TSTP Solution File: GEO474+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO474+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 20:36:44 EDT 2022
% Result : Theorem 85.09s 55.74s
% Output : Proof 86.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO474+1 : TPTP v8.1.0. Released v7.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 31 10:20:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 85.09/55.74 % SZS status Theorem
% 85.09/55.74 % SZS output start Proof
% 85.09/55.74 tff(s_type, type, (
% 85.09/55.74 s: ( $i * $i ) > $i)).
% 85.09/55.74 tff(i_type, type, (
% 85.09/55.74 i: ( $i * $i ) > $i)).
% 85.09/55.74 tff(u_0_type, type, (
% 85.09/55.74 u_0: $i)).
% 85.09/55.74 tff(num_type, type, (
% 85.09/55.74 num: $i)).
% 85.09/55.74 tff(numeral_type, type, (
% 85.09/55.74 numeral: $i)).
% 85.09/55.74 tff(fun_type, type, (
% 85.09/55.74 fun: ( $i * $i ) > $i)).
% 85.09/55.74 tff(mat_type, type, (
% 85.09/55.74 mat: $i)).
% 85.09/55.74 tff(cart_type, type, (
% 85.09/55.74 cart: ( $i * $i ) > $i)).
% 85.09/55.74 tff(tptp_fun_Q133118_3696_type, type, (
% 85.09/55.74 tptp_fun_Q133118_3696: $i)).
% 85.09/55.74 tff(tptp_fun_Q133117_3697_type, type, (
% 85.09/55.74 tptp_fun_Q133117_3697: $i)).
% 85.09/55.74 tff(real_type, type, (
% 85.09/55.74 real: $i)).
% 85.09/55.74 tff(rank_type, type, (
% 85.09/55.74 rank: $i)).
% 85.09/55.74 tff(1,plain,
% 85.09/55.74 ((~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))) <=> (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))))),
% 85.09/55.74 inference(rewrite,[status(thm)],[])).
% 85.09/55.74 tff(2,axiom,(~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aRANKu_0')).
% 85.09/55.74 tff(3,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[2, 1])).
% 85.09/55.74 tff(4,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[3, 1])).
% 85.09/55.74 tff(5,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[4, 1])).
% 85.09/55.74 tff(6,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[5, 1])).
% 85.09/55.74 tff(7,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[6, 1])).
% 85.09/55.74 tff(8,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[7, 1])).
% 85.09/55.74 tff(9,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[8, 1])).
% 85.09/55.74 tff(10,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[9, 1])).
% 85.09/55.74 tff(11,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[10, 1])).
% 85.09/55.74 tff(12,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[11, 1])).
% 85.09/55.74 tff(13,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[12, 1])).
% 85.09/55.74 tff(14,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[13, 1])).
% 85.09/55.74 tff(15,plain,
% 85.09/55.74 (~![Q133117: $i, Q133118: $i] : (s(num, i(s(fun(cart(cart(real, Q133117), Q133118), num), rank), s(cart(cart(real, Q133117), Q133118), i(s(fun(num, cart(cart(real, Q133117), Q133118)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[14, 1])).
% 85.09/55.74 tff(16,plain,(
% 85.09/55.74 ~(s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.74 inference(skolemize,[status(sab)],[15])).
% 85.09/55.74 tff(17,plain,
% 85.09/55.74 (^[M: $i, N: $i, A5: $i] : refl(((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) <=> ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))))),
% 85.09/55.74 inference(bind,[status(th)],[])).
% 85.09/55.74 tff(18,plain,
% 85.09/55.74 (![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) <=> ![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))),
% 85.09/55.74 inference(quant_intro,[status(thm)],[17])).
% 85.09/55.74 tff(19,plain,
% 85.09/55.74 (![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) <=> ![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))),
% 85.09/55.74 inference(rewrite,[status(thm)],[])).
% 85.09/55.74 tff(20,axiom,(![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','aRANKu_EQu_0')).
% 85.09/55.74 tff(21,plain,
% 85.09/55.74 (![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[20, 19])).
% 85.09/55.74 tff(22,plain,(
% 85.09/55.74 ![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))),
% 85.09/55.74 inference(skolemize,[status(sab)],[21])).
% 85.09/55.74 tff(23,plain,
% 85.09/55.74 (![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))),
% 85.09/55.74 inference(modus_ponens,[status(thm)],[22, 18])).
% 85.09/55.74 tff(24,plain,
% 85.09/55.74 (((~![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) | (s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))) <=> ((~![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) | (s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))))),
% 85.09/55.74 inference(rewrite,[status(thm)],[])).
% 85.09/55.74 tff(25,plain,
% 85.09/55.74 (((s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> $true) <=> (s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.75 inference(rewrite,[status(thm)],[])).
% 85.09/55.75 tff(26,plain,
% 85.09/55.75 ((s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))) = s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))) <=> $true),
% 85.09/55.75 inference(rewrite,[status(thm)],[])).
% 85.09/55.75 tff(27,plain,
% 85.09/55.75 (((s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))) = s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) <=> ((s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> $true)),
% 85.09/55.75 inference(monotonicity,[status(thm)],[26])).
% 85.09/55.75 tff(28,plain,
% 85.09/55.75 (((s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))) = s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) <=> (s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 85.09/55.75 inference(transitivity,[status(thm)],[27, 25])).
% 85.09/55.75 tff(29,plain,
% 85.09/55.75 (((~![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) | ((s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))) = s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) <=> ((~![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) | (s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))))),
% 86.43/57.07 inference(monotonicity,[status(thm)],[28])).
% 86.43/57.07 tff(30,plain,
% 86.43/57.07 (((~![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) | ((s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))) = s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) <=> ((~![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) | (s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))))),
% 86.43/57.07 inference(transitivity,[status(thm)],[29, 24])).
% 86.43/57.07 tff(31,plain,
% 86.43/57.07 ((~![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) | ((s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))) = s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))),
% 86.43/57.07 inference(quant_inst,[status(thm)],[])).
% 86.43/57.07 tff(32,plain,
% 86.43/57.07 ((~![M: $i, N: $i, A5: $i] : ((s(num, i(s(fun(cart(cart(real, M), N), num), rank), s(cart(cart(real, M), N), A5))) = s(num, i(s(fun(num, num), numeral), s(num, u_0)))) <=> (s(cart(cart(real, M), N), A5) = s(cart(cart(real, M), N), i(s(fun(num, cart(cart(real, M), N)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0)))))))) | (s(num, i(s(fun(cart(cart(real, Q133117!3697), Q133118!3696), num), rank), s(cart(cart(real, Q133117!3697), Q133118!3696), i(s(fun(num, cart(cart(real, Q133117!3697), Q133118!3696)), mat), s(num, i(s(fun(num, num), numeral), s(num, u_0))))))) = s(num, i(s(fun(num, num), numeral), s(num, u_0))))),
% 86.43/57.07 inference(modus_ponens,[status(thm)],[31, 30])).
% 86.43/57.07 tff(33,plain,
% 86.43/57.07 ($false),
% 86.43/57.07 inference(unit_resolution,[status(thm)],[32, 23, 16])).
% 86.43/57.07 % SZS output end Proof
%------------------------------------------------------------------------------