~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))))),
% 86.66/57.20 inference(rewrite,[status(thm)],[])).
% 86.66/57.20 tff(44,plain,
% 86.66/57.20 (((~![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))) | (p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))))) <=> ((~![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))) | ((~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))))))),
% 86.66/57.20 inference(monotonicity,[status(thm)],[43])).
% 86.66/57.20 tff(45,plain,
% 86.66/57.20 (((~![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))) | (p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))))) <=> ((~![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))))),
% 86.66/57.20 inference(transitivity,[status(thm)],[44, 42])).
% 86.66/57.20 tff(46,plain,
% 86.66/57.20 ((~![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))) | (p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))))),
% 86.66/57.20 inference(quant_inst,[status(thm)],[])).
% 86.66/57.20 tff(47,plain,
% 86.66/57.20 ((~![Q121516: $i, X: $i, C0: $i, S0: $i] : (p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), i(s(fun(cart(real, Q121516), cart(real, Q121516)), i(s(fun(real, fun(cart(real, Q121516), cart(real, Q121516))), r_), s(real, C0))), s(cart(real, Q121516), X))))), s(fun(cart(real, Q121516), bool), S0)))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), subspace), s(fun(cart(real, Q121516), bool), S0))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q121516), bool), bool), i(s(fun(cart(real, Q121516), fun(fun(cart(real, Q121516), bool), bool)), in), s(cart(real, Q121516), X))), s(fun(cart(real, Q121516), bool), S0))))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), X!3502))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500))))))) | p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), i(s(fun(cart(real, Q122108!3503), fun(fun(cart(real, Q122108!3503), bool), bool)), in), s(cart(real, Q122108!3503), i(s(fun(cart(real, Q122108!3503), cart(real, Q122108!3503)), i(s(fun(real, fun(cart(real, Q122108!3503), cart(real, Q122108!3503))), r_), s(real, C0!3501))), s(cart(real, Q122108!3503), X!3502))))), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))) | (~p(s(bool, i(s(fun(fun(cart(real, Q122108!3503), bool), bool), subspace), s(fun(cart(real, Q122108!3503), bool), i(s(fun(fun(cart(real, Q122108!3503), bool), fun(cart(real, Q122108!3503), bool)), span), s(fun(cart(real, Q122108!3503), bool), S0!3500)))))))),
% 87.87/58.31 inference(modus_ponens,[status(thm)],[46, 45])).
% 87.87/58.31 tff(48,plain,
% 87.87/58.31 ($false),
% 87.87/58.31 inference(unit_resolution,[status(thm)],[47, 41, 28, 27, 9])).
% 87.87/58.31 % SZS output end Proof
%------------------------------------------------------------------------------