0.07/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : do_CVC4 %s 0.13/0.33 % Computer : n018.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 180 0.13/0.33 % DateTime : Thu Aug 29 15:29:07 EDT 2019 0.13/0.33 % CPUTime : 0.19/0.46 %----Proving TH0_NAR 0.19/0.46 ------- cvc4-thf casc 27 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 180... 0.19/0.46 --- Run --uf-ho --ho-elim --no-ho-elim-store-ax --full-saturate-quant at 20... 20.38/20.65 --- Run --uf-ho --ho-elim --full-saturate-quant at 20... 40.49/40.79 --- Run --uf-ho --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 45.53/45.85 --- Run --uf-ho --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 50.55/50.86 --- Run --uf-ho --no-ho-matching --full-saturate-quant --fs-interleave --ho-elim-store-ax at 30... 50.63/50.90 % SZS status Theorem for theBenchmark 50.63/50.91 % SZS output start Proof for theBenchmark 50.63/50.91 (skolem (forall ((X1 $$unsorted)) (let ((_let_0 (sup ll_6))) (= _let_0 (multiplication _let_0 X1))) ) 50.63/50.91 ( skv_7 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((v (-> $$unsorted $$unsorted $$unsorted Bool))) (not (forall ((ii $$unsorted)) (= (v ii) (ite (= ii skv_7) |e_(-> $$unsorted $$unsorted Bool)_9| (|e_(-> $$unsorted $$unsorted $$unsorted Bool)_8| ii))) )) ) 50.63/50.91 ( skv_14 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((v (-> $$unsorted Bool))) (not (forall ((ii $$unsorted)) (= (v ii) (ite (= ii skv_7) false (ll_6 ii))) )) ) 50.63/50.91 ( skv_15 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((v (-> $$unsorted $$unsorted Bool))) (not (forall ((ii $$unsorted)) (= (v ii) (ite (= ii skv_7) ll_6 (|e_(-> $$unsorted $$unsorted Bool)_9| ii))) )) ) 50.63/50.91 ( skv_16 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((v (-> (-> $$unsorted Bool) Bool))) (not (forall ((ii (-> $$unsorted Bool))) (= (v ii) (ite (= ll_6 ii) false (|e_(-> (-> $$unsorted Bool) Bool)_10| ii))) )) ) 50.63/50.91 ( skv_17 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((v (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) (not (forall ((ii (-> $$unsorted Bool))) (= (v ii) (ite (= ll_6 ii) |e_(-> (-> $$unsorted Bool) $$unsorted Bool)_12| (|e_(-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)_11| ii))) )) ) 50.63/50.91 ( skv_18 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((v (-> (-> (-> $$unsorted Bool) Bool) $$unsorted Bool))) (not (forall ((ii (-> (-> $$unsorted Bool) Bool))) (= (v ii) (ite (= ii |e_(-> (-> $$unsorted Bool) Bool)_10|) ll_6 (|e_(-> (-> (-> $$unsorted Bool) Bool) $$unsorted Bool)_13| ii))) )) ) 50.63/50.91 ( skv_19 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((v (-> (-> $$unsorted Bool) $$unsorted Bool))) (not (forall ((ii (-> $$unsorted Bool))) (= (v ii) (ite (= ll_6 ii) ll_6 (|e_(-> (-> $$unsorted Bool) $$unsorted Bool)_12| ii))) )) ) 50.63/50.91 ( skv_20 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((BOUND_VARIABLE_658 $$unsorted) (BOUND_VARIABLE_659 $$unsorted)) (or (not (ll_6 BOUND_VARIABLE_658)) (not (ll_6 BOUND_VARIABLE_659)) (not (= (multiplication BOUND_VARIABLE_658 BOUND_VARIABLE_659) k_32))) ) 50.63/50.91 ( skv_37 skv_38 ) 50.63/50.91 ) 50.63/50.91 (skolem (forall ((BOUND_VARIABLE_658 $$unsorted) (BOUND_VARIABLE_659 $$unsorted)) (or (not (ll_6 BOUND_VARIABLE_658)) (not ((ll_5 skv_7) BOUND_VARIABLE_659)) (not (= (multiplication BOUND_VARIABLE_658 BOUND_VARIABLE_659) k_39))) ) 50.63/50.91 ( skv_44 skv_45 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((X $$unsorted)) (= X (multiplication one X)) ) 50.63/50.91 ( one ) 50.63/50.91 ( (sup ll_6) ) 50.63/50.91 ( skv_7 ) 50.63/50.91 ( (sup ((ll_4 skv_7) skv_7)) ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((X $$unsorted)) (= X (multiplication X one)) ) 50.63/50.91 ( one ) 50.63/50.91 ( (sup ll_6) ) 50.63/50.91 ( skv_7 ) 50.63/50.91 ( (sup ((ll_4 skv_7) skv_7)) ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((X (-> (-> $$unsorted Bool) Bool))) (= (sup (ll_1 X)) (sup (ll_2 X))) ) 50.63/50.91 ( |e_(-> (-> $$unsorted Bool) Bool)_10| ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool))) (= (multiplication (sup X) (sup Y)) (sup ((ll_3 X) Y))) ) 50.63/50.91 ( ll_6, ll_6 ) 50.63/50.91 ( ll_6, (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|) ) 50.63/50.91 ( ll_6, (ll_2 |e_(-> (-> $$unsorted Bool) Bool)_10|) ) 50.63/50.91 ( ll_6, ((ll_4 skv_7) skv_7) ) 50.63/50.91 ( ll_6, (ll_5 skv_7) ) 50.63/50.91 ( (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|), ll_6 ) 50.63/50.91 ( ((ll_4 skv_7) skv_7), ll_6 ) 50.63/50.91 ( (ll_5 skv_7), ll_6 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((X1 $$unsorted) (X2 $$unsorted)) (= (= X2 (sup ((ll_4 X1) X2))) (leq X1 X2)) ) 50.63/50.91 ( skv_7, skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((X $$unsorted)) (= X (sup (ll_5 X))) ) 50.63/50.91 ( skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_803 (-> (-> $$unsorted Bool) Bool)) (BOUND_VARIABLE_804 $$unsorted)) (= (ll_2 BOUND_VARIABLE_803 BOUND_VARIABLE_804) (not (forall ((BOUND_VARIABLE_602 (-> $$unsorted Bool))) (or (not (BOUND_VARIABLE_803 BOUND_VARIABLE_602)) (not (BOUND_VARIABLE_602 BOUND_VARIABLE_804))) ))) ) 50.63/50.91 ( |e_(-> (-> $$unsorted Bool) Bool)_10|, skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_832 $$unsorted) (BOUND_VARIABLE_833 $$unsorted) (BOUND_VARIABLE_834 $$unsorted)) (= (ll_4 BOUND_VARIABLE_832 BOUND_VARIABLE_833 BOUND_VARIABLE_834) (or (= BOUND_VARIABLE_832 BOUND_VARIABLE_834) (= BOUND_VARIABLE_833 BOUND_VARIABLE_834))) ) 50.63/50.91 ( skv_7, skv_7, skv_7 ) 50.63/50.91 ( skv_7, skv_7, k_33 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_842 $$unsorted) (BOUND_VARIABLE_843 $$unsorted)) (= (ll_5 BOUND_VARIABLE_842 BOUND_VARIABLE_843) (= BOUND_VARIABLE_842 BOUND_VARIABLE_843)) ) 50.63/50.91 ( skv_7, skv_7 ) 50.63/50.91 ( skv_7, k_34 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_790 (-> (-> $$unsorted Bool) Bool)) (BOUND_VARIABLE_791 $$unsorted)) (= (ll_1 BOUND_VARIABLE_790 BOUND_VARIABLE_791) (not (forall ((BOUND_VARIABLE_616 (-> $$unsorted Bool))) (or (not (BOUND_VARIABLE_790 BOUND_VARIABLE_616)) (not (= (sup BOUND_VARIABLE_616) BOUND_VARIABLE_791))) ))) ) 50.63/50.91 ( |e_(-> (-> $$unsorted Bool) Bool)_10|, skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_816 (-> $$unsorted Bool)) (BOUND_VARIABLE_817 (-> $$unsorted Bool)) (BOUND_VARIABLE_818 $$unsorted)) (= (ll_3 BOUND_VARIABLE_816 BOUND_VARIABLE_817 BOUND_VARIABLE_818) (not (forall ((BOUND_VARIABLE_658 $$unsorted) (BOUND_VARIABLE_659 $$unsorted)) (or (not (BOUND_VARIABLE_816 BOUND_VARIABLE_658)) (not (BOUND_VARIABLE_817 BOUND_VARIABLE_659)) (not (= (multiplication BOUND_VARIABLE_658 BOUND_VARIABLE_659) BOUND_VARIABLE_818))) ))) ) 50.63/50.91 ( ll_6, ll_6, skv_7 ) 50.63/50.91 ( ll_6, ll_6, k_32 ) 50.63/50.91 ( ll_6, (ll_5 skv_7), k_39 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_849 $$unsorted)) (not (ll_6 BOUND_VARIABLE_849)) ) 50.63/50.91 ( one ) 50.63/50.91 ( skv_7 ) 50.63/50.91 ( (sup (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|)) ) 50.63/50.91 ( (sup ((ll_4 skv_7) skv_7)) ) 50.63/50.91 ( k_32 ) 50.63/50.91 ( skv_37 ) 50.63/50.91 ( skv_38 ) 50.63/50.91 ( k_39 ) 50.63/50.91 ( skv_44 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((u (-> $$unsorted $$unsorted $$unsorted Bool)) (e (-> $$unsorted $$unsorted Bool)) (i $$unsorted)) (not (forall ((v (-> $$unsorted $$unsorted $$unsorted Bool))) (not (forall ((ii $$unsorted)) (= (v ii) (ite (= i ii) e (u ii))) )) )) ) 50.63/50.91 ( |e_(-> $$unsorted $$unsorted $$unsorted Bool)_8|, |e_(-> $$unsorted $$unsorted Bool)_9|, skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((u (-> $$unsorted Bool)) (e Bool) (i $$unsorted)) (not (forall ((v (-> $$unsorted Bool))) (not (forall ((ii $$unsorted)) (= (v ii) (ite (= i ii) e (u ii))) )) )) ) 50.63/50.91 ( ll_6, false, skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((u (-> $$unsorted $$unsorted Bool)) (e (-> $$unsorted Bool)) (i $$unsorted)) (not (forall ((v (-> $$unsorted $$unsorted Bool))) (not (forall ((ii $$unsorted)) (= (v ii) (ite (= i ii) e (u ii))) )) )) ) 50.63/50.91 ( |e_(-> $$unsorted $$unsorted Bool)_9|, ll_6, skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((u (-> (-> $$unsorted Bool) Bool)) (e Bool) (i (-> $$unsorted Bool))) (not (forall ((v (-> (-> $$unsorted Bool) Bool))) (not (forall ((ii (-> $$unsorted Bool))) (= (v ii) (ite (= i ii) e (u ii))) )) )) ) 50.63/50.91 ( |e_(-> (-> $$unsorted Bool) Bool)_10|, false, ll_6 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((u (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)) (e (-> (-> $$unsorted Bool) $$unsorted Bool)) (i (-> $$unsorted Bool))) (not (forall ((v (-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool))) (not (forall ((ii (-> $$unsorted Bool))) (= (v ii) (ite (= i ii) e (u ii))) )) )) ) 50.63/50.91 ( |e_(-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)_11|, |e_(-> (-> $$unsorted Bool) $$unsorted Bool)_12|, ll_6 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((u (-> (-> (-> $$unsorted Bool) Bool) $$unsorted Bool)) (e (-> $$unsorted Bool)) (i (-> (-> $$unsorted Bool) Bool))) (not (forall ((v (-> (-> (-> $$unsorted Bool) Bool) $$unsorted Bool))) (not (forall ((ii (-> (-> $$unsorted Bool) Bool))) (= (v ii) (ite (= i ii) e (u ii))) )) )) ) 50.63/50.91 ( |e_(-> (-> (-> $$unsorted Bool) Bool) $$unsorted Bool)_13|, ll_6, |e_(-> (-> $$unsorted Bool) Bool)_10| ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((u (-> (-> $$unsorted Bool) $$unsorted Bool)) (e (-> $$unsorted Bool)) (i (-> $$unsorted Bool))) (not (forall ((v (-> (-> $$unsorted Bool) $$unsorted Bool))) (not (forall ((ii (-> $$unsorted Bool))) (= (v ii) (ite (= i ii) e (u ii))) )) )) ) 50.63/50.91 ( |e_(-> (-> $$unsorted Bool) $$unsorted Bool)_12|, ll_6, ll_6 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_616 (-> $$unsorted Bool))) (or (not (|e_(-> (-> $$unsorted Bool) Bool)_10| BOUND_VARIABLE_616)) (not (= (sup BOUND_VARIABLE_616) skv_7))) ) 50.63/50.91 ( ll_6 ) 50.63/50.91 ( (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|) ) 50.63/50.91 ( (ll_2 |e_(-> (-> $$unsorted Bool) Bool)_10|) ) 50.63/50.91 ( ((ll_3 ll_6) ll_6) ) 50.63/50.91 ( (ll_5 skv_7) ) 50.63/50.91 ( ((ll_3 ll_6) (ll_5 skv_7)) ) 50.63/50.91 ( ((ll_3 ll_6) (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|)) ) 50.63/50.91 ( ((ll_3 (ll_5 skv_7)) ll_6) ) 50.63/50.91 ( ((ll_3 ll_6) ((ll_4 skv_7) skv_7)) ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_602 (-> $$unsorted Bool))) (or (not (|e_(-> (-> $$unsorted Bool) Bool)_10| BOUND_VARIABLE_602)) (not (BOUND_VARIABLE_602 skv_7))) ) 50.63/50.91 ( ll_6 ) 50.63/50.91 ( ((ll_4 skv_7) skv_7) ) 50.63/50.91 ( (ll_5 skv_7) ) 50.63/50.91 ( ((ll_3 ll_6) (ll_5 skv_7)) ) 50.63/50.91 ( ((ll_3 (ll_5 skv_7)) ll_6) ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_658 $$unsorted) (BOUND_VARIABLE_659 $$unsorted)) (or (not (ll_6 BOUND_VARIABLE_658)) (not (ll_6 BOUND_VARIABLE_659)) (not (= (multiplication BOUND_VARIABLE_658 BOUND_VARIABLE_659) skv_7))) ) 50.63/50.91 ( one, one ) 50.63/50.91 ( one, (sup ll_6) ) 50.63/50.91 ( (sup ll_6), (sup ll_6) ) 50.63/50.91 ( (sup (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|)), (sup (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|)) ) 50.63/50.91 ( (sup ((ll_4 skv_7) skv_7)), (sup ((ll_4 skv_7) skv_7)) ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((ii $$unsorted)) (= (ite (= ii skv_7) |e_(-> $$unsorted $$unsorted Bool)_9| (|e_(-> $$unsorted $$unsorted $$unsorted Bool)_8| ii)) (skv_14 ii)) ) 50.63/50.91 ( skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((ii $$unsorted)) (= (skv_15 ii) (ite (= ii skv_7) false (ll_6 ii))) ) 50.63/50.91 ( one ) 50.63/50.91 ( (sup ll_6) ) 50.63/50.91 ( skv_7 ) 50.63/50.91 ( k_32 ) 50.63/50.91 ( skv_37 ) 50.63/50.91 ( skv_38 ) 50.63/50.91 ( k_39 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((ii $$unsorted)) (= (ite (= ii skv_7) ll_6 (|e_(-> $$unsorted $$unsorted Bool)_9| ii)) (skv_16 ii)) ) 50.63/50.91 ( skv_7 ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((ii (-> $$unsorted Bool))) (= (skv_17 ii) (ite (= ll_6 ii) false (|e_(-> (-> $$unsorted Bool) Bool)_10| ii))) ) 50.63/50.91 ( ll_6 ) 50.63/50.91 ( (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|) ) 50.63/50.91 ( (ll_2 |e_(-> (-> $$unsorted Bool) Bool)_10|) ) 50.63/50.91 ( ((ll_3 ll_6) ll_6) ) 50.63/50.91 ( ((ll_4 skv_7) skv_7) ) 50.63/50.91 ( (ll_5 skv_7) ) 50.63/50.91 ( ((ll_3 ll_6) (ll_5 skv_7)) ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((ii (-> $$unsorted Bool))) (= (ite (= ll_6 ii) |e_(-> (-> $$unsorted Bool) $$unsorted Bool)_12| (|e_(-> (-> $$unsorted Bool) (-> $$unsorted Bool) $$unsorted Bool)_11| ii)) (skv_18 ii)) ) 50.63/50.91 ( ll_6 ) 50.63/50.91 ( (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|) ) 50.63/50.91 ( ((ll_4 skv_7) skv_7) ) 50.63/50.91 ( (ll_5 skv_7) ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((ii (-> (-> $$unsorted Bool) Bool))) (= (ite (= ii |e_(-> (-> $$unsorted Bool) Bool)_10|) ll_6 (|e_(-> (-> (-> $$unsorted Bool) Bool) $$unsorted Bool)_13| ii)) (skv_19 ii)) ) 50.63/50.91 ( |e_(-> (-> $$unsorted Bool) Bool)_10| ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((ii (-> $$unsorted Bool))) (= (ite (= ll_6 ii) ll_6 (|e_(-> (-> $$unsorted Bool) $$unsorted Bool)_12| ii)) (skv_20 ii)) ) 50.63/50.91 ( ll_6 ) 50.63/50.91 ( (ll_1 |e_(-> (-> $$unsorted Bool) Bool)_10|) ) 50.63/50.91 ( ((ll_4 skv_7) skv_7) ) 50.63/50.91 ( (ll_5 skv_7) ) 50.63/50.91 ) 50.63/50.91 (instantiation (forall ((BOUND_VARIABLE_658 $$unsorted) (BOUND_VARIABLE_659 $$unsorted)) (or (not (ll_6 BOUND_VARIABLE_658)) (not (ll_6 BOUND_VARIABLE_659)) (not (= (multiplication BOUND_VARIABLE_658 BOUND_VARIABLE_659) k_32))) ) 50.63/50.91 ( (sup ((ll_4 skv_7) skv_7)), (sup ((ll_4 skv_7) skv_7)) ) 50.63/50.91 ) 50.63/50.91 % SZS output end Proof for theBenchmark 50.63/50.91 EOF