0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.02/0.24 % Computer : n131.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Fri Jul 13 15:56:59 CDT 2018 0.02/0.24 % CPUTime : 0.07/0.28 %----Proving without arithmetic mode 0.07/0.28 ------- cvc4-fof casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ... 0.07/0.28 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 20.78/26.02 --- Run --no-e-matching --full-saturate-quant at 20... 40.79/46.04 --- Run --finite-model-find --uf-ss=no-minimal at 15... 55.79/61.08 --- Run --multi-trigger-when-single --full-saturate-quant at 5... 55.89/61.16 % SZS status Theorem for theBenchmark 55.89/61.17 % SZS output start Proof for theBenchmark 55.89/61.17 (skolem (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (or (not (precedes E1 E2 P)) (not (sequential E1 E2)) (not (shortest_path V1 V2 P)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 55.89/61.17 ( skv_1 skv_2 skv_3 skv_4 skv_5 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((E3 $$unsorted)) (or (not (= (head_of E3) (tail_of skv_3))) (not (= (tail_of E3) (head_of skv_4))) (not (edge E3))) ) 55.89/61.17 ( skv_6 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (forall ((E $$unsorted)) (or (= (and (= (path_cons E empty) skv_5) (= _let_0 skv_2)) (not (forall ((TP $$unsorted)) (or (not (path _let_0 skv_2 TP)) (not (= (path_cons E TP) skv_5))) ))) (not (= (tail_of E) skv_1)) (not (edge E))) )) 55.89/61.17 ( skv_7 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E1 skv_5)) (not (sequential E1 E2)) (not (on_path E2 skv_5)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 55.89/61.17 ( skv_8 skv_9 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_7) skv_2 TP)) (not (= skv_5 (path_cons skv_7 TP)))) ) 55.89/61.17 ( skv_10 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (forall ((E $$unsorted)) (or (= (and (= _let_0 skv_1) (= _let_1 skv_2)) (and (= _let_0 skv_2) (= _let_1 skv_1))) (not (edge E))) ))) 55.89/61.17 ( skv_11 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_3))) (let ((_let_3 (tail_of skv_3))) (forall ((E $$unsorted)) (or (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_0 _let_2) (= _let_1 _let_3))) (not (edge E))) ))))) 55.89/61.17 ( skv_12 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (forall ((E $$unsorted)) (or (= (and (= (path_cons E empty) skv_10) (= _let_0 skv_2)) (not (forall ((TP $$unsorted)) (or (not (path _let_0 skv_2 TP)) (not (= (path_cons E TP) skv_10))) ))) (not (= (tail_of E) (head_of skv_7))) (not (edge E))) )) 55.89/61.17 ( skv_13 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E1 skv_10)) (not (sequential E1 E2)) (not (on_path E2 skv_10)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 55.89/61.17 ( skv_14 skv_15 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_13) skv_2 TP)) (not (= skv_10 (path_cons skv_13 TP)))) ) 55.89/61.17 ( skv_16 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of skv_4))) (forall ((E $$unsorted)) (or (not (on_path E skv_5)) (and (not (= (tail_of E) _let_0)) (not (= (head_of E) _let_0)))) )) 55.89/61.17 ( skv_17 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (forall ((E $$unsorted)) (or (= (and (= (path_cons E empty) skv_16) (= _let_0 skv_2)) (not (forall ((TP $$unsorted)) (or (not (path _let_0 skv_2 TP)) (not (= (path_cons E TP) skv_16))) ))) (not (= (tail_of E) (head_of skv_13))) (not (edge E))) )) 55.89/61.17 ( skv_18 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((P $$unsorted)) (or (not (path (head_of skv_13) skv_2 P)) (less_or_equal (length_of skv_16) (length_of P))) ) 55.89/61.17 ( skv_19 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E1 skv_16)) (not (sequential E1 E2)) (not (on_path E2 skv_16)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 55.89/61.17 ( skv_20 skv_21 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_3))) (forall ((E $$unsorted)) (or (= (and (= _let_0 _let_2) (= _let_1 skv_2)) (and (= _let_0 skv_2) (= _let_1 _let_2))) (not (edge E))) )))) 55.89/61.17 ( skv_22 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_3))) (forall ((E $$unsorted)) (or (= (and (= _let_0 _let_2) (= _let_1 skv_1)) (and (= _let_0 skv_1) (= _let_1 _let_2))) (not (edge E))) )))) 55.89/61.17 ( skv_23 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_18) skv_2 TP)) (not (= skv_16 (path_cons skv_18 TP)))) ) 55.89/61.17 ( skv_24 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (tail_of skv_4))) (forall ((E $$unsorted)) (or (not (on_path E skv_5)) (and (not (= (tail_of E) _let_0)) (not (= (head_of E) _let_0)))) )) 55.89/61.17 ( skv_25 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((E3 $$unsorted)) (or (not (= (head_of E3) (tail_of skv_8))) (not (= (tail_of E3) (head_of skv_9))) (not (edge E3))) ) 55.89/61.17 ( skv_26 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_8))) (let ((_let_3 (tail_of skv_8))) (forall ((E $$unsorted)) (or (= (and (= _let_0 _let_3) (= _let_1 _let_2)) (and (= _let_0 _let_2) (= _let_1 _let_3))) (not (edge E))) ))))) 55.89/61.17 ( skv_27 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_4))) (forall ((E $$unsorted)) (or (= (and (= _let_0 _let_2) (= _let_1 skv_2)) (and (= _let_0 skv_2) (= _let_1 _let_2))) (not (edge E))) )))) 55.89/61.17 ( skv_28 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (forall ((E $$unsorted)) (or (= (and (= (path_cons E empty) skv_19) (= _let_0 skv_2)) (not (forall ((TP $$unsorted)) (or (not (path _let_0 skv_2 TP)) (not (= (path_cons E TP) skv_19))) ))) (not (= (tail_of E) (head_of skv_13))) (not (edge E))) )) 55.89/61.17 ( skv_29 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (forall ((E $$unsorted)) (or (= (and (= (path_cons E empty) skv_24) (= _let_0 skv_2)) (not (forall ((TP $$unsorted)) (or (not (path _let_0 skv_2 TP)) (not (= (path_cons E TP) skv_24))) ))) (not (= (tail_of E) (head_of skv_18))) (not (edge E))) )) 55.89/61.17 ( skv_30 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((P $$unsorted)) (or (not (path (head_of skv_13) skv_2 P)) (less_or_equal (length_of skv_19) (length_of P))) ) 55.89/61.17 ( skv_31 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E1 skv_19)) (not (sequential E1 E2)) (not (on_path E2 skv_19)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 55.89/61.17 ( skv_32 skv_33 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E1 skv_24)) (not (sequential E1 E2)) (not (on_path E2 skv_24)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 55.89/61.17 ( skv_34 skv_35 ) 55.89/61.17 ) 55.89/61.17 (skolem (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_13))) (forall ((E $$unsorted)) (or (= (and (= _let_0 _let_2) (= _let_1 skv_1)) (and (= _let_0 skv_1) (= _let_1 _let_2))) (not (edge E))) )))) 55.89/61.17 ( skv_36 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_29) skv_2 TP)) (not (= skv_19 (path_cons skv_29 TP)))) ) 55.89/61.17 ( skv_37 ) 55.89/61.17 ) 55.89/61.17 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_30) skv_2 TP)) (not (= skv_24 (path_cons skv_30 TP)))) ) 55.89/61.17 ( skv_38 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((Things $$unsorted) (InThese $$unsorted)) (less_or_equal (number_of_in Things InThese) (number_of_in Things graph)) ) 55.89/61.17 ( sequential_pairs, graph ) 55.89/61.17 ( sequential_pairs, skv_5 ) 55.89/61.17 ( sequential_pairs, skv_10 ) 55.89/61.17 ( sequential_pairs, skv_16 ) 55.89/61.17 ( edges, graph ) 55.89/61.17 ( edges, skv_5 ) 55.89/61.17 ( edges, skv_10 ) 55.89/61.17 ( edges, skv_16 ) 55.89/61.17 ( triangles, graph ) 55.89/61.17 ( triangles, skv_5 ) 55.89/61.17 ( triangles, skv_10 ) 55.89/61.17 ( triangles, skv_16 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((E1 $$unsorted) (E2 $$unsorted) (E3 $$unsorted)) (= (triangle E1 E2 E3) (and (edge E2) (sequential E1 E2) (sequential E3 E1) (sequential E2 E3) (edge E3) (edge E1))) ) 55.89/61.17 ( skv_3, skv_3, skv_3 ) 55.89/61.17 ( skv_3, skv_3, skv_4 ) 55.89/61.17 ( skv_3, skv_4, skv_3 ) 55.89/61.17 ( skv_3, skv_4, skv_4 ) 55.89/61.17 ( skv_3, skv_4, skv_6 ) 55.89/61.17 ( skv_3, skv_6, skv_4 ) 55.89/61.17 ( skv_3, skv_6, skv_6 ) 55.89/61.17 ( skv_3, skv_7, skv_7 ) 55.89/61.17 ( skv_4, skv_3, skv_3 ) 55.89/61.17 ( skv_4, skv_3, skv_4 ) 55.89/61.17 ( skv_4, skv_4, skv_3 ) 55.89/61.17 ( skv_4, skv_4, skv_4 ) 55.89/61.17 ( skv_4, skv_6, skv_6 ) 55.89/61.17 ( skv_6, skv_3, skv_6 ) 55.89/61.17 ( skv_6, skv_4, skv_3 ) 55.89/61.17 ( skv_6, skv_6, skv_3 ) 55.89/61.17 ( skv_6, skv_6, skv_4 ) 55.89/61.17 ( skv_6, skv_6, skv_6 ) 55.89/61.17 ( skv_7, skv_7, skv_4 ) 55.89/61.17 ( skv_7, skv_7, skv_7 ) 55.89/61.17 ( skv_8, skv_4, skv_3 ) 55.89/61.17 ( skv_8, skv_9, skv_9 ) 55.89/61.17 ( skv_8, skv_11, skv_12 ) 55.89/61.17 ( skv_11, skv_12, skv_13 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (V $$unsorted)) (or (not (in_path V P)) (not (path V1 V2 P)) (and (not (forall ((E $$unsorted)) (or (not (on_path E P)) (and (not (= V (tail_of E))) (not (= V (head_of E))))) )) (vertex V))) ) 55.89/61.17 ( skv_1, skv_2, skv_5, (tail_of skv_4) ) 55.89/61.17 ( skv_1, skv_2, skv_5, (head_of skv_4) ) 55.89/61.17 ( (head_of skv_7), skv_2, skv_10, (head_of skv_3) ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_696 $$unsorted) (BOUND_VARIABLE_697 $$unsorted) (BOUND_VARIABLE_698 $$unsorted)) (or (not (path V1 V2 P)) (not (on_path BOUND_VARIABLE_697 P)) (and (not (sequential BOUND_VARIABLE_696 BOUND_VARIABLE_697)) (or (not (sequential BOUND_VARIABLE_696 BOUND_VARIABLE_698)) (not (precedes BOUND_VARIABLE_698 BOUND_VARIABLE_697 P)))) (not (on_path BOUND_VARIABLE_696 P)) (precedes BOUND_VARIABLE_696 BOUND_VARIABLE_697 P)) ) 55.89/61.17 ( skv_5, skv_1, skv_2, skv_4, skv_3, skv_6 ) 55.89/61.17 ( skv_5, skv_1, skv_2, skv_6, skv_3, skv_4 ) 55.89/61.17 ( skv_5, skv_1, skv_2, skv_8, skv_3, skv_4 ) 55.89/61.17 ( skv_5, skv_1, skv_2, skv_8, skv_9, skv_9 ) 55.89/61.17 ( skv_10, (head_of skv_7), skv_2, skv_3, skv_4, skv_4 ) 55.89/61.17 ) 55.89/61.17 (instantiation (let ((_let_0 (head_of E))) (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (path V1 V2 P)) (and (not (forall ((E $$unsorted)) (or (= (and (= P (path_cons E empty)) (= V2 _let_0)) (not (forall ((TP $$unsorted)) (or (not (path _let_0 V2 TP)) (not (= P (path_cons E TP)))) ))) (not (= V1 (tail_of E))) (not (edge E))) )) (vertex V2) (vertex V1))) )) 55.89/61.17 ( skv_1, skv_2, skv_5 ) 55.89/61.17 ( (head_of skv_7), skv_2, skv_10 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_16 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_19 ) 55.89/61.17 ( (head_of skv_18), skv_2, skv_24 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_772 $$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_772))) (not (= (tail_of E1) (tail_of BOUND_VARIABLE_772)))))) ) 55.89/61.17 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_3 ) 55.89/61.17 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_7 ) 55.89/61.17 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_8 ) 55.89/61.17 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_14 ) 55.89/61.17 ) 55.89/61.17 (instantiation (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (forall ((V1 $$unsorted) (V2 $$unsorted)) (or (= V1 V2) (not (vertex V2)) (not (vertex V1)) (not (forall ((E $$unsorted)) (or (= (and (= V1 _let_0) (= V2 _let_1)) (and (= V2 _let_0) (= V1 _let_1))) (not (edge E))) ))) ))) 55.89/61.17 ( skv_1, skv_2 ) 55.89/61.17 ( skv_1, (tail_of skv_3) ) 55.89/61.17 ( skv_1, (head_of skv_13) ) 55.89/61.17 ( skv_2, skv_1 ) 55.89/61.17 ( skv_2, (head_of skv_3) ) 55.89/61.17 ( skv_2, (head_of skv_4) ) 55.89/61.17 ( (head_of skv_3), skv_2 ) 55.89/61.17 ( (head_of skv_3), (tail_of skv_3) ) 55.89/61.17 ( (tail_of skv_3), skv_1 ) 55.89/61.17 ( (tail_of skv_3), (head_of skv_3) ) 55.89/61.17 ( (head_of skv_4), skv_2 ) 55.89/61.17 ( (head_of skv_8), (tail_of skv_8) ) 55.89/61.17 ( (tail_of skv_8), (head_of skv_8) ) 55.89/61.17 ( (head_of skv_13), skv_1 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (SP $$unsorted)) (= (and (path V1 V2 SP) (not (= V1 V2)) (forall ((P $$unsorted)) (or (not (path V1 V2 P)) (less_or_equal (length_of SP) (length_of P))) )) (shortest_path V1 V2 SP)) ) 55.89/61.17 ( skv_1, skv_2, skv_5 ) 55.89/61.17 ( skv_1, skv_2, skv_10 ) 55.89/61.17 ( (head_of skv_7), skv_2, skv_10 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_16 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_19 ) 55.89/61.17 ( (head_of skv_18), skv_2, skv_24 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_838 $$unsorted) (BOUND_VARIABLE_839 $$unsorted)) (or (not (path V1 V2 P)) (not (precedes BOUND_VARIABLE_838 BOUND_VARIABLE_839 P)) (and (= (forall ((E3 $$unsorted)) (or (not (sequential BOUND_VARIABLE_838 E3)) (not (precedes E3 BOUND_VARIABLE_839 P))) ) (sequential BOUND_VARIABLE_838 BOUND_VARIABLE_839)) (on_path BOUND_VARIABLE_839 P) (on_path BOUND_VARIABLE_838 P))) ) 55.89/61.17 ( skv_5, skv_1, skv_2, skv_3, skv_4 ) 55.89/61.17 ( skv_5, skv_1, skv_2, skv_8, skv_4 ) 55.89/61.17 ( skv_5, skv_1, skv_2, skv_9, skv_4 ) 55.89/61.17 ( skv_10, (head_of skv_7), skv_2, skv_3, skv_4 ) 55.89/61.17 ( skv_10, (head_of skv_7), skv_2, skv_4, skv_4 ) 55.89/61.17 ( skv_16, (head_of skv_13), skv_2, skv_20, skv_20 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted) (E $$unsorted)) (or (not (path V1 V2 P)) (not (on_path E P)) (and (edge E) (in_path (head_of E) P) (in_path (tail_of E) P))) ) 55.89/61.17 ( skv_1, skv_2, skv_5, skv_3 ) 55.89/61.17 ( skv_1, skv_2, skv_5, skv_4 ) 55.89/61.17 ( skv_1, skv_2, skv_5, skv_8 ) 55.89/61.17 ( skv_1, skv_2, skv_5, skv_17 ) 55.89/61.17 ( (head_of skv_7), skv_2, skv_10, skv_3 ) 55.89/61.17 ( (head_of skv_7), skv_2, skv_10, skv_14 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_16, skv_20 ) 55.89/61.17 ) 55.89/61.17 (instantiation (let ((_let_0 (tail_of BOUND_VARIABLE_916))) (let ((_let_1 (head_of BOUND_VARIABLE_916))) (forall ((V2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_916 $$unsorted) (BOUND_VARIABLE_917 $$unsorted)) (or (not (vertex _let_0)) (not (vertex V2)) (path _let_0 V2 P) (not (edge BOUND_VARIABLE_916)) (and (or (not (= P (path_cons BOUND_VARIABLE_916 BOUND_VARIABLE_917))) (not (path _let_1 V2 BOUND_VARIABLE_917))) (or (not (= V2 _let_1)) (not (= P (path_cons BOUND_VARIABLE_916 empty)))))) ))) 55.89/61.17 ( skv_2, skv_10, skv_7, skv_10 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((E $$unsorted)) (or (not (edge E)) (and (vertex (head_of E)) (vertex (tail_of E)))) ) 55.89/61.17 ( skv_3 ) 55.89/61.17 ( skv_4 ) 55.89/61.17 ( skv_6 ) 55.89/61.17 ( skv_7 ) 55.89/61.17 ( skv_8 ) 55.89/61.17 ( skv_9 ) 55.89/61.17 ( skv_13 ) 55.89/61.17 ( skv_14 ) 55.89/61.17 ( skv_15 ) 55.89/61.17 ( skv_17 ) 55.89/61.17 ( skv_18 ) 55.89/61.17 ( skv_22 ) 55.89/61.17 ( skv_23 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((E $$unsorted)) (or (not (edge E)) (not (= (tail_of E) (head_of E)))) ) 55.89/61.17 ( skv_3 ) 55.89/61.17 ( skv_4 ) 55.89/61.17 ( skv_6 ) 55.89/61.17 ( skv_7 ) 55.89/61.17 ( skv_8 ) 55.89/61.17 ( skv_9 ) 55.89/61.17 ( skv_13 ) 55.89/61.17 ( skv_14 ) 55.89/61.17 ( skv_15 ) 55.89/61.17 ( skv_17 ) 55.89/61.17 ( skv_18 ) 55.89/61.17 ( skv_22 ) 55.89/61.17 ( skv_23 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (sequential E1 E2) (and (edge E1) (= (tail_of E2) (head_of E1)) (not (= E1 E2)) (edge E2))) ) 55.89/61.17 ( skv_3, skv_3 ) 55.89/61.17 ( skv_3, skv_4 ) 55.89/61.17 ( skv_3, skv_6 ) 55.89/61.17 ( skv_3, skv_7 ) 55.89/61.17 ( skv_3, skv_9 ) 55.89/61.17 ( skv_4, skv_3 ) 55.89/61.17 ( skv_4, skv_4 ) 55.89/61.17 ( skv_4, skv_6 ) 55.89/61.17 ( skv_4, skv_7 ) 55.89/61.17 ( skv_6, skv_3 ) 55.89/61.17 ( skv_6, skv_4 ) 55.89/61.17 ( skv_6, skv_6 ) 55.89/61.17 ( skv_6, skv_11 ) 55.89/61.17 ( skv_7, skv_3 ) 55.89/61.17 ( skv_7, skv_4 ) 55.89/61.17 ( skv_7, skv_7 ) 55.89/61.17 ( skv_8, skv_4 ) 55.89/61.17 ( skv_8, skv_6 ) 55.89/61.17 ( skv_8, skv_9 ) 55.89/61.17 ( skv_8, skv_11 ) 55.89/61.17 ( skv_9, skv_4 ) 55.89/61.17 ( skv_9, skv_9 ) 55.89/61.17 ( skv_11, skv_12 ) 55.89/61.17 ( skv_11, skv_13 ) 55.89/61.17 ( skv_12, skv_12 ) 55.89/61.17 ( skv_12, skv_13 ) 55.89/61.17 ( skv_13, skv_8 ) 55.89/61.17 ( skv_14, skv_15 ) 55.89/61.17 ( skv_14, skv_17 ) 55.89/61.17 ( skv_15, skv_15 ) 55.89/61.17 ( skv_18, skv_18 ) 55.89/61.17 ( skv_20, skv_21 ) 55.89/61.17 ( skv_22, skv_22 ) 55.89/61.17 ( skv_23, skv_23 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (path V1 V2 P)) (= (number_of_in sequential_pairs P) (minus (length_of P) n1))) ) 55.89/61.17 ( skv_1, skv_2, skv_5 ) 55.89/61.17 ( (head_of skv_7), skv_2, skv_10 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_16 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_19 ) 55.89/61.17 ( (head_of skv_18), skv_2, skv_24 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (path V1 V2 P)) (= (number_of_in edges P) (length_of P))) ) 55.89/61.17 ( skv_1, skv_2, skv_5 ) 55.89/61.17 ( (head_of skv_7), skv_2, skv_10 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_16 ) 55.89/61.17 ( (head_of skv_13), skv_2, skv_19 ) 55.89/61.17 ( (head_of skv_18), skv_2, skv_24 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (or (not (path V1 V2 P)) (not (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E1 P)) (not (sequential E1 E2)) (not (on_path E2 P)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) )) (= (number_of_in sequential_pairs P) (number_of_in triangles P))) ) 55.89/61.17 ( skv_5, skv_1, skv_2 ) 55.89/61.17 ( skv_10, (head_of skv_7), skv_2 ) 55.89/61.17 ( skv_16, (head_of skv_13), skv_2 ) 55.89/61.17 ( skv_19, (head_of skv_13), skv_2 ) 55.89/61.17 ( skv_24, (head_of skv_18), skv_2 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted)) (or (not (shortest_path V1 V2 P)) (not (precedes E1 E2 P)) (not (forall ((E3 $$unsorted)) (or (not (= (tail_of E1) (head_of E3))) (not (= (head_of E2) (tail_of E3))) (not (edge E3))) ))) ) 55.89/61.17 ( skv_1, skv_2, skv_3, skv_4, skv_5 ) 55.89/61.17 ( skv_1, skv_2, skv_8, skv_9, skv_5 ) 55.89/61.17 ( skv_1, skv_2, skv_9, skv_9, skv_5 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((E3 $$unsorted)) (not (triangle skv_3 skv_4 E3)) ) 55.89/61.17 ( skv_6 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((P $$unsorted)) (or (not (path skv_1 skv_2 P)) (less_or_equal (length_of skv_5) (length_of P))) ) 55.89/61.17 ( skv_5 ) 55.89/61.17 ( skv_10 ) 55.89/61.17 ( skv_16 ) 55.89/61.17 ( skv_19 ) 55.89/61.17 ) 55.89/61.17 (instantiation (forall ((E3 $$unsorted)) (or (not (sequential skv_3 E3)) (not (precedes E3 skv_4 skv_5))) ) 55.89/61.17 ( skv_4 ) 55.89/61.17 ) 55.89/61.17 (instantiation (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (head_of skv_3))) (forall ((E $$unsorted)) (or (= (and (= _let_0 _let_2) (= _let_1 skv_2)) (and (= _let_0 skv_2) (= _let_1 _let_2))) (not (edge E))) )))) 55.89/61.17 ( skv_8 ) 55.89/61.17 ( skv_9 ) 55.89/61.17 ( skv_14 ) 55.89/61.17 ( skv_15 ) 55.89/61.17 ( skv_22 ) 55.89/61.17 ( skv_23 ) 55.89/61.17 ) 55.89/61.17 (instantiation (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (let ((_let_2 (tail_of skv_3))) (forall ((E $$unsorted)) (or (= (and (= _let_0 _let_2) (= _let_1 skv_1)) (and (= _let_0 skv_1) (= _let_1 _let_2))) (not (edge E))) )))) 55.89/61.17 ( skv_14 ) 55.89/61.17 ( skv_15 ) 55.89/61.17 ( skv_18 ) 55.89/61.17 ( skv_22 ) 55.89/61.17 ( skv_23 ) 55.89/61.17 ) 55.89/61.17 % SZS output end Proof for theBenchmark 55.89/61.18 EOF