TSTP Solution File: SWV232+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV232+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 : Thu Sep 29 15:10:28 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV232+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n027.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 : Sun Sep 4 02:02:06 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.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% 0.21/0.44 tff(tptp_fun_D_13_type, type, (
% 0.21/0.44 tptp_fun_D_13: $i)).
% 0.21/0.44 tff(succ_type, type, (
% 0.21/0.44 succ: $i > $i)).
% 0.21/0.44 tff(tptp_minus_1_type, type, (
% 0.21/0.44 tptp_minus_1: $i)).
% 0.21/0.44 tff(tptp_fun_C_14_type, type, (
% 0.21/0.44 tptp_fun_C_14: $i)).
% 0.21/0.44 tff(leq_type, type, (
% 0.21/0.44 leq: ( $i * $i ) > $o)).
% 0.21/0.44 tff(a_select2_type, type, (
% 0.21/0.44 a_select2: ( $i * $i ) > $i)).
% 0.21/0.44 tff(rho_type, type, (
% 0.21/0.44 rho: $i)).
% 0.21/0.44 tff(n2_type, type, (
% 0.21/0.44 n2: $i)).
% 0.21/0.44 tff(n0_type, type, (
% 0.21/0.44 n0: $i)).
% 0.21/0.44 tff(n1_type, type, (
% 0.21/0.44 n1: $i)).
% 0.21/0.44 tff(a_select3_type, type, (
% 0.21/0.44 a_select3: ( $i * $i * $i ) > $i)).
% 0.21/0.44 tff(q_ds1_filter_type, type, (
% 0.21/0.44 q_ds1_filter: $i)).
% 0.21/0.44 tff(n5_type, type, (
% 0.21/0.44 n5: $i)).
% 0.21/0.44 tff(1,plain,
% 0.21/0.44 ((~((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(tptp_minus_1) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(succ(tptp_minus_1))) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (succ(tptp_minus_1) = D!13) & (succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) | (~(leq(succ(tptp_minus_1), C!14) & leq(succ(tptp_minus_1), D!13) & leq(C!14, succ(succ(succ(tptp_minus_1)))) & leq(D!13, succ(succ(succ(tptp_minus_1)))))))) <=> (~((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(tptp_minus_1) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(succ(tptp_minus_1))) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (succ(tptp_minus_1) = D!13) & (succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) | (~(leq(succ(tptp_minus_1), C!14) & leq(succ(tptp_minus_1), D!13) & leq(C!14, succ(succ(succ(tptp_minus_1)))) & leq(D!13, succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(2,plain,
% 0.21/0.44 ((~![C: $i, D: $i] : ((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(tptp_minus_1) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(tptp_minus_1) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(succ(tptp_minus_1))) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (succ(tptp_minus_1) = D) & (succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) | (~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, succ(succ(succ(tptp_minus_1)))))))) <=> (~![C: $i, D: $i] : ((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(tptp_minus_1) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(tptp_minus_1) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(succ(tptp_minus_1))) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (succ(tptp_minus_1) = D) & (succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) | (~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(3,plain,
% 0.21/0.44 ((~![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))))) <=> (~![C: $i, D: $i] : ((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(tptp_minus_1) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(tptp_minus_1) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(succ(tptp_minus_1))) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (succ(tptp_minus_1) = D) & (succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) | (~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, succ(succ(succ(tptp_minus_1))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(4,plain,
% 0.21/0.44 ((~![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))))) <=> (~![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(5,plain,
% 0.21/0.44 ((~(![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n5)) & leq(B, n5)) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) => ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, n2)) => ((((((((((((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D)))) & (~((n0 = D) & (n2 = C)))) & (~((n1 = C) & (n1 = D)))) & (~((n1 = C) & (n2 = D)))) & (~((n1 = D) & (n2 = C)))) & (~((n2 = C) & (n2 = D)))) & (n0 = D)) & (n1 = C)) & (n1 = D)) & (n2 = C)) => (a_select2(rho, n1) = n0))))) <=> (~((~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n5) & leq(B, n5))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) | ![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(6,axiom,(~(![A: $i, B: $i] : ((((leq(n0, A) & leq(n0, B)) & leq(A, n5)) & leq(B, n5)) => (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A))) => ![C: $i, D: $i] : ((((leq(n0, C) & leq(n0, D)) & leq(C, n2)) & leq(D, n2)) => ((((((((((((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D)))) & (~((n0 = D) & (n2 = C)))) & (~((n1 = C) & (n1 = D)))) & (~((n1 = C) & (n2 = D)))) & (~((n1 = D) & (n2 = C)))) & (~((n2 = C) & (n2 = D)))) & (n0 = D)) & (n1 = C)) & (n1 = D)) & (n2 = C)) => (a_select2(rho, n1) = n0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quaternion_ds1_symm_0841')).
% 0.21/0.44 tff(7,plain,
% 0.21/0.44 (~((~![A: $i, B: $i] : ((~(leq(n0, A) & leq(n0, B) & leq(A, n5) & leq(B, n5))) | (a_select3(q_ds1_filter, A, B) = a_select3(q_ds1_filter, B, A)))) | ![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.44 tff(8,plain,
% 0.21/0.44 (~![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))))),
% 0.21/0.44 inference(or_elim,[status(thm)],[7])).
% 0.21/0.44 tff(9,plain,
% 0.21/0.44 (~![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.44 tff(10,plain,
% 0.21/0.44 (~![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.21/0.44 tff(11,plain,
% 0.21/0.44 (~![C: $i, D: $i] : ((a_select2(rho, n1) = n0) | (~((~((n0 = C) & (n1 = D))) & (~((n0 = C) & (n2 = D))) & (~((n0 = D) & (n2 = C))) & (~((n1 = C) & (n1 = D))) & (~((n1 = C) & (n2 = D))) & (~((n1 = D) & (n2 = C))) & (~((n2 = C) & (n2 = D))) & (n0 = D) & (n1 = C) & (n1 = D) & (n2 = C))) | (~(leq(n0, C) & leq(n0, D) & leq(C, n2) & leq(D, n2))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.21/0.44 tff(12,plain,
% 0.21/0.44 (~![C: $i, D: $i] : ((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(tptp_minus_1) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(tptp_minus_1) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(succ(tptp_minus_1))) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (succ(tptp_minus_1) = D) & (succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) | (~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, succ(succ(succ(tptp_minus_1)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.21/0.44 tff(13,plain,
% 0.21/0.44 (~![C: $i, D: $i] : ((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(tptp_minus_1) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(tptp_minus_1) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(succ(tptp_minus_1))) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (succ(tptp_minus_1) = D) & (succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) | (~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, succ(succ(succ(tptp_minus_1)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.21/0.44 tff(14,plain,
% 0.21/0.44 (~![C: $i, D: $i] : ((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(tptp_minus_1) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(tptp_minus_1) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(succ(tptp_minus_1))) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (succ(tptp_minus_1) = D) & (succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) | (~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, succ(succ(succ(tptp_minus_1)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (~![C: $i, D: $i] : ((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(tptp_minus_1) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(tptp_minus_1) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D))) & (~((succ(succ(tptp_minus_1)) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (~((succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) & (~((succ(succ(succ(tptp_minus_1))) = C) & (succ(succ(succ(tptp_minus_1))) = D))) & (succ(tptp_minus_1) = D) & (succ(succ(tptp_minus_1)) = C) & (succ(succ(tptp_minus_1)) = D) & (succ(succ(succ(tptp_minus_1))) = C))) | (~(leq(succ(tptp_minus_1), C) & leq(succ(tptp_minus_1), D) & leq(C, succ(succ(succ(tptp_minus_1)))) & leq(D, succ(succ(succ(tptp_minus_1)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.21/0.45 tff(16,plain,(
% 0.21/0.45 ~((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(tptp_minus_1) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(succ(tptp_minus_1))) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (succ(tptp_minus_1) = D!13) & (succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) | (~(leq(succ(tptp_minus_1), C!14) & leq(succ(tptp_minus_1), D!13) & leq(C!14, succ(succ(succ(tptp_minus_1)))) & leq(D!13, succ(succ(succ(tptp_minus_1)))))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[15])).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (~((a_select2(rho, succ(succ(tptp_minus_1))) = succ(tptp_minus_1)) | (~((~((succ(tptp_minus_1) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(tptp_minus_1) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(succ(tptp_minus_1))) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (succ(tptp_minus_1) = D!13) & (succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) | (~(leq(succ(tptp_minus_1), C!14) & leq(succ(tptp_minus_1), D!13) & leq(C!14, succ(succ(succ(tptp_minus_1)))) & leq(D!13, succ(succ(succ(tptp_minus_1)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[16, 1])).
% 0.21/0.45 tff(18,plain,
% 0.21/0.45 ((~((succ(tptp_minus_1) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(tptp_minus_1) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13))) & (~((succ(succ(tptp_minus_1)) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (~((succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) & (~((succ(succ(succ(tptp_minus_1))) = C!14) & (succ(succ(succ(tptp_minus_1))) = D!13))) & (succ(tptp_minus_1) = D!13) & (succ(succ(tptp_minus_1)) = C!14) & (succ(succ(tptp_minus_1)) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14)),
% 0.21/0.46 inference(or_elim,[status(thm)],[17])).
% 0.21/0.46 tff(19,plain,
% 0.21/0.46 (succ(tptp_minus_1) = D!13),
% 0.21/0.46 inference(and_elim,[status(thm)],[18])).
% 0.21/0.46 tff(20,plain,
% 0.21/0.46 (succ(succ(succ(tptp_minus_1))) = C!14),
% 0.21/0.46 inference(and_elim,[status(thm)],[18])).
% 0.21/0.46 tff(21,plain,
% 0.21/0.46 ((~(~((~(succ(tptp_minus_1) = D!13)) | (~(succ(succ(succ(tptp_minus_1))) = C!14))))) <=> ((~(succ(tptp_minus_1) = D!13)) | (~(succ(succ(succ(tptp_minus_1))) = C!14)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(22,plain,
% 0.21/0.46 (((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14)) <=> (~((~(succ(tptp_minus_1) = D!13)) | (~(succ(succ(succ(tptp_minus_1))) = C!14))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(23,plain,
% 0.21/0.46 ((~((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) <=> (~(~((~(succ(tptp_minus_1) = D!13)) | (~(succ(succ(succ(tptp_minus_1))) = C!14)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.46 tff(24,plain,
% 0.21/0.46 ((~((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))) <=> ((~(succ(tptp_minus_1) = D!13)) | (~(succ(succ(succ(tptp_minus_1))) = C!14)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[23, 21])).
% 0.21/0.46 tff(25,plain,
% 0.21/0.46 (~((succ(tptp_minus_1) = D!13) & (succ(succ(succ(tptp_minus_1))) = C!14))),
% 0.21/0.46 inference(and_elim,[status(thm)],[18])).
% 0.21/0.46 tff(26,plain,
% 0.21/0.46 ((~(succ(tptp_minus_1) = D!13)) | (~(succ(succ(succ(tptp_minus_1))) = C!14))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.46 tff(27,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[26, 20, 19])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------