0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : do_CVC4 %s %d 0.12/0.33 % Computer : n021.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 960 0.12/0.33 % WCLimit : 120 0.12/0.33 % DateTime : Thu Jul 2 08:37:22 EDT 2020 0.12/0.33 % CPUTime : 0.18/0.45 %----Proving TF0_ARI 0.18/0.46 ------- cvc4-tfa casc j10 : /export/starexec/sandbox/benchmark/theBenchmark.p at 960... 0.18/0.46 --- Run --finite-model-find --decision=internal at 15... 0.39/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 15... 0.40/0.71 % SZS status Theorem for theBenchmark 0.40/0.71 % SZS output start Proof for theBenchmark 0.40/0.71 (skolem (forall ((N Int)) (or (not (>= N 1)) (not (p1 (+ (- 1) N))) (not (= (mod1 N 3) 0)) (not (= (mod1 N 5) 0)) (p1 N)) ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ) 0.40/0.71 (skolem (forall ((BOUND_VARIABLE_1179 Int)) (not (= INST_CONSTANT_2058 (+ 1 (* 2 BOUND_VARIABLE_1179)))) ) 0.40/0.71 ( skv_44 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (or (not (>= N 1)) (not (p1 (+ (- 1) N))) (= (mod1 N 3) 0) (not (= (mod1 N 5) 0)) (p1 N)) ) 0.40/0.71 ( 0 ) 0.40/0.71 ( 1 ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ( (+ 1 skv_5) ) 0.40/0.71 ( (+ 2 skv_5) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (>= (+ (abs1 X) (* (- 1) (abs1 (* Y (div1 X Y))))) 0)) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ (- 1) skv_5), 3 ) 0.40/0.71 ( (+ (- 1) skv_5), 5 ) 0.40/0.71 ( (+ (- 1) skv_5), 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (let ((_let_0 (+ 1 X))) (let ((_let_1 (mod1 _let_0 Y))) (or (not (>= X 0)) (not (>= Y 1)) (= _let_1 0) (= (mod1 X Y) (+ (- 1) _let_1))))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( 1, 3 ) 0.40/0.71 ( 1, 5 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ( (+ 1 skv_5), 15 ) 0.40/0.71 ( (+ 2 skv_5), 3 ) 0.40/0.71 ( (+ 2 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (= (p1 N) (= (closed_formula_aux1 N) (sum_multiple_3_5_lt1 (+ 1 N)))) ) 0.40/0.71 ( 0 ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ( (+ (- 1) skv_5) ) 0.40/0.71 ( (+ 1 skv_5) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (or (not (>= N 0)) (= N (+ (* 2 (tr1 N)) (* (- 1) (* N N))))) ) 0.40/0.71 ( (div1 skv_5 3) ) 0.40/0.71 ( (div1 skv_5 5) ) 0.40/0.71 ( (div1 0 5) ) 0.40/0.71 ( (div1 skv_5 15) ) 0.40/0.71 ( (div1 0 15) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 3) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 5) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 15) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (not (>= Y 1)) (not (>= X 0)) (>= (div1 X Y) 0)) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ (- 1) skv_5), 3 ) 0.40/0.71 ( (+ (- 1) skv_5), 5 ) 0.40/0.71 ( (+ (- 1) skv_5), 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (>= (+ X (* (- 1) Y)) 1) (not (>= Z 0)) (not (>= (+ (* X Z) (* (- 1) (* Y Z))) 1))) ) 0.40/0.71 ( 0, 0, 0 ) 0.40/0.71 ( (- 1), 0, 0 ) 0.40/0.71 ( (- 1), 0, 1 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (or (not (>= N 0)) (= (mod1 N 5) 0) (= (mod1 N 3) 0) (= (sum_multiple_3_5_lt1 N) (sum_multiple_3_5_lt1 (+ 1 N)))) ) 0.40/0.71 ( 0 ) 0.40/0.71 ( 1 ) 0.40/0.71 ( 2 ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ( (+ 1 skv_5) ) 0.40/0.71 ( (+ 2 skv_5) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (= (and (= (mod1 N 5) 0) (= (mod1 N 3) 0)) (= (mod1 N 15) 0)) ) 0.40/0.71 ( 0 ) 0.40/0.71 ( 1 ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ( (+ 1 skv_5) ) 0.40/0.71 ( (+ 2 skv_5) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (= X (+ (mod1 X Y) (* Y (div1 X Y))))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( 1, 3 ) 0.40/0.71 ( 1, 5 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ (- 1) skv_5), 3 ) 0.40/0.71 ( (+ (- 1) skv_5), 5 ) 0.40/0.71 ( (+ (- 1) skv_5), 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ( (+ 1 skv_5), 15 ) 0.40/0.71 ( (+ 2 skv_5), 3 ) 0.40/0.71 ( (+ 2 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (= (tr1 N) (div1 (+ N (* N N)) 2)) ) 0.40/0.71 ( (div1 skv_5 3) ) 0.40/0.71 ( (div1 skv_5 5) ) 0.40/0.71 ( (div1 0 5) ) 0.40/0.71 ( (div1 skv_5 15) ) 0.40/0.71 ( (div1 0 15) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 3) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 5) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 15) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (= Y 0) (>= X 1) (not (>= (mod1 X Y) 1))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( 1, 3 ) 0.40/0.71 ( 1, 5 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ( (+ 1 skv_5), 15 ) 0.40/0.71 ( (+ 2 skv_5), 3 ) 0.40/0.71 ( (+ 2 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (let ((_let_0 (abs1 Y))) (let ((_let_1 (mod1 X Y))) (or (= Y 0) (and (>= (+ _let_0 _let_1) 1) (>= (+ _let_0 (* (- 1) _let_1)) 1))))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( 1, 3 ) 0.40/0.71 ( 1, 5 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ( (+ 1 skv_5), 15 ) 0.40/0.71 ( (+ 2 skv_5), 3 ) 0.40/0.71 ( (+ 2 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (not (>= X 0)) (>= (+ X (* (- 1) Y)) 0) (= (div1 X Y) 0)) ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ (- 1) skv_5), 3 ) 0.40/0.71 ( (+ (- 1) skv_5), 5 ) 0.40/0.71 ( (+ (- 1) skv_5), 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (= (closed_formula_aux1 N) (+ (* 3 (tr1 (div1 N 3))) (* 5 (tr1 (div1 N 5))) (* (- 15) (tr1 (div1 N 15))))) ) 0.40/0.71 ( 0 ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ( (+ (- 1) skv_5) ) 0.40/0.71 ( (+ 1 skv_5) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (or (not (>= N 0)) (= N (+ (- 1) (* (- 1) (tr1 N)) (tr1 (+ 1 N))))) ) 0.40/0.71 ( (div1 skv_5 3) ) 0.40/0.71 ( (div1 skv_5 5) ) 0.40/0.71 ( (div1 0 5) ) 0.40/0.71 ( (div1 skv_5 15) ) 0.40/0.71 ( (div1 0 15) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 3) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 5) ) 0.40/0.71 ( (div1 (+ (- 1) skv_5) 15) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (not (>= X 0)) (not (>= Y 1)) (not (= (mod1 (+ 1 X) Y) 0)) (= Y (+ 1 (mod1 X Y)))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( 1, 3 ) 0.40/0.71 ( 1, 5 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ( (+ 1 skv_5), 15 ) 0.40/0.71 ( (+ 2 skv_5), 3 ) 0.40/0.71 ( (+ 2 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (>= (+ X (* (- 1) Y)) 0) (not (>= X 0)) (= X (mod1 X Y))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( 1, 3 ) 0.40/0.71 ( 1, 5 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ( (+ 1 skv_5), 15 ) 0.40/0.71 ( (+ 2 skv_5), 3 ) 0.40/0.71 ( (+ 2 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (or (not (>= N 1)) (not (p1 (+ (- 1) N))) (= (mod1 N 3) 0) (= (mod1 N 5) 0) (p1 N)) ) 0.40/0.71 ( 0 ) 0.40/0.71 ( 1 ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ( (+ 1 skv_5) ) 0.40/0.71 ( (+ 2 skv_5) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (not (>= X 0)) (= Y 0) (>= (mod1 X Y) 0)) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( 1, 3 ) 0.40/0.71 ( 1, 5 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ( (+ 1 skv_5), 15 ) 0.40/0.71 ( (+ 2 skv_5), 3 ) 0.40/0.71 ( (+ 2 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((BOUND_VARIABLE_1616 Int)) (or (>= BOUND_VARIABLE_1616 0) (= BOUND_VARIABLE_1616 (* (- 1) (abs1 BOUND_VARIABLE_1616)))) ) 0.40/0.71 ( 3 ) 0.40/0.71 ( 5 ) 0.40/0.71 ( (* 3 (div1 skv_5 3)) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((BOUND_VARIABLE_1624 Int)) (or (not (>= BOUND_VARIABLE_1624 0)) (= BOUND_VARIABLE_1624 (abs1 BOUND_VARIABLE_1624))) ) 0.40/0.71 ( 3 ) 0.40/0.71 ( 5 ) 0.40/0.71 ( (* 3 (div1 skv_5 3)) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (let ((_let_0 (+ 1 X))) (or (not (>= X 0)) (not (>= Y 1)) (= (mod1 _let_0 Y) 0) (= (div1 X Y) (div1 _let_0 Y)))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ (- 1) skv_5), 3 ) 0.40/0.71 ( (+ (- 1) skv_5), 5 ) 0.40/0.71 ( (+ (- 1) skv_5), 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (or (not (>= N 0)) (and (not (= (mod1 N 3) 0)) (not (= (mod1 N 5) 0))) (= N (+ (* (- 1) (sum_multiple_3_5_lt1 N)) (sum_multiple_3_5_lt1 (+ 1 N))))) ) 0.40/0.71 ( 0 ) 0.40/0.71 ( 1 ) 0.40/0.71 ( 2 ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ( (+ 1 skv_5) ) 0.40/0.71 ( (+ 2 skv_5) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((N Int)) (or (not (>= N 1)) (not (p1 (+ (- 1) N))) (= (mod1 N 5) 0) (not (= (mod1 N 3) 0)) (p1 N)) ) 0.40/0.71 ( 0 ) 0.40/0.71 ( 1 ) 0.40/0.71 ( skv_5 ) 0.40/0.71 ( (+ 1 skv_5) ) 0.40/0.71 ( (+ 2 skv_5) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (let ((_let_0 (div1 X Y))) (or (not (>= X 0)) (not (>= Y 1)) (and (>= (+ X (* (- 1) _let_0)) 0) (>= _let_0 0)))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ (- 1) skv_5), 3 ) 0.40/0.71 ( (+ (- 1) skv_5), 5 ) 0.40/0.71 ( (+ (- 1) skv_5), 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (or (not (>= Y 1)) (>= X 1) (not (>= (div1 X Y) 1))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ (- 1) skv_5), 3 ) 0.40/0.71 ( (+ (- 1) skv_5), 5 ) 0.40/0.71 ( (+ (- 1) skv_5), 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int)) (>= (abs1 X) 0) ) 0.40/0.71 ( 3 ) 0.40/0.71 ( 5 ) 0.40/0.71 ( (* 3 (div1 skv_5 3)) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((X Int) (Y Int)) (let ((_let_0 (+ 1 X))) (or (not (>= X 0)) (not (>= Y 1)) (not (= (mod1 _let_0 Y) 0)) (= (div1 X Y) (+ (- 1) (div1 _let_0 Y))))) ) 0.40/0.71 ( 0, 3 ) 0.40/0.71 ( 0, 5 ) 0.40/0.71 ( 0, 15 ) 0.40/0.71 ( skv_5, 3 ) 0.40/0.71 ( skv_5, 5 ) 0.40/0.71 ( skv_5, 15 ) 0.40/0.71 ( (+ (- 1) skv_5), 3 ) 0.40/0.71 ( (+ (- 1) skv_5), 5 ) 0.40/0.71 ( (+ (- 1) skv_5), 15 ) 0.40/0.71 ( (+ 1 skv_5), 3 ) 0.40/0.71 ( (+ 1 skv_5), 5 ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((BOUND_VARIABLE_1173 Int)) (not (= INST_CONSTANT_2058 (* 2 BOUND_VARIABLE_1173))) ) 0.40/0.71 ( (div INST_CONSTANT_2058 2) ) 0.40/0.71 ) 0.40/0.71 (instantiation (forall ((BOUND_VARIABLE_1179 Int)) (not (= INST_CONSTANT_2058 (+ 1 (* 2 BOUND_VARIABLE_1179)))) ) 0.40/0.71 ( (div (+ (- 1) INST_CONSTANT_2058) 2) ) 0.40/0.71 ) 0.40/0.71 % SZS output end Proof for theBenchmark 0.40/0.71 EOF