0.06/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : do_CVC4 %s %d 0.11/0.30 % Computer : n023.cluster.edu 0.11/0.30 % Model : x86_64 x86_64 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.30 % Memory : 8042.1875MB 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.30 % CPULimit : 960 0.11/0.30 % WCLimit : 120 0.11/0.30 % DateTime : Thu Jul 2 08:26:43 EDT 2020 0.11/0.30 % CPUTime : 0.16/0.41 %----Proving TF0_NAR, FOF, or CNF 0.16/0.41 ------- cvc4-fof casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 0.16/0.41 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 0.16/0.53 % SZS status Theorem for theBenchmark 0.16/0.53 % SZS output start Proof for theBenchmark 0.16/0.53 (skolem (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (or (not (precedes E1 E2 P)) (not (shortest_path V1 V2 P)) (= (forall ((E3 $$unsorted)) (or (not (= (tail_of E3) (head_of E2))) (not (= (head_of E3) (tail_of E1))) (not (edge E3))) ) (not (forall ((E3 $$unsorted)) (or (not (edge E3)) (not (= (tail_of E1) (tail_of E3))) (not (= (head_of E2) (head_of E3)))) )))) ) 0.16/0.53 ( skv_1 skv_2 skv_3 skv_4 skv_5 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E3 $$unsorted)) (or (not (= (tail_of E3) (head_of skv_4))) (not (= (head_of E3) (tail_of skv_3))) (not (edge E3))) ) 0.16/0.53 ( skv_6 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E3 $$unsorted)) (or (not (edge E3)) (not (= (tail_of E3) (tail_of skv_3))) (not (= (head_of E3) (head_of skv_4)))) ) 0.16/0.53 ( skv_7 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (or (not (edge E)) (not (= (tail_of E) skv_1)) (= (not (forall ((TP $$unsorted)) (or (not (path (head_of E) skv_2 TP)) (not (= (path_cons E TP) skv_5))) )) (and (= (path_cons E empty) skv_5) (= (head_of E) skv_2)))) ) 0.16/0.53 ( skv_8 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_6))) (let ((_let_3 (head_of skv_6))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_9 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_6))) (let ((_let_3 (head_of skv_6))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_10 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_7))) (let ((_let_3 (head_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_11 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_7))) (let ((_let_3 (head_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_12 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_4))) (let ((_let_3 (tail_of skv_3))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_13 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_4))) (let ((_let_3 (tail_of skv_3))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_14 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_8) skv_2 TP)) (not (= skv_5 (path_cons skv_8 TP)))) ) 0.16/0.53 ( skv_15 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (sequential E1 E2)) (not (on_path E2 skv_5)) (not (on_path E1 skv_5)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 0.16/0.53 ( skv_16 skv_17 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E3 $$unsorted)) (or (not (precedes E3 skv_4 skv_5)) (not (sequential skv_3 E3))) ) 0.16/0.53 ( skv_18 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((P $$unsorted)) (or (not (path (head_of skv_8) skv_2 P)) (less_or_equal (length_of skv_15) (length_of P))) ) 0.16/0.53 ( skv_19 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (or (not (edge E)) (not (= (tail_of E) (head_of skv_8))) (= (not (forall ((TP $$unsorted)) (or (not (path (head_of E) skv_2 TP)) (not (= (path_cons E TP) skv_15))) )) (and (= (path_cons E empty) skv_15) (= (head_of E) skv_2)))) ) 0.16/0.53 ( skv_20 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_20) skv_2 TP)) (not (= skv_15 (path_cons skv_20 TP)))) ) 0.16/0.53 ( skv_21 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_6))) (let ((_let_3 (head_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_22 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_6))) (let ((_let_3 (head_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_23 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_6))) (let ((_let_3 (tail_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_24 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_6))) (let ((_let_3 (tail_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_25 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (sequential E1 E2)) (not (on_path E2 skv_15)) (not (on_path E1 skv_15)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 0.16/0.53 ( skv_26 skv_27 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_3))) (or (not (edge E)) (= (and (= _let_0 skv_2) (= _let_1 _let_2)) (and (= _let_1 skv_2) (= _let_0 _let_2))))))) ) 0.16/0.53 ( skv_28 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_4))) (or (not (edge E)) (= (and (= _let_0 skv_1) (= _let_1 _let_2)) (and (= _let_1 skv_1) (= _let_0 _let_2))))))) ) 0.16/0.53 ( skv_29 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_3))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 skv_2)) (and (= _let_1 _let_2) (= _let_0 skv_2))))))) ) 0.16/0.53 ( skv_30 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_4))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 skv_1)) (and (= _let_1 _let_2) (= _let_0 skv_1))))))) ) 0.16/0.53 ( skv_31 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E3 $$unsorted)) (or (not (precedes E3 skv_4 skv_5)) (not (sequential skv_18 E3))) ) 0.16/0.53 ( skv_32 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_4))) (let ((_let_3 (tail_of skv_4))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_33 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_4))) (let ((_let_3 (tail_of skv_4))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_34 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (or (not (edge E)) (= (and (= _let_0 skv_1) (= _let_1 skv_2)) (and (= _let_1 skv_1) (= _let_0 skv_2)))))) ) 0.16/0.53 ( skv_35 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (or (not (edge E)) (= (and (= _let_0 skv_2) (= _let_1 skv_1)) (and (= _let_1 skv_2) (= _let_0 skv_1)))))) ) 0.16/0.53 ( skv_36 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_8))) (let ((_let_3 (head_of skv_8))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_37 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_8))) (let ((_let_3 (head_of skv_8))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_38 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of skv_4))) (or (not (on_path E skv_5)) (and (not (= (tail_of E) _let_0)) (not (= (head_of E) _let_0))))) ) 0.16/0.53 ( skv_39 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (sequential E1 E2)) (not (on_path E2 skv_21)) (not (on_path E1 skv_21)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 0.16/0.53 ( skv_40 skv_41 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (sequential E1 E2)) (not (on_path E2 skv_19)) (not (on_path E1 skv_19)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 0.16/0.53 ( skv_42 skv_43 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_14))) (let ((_let_3 (tail_of skv_14))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_44 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_14))) (let ((_let_3 (tail_of skv_14))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_45 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_13))) (let ((_let_3 (tail_of skv_13))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_46 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_13))) (let ((_let_3 (tail_of skv_13))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_47 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_12))) (let ((_let_3 (tail_of skv_12))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_48 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_12))) (let ((_let_3 (tail_of skv_12))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_49 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_11))) (let ((_let_3 (tail_of skv_11))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_50 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_11))) (let ((_let_3 (tail_of skv_11))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_51 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_10))) (let ((_let_3 (tail_of skv_10))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_52 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_10))) (let ((_let_3 (tail_of skv_10))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_53 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_9))) (let ((_let_3 (tail_of skv_9))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_54 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_9))) (let ((_let_3 (tail_of skv_9))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_55 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_3))) (let ((_let_3 (head_of skv_3))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_56 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_3))) (let ((_let_3 (head_of skv_3))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_57 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_6))) (let ((_let_3 (tail_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_58 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_6))) (let ((_let_3 (head_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_1 _let_3) (= _let_0 _let_2)))))))) ) 0.16/0.53 ( skv_59 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_6))) (let ((_let_3 (head_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_60 ) 0.16/0.53 ) 0.16/0.53 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_6))) (let ((_let_3 (tail_of skv_7))) (or (not (edge E)) (= (and (= _let_0 _let_2) (= _let_1 _let_3)) (and (= _let_1 _let_2) (= _let_0 _let_3)))))))) ) 0.16/0.53 ( skv_61 ) 0.16/0.53 ) 0.16/0.53 (instantiation (forall ((Things $$unsorted) (InThese $$unsorted)) (less_or_equal (number_of_in Things InThese) (number_of_in Things graph)) ) 0.16/0.53 ( sequential_pairs, graph ) 0.16/0.53 ( sequential_pairs, skv_5 ) 0.16/0.53 ( sequential_pairs, skv_15 ) 0.16/0.53 ( triangles, graph ) 0.16/0.53 ( triangles, skv_5 ) 0.16/0.53 ( triangles, skv_15 ) 0.16/0.53 ( edges, graph ) 0.16/0.53 ( edges, skv_5 ) 0.16/0.53 ( edges, skv_15 ) 0.16/0.53 ) 0.16/0.53 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted)) (or (not (vertex V1)) (= V1 V2) (not (vertex V2)) (not (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (or (not (edge E)) (= (and (= V1 _let_0) (= V2 _let_1)) (and (= V1 _let_1) (= V2 _let_0)))))) ))) ) 0.16/0.53 ( skv_1, skv_1 ) 0.16/0.53 ( skv_1, skv_2 ) 0.16/0.53 ( skv_1, (head_of skv_4) ) 0.16/0.53 ( skv_2, skv_1 ) 0.16/0.53 ( skv_2, (tail_of skv_3) ) 0.16/0.53 ( (head_of skv_4), skv_1 ) 0.16/0.53 ( (head_of skv_4), (head_of skv_4) ) 0.16/0.53 ( (head_of skv_4), (tail_of skv_3) ) 0.16/0.53 ( (head_of skv_4), (tail_of skv_4) ) 0.16/0.53 ( (tail_of skv_3), skv_2 ) 0.16/0.53 ( (tail_of skv_3), (head_of skv_4) ) 0.16/0.53 ( (tail_of skv_3), (tail_of skv_3) ) 0.16/0.53 ( (tail_of skv_3), (head_of skv_3) ) 0.16/0.53 ( (tail_of skv_6), (tail_of skv_6) ) 0.16/0.53 ( (tail_of skv_6), (head_of skv_6) ) 0.16/0.53 ( (tail_of skv_6), (tail_of skv_7) ) 0.16/0.53 ( (tail_of skv_6), (head_of skv_7) ) 0.16/0.53 ( (head_of skv_6), (tail_of skv_6) ) 0.16/0.53 ( (head_of skv_6), (head_of skv_6) ) 0.16/0.53 ( (head_of skv_6), (tail_of skv_7) ) 0.16/0.53 ( (head_of skv_6), (head_of skv_7) ) 0.16/0.53 ( (tail_of skv_7), (tail_of skv_6) ) 0.16/0.53 ( (tail_of skv_7), (head_of skv_6) ) 0.16/0.53 ( (tail_of skv_7), (head_of skv_7) ) 0.16/0.53 ( (head_of skv_7), (tail_of skv_6) ) 0.16/0.53 ( (head_of skv_7), (head_of skv_6) ) 0.16/0.53 ( (head_of skv_7), (tail_of skv_7) ) 0.16/0.53 ( (head_of skv_7), (head_of skv_7) ) 0.16/0.53 ( (tail_of skv_4), (head_of skv_4) ) 0.16/0.53 ( (head_of skv_3), (tail_of skv_3) ) 0.16/0.53 ( (head_of skv_3), (head_of skv_3) ) 0.16/0.53 ( (tail_of skv_8), (head_of skv_8) ) 0.16/0.53 ( (head_of skv_8), (tail_of skv_8) ) 0.16/0.53 ( (head_of skv_8), (head_of skv_8) ) 0.16/0.53 ( (head_of skv_9), (head_of skv_9) ) 0.16/0.53 ( (head_of skv_9), (tail_of skv_9) ) 0.16/0.53 ( (tail_of skv_9), (head_of skv_9) ) 0.16/0.53 ( (head_of skv_10), (head_of skv_10) ) 0.16/0.53 ( (head_of skv_10), (tail_of skv_10) ) 0.16/0.53 ( (tail_of skv_10), (head_of skv_10) ) 0.16/0.53 ( (head_of skv_11), (head_of skv_11) ) 0.16/0.53 ( (head_of skv_11), (tail_of skv_11) ) 0.16/0.53 ( (tail_of skv_11), (head_of skv_11) ) 0.16/0.53 ( (head_of skv_12), (head_of skv_12) ) 0.16/0.53 ( (head_of skv_12), (tail_of skv_12) ) 0.16/0.53 ( (tail_of skv_12), (head_of skv_12) ) 0.16/0.53 ( (head_of skv_13), (head_of skv_13) ) 0.16/0.53 ( (head_of skv_13), (tail_of skv_13) ) 0.16/0.53 ( (tail_of skv_13), (head_of skv_13) ) 0.16/0.53 ( (head_of skv_14), (head_of skv_14) ) 0.16/0.53 ( (head_of skv_14), (tail_of skv_14) ) 0.16/0.53 ( (tail_of skv_14), (head_of skv_14) ) 0.16/0.53 ) 0.16/0.53 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (and (path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (or (not (path V1 V2 P)) (less_or_equal (length_of SP) (length_of P))) )) (shortest_path V1 V2 SP)) ) 0.16/0.53 ( skv_1, skv_2, skv_5 ) 0.16/0.53 ( (head_of skv_8), skv_2, skv_15 ) 0.16/0.53 ( (head_of skv_8), skv_2, skv_19 ) 0.16/0.53 ( (head_of skv_20), skv_2, skv_21 ) 0.16/0.53 ) 0.16/0.53 (instantiation (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (sequential E1 E2) (and (edge E1) (edge E2) (= (tail_of E2) (head_of E1)) (not (= E1 E2)))) ) 0.16/0.53 ( skv_3, skv_4 ) 0.16/0.53 ( skv_3, skv_18 ) 0.16/0.54 ( skv_4, skv_3 ) 0.16/0.54 ( skv_4, skv_4 ) 0.16/0.54 ( skv_16, skv_17 ) 0.16/0.54 ( skv_18, skv_4 ) 0.16/0.54 ( skv_18, skv_32 ) 0.16/0.54 ( skv_26, skv_27 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (V $$unsorted)) (or (not (in_path V P)) (not (path V1 V2 P)) (and (vertex V) (not (forall ((E $$unsorted)) (or (not (on_path E P)) (and (not (= V (tail_of E))) (not (= V (head_of E))))) )))) ) 0.16/0.54 ( skv_1, skv_2, skv_5, (head_of skv_4) ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (path V1 V2 P)) (and (vertex V1) (not (forall ((E $$unsorted)) (or (not (edge E)) (not (= V1 (tail_of E))) (= (not (forall ((TP $$unsorted)) (or (not (path (head_of E) V2 TP)) (not (= P (path_cons E TP)))) )) (and (= P (path_cons E empty)) (= V2 (head_of E))))) )) (vertex V2))) ) 0.16/0.54 ( skv_1, skv_2, skv_5 ) 0.16/0.54 ( (head_of skv_8), skv_2, skv_15 ) 0.16/0.54 ( (head_of skv_8), skv_2, skv_19 ) 0.16/0.54 ( (head_of skv_20), skv_2, skv_21 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_775 $$unsorted) (BOUND_VARIABLE_776 $$unsorted) (BOUND_VARIABLE_777 $$unsorted)) (or (not (path V1 V2 P)) (not (on_path BOUND_VARIABLE_775 P)) (and (or (not (precedes BOUND_VARIABLE_777 BOUND_VARIABLE_776 P)) (not (sequential BOUND_VARIABLE_775 BOUND_VARIABLE_777))) (not (sequential BOUND_VARIABLE_775 BOUND_VARIABLE_776))) (not (on_path BOUND_VARIABLE_776 P)) (precedes BOUND_VARIABLE_775 BOUND_VARIABLE_776 P)) ) 0.16/0.54 ( skv_5, skv_1, skv_2, skv_4, skv_3, skv_4 ) 0.16/0.54 ( skv_5, skv_1, skv_2, skv_4, skv_4, skv_3 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_819 $$unsorted) (BOUND_VARIABLE_820 $$unsorted)) (or (not (path V1 V2 P)) (not (precedes BOUND_VARIABLE_819 BOUND_VARIABLE_820 P)) (and (on_path BOUND_VARIABLE_820 P) (on_path BOUND_VARIABLE_819 P) (= (forall ((E3 $$unsorted)) (or (not (precedes E3 BOUND_VARIABLE_820 P)) (not (sequential BOUND_VARIABLE_819 E3))) ) (sequential BOUND_VARIABLE_819 BOUND_VARIABLE_820)))) ) 0.16/0.54 ( skv_5, skv_1, skv_2, skv_3, skv_4 ) 0.16/0.54 ( skv_5, skv_1, skv_2, skv_18, skv_4 ) 0.16/0.54 ( skv_5, skv_1, skv_2, skv_32, skv_4 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (E $$unsorted)) (or (not (path V1 V2 P)) (not (on_path E P)) (and (in_path (head_of E) P) (edge E) (in_path (tail_of E) P))) ) 0.16/0.54 ( skv_1, skv_2, skv_5, skv_4 ) 0.16/0.54 ( skv_1, skv_2, skv_5, skv_29 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_953 $$unsorted)) (or (not (shortest_path V1 V2 P)) (not (precedes E1 E2 P)) (and (not (precedes E2 E1 P)) (or (not (= (head_of E2) (head_of BOUND_VARIABLE_953))) (not (= (tail_of E1) (tail_of BOUND_VARIABLE_953)))))) ) 0.16/0.54 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_4 ) 0.16/0.54 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_6 ) 0.16/0.54 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_7 ) 0.16/0.54 ( skv_1, skv_2, skv_4, skv_3, skv_5, skv_4 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((E $$unsorted)) (or (not (edge E)) (and (vertex (head_of E)) (vertex (tail_of E)))) ) 0.16/0.54 ( skv_3 ) 0.16/0.54 ( skv_4 ) 0.16/0.54 ( skv_6 ) 0.16/0.54 ( skv_7 ) 0.16/0.54 ( skv_8 ) 0.16/0.54 ( skv_9 ) 0.16/0.54 ( skv_10 ) 0.16/0.54 ( skv_11 ) 0.16/0.54 ( skv_12 ) 0.16/0.54 ( skv_13 ) 0.16/0.54 ( skv_14 ) 0.16/0.54 ( skv_16 ) 0.16/0.54 ( skv_17 ) 0.16/0.54 ( skv_18 ) 0.16/0.54 ( skv_20 ) 0.16/0.54 ( skv_22 ) 0.16/0.54 ( skv_23 ) 0.16/0.54 ( skv_24 ) 0.16/0.54 ( skv_25 ) 0.16/0.54 ( skv_28 ) 0.16/0.54 ( skv_29 ) 0.16/0.54 ( skv_30 ) 0.16/0.54 ( skv_31 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((E $$unsorted)) (or (not (edge E)) (not (= (head_of E) (tail_of E)))) ) 0.16/0.54 ( skv_3 ) 0.16/0.54 ( skv_4 ) 0.16/0.54 ( skv_6 ) 0.16/0.54 ( skv_7 ) 0.16/0.54 ( skv_8 ) 0.16/0.54 ( skv_9 ) 0.16/0.54 ( skv_10 ) 0.16/0.54 ( skv_11 ) 0.16/0.54 ( skv_12 ) 0.16/0.54 ( skv_13 ) 0.16/0.54 ( skv_14 ) 0.16/0.54 ( skv_16 ) 0.16/0.54 ( skv_17 ) 0.16/0.54 ( skv_18 ) 0.16/0.54 ( skv_20 ) 0.16/0.54 ( skv_22 ) 0.16/0.54 ( skv_23 ) 0.16/0.54 ( skv_24 ) 0.16/0.54 ( skv_25 ) 0.16/0.54 ( skv_28 ) 0.16/0.54 ( skv_29 ) 0.16/0.54 ( skv_30 ) 0.16/0.54 ( skv_31 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (path V1 V2 P)) (= (number_of_in sequential_pairs P) (minus (length_of P) n1))) ) 0.16/0.54 ( skv_1, skv_2, skv_5 ) 0.16/0.54 ( (head_of skv_8), skv_2, skv_15 ) 0.16/0.54 ( (head_of skv_8), skv_2, skv_19 ) 0.16/0.54 ( (head_of skv_20), skv_2, skv_21 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (or (not (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (sequential E1 E2)) (not (on_path E2 P)) (not (on_path E1 P)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) )) (not (path V1 V2 P)) (= (number_of_in sequential_pairs P) (number_of_in triangles P))) ) 0.16/0.54 ( skv_5, skv_1, skv_2 ) 0.16/0.54 ( skv_15, (head_of skv_8), skv_2 ) 0.16/0.54 ( skv_19, (head_of skv_8), skv_2 ) 0.16/0.54 ( skv_21, (head_of skv_20), skv_2 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (path V1 V2 P)) (= (number_of_in edges P) (length_of P))) ) 0.16/0.54 ( skv_1, skv_2, skv_5 ) 0.16/0.54 ( (head_of skv_8), skv_2, skv_15 ) 0.16/0.54 ( (head_of skv_8), skv_2, skv_19 ) 0.16/0.54 ( (head_of skv_20), skv_2, skv_21 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((E3 $$unsorted)) (or (not (= (tail_of E3) (head_of skv_4))) (not (= (head_of E3) (tail_of skv_3))) (not (edge E3))) ) 0.16/0.54 ( skv_3 ) 0.16/0.54 ( skv_4 ) 0.16/0.54 ( skv_6 ) 0.16/0.54 ( skv_7 ) 0.16/0.54 ( skv_8 ) 0.16/0.54 ( skv_9 ) 0.16/0.54 ( skv_10 ) 0.16/0.54 ( skv_11 ) 0.16/0.54 ( skv_12 ) 0.16/0.54 ( skv_13 ) 0.16/0.54 ( skv_14 ) 0.16/0.54 ( skv_16 ) 0.16/0.54 ( skv_17 ) 0.16/0.54 ( skv_18 ) 0.16/0.54 ( skv_20 ) 0.16/0.54 ( skv_22 ) 0.16/0.54 ( skv_23 ) 0.16/0.54 ( skv_24 ) 0.16/0.54 ( skv_25 ) 0.16/0.54 ( skv_28 ) 0.16/0.54 ( skv_29 ) 0.16/0.54 ( skv_30 ) 0.16/0.54 ( skv_31 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((E3 $$unsorted)) (or (not (edge E3)) (not (= (tail_of E3) (tail_of skv_3))) (not (= (head_of E3) (head_of skv_4)))) ) 0.16/0.54 ( skv_3 ) 0.16/0.54 ( skv_4 ) 0.16/0.54 ( skv_6 ) 0.16/0.54 ( skv_7 ) 0.16/0.54 ( skv_8 ) 0.16/0.54 ( skv_9 ) 0.16/0.54 ( skv_10 ) 0.16/0.54 ( skv_11 ) 0.16/0.54 ( skv_12 ) 0.16/0.54 ( skv_13 ) 0.16/0.54 ( skv_14 ) 0.16/0.54 ( skv_16 ) 0.16/0.54 ( skv_17 ) 0.16/0.54 ( skv_18 ) 0.16/0.54 ( skv_20 ) 0.16/0.54 ( skv_22 ) 0.16/0.54 ( skv_23 ) 0.16/0.54 ( skv_24 ) 0.16/0.54 ( skv_25 ) 0.16/0.54 ( skv_28 ) 0.16/0.54 ( skv_29 ) 0.16/0.54 ( skv_30 ) 0.16/0.54 ( skv_31 ) 0.16/0.54 ) 0.16/0.54 (instantiation (forall ((P $$unsorted)) (or (not (path skv_1 skv_2 P)) (less_or_equal (length_of skv_5) (length_of P))) ) 0.16/0.54 ( skv_5 ) 0.16/0.54 ( skv_15 ) 0.16/0.54 ( skv_19 ) 0.16/0.54 ) 0.16/0.54 % SZS output end Proof for theBenchmark 0.16/0.54 EOF