0.04/0.07 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.08 % Command : do_CVC4 %s %d 0.07/0.27 % Computer : n032.cluster.edu 0.07/0.27 % Model : x86_64 x86_64 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.07/0.27 % Memory : 8042.1875MB 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64 0.07/0.27 % CPULimit : 960 0.07/0.27 % WCLimit : 120 0.07/0.27 % DateTime : Thu Jul 2 07:04:04 EDT 2020 0.07/0.27 % CPUTime : 0.11/0.37 %----Proving TF0_NAR, FOF, or CNF 0.11/0.38 ------- cvc4-fof casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 0.11/0.38 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 0.11/0.43 % SZS status Theorem for theBenchmark 0.11/0.43 % SZS output start Proof for theBenchmark 0.11/0.43 (skolem (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_1034 $$unsorted)) (let ((_let_0 (tail_of E1))) (let ((_let_1 (head_of E2))) (or (not (shortest_path V1 V2 P)) (not (precedes E1 E2 P)) (and (or (not (= _let_0 (tail_of BOUND_VARIABLE_1034))) (not (= _let_1 (head_of BOUND_VARIABLE_1034)))) (not (= _let_1 (head_of E1))) (not (= _let_0 _let_1)))))) ) 0.11/0.43 ( skv_1 skv_2 skv_3 skv_4 skv_5 skv_6 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((V1 $$unsorted) (V2 $$unsorted)) (or (not (vertex V1)) (= V1 V2) (not (vertex V2)) (not (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (or (not (edge E)) (= (and (= V1 _let_0) (= V2 _let_1)) (and (= V1 _let_1) (= V2 _let_0)))))) ))) ) 0.11/0.43 ( skv_7 skv_8 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((E $$unsorted)) (or (not (edge E)) (not (= (tail_of E) skv_1)) (= (not (forall ((TP $$unsorted)) (or (not (path (head_of E) skv_2 TP)) (not (= (path_cons E TP) skv_5))) )) (and (= (path_cons E empty) skv_5) (= (head_of E) skv_2)))) ) 0.11/0.43 ( skv_9 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_9) skv_2 TP)) (not (= skv_5 (path_cons skv_9 TP)))) ) 0.11/0.43 ( skv_10 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E2 skv_5)) (not (sequential E1 E2)) (not (on_path E1 skv_5)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 0.11/0.43 ( skv_11 skv_12 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((E3 $$unsorted)) (or (not (precedes E3 skv_4 skv_5)) (not (sequential skv_3 E3))) ) 0.11/0.43 ( skv_13 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((E $$unsorted)) (or (not (edge E)) (not (= (tail_of E) (head_of skv_9))) (= (not (forall ((TP $$unsorted)) (or (not (path (head_of E) skv_2 TP)) (not (= (path_cons E TP) skv_10))) )) (and (= (path_cons E empty) skv_10) (= (head_of E) skv_2)))) ) 0.11/0.43 ( skv_14 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((TP $$unsorted)) (or (not (path (head_of skv_14) skv_2 TP)) (not (= skv_10 (path_cons skv_14 TP)))) ) 0.11/0.43 ( skv_15 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (or (not (edge E)) (= (and (= _let_0 skv_7) (= _let_1 skv_8)) (and (= _let_1 skv_7) (= _let_0 skv_8)))))) ) 0.11/0.43 ( skv_16 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E2 skv_10)) (not (sequential E1 E2)) (not (on_path E1 skv_10)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) ) 0.11/0.43 ( skv_17 skv_18 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((E3 $$unsorted)) (or (not (precedes E3 skv_4 skv_5)) (not (sequential skv_13 E3))) ) 0.11/0.43 ( skv_19 ) 0.11/0.43 ) 0.11/0.43 (skolem (forall ((P $$unsorted)) (or (not (path (head_of skv_9) skv_2 P)) (less_or_equal (length_of skv_10) (length_of P))) ) 0.11/0.43 ( skv_20 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((Things $$unsorted) (InThese $$unsorted)) (less_or_equal (number_of_in Things InThese) (number_of_in Things graph)) ) 0.11/0.43 ( sequential_pairs, graph ) 0.11/0.43 ( sequential_pairs, skv_5 ) 0.11/0.43 ( sequential_pairs, skv_10 ) 0.11/0.43 ( triangles, graph ) 0.11/0.43 ( triangles, skv_5 ) 0.11/0.43 ( triangles, skv_10 ) 0.11/0.43 ( edges, graph ) 0.11/0.43 ( edges, skv_5 ) 0.11/0.43 ( edges, skv_10 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((V1 $$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)))))) ))) ) 0.11/0.43 ( skv_1, skv_1 ) 0.11/0.43 ( skv_1, skv_2 ) 0.11/0.43 ( skv_2, skv_1 ) 0.11/0.43 ( (tail_of skv_3), (head_of skv_3) ) 0.11/0.43 ( (tail_of skv_6), (head_of skv_6) ) 0.11/0.43 ( (head_of skv_4), (head_of skv_4) ) 0.11/0.43 ( (head_of skv_4), (tail_of skv_4) ) 0.11/0.43 ( (head_of skv_6), (tail_of skv_6) ) 0.11/0.43 ( (head_of skv_6), (head_of skv_6) ) 0.11/0.43 ( (head_of skv_3), (tail_of skv_3) ) 0.11/0.43 ( (head_of skv_3), (head_of skv_3) ) 0.11/0.43 ( skv_7, skv_7 ) 0.11/0.43 ( skv_7, skv_8 ) 0.11/0.43 ( skv_8, skv_7 ) 0.11/0.43 ( (tail_of skv_4), (head_of skv_4) ) 0.11/0.43 ( (tail_of skv_9), (head_of skv_9) ) 0.11/0.43 ( (head_of skv_9), (tail_of skv_9) ) 0.11/0.43 ( (head_of skv_9), (head_of skv_9) ) 0.11/0.43 ) 0.11/0.43 (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)) ) 0.11/0.43 ( skv_1, skv_2, skv_5 ) 0.11/0.43 ( (head_of skv_9), skv_2, skv_10 ) 0.11/0.43 ( (head_of skv_9), skv_2, skv_20 ) 0.11/0.43 ( (head_of skv_14), skv_2, skv_15 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((E1 $$unsorted) (E2 $$unsorted)) (= (sequential E1 E2) (and (edge E1) (edge E2) (= (tail_of E2) (head_of E1)) (not (= E1 E2)))) ) 0.11/0.43 ( skv_3, skv_4 ) 0.11/0.43 ( skv_3, skv_13 ) 0.11/0.43 ( skv_4, skv_3 ) 0.11/0.43 ( skv_4, skv_4 ) 0.11/0.43 ( skv_11, skv_12 ) 0.11/0.43 ( skv_13, skv_4 ) 0.11/0.43 ( skv_13, skv_19 ) 0.11/0.43 ( skv_17, skv_18 ) 0.11/0.43 ) 0.11/0.43 (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 $$unsorted)) (or (not (on_path E P)) (and (not (= V (tail_of E))) (not (= V (head_of E))))) )))) ) 0.11/0.43 ( skv_1, skv_2, skv_5, (head_of skv_4) ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((V1 $$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))) ) 0.11/0.43 ( skv_1, skv_2, skv_5 ) 0.11/0.43 ( (head_of skv_9), skv_2, skv_10 ) 0.11/0.43 ( (head_of skv_9), skv_2, skv_20 ) 0.11/0.43 ( (head_of skv_14), skv_2, skv_15 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_770 $$unsorted) (BOUND_VARIABLE_771 $$unsorted) (BOUND_VARIABLE_772 $$unsorted)) (or (not (path V1 V2 P)) (not (on_path BOUND_VARIABLE_770 P)) (and (or (not (precedes BOUND_VARIABLE_772 BOUND_VARIABLE_771 P)) (not (sequential BOUND_VARIABLE_770 BOUND_VARIABLE_772))) (not (sequential BOUND_VARIABLE_770 BOUND_VARIABLE_771))) (not (on_path BOUND_VARIABLE_771 P)) (precedes BOUND_VARIABLE_770 BOUND_VARIABLE_771 P)) ) 0.11/0.43 ( skv_5, skv_1, skv_2, skv_4, skv_3, skv_4 ) 0.11/0.43 ( skv_5, skv_1, skv_2, skv_4, skv_4, skv_3 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted) (BOUND_VARIABLE_814 $$unsorted) (BOUND_VARIABLE_815 $$unsorted)) (or (not (path V1 V2 P)) (not (precedes BOUND_VARIABLE_814 BOUND_VARIABLE_815 P)) (and (on_path BOUND_VARIABLE_815 P) (on_path BOUND_VARIABLE_814 P) (= (forall ((E3 $$unsorted)) (or (not (precedes E3 BOUND_VARIABLE_815 P)) (not (sequential BOUND_VARIABLE_814 E3))) ) (sequential BOUND_VARIABLE_814 BOUND_VARIABLE_815)))) ) 0.11/0.43 ( skv_5, skv_1, skv_2, skv_3, skv_4 ) 0.11/0.43 ( skv_5, skv_1, skv_2, skv_13, skv_4 ) 0.11/0.43 ( skv_5, skv_1, skv_2, skv_19, skv_4 ) 0.11/0.43 ) 0.11/0.43 (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))) ) 0.11/0.43 ( skv_1, skv_2, skv_5, skv_3 ) 0.11/0.43 ( skv_1, skv_2, skv_5, skv_4 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (E1 $$unsorted) (E2 $$unsorted) (P $$unsorted) (BOUND_VARIABLE_948 $$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_948))) (not (= (tail_of E1) (tail_of BOUND_VARIABLE_948)))))) ) 0.11/0.43 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_3 ) 0.11/0.43 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_4 ) 0.11/0.43 ( skv_1, skv_2, skv_3, skv_4, skv_5, skv_6 ) 0.11/0.43 ( skv_1, skv_2, skv_4, skv_3, skv_5, skv_6 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((E $$unsorted)) (or (not (edge E)) (and (vertex (head_of E)) (vertex (tail_of E)))) ) 0.11/0.43 ( skv_3 ) 0.11/0.43 ( skv_4 ) 0.11/0.43 ( skv_6 ) 0.11/0.43 ( skv_9 ) 0.11/0.43 ( skv_11 ) 0.11/0.43 ( skv_12 ) 0.11/0.43 ( skv_13 ) 0.11/0.43 ( skv_14 ) 0.11/0.43 ( skv_16 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((E $$unsorted)) (or (not (edge E)) (not (= (head_of E) (tail_of E)))) ) 0.11/0.43 ( skv_3 ) 0.11/0.43 ( skv_4 ) 0.11/0.43 ( skv_6 ) 0.11/0.43 ( skv_9 ) 0.11/0.43 ( skv_11 ) 0.11/0.43 ( skv_12 ) 0.11/0.43 ( skv_13 ) 0.11/0.43 ( skv_14 ) 0.11/0.43 ( skv_16 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (path V1 V2 P)) (= (number_of_in sequential_pairs P) (minus (length_of P) n1))) ) 0.11/0.43 ( skv_1, skv_2, skv_5 ) 0.11/0.43 ( (head_of skv_9), skv_2, skv_10 ) 0.11/0.43 ( (head_of skv_9), skv_2, skv_20 ) 0.11/0.43 ( (head_of skv_14), skv_2, skv_15 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((P $$unsorted) (V1 $$unsorted) (V2 $$unsorted)) (or (not (forall ((E1 $$unsorted) (E2 $$unsorted)) (or (not (on_path E2 P)) (not (sequential E1 E2)) (not (on_path E1 P)) (not (forall ((E3 $$unsorted)) (not (triangle E1 E2 E3)) ))) )) (not (path V1 V2 P)) (= (number_of_in triangles P) (number_of_in sequential_pairs P))) ) 0.11/0.43 ( skv_5, skv_1, skv_2 ) 0.11/0.43 ( skv_10, (head_of skv_9), skv_2 ) 0.11/0.43 ( skv_15, (head_of skv_14), skv_2 ) 0.11/0.43 ( skv_20, (head_of skv_9), skv_2 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((V1 $$unsorted) (V2 $$unsorted) (P $$unsorted)) (or (not (path V1 V2 P)) (= (number_of_in edges P) (length_of P))) ) 0.11/0.43 ( skv_1, skv_2, skv_5 ) 0.11/0.43 ( (head_of skv_9), skv_2, skv_10 ) 0.11/0.43 ( (head_of skv_9), skv_2, skv_20 ) 0.11/0.43 ( (head_of skv_14), skv_2, skv_15 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((E $$unsorted)) (let ((_let_0 (head_of E))) (let ((_let_1 (tail_of E))) (or (not (edge E)) (= (and (= _let_0 skv_7) (= _let_1 skv_8)) (and (= _let_1 skv_7) (= _let_0 skv_8)))))) ) 0.11/0.43 ( skv_3 ) 0.11/0.43 ( skv_4 ) 0.11/0.43 ( skv_6 ) 0.11/0.43 ( skv_9 ) 0.11/0.43 ) 0.11/0.43 (instantiation (forall ((P $$unsorted)) (or (not (path skv_1 skv_2 P)) (less_or_equal (length_of skv_5) (length_of P))) ) 0.11/0.43 ( skv_5 ) 0.11/0.43 ( skv_10 ) 0.11/0.43 ( skv_20 ) 0.11/0.43 ) 0.11/0.43 % SZS output end Proof for theBenchmark 0.11/0.44 EOF