TSTP Solution File: GEG023_1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GEG023_1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n023.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 May 3 02:15:56 EDT 2024
% Result : Theorem 27.22s 4.20s
% Output : CNFRefutation 27.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEG023_1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 22:51:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running TFA theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 27.22/4.20 % SZS status Started for theBenchmark.p
% 27.22/4.20 % SZS status Theorem for theBenchmark.p
% 27.22/4.20
% 27.22/4.20 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 27.22/4.20
% 27.22/4.20 ------ iProver source info
% 27.22/4.20
% 27.22/4.20 git: date: 2024-05-02 19:28:25 +0000
% 27.22/4.20 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 27.22/4.20 git: non_committed_changes: false
% 27.22/4.20
% 27.22/4.20 ------ Parsing...
% 27.22/4.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 27.22/4.20
% 27.22/4.20 ------ Preprocessing... sup_sim: 9 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 27.22/4.20
% 27.22/4.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 27.22/4.20
% 27.22/4.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.22/4.20 ------ Proving...
% 27.22/4.20 ------ Problem Properties
% 27.22/4.20
% 27.22/4.20
% 27.22/4.20 clauses 40
% 27.22/4.20 conjectures 8
% 27.22/4.20 EPR 16
% 27.22/4.20 Horn 38
% 27.22/4.20 unary 36
% 27.22/4.20 binary 2
% 27.22/4.20 lits 46
% 27.22/4.20 lits eq 21
% 27.22/4.20 fd_pure 0
% 27.22/4.20 fd_pseudo 0
% 27.22/4.20 fd_cond 0
% 27.22/4.20 fd_pseudo_cond 1
% 27.22/4.20 AC symbols 1
% 27.22/4.20
% 27.22/4.20 ------ Input Options Time Limit: Unbounded
% 27.22/4.20
% 27.22/4.20
% 27.22/4.20 ------
% 27.22/4.20 Current options:
% 27.22/4.20 ------
% 27.22/4.20
% 27.22/4.20
% 27.22/4.20
% 27.22/4.20
% 27.22/4.20 ------ Proving...
% 27.22/4.20
% 27.22/4.20
% 27.22/4.20 % SZS status Theorem for theBenchmark.p
% 27.22/4.20
% 27.22/4.20 % SZS output start CNFRefutation for theBenchmark.p
% 27.22/4.20
% 27.22/4.20 tff(f1,conjecture,(
% 27.22/4.20 (360 = d(munich,saarbruecken) & d(munich,frankfurt) = 300 & d(hamburg,berlin) = 250 & d(hamburg,kiel) = 90 & d(cologne,frankfurt) = 150 & d(hamburg,frankfurt) = 390 & d(hamburg,cologne) = 360 & d(saarbruecken,cologne) = 190 & d(saarbruecken,frankfurt) = 160 & d(berlin,frankfurt) = 420 & d(berlin,cologne) = 480 & d(berlin,munich) = 510 & ! [X0 : city] : d(X0,X0) = 0 & ! [X0 : city,X1 : city,X2 : city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2))) & ! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0)) => $lesseq(d(kiel,saarbruecken),640)),
% 27.22/4.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',city_distance_3)).
% 27.22/4.20
% 27.22/4.20 tff(f2,negated_conjecture,(
% 27.22/4.20 ~((360 = d(munich,saarbruecken) & d(munich,frankfurt) = 300 & d(hamburg,berlin) = 250 & d(hamburg,kiel) = 90 & d(cologne,frankfurt) = 150 & d(hamburg,frankfurt) = 390 & d(hamburg,cologne) = 360 & d(saarbruecken,cologne) = 190 & d(saarbruecken,frankfurt) = 160 & d(berlin,frankfurt) = 420 & d(berlin,cologne) = 480 & d(berlin,munich) = 510 & ! [X0 : city] : d(X0,X0) = 0 & ! [X0 : city,X1 : city,X2 : city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2))) & ! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0)) => $lesseq(d(kiel,saarbruecken),640))),
% 27.22/4.20 inference(negated_conjecture,[],[f1])).
% 27.22/4.20
% 27.22/4.20 tff(f3,plain,(
% 27.22/4.20 ~((360 = d(munich,saarbruecken) & d(munich,frankfurt) = 300 & d(hamburg,berlin) = 250 & d(hamburg,kiel) = 90 & d(cologne,frankfurt) = 150 & d(hamburg,frankfurt) = 390 & d(hamburg,cologne) = 360 & d(saarbruecken,cologne) = 190 & d(saarbruecken,frankfurt) = 160 & d(berlin,frankfurt) = 420 & d(berlin,cologne) = 480 & d(berlin,munich) = 510 & ! [X0 : city] : d(X0,X0) = 0 & ! [X0 : city,X1 : city,X2 : city] : ~$less($sum(d(X0,X1),d(X1,X2)),d(X0,X2)) & ! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0)) => ~$less(640,d(kiel,saarbruecken)))),
% 27.22/4.20 inference(theory_normalization,[],[f2])).
% 27.22/4.20
% 27.22/4.20 tff(f4,plain,(
% 27.22/4.20 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 27.22/4.20 introduced(theory_axiom_138,[])).
% 27.22/4.20
% 27.22/4.20 tff(f5,plain,(
% 27.22/4.20 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 27.22/4.20 introduced(theory_axiom_139,[])).
% 27.22/4.20
% 27.22/4.20 tff(f6,plain,(
% 27.22/4.20 ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
% 27.22/4.20 introduced(theory_axiom_140,[])).
% 27.22/4.20
% 27.22/4.20 tff(f7,plain,(
% 27.22/4.20 ( ! [X0 : $int,X1 : $int] : ($uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0))) )),
% 27.22/4.20 introduced(theory_axiom_142,[])).
% 27.22/4.20
% 27.22/4.20 tff(f8,plain,(
% 27.22/4.20 ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
% 27.22/4.20 introduced(theory_axiom_143,[])).
% 27.22/4.20
% 27.22/4.20 tff(f10,plain,(
% 27.22/4.20 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,X2) | $less(X0,X2)) )),
% 27.22/4.20 introduced(theory_axiom_146,[])).
% 27.22/4.20
% 27.22/4.20 tff(f11,plain,(
% 27.22/4.20 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
% 27.22/4.20 introduced(theory_axiom_147,[])).
% 27.22/4.20
% 27.22/4.20 tff(f14,plain,(
% 27.22/4.20 ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
% 27.22/4.20 introduced(theory_axiom_151,[])).
% 27.22/4.20
% 27.22/4.20 tff(f16,plain,(
% 27.22/4.20 ~((360 = d(munich,saarbruecken) & d(munich,frankfurt) = 300 & d(hamburg,berlin) = 250 & d(hamburg,kiel) = 90 & d(cologne,frankfurt) = 150 & d(hamburg,frankfurt) = 390 & d(hamburg,cologne) = 360 & d(saarbruecken,cologne) = 190 & d(saarbruecken,frankfurt) = 160 & d(berlin,frankfurt) = 420 & d(berlin,cologne) = 480 & d(berlin,munich) = 510 & ! [X0 : city] : d(X0,X0) = 0 & ! [X1 : city,X2 : city,X3 : city] : ~$less($sum(d(X1,X2),d(X2,X3)),d(X1,X3)) & ! [X4 : city,X5 : city] : d(X4,X5) = d(X5,X4)) => ~$less(640,d(kiel,saarbruecken)))),
% 27.22/4.20 inference(rectify,[],[f3])).
% 27.22/4.20
% 27.22/4.20 tff(f17,plain,(
% 27.22/4.20 $less(640,d(kiel,saarbruecken)) & (360 = d(munich,saarbruecken) & d(munich,frankfurt) = 300 & d(hamburg,berlin) = 250 & d(hamburg,kiel) = 90 & d(cologne,frankfurt) = 150 & d(hamburg,frankfurt) = 390 & d(hamburg,cologne) = 360 & d(saarbruecken,cologne) = 190 & d(saarbruecken,frankfurt) = 160 & d(berlin,frankfurt) = 420 & d(berlin,cologne) = 480 & d(berlin,munich) = 510 & ! [X0 : city] : d(X0,X0) = 0 & ! [X1 : city,X2 : city,X3 : city] : ~$less($sum(d(X1,X2),d(X2,X3)),d(X1,X3)) & ! [X4 : city,X5 : city] : d(X4,X5) = d(X5,X4))),
% 27.22/4.20 inference(ennf_transformation,[],[f16])).
% 27.22/4.20
% 27.22/4.20 tff(f18,plain,(
% 27.22/4.20 $less(640,d(kiel,saarbruecken)) & 360 = d(munich,saarbruecken) & d(munich,frankfurt) = 300 & d(hamburg,berlin) = 250 & d(hamburg,kiel) = 90 & d(cologne,frankfurt) = 150 & d(hamburg,frankfurt) = 390 & d(hamburg,cologne) = 360 & d(saarbruecken,cologne) = 190 & d(saarbruecken,frankfurt) = 160 & d(berlin,frankfurt) = 420 & d(berlin,cologne) = 480 & d(berlin,munich) = 510 & ! [X0 : city] : d(X0,X0) = 0 & ! [X1 : city,X2 : city,X3 : city] : ~$less($sum(d(X1,X2),d(X2,X3)),d(X1,X3)) & ! [X4 : city,X5 : city] : d(X4,X5) = d(X5,X4)),
% 27.22/4.20 inference(flattening,[],[f17])).
% 27.22/4.20
% 27.22/4.20 tff(f19,plain,(
% 27.22/4.20 ( ! [X4 : city,X5 : city] : (d(X4,X5) = d(X5,X4)) )),
% 27.22/4.20 inference(cnf_transformation,[],[f18])).
% 27.22/4.20
% 27.22/4.20 tff(f20,plain,(
% 27.22/4.20 ( ! [X2 : city,X3 : city,X1 : city] : (~$less($sum(d(X1,X2),d(X2,X3)),d(X1,X3))) )),
% 27.22/4.20 inference(cnf_transformation,[],[f18])).
% 27.22/4.20
% 27.22/4.20 tff(f25,plain,(
% 27.22/4.20 d(saarbruecken,frankfurt) = 160),
% 27.22/4.20 inference(cnf_transformation,[],[f18])).
% 27.22/4.20
% 27.22/4.20 tff(f26,plain,(
% 27.22/4.20 d(saarbruecken,cologne) = 190),
% 27.22/4.20 inference(cnf_transformation,[],[f18])).
% 27.22/4.20
% 27.22/4.20 tff(f27,plain,(
% 27.22/4.20 d(hamburg,cologne) = 360),
% 27.22/4.20 inference(cnf_transformation,[],[f18])).
% 27.22/4.20
% 27.22/4.20 tff(f28,plain,(
% 27.22/4.20 d(hamburg,frankfurt) = 390),
% 27.22/4.20 inference(cnf_transformation,[],[f18])).
% 27.22/4.20
% 27.22/4.20 tff(f30,plain,(
% 27.22/4.20 d(hamburg,kiel) = 90),
% 27.22/4.20 inference(cnf_transformation,[],[f18])).
% 27.22/4.20
% 27.22/4.20 tff(f34,plain,(
% 27.22/4.20 $less(640,d(kiel,saarbruecken))),
% 27.22/4.20 inference(cnf_transformation,[],[f18])).
% 27.22/4.20
% 27.22/4.20 cnf(c_50,plain,
% 27.22/4.20 ($uminus_int($uminus_int(X0_3)) = X0_3),
% 27.22/4.20 inference(cnf_transformation,[],[f14])).
% 27.22/4.20
% 27.22/4.20 cnf(c_53,plain,
% 27.22/4.20 (X0_3 = X1_3|$less_int(X0_3,X1_3)|$less_int(X1_3,X0_3)),
% 27.22/4.20 inference(cnf_transformation,[],[f11])).
% 27.22/4.20
% 27.22/4.20 cnf(c_54,plain,
% 27.22/4.20 (~$less_int(X0_3,X1_3)|~$less_int(X1_3,X2_3)|$less_int(X0_3,X2_3)),
% 27.22/4.20 inference(cnf_transformation,[],[f10])).
% 27.22/4.20
% 27.22/4.20 cnf(c_56,plain,
% 27.22/4.20 ($sum_int(X0_3,$uminus_int(X0_3)) = 0),
% 27.22/4.20 inference(cnf_transformation,[],[f8])).
% 27.22/4.20
% 27.22/4.20 cnf(c_57,plain,
% 27.22/4.20 ($sum_int($uminus_int(X0_3),$uminus_int(X1_3)) = $uminus_int($sum_int(X1_3,X0_3))),
% 27.22/4.20 inference(cnf_transformation,[],[f7])).
% 27.22/4.20
% 27.22/4.20 cnf(c_58,plain,
% 27.22/4.20 ($sum_int(X0_3,0) = X0_3),
% 27.22/4.20 inference(cnf_transformation,[],[f6])).
% 27.22/4.20
% 27.22/4.20 cnf(c_59,plain,
% 27.22/4.20 ($sum_int($sum_int(X0_3,X1_3),X2_3) = $sum_int(X0_3,$sum_int(X1_3,X2_3))),
% 27.22/4.20 inference(cnf_transformation,[],[f5])).
% 27.22/4.20
% 27.22/4.20 cnf(c_60,plain,
% 27.22/4.20 ($sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3)),
% 27.22/4.20 inference(cnf_transformation,[],[f4])).
% 27.22/4.20
% 27.22/4.20 cnf(c_61,negated_conjecture,
% 27.22/4.20 ($less_int(640,d(kiel,saarbruecken))),
% 27.22/4.20 inference(cnf_transformation,[],[f34])).
% 27.22/4.20
% 27.22/4.20 cnf(c_65,negated_conjecture,
% 27.22/4.20 (d(hamburg,kiel) = 90),
% 27.22/4.20 inference(cnf_transformation,[],[f30])).
% 27.22/4.20
% 27.22/4.20 cnf(c_67,negated_conjecture,
% 27.22/4.20 (d(hamburg,frankfurt) = 390),
% 27.22/4.20 inference(cnf_transformation,[],[f28])).
% 27.22/4.20
% 27.22/4.20 cnf(c_68,negated_conjecture,
% 27.22/4.20 (d(hamburg,cologne) = 360),
% 27.22/4.20 inference(cnf_transformation,[],[f27])).
% 27.22/4.20
% 27.22/4.20 cnf(c_69,negated_conjecture,
% 27.22/4.20 (d(saarbruecken,cologne) = 190),
% 27.22/4.20 inference(cnf_transformation,[],[f26])).
% 27.22/4.20
% 27.22/4.20 cnf(c_70,negated_conjecture,
% 27.22/4.20 (d(saarbruecken,frankfurt) = 160),
% 27.22/4.20 inference(cnf_transformation,[],[f25])).
% 27.22/4.20
% 27.22/4.20 cnf(c_75,negated_conjecture,
% 27.22/4.20 (~$less_int($sum_int(d(X0_13,X1_13),d(X1_13,X2_13)),d(X0_13,X2_13))),
% 27.22/4.20 inference(cnf_transformation,[],[f20])).
% 27.22/4.20
% 27.22/4.20 cnf(c_76,negated_conjecture,
% 27.22/4.20 (d(X0_13,X1_13) = d(X1_13,X0_13)),
% 27.22/4.20 inference(cnf_transformation,[],[f19])).
% 27.22/4.20
% 27.22/4.20 cnf(c_254,plain,
% 27.22/4.20 ($less_int(640,d(saarbruecken,kiel))),
% 27.22/4.20 inference(demodulation,[status(thm)],[c_61,c_76])).
% 27.22/4.20
% 27.22/4.20 cnf(c_255,plain,
% 27.22/4.20 (d(frankfurt,saarbruecken) = 160),
% 27.22/4.20 inference(demodulation,[status(thm)],[c_70,c_76])).
% 27.22/4.20
% 27.22/4.20 cnf(c_256,plain,
% 27.22/4.20 (d(cologne,saarbruecken) = 190),
% 27.22/4.20 inference(demodulation,[status(thm)],[c_69,c_76])).
% 27.22/4.20
% 27.22/4.20 cnf(c_259,plain,
% 27.22/4.20 (d(frankfurt,hamburg) = 390),
% 27.22/4.20 inference(demodulation,[status(thm)],[c_67,c_76])).
% 27.22/4.20
% 27.22/4.20 cnf(c_828,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int(X1_3,X2_3)) = $sum_int(X1_3,$sum_int(X0_3,X2_3))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_59,c_60])).
% 27.22/4.20
% 27.22/4.20 cnf(c_833,plain,
% 27.22/4.20 (~$less_int($sum_int(360,d(cologne,X0_13)),d(hamburg,X0_13))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_68,c_75])).
% 27.22/4.20
% 27.22/4.20 cnf(c_837,plain,
% 27.22/4.20 (~$less_int($sum_int(d(X0_13,X1_13),d(X0_13,X2_13)),d(X1_13,X2_13))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_76,c_75])).
% 27.22/4.20
% 27.22/4.20 cnf(c_982,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int(X1_3,$uminus_int(X0_3))) = $sum_int(X1_3,0)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_56,c_828])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1092,plain,
% 27.22/4.20 (~$less_int($sum_int(360,d(cologne,X0_13)),d(X0_13,hamburg))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_76,c_833])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1102,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int(X1_3,$uminus_int(X0_3))) = X1_3),
% 27.22/4.20 inference(demodulation,[status(thm)],[c_982,c_58])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1108,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int($uminus_int(X0_3),X1_3)) = X1_3),
% 27.22/4.20 inference(superposition,[status(thm)],[c_60,c_1102])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1111,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int(X1_3,$sum_int(X2_3,$uminus_int(X0_3)))) = $sum_int(X1_3,X2_3)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_1102,c_828])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1147,plain,
% 27.22/4.20 ($sum_int(d(X0_13,X1_13),d(X1_13,X2_13)) = d(X0_13,X2_13)|$less_int(d(X0_13,X2_13),$sum_int(d(X0_13,X1_13),d(X1_13,X2_13)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_53,c_75])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1247,plain,
% 27.22/4.20 (~$less_int(d(saarbruecken,kiel),X0_3)|$less_int(640,X0_3)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_254,c_54])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1326,plain,
% 27.22/4.20 ($sum_int($uminus_int(X0_3),$sum_int(X1_3,$uminus_int(X2_3))) = $sum_int(X1_3,$uminus_int($sum_int(X2_3,X0_3)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_57,c_828])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1330,plain,
% 27.22/4.20 ($sum_int(X0_3,$uminus_int($sum_int(X0_3,X1_3))) = $uminus_int(X1_3)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_57,c_1102])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1359,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int($sum_int(X1_3,$uminus_int(X0_3)),X2_3)) = $sum_int(X1_3,X2_3)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_1102,c_59])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1370,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int(X1_3,$sum_int($uminus_int(X0_3),X2_3))) = $sum_int(X1_3,X2_3)),
% 27.22/4.20 inference(theory_normalisation,[status(thm)],[c_1359,c_59,c_60])).
% 27.22/4.20
% 27.22/4.20 cnf(c_1802,plain,
% 27.22/4.20 ($sum_int(X0_3,$uminus_int($sum_int(X1_3,X0_3))) = $uminus_int(X1_3)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_57,c_1108])).
% 27.22/4.20
% 27.22/4.20 cnf(c_2218,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int(X1_3,$sum_int(X2_3,$sum_int(X3_3,$uminus_int(X0_3))))) = $sum_int(X1_3,$sum_int(X2_3,X3_3))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_1111,c_828])).
% 27.22/4.20
% 27.22/4.20 cnf(c_3292,plain,
% 27.22/4.20 (~$less_int($sum_int(360,190),d(saarbruecken,hamburg))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_256,c_1092])).
% 27.22/4.20
% 27.22/4.20 cnf(c_4293,plain,
% 27.22/4.20 ($sum_int(X0_3,$uminus_int($sum_int(X1_3,$sum_int(X0_3,X2_3)))) = $uminus_int($sum_int(X1_3,X2_3))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_828,c_1330])).
% 27.22/4.20
% 27.22/4.20 cnf(c_5542,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int(X1_3,$sum_int(X2_3,$uminus_int($sum_int(X3_3,X0_3))))) = $sum_int(X1_3,$sum_int(X2_3,$uminus_int(X3_3)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_1326,c_1370])).
% 27.22/4.20
% 27.22/4.20 cnf(c_5896,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int($uminus_int($sum_int(X1_3,X0_3)),X2_3)) = $sum_int($uminus_int(X1_3),X2_3)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_1802,c_59])).
% 27.22/4.20
% 27.22/4.20 cnf(c_7160,plain,
% 27.22/4.20 (~$less_int($sum_int(390,d(frankfurt,X0_13)),d(hamburg,X0_13))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_259,c_837])).
% 27.22/4.20
% 27.22/4.20 cnf(c_8743,plain,
% 27.22/4.20 ($sum_int(d(X0_13,X1_13),d(X1_13,X2_13)) = d(X0_13,X2_13)|$less_int(d(X2_13,X0_13),$sum_int(d(X0_13,X1_13),d(X1_13,X2_13)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_76,c_1147])).
% 27.22/4.20
% 27.22/4.20 cnf(c_8967,plain,
% 27.22/4.20 ($sum_int(d(X0_13,X1_13),d(X1_13,X2_13)) = d(X0_13,X2_13)|$less_int(d(X2_13,X0_13),$sum_int(d(X1_13,X0_13),d(X1_13,X2_13)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_76,c_8743])).
% 27.22/4.20
% 27.22/4.20 cnf(c_17499,plain,
% 27.22/4.20 ($sum_int(d(kiel,hamburg),d(hamburg,X0_13)) = d(kiel,X0_13)|$less_int(d(X0_13,kiel),$sum_int(90,d(hamburg,X0_13)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_65,c_8967])).
% 27.22/4.20
% 27.22/4.20 cnf(c_18070,plain,
% 27.22/4.20 ($sum_int(90,d(hamburg,X0_13)) = d(kiel,X0_13)|$less_int(d(X0_13,kiel),$sum_int(90,d(hamburg,X0_13)))),
% 27.22/4.20 inference(demodulation,[status(thm)],[c_17499,c_65,c_76])).
% 27.22/4.20
% 27.22/4.20 cnf(c_18083,plain,
% 27.22/4.20 ($sum_int(90,d(hamburg,X0_13)) = d(kiel,X0_13)|$less_int(d(X0_13,kiel),$sum_int(90,d(X0_13,hamburg)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_76,c_18070])).
% 27.22/4.20
% 27.22/4.20 cnf(c_25621,plain,
% 27.22/4.20 (~$less_int(550,d(saarbruecken,hamburg))),
% 27.22/4.20 inference(smt_theory_normalisation,[status(thm)],[c_3292])).
% 27.22/4.20
% 27.22/4.20 cnf(c_32390,plain,
% 27.22/4.20 ($sum_int(90,d(hamburg,saarbruecken)) = d(kiel,saarbruecken)|$less_int(640,$sum_int(90,d(saarbruecken,hamburg)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_18083,c_1247])).
% 27.22/4.20
% 27.22/4.20 cnf(c_37902,plain,
% 27.22/4.20 (~$less_int($sum_int(390,160),d(hamburg,saarbruecken))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_255,c_7160])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51280,plain,
% 27.22/4.20 ($sum_int(90,d(hamburg,saarbruecken)) = d(kiel,saarbruecken)|$less_int(550,d(saarbruecken,hamburg))),
% 27.22/4.20 inference(smt_theory_normalisation,[status(thm)],[c_32390])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51281,plain,
% 27.22/4.20 ($sum_int(90,d(hamburg,saarbruecken)) = d(kiel,saarbruecken)),
% 27.22/4.20 inference(global_subsumption_just,
% 27.22/4.20 [status(thm)],
% 27.22/4.20 [c_51280,c_25621,c_51280])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51283,plain,
% 27.22/4.20 ($sum_int(90,d(hamburg,saarbruecken)) = d(saarbruecken,kiel)),
% 27.22/4.20 inference(demodulation,[status(thm)],[c_51281,c_76])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51284,plain,
% 27.22/4.20 ($sum_int(d(hamburg,saarbruecken),$sum_int($uminus_int(d(saarbruecken,kiel)),X0_3)) = $sum_int($uminus_int(90),X0_3)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51283,c_5896])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51289,plain,
% 27.22/4.20 ($sum_int(90,$uminus_int($sum_int(X0_3,d(saarbruecken,kiel)))) = $uminus_int($sum_int(X0_3,d(hamburg,saarbruecken)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51283,c_4293])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51292,plain,
% 27.22/4.20 ($sum_int(90,$sum_int(X0_3,d(hamburg,saarbruecken))) = $sum_int(X0_3,d(saarbruecken,kiel))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51283,c_828])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51296,plain,
% 27.22/4.20 ($sum_int(90,$uminus_int(d(saarbruecken,kiel))) = $uminus_int(d(hamburg,saarbruecken))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51283,c_1330])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51646,plain,
% 27.22/4.20 ($sum_int(d(saarbruecken,kiel),$uminus_int(d(hamburg,saarbruecken))) = 90),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51296,c_1102])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51654,plain,
% 27.22/4.20 ($sum_int(d(saarbruecken,kiel),$sum_int(X0_3,$sum_int(X1_3,$uminus_int(d(hamburg,saarbruecken))))) = $sum_int(X0_3,$sum_int(X1_3,90))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51296,c_2218])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51685,plain,
% 27.22/4.20 ($sum_int(-90,d(saarbruecken,kiel)) = d(hamburg,saarbruecken)),
% 27.22/4.20 inference(smt_theory_normalisation,[status(thm)],[c_51292])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51687,plain,
% 27.22/4.20 ($sum_int(d(saarbruecken,kiel),$uminus_int(d(hamburg,saarbruecken))) = $uminus_int(-90)),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51685,c_1802])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51700,plain,
% 27.22/4.20 ($sum_int(d(saarbruecken,kiel),$sum_int(X0_3,$sum_int(X1_3,$uminus_int(d(hamburg,saarbruecken))))) = $sum_int(X0_3,$sum_int(X1_3,$uminus_int(-90)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51685,c_5542])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51704,plain,
% 27.22/4.20 ($uminus_int(-90) = 90),
% 27.22/4.20 inference(light_normalisation,[status(thm)],[c_51687,c_51646])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51706,plain,
% 27.22/4.20 ($sum_int(X0_3,$sum_int(X1_3,$uminus_int(-90))) = $sum_int(X0_3,$sum_int(X1_3,90))),
% 27.22/4.20 inference(light_normalisation,[status(thm)],[c_51700,c_51654])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51984,plain,
% 27.22/4.20 ($sum_int(d(hamburg,saarbruecken),$product_int(-1,d(saarbruecken,kiel))) = -90),
% 27.22/4.20 inference(smt_theory_normalisation,[status(thm)],[c_51284])).
% 27.22/4.20
% 27.22/4.20 cnf(c_51997,plain,
% 27.22/4.20 ($sum_int(d(hamburg,saarbruecken),$uminus_int(-90)) = $uminus_int($product_int(-1,d(saarbruecken,kiel)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_51984,c_1330])).
% 27.22/4.20
% 27.22/4.20 cnf(c_52003,plain,
% 27.22/4.20 ($sum_int($uminus_int(-90),d(hamburg,saarbruecken)) = $uminus_int($product_int(-1,d(saarbruecken,kiel)))),
% 27.22/4.20 inference(theory_normalisation,[status(thm)],[c_51997,c_59,c_60])).
% 27.22/4.20
% 27.22/4.20 cnf(c_52004,plain,
% 27.22/4.20 ($uminus_int($product_int(-1,d(saarbruecken,kiel))) = d(saarbruecken,kiel)),
% 27.22/4.20 inference(light_normalisation,[status(thm)],[c_52003,c_51283,c_51704])).
% 27.22/4.20
% 27.22/4.20 cnf(c_52200,plain,
% 27.22/4.20 ($product_int(-1,d(saarbruecken,kiel)) = $uminus_int(d(saarbruecken,kiel))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_52004,c_50])).
% 27.22/4.20
% 27.22/4.20 cnf(c_52410,plain,
% 27.22/4.20 ($sum_int(-90,$product_int(-1,d(hamburg,saarbruecken))) = $product_int(-1,d(saarbruecken,kiel))),
% 27.22/4.20 inference(smt_theory_normalisation,[status(thm)],[c_51289])).
% 27.22/4.20
% 27.22/4.20 cnf(c_52411,plain,
% 27.22/4.20 ($sum_int(-90,$product_int(-1,d(hamburg,saarbruecken))) = $uminus_int(d(saarbruecken,kiel))),
% 27.22/4.20 inference(light_normalisation,[status(thm)],[c_52410,c_52200])).
% 27.22/4.20
% 27.22/4.20 cnf(c_52426,plain,
% 27.22/4.20 ($sum_int($product_int(-1,d(hamburg,saarbruecken)),$sum_int(X0_3,$sum_int(X1_3,$uminus_int($uminus_int(d(saarbruecken,kiel)))))) = $sum_int(X0_3,$sum_int(X1_3,$uminus_int(-90)))),
% 27.22/4.20 inference(superposition,[status(thm)],[c_52411,c_5542])).
% 27.22/4.20
% 27.22/4.20 cnf(c_52436,plain,
% 27.22/4.20 ($sum_int($uminus_int($uminus_int(d(saarbruecken,kiel))),$sum_int(X0_3,$sum_int(X1_3,$product_int(-1,d(hamburg,saarbruecken))))) = $sum_int(X0_3,$sum_int(X1_3,$uminus_int(-90)))),
% 27.22/4.20 inference(theory_normalisation,[status(thm)],[c_52426,c_59,c_60])).
% 27.22/4.20
% 27.22/4.20 cnf(c_52437,plain,
% 27.22/4.20 ($sum_int($uminus_int($uminus_int(d(saarbruecken,kiel))),$sum_int(X0_3,$sum_int(X1_3,$product_int(-1,d(hamburg,saarbruecken))))) = $sum_int(X0_3,$sum_int(X1_3,90))),
% 27.22/4.20 inference(light_normalisation,[status(thm)],[c_52436,c_51706])).
% 27.22/4.20
% 27.22/4.20 cnf(c_53318,plain,
% 27.22/4.20 ($false),
% 27.22/4.20 inference(smt_impl_just,[status(thm)],[c_52437,c_37902,c_254])).
% 27.22/4.20
% 27.22/4.20
% 27.22/4.20 % SZS output end CNFRefutation for theBenchmark.p
% 27.22/4.20
% 27.22/4.21
%------------------------------------------------------------------------------