0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : do_CVC4 %s %d 0.13/0.33 % Computer : n026.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 : 960 0.13/0.33 % WCLimit : 120 0.13/0.33 % DateTime : Thu Jul 2 06:51:09 EDT 2020 0.13/0.33 % CPUTime : 0.18/0.46 %----Proving TF0_ARI 0.18/0.47 ------- cvc4-tfa casc j10 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 960... 0.18/0.47 --- Run --finite-model-find --decision=internal at 15... 15.24/15.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 15... 15.33/15.56 % SZS status Theorem for theBenchmark 15.33/15.56 % SZS output start Proof for theBenchmark 15.33/15.56 (skolem (forall ((X elt) (X1 list_elt)) (let ((_let_0 (t2tb1 X))) (let ((_let_1 (t2tb X1))) (let ((_let_2 (cons elt1 _let_0 _let_1))) (or (not (permut elt1 (prefix elt1 (length elt1 _let_1) _let_1) _let_1)) (permut elt1 (prefix elt1 (length elt1 _let_2) _let_2) _let_2))))) ) 15.33/15.56 ( skv_2 skv_3 ) 15.33/15.56 ) 15.33/15.56 (skolem (forall ((Y elt)) (or (not (mem elt1 (t2tb1 Y) (t2tb skv_3))) (le skv_2 Y)) ) 15.33/15.56 ( skv_4 ) 15.33/15.56 ) 15.33/15.56 (skolem (forall ((X elt)) (or (not (mem elt1 (t2tb1 X) (t2tb skv_3))) (le X skv_2)) ) 15.33/15.56 ( skv_5 ) 15.33/15.56 ) 15.33/15.56 (skolem (forall ((X uni)) (let ((_let_0 (t2tb skv_3))) (let ((_let_1 (t2tb1 skv_2))) (let ((_let_2 (cons elt1 _let_1 _let_0))) (or (not (sort elt1 X)) (= (num_occ elt1 X _let_2) (num_occ elt1 X (prefix elt1 (length elt1 _let_2) _let_2))))))) ) 15.33/15.56 ( skv_6 ) 15.33/15.56 ) 15.33/15.56 (skolem (forall ((X uni)) (let ((_let_0 (nil elt1))) (or (not (sort elt1 X)) (= (num_occ elt1 X _let_0) (num_occ elt1 X (prefix elt1 (length elt1 _let_0) _let_0))))) ) 15.33/15.56 ( skv_7 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni)) (sort (list A) (cons_proj_2 A X)) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni) (X1 uni)) (sort (list A) (cons A X X1)) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (nil elt1) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((I elt)) (= I (tb2t1 (t2tb1 I))) ) 15.33/15.56 ( skv_2 ) 15.33/15.56 ( skv_4 ) 15.33/15.56 ( skv_5 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni)) (sort (list A) (reverse A X)) ) 15.33/15.56 ( elt1, (nil elt1) ) 15.33/15.56 ( elt1, (t2tb skv_3) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X elt)) (le X X) ) 15.33/15.56 ( skv_2 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni) (X1 uni)) (sort (list A) (infix_plpl A X X1)) ) 15.33/15.56 ( elt1, (reverse elt1 (t2tb skv_3)), (cons elt1 (t2tb1 skv_2) (nil elt1)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni)) (sort A (cons_proj_1 A X)) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X elt)) (sort elt1 (t2tb1 X)) ) 15.33/15.56 ( skv_2 ) 15.33/15.56 ( skv_4 ) 15.33/15.56 ( skv_5 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((J uni)) (= J (t2tb (tb2t J))) ) 15.33/15.56 ( (nil elt1) ) 15.33/15.56 ( (t2tb skv_3) ) 15.33/15.56 ( (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ( (reverse elt1 (t2tb skv_3)) ) 15.33/15.56 ( (cons elt1 (t2tb1 skv_2) (nil elt1)) ) 15.33/15.56 ( (reverse elt1 (cons elt1 (t2tb1 skv_2) (t2tb skv_3))) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni) (L1 uni) (L2 uni)) (permut A (infix_plpl A (cons A X L1) L2) (infix_plpl A L1 (cons A X L2))) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (reverse elt1 (t2tb skv_3)), (nil elt1) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L1 uni) (L2 uni)) (permut A (infix_plpl A L1 L2) (infix_plpl A L2 L1)) ) 15.33/15.56 ( elt1, (reverse elt1 (t2tb skv_3)), (cons elt1 (t2tb1 skv_2) (nil elt1)) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (nil elt1)), (reverse elt1 (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X elt) (Y elt)) (or (le Y X) (le X Y)) ) 15.33/15.56 ( skv_2, skv_2 ) 15.33/15.56 ( skv_2, skv_4 ) 15.33/15.56 ( skv_2, skv_5 ) 15.33/15.56 ( skv_4, skv_2 ) 15.33/15.56 ( skv_5, skv_2 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty)) (sort (list A) (nil A)) ) 15.33/15.56 ( elt1 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X list_elt)) (sort (list elt1) (t2tb X)) ) 15.33/15.56 ( (tb2t (nil elt1)) ) 15.33/15.56 ( skv_3 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X elt)) (sorted (tb2t (cons elt1 (t2tb1 X) (nil elt1)))) ) 15.33/15.56 ( skv_2 ) 15.33/15.56 ( skv_4 ) 15.33/15.56 ( skv_5 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X Int) (X1 uni)) (sort (list A) (prefix A X X1)) ) 15.33/15.56 ( elt1, (length elt1 (nil elt1)), (nil elt1) ) 15.33/15.56 ( elt1, (length elt1 (t2tb skv_3)), (t2tb skv_3) ) 15.33/15.56 ( elt1, (length elt1 (cons elt1 (t2tb1 skv_2) (t2tb skv_3))), (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (U uni) (U1 uni)) (or (not (sort A U)) (= U (cons_proj_1 A (cons A U U1)))) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (nil elt1) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L uni)) (= (length A L) (length A (reverse A L))) ) 15.33/15.56 ( elt1, (nil elt1) ) 15.33/15.56 ( elt1, (t2tb skv_3) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((BOUND_VARIABLE_1567 ty) (X uni) (X1 uni)) (= (infix_plpl BOUND_VARIABLE_1567 (reverse BOUND_VARIABLE_1567 X1) (cons BOUND_VARIABLE_1567 X (nil BOUND_VARIABLE_1567))) (reverse BOUND_VARIABLE_1567 (cons BOUND_VARIABLE_1567 X X1))) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (nil elt1) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((BOUND_VARIABLE_1578 ty)) (let ((_let_0 (nil BOUND_VARIABLE_1578))) (= _let_0 (reverse BOUND_VARIABLE_1578 _let_0))) ) 15.33/15.56 ( elt1 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L uni)) (>= (length A L) 0) ) 15.33/15.56 ( elt1, (nil elt1) ) 15.33/15.56 ( elt1, (let ((_let_0 (nil elt1))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ( elt1, (t2tb skv_3) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (let ((_let_1 (t2tb1 skv_2))) (let ((_let_2 (cons elt1 _let_1 _let_0))) (prefix elt1 (length elt1 _let_2) _let_2)))) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni) (BOUND_VARIABLE_1619 uni) (BOUND_VARIABLE_1620 uni)) (let ((_let_0 (= X BOUND_VARIABLE_1619))) (let ((_let_1 (num_occ A X BOUND_VARIABLE_1620))) (let ((_let_2 (cons A BOUND_VARIABLE_1619 BOUND_VARIABLE_1620))) (let ((_let_3 (num_occ A X _let_2))) (or (not (sort A X)) (and (= (num_occ A X (nil A)) 0) (or (not (sort A BOUND_VARIABLE_1619)) (and (or (not _let_0) (= _let_1 (+ (- 1) _let_3))) (or _let_0 (= _let_1 _let_3)))))))))) ) 15.33/15.56 ( elt1, skv_6, (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ( elt1, skv_6, (t2tb1 skv_2), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L1 uni) (L2 uni) (X uni)) (= (infix_plpl A (reverse A (cons A X L1)) L2) (infix_plpl A (reverse A L1) (cons A X L2))) ) 15.33/15.56 ( elt1, (t2tb skv_3), (nil elt1), (t2tb1 skv_2) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L1 uni) (L2 uni)) (= (length A L1) (+ (* (- 1) (length A L2)) (length A (infix_plpl A L1 L2)))) ) 15.33/15.56 ( elt1, (reverse elt1 (t2tb skv_3)), (cons elt1 (t2tb1 skv_2) (nil elt1)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((I list_elt)) (= I (tb2t (t2tb I))) ) 15.33/15.56 ( (tb2t (nil elt1)) ) 15.33/15.56 ( skv_3 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((BOUND_VARIABLE_1699 ty)) (= (length BOUND_VARIABLE_1699 (nil BOUND_VARIABLE_1699)) 0) ) 15.33/15.56 ( elt1 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((BOUND_VARIABLE_1705 ty) (X uni) (X1 uni)) (= (length BOUND_VARIABLE_1705 X1) (+ (- 1) (length BOUND_VARIABLE_1705 (cons BOUND_VARIABLE_1705 X X1)))) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (nil elt1) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L uni)) (= (= L (nil A)) (= (length A L) 0)) ) 15.33/15.56 ( elt1, (nil elt1) ) 15.33/15.56 ( elt1, (let ((_let_0 (nil elt1))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ( elt1, (t2tb skv_3) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (let ((_let_1 (t2tb1 skv_2))) (let ((_let_2 (cons elt1 _let_1 _let_0))) (prefix elt1 (length elt1 _let_2) _let_2)))) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L1 uni) (L2 uni)) (or (not (permut A L1 L2)) (permut A L2 L1)) ) 15.33/15.56 ( elt1, (nil elt1), (let ((_let_0 (nil elt1))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ( elt1, (let ((_let_0 (nil elt1))) (prefix elt1 (length elt1 _let_0) _let_0)), (nil elt1) ) 15.33/15.56 ( elt1, (t2tb skv_3), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (prefix elt1 (length elt1 _let_0) _let_0)), (t2tb skv_3) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)), (let ((_let_0 (t2tb skv_3))) (let ((_let_1 (t2tb1 skv_2))) (let ((_let_2 (cons elt1 _let_1 _let_0))) (prefix elt1 (length elt1 _let_2) _let_2)))) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (let ((_let_1 (t2tb1 skv_2))) (let ((_let_2 (cons elt1 _let_1 _let_0))) (prefix elt1 (length elt1 _let_2) _let_2)))), (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni) (L1 uni) (L2 uni)) (or (not (permut A L1 L2)) (permut A (cons A X L1) (cons A X L2))) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (t2tb skv_3), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)), (t2tb skv_3) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (V uni) (V1 uni)) (not (= (cons A V V1) (nil A))) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (nil elt1) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni) (L uni)) (= (num_occ A X (reverse A L)) (num_occ A X L)) ) 15.33/15.56 ( elt1, skv_7, (nil elt1) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((BOUND_VARIABLE_1798 ty) (BOUND_VARIABLE_1799 uni) (BOUND_VARIABLE_1800 uni)) (or (not (forall ((X uni)) (or (not (sort BOUND_VARIABLE_1798 X)) (= (num_occ BOUND_VARIABLE_1798 X BOUND_VARIABLE_1800) (num_occ BOUND_VARIABLE_1798 X BOUND_VARIABLE_1799))) )) (permut BOUND_VARIABLE_1798 BOUND_VARIABLE_1799 BOUND_VARIABLE_1800)) ) 15.33/15.56 ( elt1, (nil elt1), (let ((_let_0 (nil elt1))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ( elt1, (let ((_let_0 (nil elt1))) (prefix elt1 (length elt1 _let_0) _let_0)), (nil elt1) ) 15.33/15.56 ( elt1, (t2tb skv_3), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (prefix elt1 (length elt1 _let_0) _let_0)), (t2tb skv_3) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)), (let ((_let_0 (t2tb skv_3))) (let ((_let_1 (t2tb1 skv_2))) (let ((_let_2 (cons elt1 _let_1 _let_0))) (prefix elt1 (length elt1 _let_2) _let_2)))) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (let ((_let_1 (t2tb1 skv_2))) (let ((_let_2 (cons elt1 _let_1 _let_0))) (prefix elt1 (length elt1 _let_2) _let_2)))), (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((Acc list_elt) (X1 elt)) (let ((_let_0 (t2tb Acc))) (or (not (sorted (tb2t (reverse elt1 _let_0)))) (not (forall ((X elt)) (or (not (mem elt1 (t2tb1 X) _let_0)) (le X X1)) )) (sorted (tb2t (reverse elt1 (cons elt1 (t2tb1 X1) _let_0)))))) ) 15.33/15.56 ( (tb2t (nil elt1)), skv_2 ) 15.33/15.56 ( skv_3, skv_2 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (U uni)) (or (= U (nil A)) (= U (cons A (cons_proj_1 A U) (cons_proj_2 A U)))) ) 15.33/15.56 ( elt1, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni) (L uni)) (or (not (mem A X L)) (not (forall ((L1 uni) (L2 uni)) (let ((_let_0 (list A))) (or (not (sort _let_0 L1)) (not (= L (infix_plpl A L1 (cons A X L2)))) (not (sort _let_0 L2)))) ))) ) 15.33/15.56 ( elt1, (t2tb1 skv_4), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_5), (t2tb skv_3) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (R uni) (S uni)) (= (rev_append A R S) (infix_plpl A (reverse A R) S)) ) 15.33/15.56 ( elt1, (t2tb skv_3), (cons elt1 (t2tb1 skv_2) (nil elt1)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L1 uni) (L2 uni)) (or (not (permut A L1 L2)) (= (length A L2) (length A L1))) ) 15.33/15.56 ( elt1, (let ((_let_0 (t2tb skv_3))) (prefix elt1 (length elt1 _let_0) _let_0)), (t2tb skv_3) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L uni)) (= (nil A) (prefix A 0 L)) ) 15.33/15.56 ( elt1, (nil elt1) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X elt) (L list_elt) (BOUND_VARIABLE_2071 elt)) (let ((_let_0 (t2tb L))) (or (not (sorted (tb2t (reverse elt1 (cons elt1 (t2tb1 X) _let_0))))) (not (mem elt1 (t2tb1 BOUND_VARIABLE_2071) _let_0)) (le BOUND_VARIABLE_2071 X))) ) 15.33/15.56 ( skv_2, skv_3, skv_2 ) 15.33/15.56 ( skv_2, skv_3, skv_4 ) 15.33/15.56 ( skv_4, (tb2t (nil elt1)), skv_2 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X Int) (Y Int) (Z Int)) (or (>= (+ X (* (- 1) Y)) 1) (not (>= Z 0)) (not (>= (+ (* X Z) (* (- 1) (* Y Z))) 1))) ) 15.33/15.56 ( 0, 0, 0 ) 15.33/15.56 ( (- 1), 0, 0 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (N Int) (X uni) (L uni)) (or (not (>= N 1)) (= (prefix A N (cons A X L)) (cons A X (prefix A (+ (- 1) N) L)))) ) 15.33/15.56 ( elt1, (length elt1 (cons elt1 (t2tb1 skv_2) (t2tb skv_3))), (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((Z list_elt)) (or (not (sorted Z)) (not (forall ((X elt) (Y elt) (L list_elt)) (let ((_let_0 (t2tb1 Y))) (let ((_let_1 (t2tb L))) (let ((_let_2 (cons elt1 _let_0 _let_1))) (or (not (= Z (tb2t (cons elt1 (t2tb1 X) _let_2)))) (not (sorted (tb2t _let_2))) (not (le X Y)))))) )) (not (forall ((X elt)) (not (= Z (tb2t (cons elt1 (t2tb1 X) (nil elt1))))) )) (= (tb2t (nil elt1)) Z)) ) 15.33/15.56 ( (tb2t (nil elt1)) ) 15.33/15.56 ( (tb2t (cons elt1 (t2tb1 skv_2) (nil elt1))) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (L uni)) (= L (reverse A (reverse A L))) ) 15.33/15.56 ( elt1, (nil elt1) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (X uni) (L uni)) (= (mem A X L) (>= (num_occ A X L) 1)) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_4), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_5), (t2tb skv_3) ) 15.33/15.56 ( elt1, skv_6, (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ( elt1, skv_6, (let ((_let_0 (t2tb skv_3))) (let ((_let_1 (t2tb1 skv_2))) (let ((_let_2 (cons elt1 _let_1 _let_0))) (prefix elt1 (length elt1 _let_2) _let_2)))) ) 15.33/15.56 ( elt1, skv_7, (nil elt1) ) 15.33/15.56 ( elt1, skv_7, (let ((_let_0 (nil elt1))) (prefix elt1 (length elt1 _let_0) _let_0)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X elt) (X1 list_elt)) (let ((_let_0 (t2tb1 X))) (let ((_let_1 (t2tb X1))) (let ((_let_2 (cons elt1 _let_0 _let_1))) (or (not (permut elt1 (prefix elt1 (length elt1 _let_1) _let_1) _let_1)) (permut elt1 (prefix elt1 (length elt1 _let_2) _let_2) _let_2))))) ) 15.33/15.56 ( skv_2, (tb2t (nil elt1)) ) 15.33/15.56 ( skv_2, skv_3 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (U uni) (U1 uni)) (= U1 (cons_proj_2 A (cons A U U1))) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (nil elt1) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (t2tb skv_3) ) 15.33/15.56 ( elt1, (t2tb1 skv_2), (let ((_let_0 (t2tb skv_3))) (prefix elt1 (+ (- 1) (length elt1 (cons elt1 (t2tb1 skv_2) _let_0))) _let_0)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((A ty) (N Int) (L uni)) (or (>= (+ N (* (- 1) (length A L))) 1) (not (>= N 0)) (= N (length A (prefix A N L)))) ) 15.33/15.56 ( elt1, (length elt1 (nil elt1)), (nil elt1) ) 15.33/15.56 ( elt1, (length elt1 (t2tb skv_3)), (t2tb skv_3) ) 15.33/15.56 ( elt1, (length elt1 (cons elt1 (t2tb1 skv_2) (t2tb skv_3))), (cons elt1 (t2tb1 skv_2) (t2tb skv_3)) ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X elt) (L list_elt)) (= (and (sorted L) (forall ((Y elt)) (or (not (mem elt1 (t2tb1 Y) (t2tb L))) (le X Y)) )) (sorted (tb2t (cons elt1 (t2tb1 X) (t2tb L))))) ) 15.33/15.56 ( skv_2, (tb2t (nil elt1)) ) 15.33/15.56 ( skv_2, skv_3 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((X elt) (L list_elt)) (let ((_let_0 (t2tb L))) (or (not (sorted (tb2t (reverse elt1 (cons elt1 (t2tb1 X) _let_0))))) (sorted (tb2t (reverse elt1 _let_0))))) ) 15.33/15.56 ( skv_2, (tb2t (nil elt1)) ) 15.33/15.56 ( skv_2, skv_3 ) 15.33/15.56 ) 15.33/15.56 (instantiation (forall ((J uni)) (or (not (sort elt1 J)) (= J (t2tb1 (tb2t1 J)))) ) 15.33/15.56 ( (t2tb1 skv_2) ) 15.33/15.56 ( skv_6 ) 15.33/15.56 ( skv_7 ) 15.33/15.56 ) 15.33/15.56 % SZS output end Proof for theBenchmark 15.33/15.56 EOF