0.04/0.15 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.14/0.16 % Command : do_CVC4 %s 0.15/0.38 % Computer : n005.cluster.edu 0.15/0.38 % Model : x86_64 x86_64 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.38 % Memory : 8042.1875MB 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.38 % CPULimit : 180 0.15/0.38 % DateTime : Thu Aug 29 10:52:55 EDT 2019 0.15/0.38 % CPUTime : 0.23/0.53 %----Proving TH0_NAR 0.36/0.54 ------- cvc4-thf casc 27 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 180... 0.36/0.54 --- Run --uf-ho --ho-elim --no-ho-elim-store-ax --full-saturate-quant at 20... 2.24/2.45 % SZS status Theorem for theBenchmark 2.24/2.45 % SZS output start Proof for theBenchmark 2.24/2.45 (skolem (forall ((z frac)) (= (ho_7 (ho_6 k_5 y) z) (ho_7 (ho_6 k_5 x) z)) ) 2.24/2.45 ( skv_8 ) 2.24/2.45 ) 2.24/2.45 (skolem (forall ((z frac)) (= (ho_3 (ho_2 k_1 x) z) (ho_3 (ho_2 k_1 (ho_7 (ho_6 k_5 x) z)) z)) ) 2.24/2.45 ( skv_9 ) 2.24/2.45 ) 2.24/2.45 (skolem (forall ((z frac)) (= (ho_2 k_1 z) (ho_2 k_4 z)) ) 2.24/2.45 ( skv_10 ) 2.24/2.45 ) 2.24/2.45 (skolem (forall ((z frac)) (= (ho_3 (ho_2 k_1 x) z) (ho_3 (ho_2 k_1 z) z)) ) 2.24/2.45 ( skv_11 ) 2.24/2.45 ) 2.24/2.45 (instantiation (forall ((Xx frac) (Xy frac) (Xz frac) (Xu frac)) (or (not (ho_3 (ho_2 k_1 Xx) Xy)) (not (ho_3 (ho_2 k_4 Xx) Xz)) (not (ho_3 (ho_2 k_4 Xy) Xu)) (ho_3 (ho_2 k_1 Xz) Xu)) ) 2.24/2.45 ( x, x, x, x ) 2.24/2.45 ( x, y, x, x ) 2.24/2.45 ( x, y, x, z ) 2.24/2.45 ( x, y, x, u ) 2.24/2.45 ( x, y, x, (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( x, y, x, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( x, y, x, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( x, y, x, skv_8 ) 2.24/2.45 ( x, y, x, skv_9 ) 2.24/2.45 ( x, y, x, skv_10 ) 2.24/2.45 ( x, y, x, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( x, y, x, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( x, y, x, (ho_7 (ho_6 k_5 x) y) ) 2.24/2.45 ( x, y, x, skv_11 ) 2.24/2.45 ( x, y, y, y ) 2.24/2.45 ( x, y, z, u ) 2.24/2.45 ( x, y, u, y ) 2.24/2.45 ( x, y, (ho_7 (ho_6 k_5 y) u), y ) 2.24/2.45 ( x, y, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( x, y, (ho_7 (ho_6 k_5 x) x), y ) 2.24/2.45 ( x, y, skv_8, y ) 2.24/2.45 ( x, y, skv_9, y ) 2.24/2.45 ( x, y, skv_10, y ) 2.24/2.45 ( x, y, (ho_7 (ho_6 k_5 y) x), y ) 2.24/2.45 ( x, y, (ho_7 (ho_6 k_5 y) y), y ) 2.24/2.45 ( x, y, (ho_7 (ho_6 k_5 x) y), y ) 2.24/2.45 ( x, z, x, u ) 2.24/2.45 ( x, u, x, x ) 2.24/2.45 ( x, (ho_7 (ho_6 k_5 y) u), skv_9, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( x, (ho_7 (ho_6 k_5 x) z), x, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( x, (ho_7 (ho_6 k_5 x) x), x, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( x, skv_8, x, skv_8 ) 2.24/2.45 ( x, skv_10, x, skv_10 ) 2.24/2.45 ( x, (ho_7 (ho_6 k_5 y) x), x, (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( x, (ho_7 (ho_6 k_5 y) y), x, skv_9 ) 2.24/2.45 ( x, (ho_7 (ho_6 k_5 x) y), x, z ) 2.24/2.45 ( y, x, (ho_7 (ho_6 k_5 y) u), x ) 2.24/2.45 ( y, y, y, y ) 2.24/2.45 ( y, z, (ho_7 (ho_6 k_5 y) u), u ) 2.24/2.45 ( y, u, y, z ) 2.24/2.45 ( y, (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( y, (ho_7 (ho_6 k_5 x) z), y, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( y, (ho_7 (ho_6 k_5 x) x), y, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( y, skv_8, y, z ) 2.24/2.45 ( y, skv_9, y, skv_9 ) 2.24/2.45 ( y, skv_10, y, skv_10 ) 2.24/2.45 ( y, (ho_7 (ho_6 k_5 y) x), y, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( y, (ho_7 (ho_6 k_5 y) y), y, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( y, (ho_7 (ho_6 k_5 x) y), y, z ) 2.24/2.45 ( z, x, u, x ) 2.24/2.45 ( z, y, u, (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( z, z, u, u ) 2.24/2.45 ( z, (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( z, (ho_7 (ho_6 k_5 x) z), u, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( z, (ho_7 (ho_6 k_5 y) z), u, (ho_7 (ho_6 k_5 y) z) ) 2.24/2.45 ( z, (ho_7 (ho_6 k_5 x) x), z, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( z, skv_8, (ho_7 (ho_6 k_5 x) x), z ) 2.24/2.45 ( z, (ho_7 (ho_6 k_5 x) skv_8), z, (ho_7 (ho_6 k_5 x) skv_8) ) 2.24/2.45 ( z, skv_9, z, z ) 2.24/2.45 ( z, skv_10, u, skv_10 ) 2.24/2.45 ( z, (ho_7 (ho_6 k_5 y) x), z, skv_9 ) 2.24/2.45 ( z, (ho_7 (ho_6 k_5 y) y), u, skv_10 ) 2.24/2.45 ( z, (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) y) ) 2.24/2.45 ( u, x, u, u ) 2.24/2.45 ( u, y, u, y ) 2.24/2.45 ( u, z, z, z ) 2.24/2.45 ( u, u, z, u ) 2.24/2.45 ( u, (ho_7 (ho_6 k_5 y) u), x, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( u, (ho_7 (ho_6 k_5 x) z), z, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( u, (ho_7 (ho_6 k_5 x) x), z, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( u, skv_8, x, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( u, (ho_7 (ho_6 k_5 x) skv_8), z, u ) 2.24/2.45 ( u, skv_9, x, skv_9 ) 2.24/2.45 ( u, skv_9, (ho_7 (ho_6 k_5 x) x), u ) 2.24/2.45 ( u, skv_10, (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( u, (ho_7 (ho_6 k_5 y) x), z, (ho_7 (ho_6 k_5 x) y) ) 2.24/2.45 ( u, (ho_7 (ho_6 k_5 y) y), x, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( u, (ho_7 (ho_6 k_5 x) y), x, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), x, z, x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), y, (ho_7 (ho_6 k_5 x) z), y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), z, (ho_7 (ho_6 k_5 x) z), u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), u, x, z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 y) u), z, u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) z), x, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) x), u, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), skv_8, x, skv_8 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), skv_9, x, skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), skv_10, z, z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 y) x), z, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 y) y), x, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), x, (ho_7 (ho_6 k_5 x) z), x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), y, (ho_7 (ho_6 k_5 x) z), y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), z, (ho_7 (ho_6 k_5 x) z), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), u, (ho_7 (ho_6 k_5 x) z), u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) z), x, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) z), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_8, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, x, skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, y, skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, z, z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, u, u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 y) u), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), skv_8 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), skv_10 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) x), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, skv_8, skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, skv_9, skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, skv_10, skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 y) x), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 y) y), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_9, (ho_7 (ho_6 k_5 x) y), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), skv_10, (ho_7 (ho_6 k_5 x) z), skv_10 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) z), x, x, x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) z), z, (ho_7 (ho_6 k_5 y) z), u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), x, (ho_7 (ho_6 k_5 x) x), x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), y, (ho_7 (ho_6 k_5 x) x), y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), z, (ho_7 (ho_6 k_5 x) x), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), u, (ho_7 (ho_6 k_5 x) x), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) z), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), skv_8, skv_10, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), skv_9, (ho_7 (ho_6 k_5 x) x), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), skv_10, (ho_7 (ho_6 k_5 x) x), skv_10 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), x, x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), y, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), z, u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), skv_8 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), skv_10 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), skv_8, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), skv_9, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), skv_10, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), u, u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), skv_8 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), skv_10 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), skv_10, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( skv_8, x, (ho_7 (ho_6 k_5 x) z), x ) 2.24/2.45 ( skv_8, y, (ho_7 (ho_6 k_5 x) z), y ) 2.24/2.45 ( skv_8, z, z, u ) 2.24/2.45 ( skv_8, u, z, u ) 2.24/2.45 ( skv_8, (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( skv_8, (ho_7 (ho_6 k_5 x) z), z, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( skv_8, (ho_7 (ho_6 k_5 x) x), skv_8, (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( skv_8, skv_8, skv_8, (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( skv_8, skv_9, z, skv_8 ) 2.24/2.45 ( skv_8, skv_10, skv_8, (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( skv_8, (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( skv_8, (ho_7 (ho_6 k_5 y) y), x, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( skv_8, (ho_7 (ho_6 k_5 x) y), skv_8, (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) skv_8), z, (ho_7 (ho_6 k_5 x) skv_8), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) skv_8), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( skv_9, x, z, x ) 2.24/2.45 ( skv_9, x, skv_9, u ) 2.24/2.45 ( skv_9, y, skv_10, y ) 2.24/2.45 ( skv_9, z, z, u ) 2.24/2.45 ( skv_9, u, u, x ) 2.24/2.45 ( skv_9, (ho_7 (ho_6 k_5 y) u), x, x ) 2.24/2.45 ( skv_9, (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( skv_9, (ho_7 (ho_6 k_5 x) x), skv_9, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( skv_9, skv_8, skv_9, x ) 2.24/2.45 ( skv_9, skv_9, skv_9, skv_9 ) 2.24/2.45 ( skv_9, skv_10, skv_9, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( skv_9, (ho_7 (ho_6 k_5 y) x), skv_9, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( skv_9, (ho_7 (ho_6 k_5 y) y), skv_9, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( skv_9, (ho_7 (ho_6 k_5 x) y), skv_9, x ) 2.24/2.45 ( skv_10, x, skv_10, x ) 2.24/2.45 ( skv_10, y, skv_10, y ) 2.24/2.45 ( skv_10, z, skv_10, u ) 2.24/2.45 ( skv_10, u, x, skv_9 ) 2.24/2.45 ( skv_10, (ho_7 (ho_6 k_5 y) u), z, (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( skv_10, (ho_7 (ho_6 k_5 x) z), skv_10, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( skv_10, (ho_7 (ho_6 k_5 x) x), skv_10, (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( skv_10, skv_8, x, skv_8 ) 2.24/2.45 ( skv_10, skv_9, (ho_7 (ho_6 k_5 x) x), skv_9 ) 2.24/2.45 ( skv_10, skv_9, skv_10, z ) 2.24/2.45 ( skv_10, skv_10, x, x ) 2.24/2.45 ( skv_10, skv_10, (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( skv_10, (ho_7 (ho_6 k_5 y) x), skv_10, skv_8 ) 2.24/2.45 ( skv_10, (ho_7 (ho_6 k_5 y) y), skv_10, (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( skv_10, (ho_7 (ho_6 k_5 x) y), z, z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), x, (ho_7 (ho_6 k_5 y) x), x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), y, (ho_7 (ho_6 k_5 y) y), y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), z, skv_10, z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), u, (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) u), y, z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), skv_8, (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), skv_9, (ho_7 (ho_6 k_5 y) x), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), skv_10, (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), x, x, x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), y, (ho_7 (ho_6 k_5 y) y), y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), z, z, z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), u, (ho_7 (ho_6 k_5 y) y), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), skv_8, (ho_7 (ho_6 k_5 y) y), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), skv_9, (ho_7 (ho_6 k_5 y) x), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), skv_10, (ho_7 (ho_6 k_5 y) y), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), x, z, x ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), y, z, y ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), z, z, u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), u, z, z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 x) z), z, (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 x) x), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), skv_8, (ho_7 (ho_6 k_5 x) y), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), skv_9, (ho_7 (ho_6 k_5 x) x), skv_9 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), skv_10, (ho_7 (ho_6 k_5 x) y), z ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) x), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), x, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), y, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), z, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), u, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) u), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) z), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), skv_8, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), skv_9, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), skv_10, (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) y), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 x) y), (ho_7 (ho_6 k_5 x) y), z ) 2.24/2.45 ( (let ((_let_0 (ho_6 k_5 x))) (ho_7 _let_0 (ho_7 _let_0 z))), z, z, z ) 2.24/2.45 ) 2.24/2.45 (instantiation (forall ((Xx frac) (Xy frac) (Xz frac)) (or (not (ho_3 (ho_2 k_1 Xx) Xy)) (ho_3 (ho_2 k_1 (ho_7 (ho_6 k_5 Xx) Xz)) (ho_7 (ho_6 k_5 Xy) Xz))) ) 2.24/2.45 ( x, x, x ) 2.24/2.45 ( x, y, x ) 2.24/2.45 ( x, y, y ) 2.24/2.45 ( x, y, z ) 2.24/2.45 ) 2.24/2.45 (instantiation (forall ((Xx frac) (Xy frac) (Xz frac) (Xu frac)) (or (not (ho_3 (ho_2 k_1 Xx) Xy)) (not (ho_3 (ho_2 k_1 Xz) Xu)) (ho_3 (ho_2 k_1 (ho_7 (ho_6 k_5 Xx) Xz)) (ho_7 (ho_6 k_5 Xy) Xu))) ) 2.24/2.45 ( x, x, x, x ) 2.24/2.45 ( x, y, x, y ) 2.24/2.45 ( x, y, z, u ) 2.24/2.45 ( x, y, (ho_7 (ho_6 k_5 x) z), skv_9 ) 2.24/2.45 ) 2.24/2.45 (instantiation (forall ((Xx frac)) (ho_3 (ho_2 k_4 Xx) Xx) ) 2.24/2.45 ( x ) 2.24/2.45 ( y ) 2.24/2.45 ( z ) 2.24/2.45 ( u ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) u) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) z) ) 2.24/2.45 ( skv_8 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 x) skv_8) ) 2.24/2.45 ( skv_9 ) 2.24/2.45 ( skv_10 ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) x) ) 2.24/2.45 ( (ho_7 (ho_6 k_5 y) y) ) 2.24/2.45 ) 2.24/2.45 (instantiation (forall ((Xx frac) (Xy frac) (Xz frac) (Xu frac)) (or (not (ho_3 (ho_2 k_4 Xx) Xy)) (not (ho_3 (ho_2 k_4 Xz) Xu)) (ho_3 (ho_2 k_4 (ho_7 (ho_6 k_5 Xx) Xz)) (ho_7 (ho_6 k_5 Xy) Xu))) ) 2.24/2.45 ( x, x, x, x ) 2.24/2.45 ( x, x, y, y ) 2.24/2.45 ( x, x, z, x ) 2.24/2.45 ( x, x, z, y ) 2.24/2.45 ( y, y, z, z ) 2.24/2.45 ( y, y, z, u ) 2.24/2.45 ) 2.24/2.45 (instantiation (forall ((x |u_(-> frac frac)|) (y |u_(-> frac frac)|)) (or (not (forall ((z frac)) (= (ho_7 x z) (ho_7 y z)) )) (= x y)) ) 2.24/2.45 ( (ho_6 k_5 y), (ho_6 k_5 x) ) 2.24/2.45 ( (ho_6 k_5 x), (ho_6 k_5 y) ) 2.24/2.45 ) 2.24/2.45 (instantiation (forall ((x |u_(-> frac Bool)|) (y |u_(-> frac Bool)|)) (or (not (forall ((z frac)) (= (ho_3 x z) (ho_3 y z)) )) (= x y)) ) 2.24/2.45 ( (ho_2 k_1 x), (ho_2 k_1 (ho_7 (ho_6 k_5 x) z)) ) 2.24/2.45 ( (ho_2 k_1 x), (ho_2 k_1 z) ) 2.24/2.45 ( (ho_2 k_1 (ho_7 (ho_6 k_5 x) z)), (ho_2 k_1 x) ) 2.24/2.45 ) 2.24/2.45 (instantiation (forall ((x |u_(-> frac frac Bool)|) (y |u_(-> frac frac Bool)|)) (or (not (forall ((z frac)) (= (ho_2 x z) (ho_2 y z)) )) (= x y)) ) 2.24/2.45 ( k_1, k_4 ) 2.24/2.45 ( k_4, k_1 ) 2.24/2.45 ) 2.24/2.45 % SZS output end Proof for theBenchmark 2.24/2.45 EOF