0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : do_CVC4 %s 0.03/0.24 % Computer : n130.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 05:18:39 CDT 2018 0.03/0.24 % CPUTime : 0.03/0.28 %----Proving without arithmetic mode 0.03/0.28 ------- cvc4-fof casc j9 : /export/starexec/sandbox2/benchmark/theBenchmark.p at ... 0.03/0.28 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-quant-cf --full-saturate-quant at 20... 20.19/21.14 --- Run --no-e-matching --full-saturate-quant at 20... 40.13/41.17 --- Run --finite-model-find --uf-ss=no-minimal at 15... 42.33/43.35 % SZS status Theorem for theBenchmark 42.33/43.35 % SZS output start Proof for theBenchmark 42.33/43.35 (skolem (let ((_let_0 (strong_iteration X0))) (forall ((X0 $$unsorted)) (leq (multiplication _let_0 _let_0) _let_0) )) 42.33/43.35 ( skv_1 ) 42.33/43.35 ) 42.33/43.35 (skolem (let ((_let_0 (strong_iteration X0))) (forall ((X0 $$unsorted)) (leq _let_0 (multiplication _let_0 _let_0)) )) 42.33/43.35 ( skv_21 ) 42.33/43.35 ) 42.33/43.35 (instantiation (forall ((A $$unsorted)) (= A (multiplication one A)) ) 42.33/43.35 ( zero ) 42.33/43.35 ( skv_1 ) 42.33/43.35 ( (strong_iteration skv_1) ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( (addition (multiplication (addition skv_1 skv_1) skv_1) skv_1) ) 42.33/43.35 ( (strong_iteration one) ) 42.33/43.35 ( (strong_iteration skv_21) ) 42.33/43.35 ) 42.33/43.35 (instantiation (forall ((A $$unsorted) (B $$unsorted)) (= (leq A B) (= B (addition A B))) ) 42.33/43.35 ( one, one ) 42.33/43.35 ( one, skv_1 ) 42.33/43.35 ( one, (strong_iteration skv_21) ) 42.33/43.35 ( zero, one ) 42.33/43.35 ( zero, zero ) 42.33/43.35 ( zero, skv_1 ) 42.33/43.35 ( zero, (star skv_1) ) 42.33/43.35 ( zero, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( zero, (addition (multiplication zero zero) (strong_iteration skv_21)) ) 42.33/43.35 ( skv_1, zero ) 42.33/43.35 ( skv_1, skv_1 ) 42.33/43.35 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( skv_1, (addition (multiplication skv_1 skv_1) skv_1) ) 42.33/43.35 ( skv_1, (addition (multiplication (star skv_1) skv_1) (addition skv_1 (strong_iteration skv_1))) ) 42.33/43.35 ( skv_1, (addition (multiplication skv_1 skv_1) (multiplication skv_1 (addition skv_1 (strong_iteration skv_1)))) ) 42.33/43.35 ( skv_1, (multiplication (strong_iteration (multiplication (addition skv_1 skv_1) skv_1)) zero) ) 42.33/43.35 ( skv_1, (addition (multiplication (multiplication (addition skv_1 skv_1) skv_1) skv_1) (star skv_1)) ) 42.33/43.35 ( skv_1, (strong_iteration skv_21) ) 42.33/43.35 ( (strong_iteration skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1) ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (let ((_let_0 (strong_iteration skv_1))) (addition (multiplication skv_1 (multiplication _let_0 _let_0)) zero)) ) 42.33/43.35 ( (star skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( (star skv_1), (star skv_1) ) 42.33/43.35 ( (star skv_1), (multiplication (strong_iteration skv_1) one) ) 42.33/43.35 ( (star skv_1), (multiplication (strong_iteration skv_1) (multiplication skv_1 one)) ) 42.33/43.35 ( (addition (multiplication skv_1 skv_1) skv_1), skv_1 ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), (star skv_1) ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( (multiplication skv_1 (star (multiplication (addition skv_1 skv_1) skv_1))), skv_1 ) 42.33/43.35 ( (multiplication (star zero) skv_1), skv_1 ) 42.33/43.35 ( (let ((_let_0 (star skv_1))) (multiplication (multiplication _let_0 skv_1) _let_0)), (star skv_1) ) 42.33/43.35 ( (strong_iteration skv_21), skv_1 ) 42.33/43.35 ( (strong_iteration skv_21), (let ((_let_0 (strong_iteration skv_21))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ) 42.33/43.35 (instantiation (let ((_let_0 (star A))) (forall ((A $$unsorted)) (= _let_0 (addition one (multiplication A _let_0))) )) 42.33/43.35 ( zero ) 42.33/43.35 ( (strong_iteration skv_21) ) 42.33/43.35 ) 42.33/43.35 (instantiation (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (multiplication A (addition B C)) (addition (multiplication A B) (multiplication A C))) ) 42.33/43.35 ( one, skv_21, one ) 42.33/43.35 ( zero, zero, skv_1 ) 42.33/43.35 ( zero, skv_1, zero ) 42.33/43.35 ( zero, skv_1, skv_1 ) 42.33/43.35 ( zero, skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( zero, (multiplication (addition skv_1 skv_1) skv_1), skv_1 ) 42.33/43.35 ( skv_1, one, one ) 42.33/43.35 ( skv_1, one, zero ) 42.33/43.35 ( skv_1, zero, skv_1 ) 42.33/43.35 ( skv_1, zero, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( skv_1, skv_1, skv_1 ) 42.33/43.35 ( skv_1, skv_1, (strong_iteration skv_1) ) 42.33/43.35 ( skv_1, skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( skv_1, skv_1, (addition skv_1 (strong_iteration skv_1)) ) 42.33/43.35 ( skv_1, (strong_iteration skv_1), one ) 42.33/43.35 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1 ) 42.33/43.35 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1) ) 42.33/43.35 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 (multiplication _let_0 _let_0))) ) 42.33/43.35 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( skv_1, (multiplication skv_1 (strong_iteration skv_1)), skv_1 ) 42.33/43.35 ( skv_1, (multiplication skv_1 skv_1), one ) 42.33/43.35 ( skv_1, (multiplication skv_1 skv_1), (multiplication skv_1 (strong_iteration skv_1)) ) 42.33/43.35 ( skv_1, (multiplication skv_1 skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication (multiplication _let_0 _let_0) skv_1)) ) 42.33/43.35 ( skv_1, (multiplication skv_1 skv_1), (multiplication skv_1 (addition skv_1 (strong_iteration skv_1))) ) 42.33/43.35 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), zero ) 42.33/43.35 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( skv_1, (multiplication (star skv_1) skv_1), one ) 42.33/43.35 ( skv_1, (multiplication (star skv_1) skv_1), (multiplication skv_1 one) ) 42.33/43.35 ( skv_1, (multiplication (star skv_1) skv_1), (multiplication (star skv_1) (multiplication (addition skv_1 skv_1) skv_1)) ) 42.33/43.35 ( skv_1, (multiplication (star skv_1) skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication (star skv_1) (multiplication _let_0 _let_0))) ) 42.33/43.35 ( skv_1, (addition skv_1 (strong_iteration skv_1)), (multiplication (star skv_1) skv_1) ) 42.33/43.35 ( skv_1, skv_21, zero ) 42.33/43.35 ( (strong_iteration skv_1), one, one ) 42.33/43.35 ( (strong_iteration skv_1), skv_1, skv_1 ) 42.33/43.35 ( (strong_iteration skv_1), skv_1, (strong_iteration skv_1) ) 42.33/43.35 ( (strong_iteration skv_1), skv_1, (multiplication skv_1 skv_1) ) 42.33/43.35 ( (strong_iteration skv_1), (strong_iteration skv_1), one ) 42.33/43.35 ( (strong_iteration skv_1), (strong_iteration skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( (strong_iteration skv_1), (multiplication skv_1 skv_1), one ) 42.33/43.35 ( (strong_iteration skv_1), (star skv_1), (star skv_1) ) 42.33/43.35 ( (strong_iteration skv_1), (multiplication (strong_iteration skv_1) skv_1), (multiplication skv_1 skv_1) ) 42.33/43.35 ( (strong_iteration skv_1), (addition (multiplication (star skv_1) skv_1) one), one ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1, (star skv_1) ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (star skv_1), skv_1 ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (multiplication (addition skv_1 skv_1) skv_1), skv_1 ) 42.33/43.35 ( (star skv_1), zero, skv_1 ) 42.33/43.35 ( (star skv_1), zero, (star skv_1) ) 42.33/43.35 ( (star skv_1), zero, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( (star skv_1), skv_1, zero ) 42.33/43.35 ( (star skv_1), skv_1, skv_1 ) 42.33/43.35 ( (star skv_1), skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( (star skv_1), skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( (star skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1 ) 42.33/43.35 ( (star skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( (star skv_1), (star skv_1), zero ) 42.33/43.35 ( (star skv_1), (multiplication (addition skv_1 skv_1) skv_1), zero ) 42.33/43.35 ( (star skv_1), (multiplication (addition skv_1 skv_1) skv_1), skv_1 ) 42.33/43.35 ( (star skv_1), (addition skv_1 (strong_iteration skv_1)), (multiplication (star skv_1) skv_1) ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), one, (multiplication skv_1 skv_1) ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), zero, skv_1 ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, zero ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, (star skv_1) ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), (star skv_1), skv_1 ) 42.33/43.35 ( (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1), skv_1 ) 42.33/43.35 ( (strong_iteration (star skv_1)), one, one ) 42.33/43.35 ( (strong_iteration (multiplication (addition skv_1 skv_1) skv_1)), one, one ) 42.33/43.35 ( (strong_iteration (multiplication (addition skv_1 skv_1) skv_1)), skv_1, (multiplication skv_1 skv_1) ) 42.33/43.35 ( (strong_iteration (multiplication (addition skv_1 skv_1) skv_1)), (multiplication skv_1 skv_1), skv_1 ) 42.33/43.35 ( skv_21, skv_21, one ) 42.33/43.35 ( skv_21, (strong_iteration skv_21), skv_1 ) 42.33/43.35 ( (strong_iteration skv_21), one, one ) 42.33/43.35 ( (strong_iteration skv_21), one, zero ) 42.33/43.35 ( (strong_iteration skv_21), one, (strong_iteration skv_21) ) 42.33/43.35 ( (strong_iteration skv_21), zero, one ) 42.33/43.35 ( (strong_iteration skv_21), skv_1, skv_1 ) 42.33/43.35 ( (strong_iteration skv_21), skv_21, one ) 42.33/43.35 ( (strong_iteration skv_21), (strong_iteration skv_21), one ) 42.33/43.35 ) 42.33/43.35 (instantiation (forall ((C $$unsorted) (B $$unsorted) (A $$unsorted)) (= (addition (addition A B) C) (addition A (addition B C))) ) 42.33/43.35 ( one, one, (multiplication skv_1 (strong_iteration skv_1)) ) 42.33/43.35 ( one, one, (multiplication (star skv_1) skv_1) ) 42.33/43.35 ( one, one, (multiplication skv_21 (strong_iteration skv_21)) ) 42.33/43.35 ( one, one, (let ((_let_0 (strong_iteration skv_21))) (multiplication _let_0 (strong_iteration _let_0))) ) 42.33/43.35 ( one, zero, skv_1 ) 42.33/43.35 ( one, zero, (strong_iteration skv_21) ) 42.33/43.35 ( one, skv_1, (strong_iteration skv_1) ) 42.33/43.35 ( one, skv_1, (multiplication skv_1 (strong_iteration skv_1)) ) 42.33/43.35 ( one, skv_1, (multiplication skv_1 skv_1) ) 42.33/43.35 ( one, skv_1, (addition (multiplication skv_1 (multiplication (star skv_1) skv_1)) (multiplication skv_1 one)) ) 42.33/43.35 ( one, skv_1, (multiplication skv_1 (multiplication (addition skv_1 skv_1) skv_1)) ) 42.33/43.35 ( one, (strong_iteration skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( one, (multiplication skv_1 (strong_iteration skv_1)), (let ((_let_0 (strong_iteration skv_1))) (multiplication skv_1 (multiplication _let_0 _let_0))) ) 42.33/43.35 ( one, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 (multiplication _let_0 _let_0))), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( one, (multiplication skv_1 skv_1), skv_1 ) 42.33/43.35 ( one, (multiplication skv_1 skv_1), (multiplication skv_1 skv_1) ) 42.33/43.35 ( one, (multiplication (strong_iteration skv_1) skv_1), (multiplication skv_1 skv_1) ) 42.33/43.35 ( one, (multiplication (strong_iteration skv_1) skv_1), (multiplication (strong_iteration skv_1) skv_1) ) 42.33/43.35 ( one, (multiplication one skv_1), (let ((_let_0 (strong_iteration skv_21))) (multiplication (multiplication _let_0 _let_0) skv_1)) ) 42.33/43.35 ( one, (multiplication (star skv_1) skv_1), (addition one (multiplication skv_1 skv_1)) ) 42.33/43.35 ( one, (addition skv_1 (strong_iteration skv_1)), skv_1 ) 42.33/43.35 ( one, (multiplication skv_1 (multiplication skv_1 (addition skv_1 (strong_iteration skv_1)))), (multiplication skv_1 (multiplication skv_1 skv_1)) ) 42.33/43.35 ( one, (multiplication skv_1 (multiplication skv_1 one)), (multiplication skv_1 (multiplication (star skv_1) skv_1)) ) 42.33/43.35 ( one, (multiplication (strong_iteration (multiplication (addition skv_1 skv_1) skv_1)) (multiplication skv_1 skv_1)), (multiplication (strong_iteration (multiplication (addition skv_1 skv_1) skv_1)) skv_1) ) 42.33/43.35 ( one, skv_21, skv_1 ) 42.33/43.35 ( zero, one, (strong_iteration skv_21) ) 42.33/43.35 ( zero, zero, skv_1 ) 42.33/43.35 ( zero, zero, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( zero, skv_1, (star skv_1) ) 42.33/43.35 ( zero, skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.35 ( zero, (multiplication (addition skv_1 skv_1) skv_1), skv_1 ) 42.33/43.35 ( zero, (multiplication (addition skv_1 skv_1) skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( zero, (multiplication (addition skv_1 skv_1) skv_1), (star skv_1) ) 42.33/43.35 ( skv_1, one, (multiplication skv_1 (strong_iteration skv_1)) ) 42.33/43.35 ( skv_1, one, (addition (addition (multiplication skv_1 (multiplication (star skv_1) skv_1)) (multiplication skv_1 one)) skv_1) ) 42.33/43.35 ( skv_1, zero, zero ) 42.33/43.35 ( skv_1, zero, (star skv_1) ) 42.33/43.35 ( skv_1, skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( skv_1, skv_1, (multiplication skv_1 skv_1) ) 42.33/43.35 ( skv_1, skv_1, skv_21 ) 42.33/43.35 ( skv_1, (strong_iteration skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( skv_1, (multiplication skv_1 (strong_iteration skv_1)), (multiplication skv_1 skv_1) ) 42.33/43.35 ( skv_1, (addition skv_1 one), (addition (multiplication skv_1 (multiplication (star skv_1) skv_1)) (multiplication skv_1 one)) ) 42.33/43.35 ( skv_1, (multiplication skv_1 skv_1), (strong_iteration skv_1) ) 42.33/43.35 ( skv_1, (multiplication skv_1 skv_1), (addition (multiplication (star skv_1) skv_1) one) ) 42.33/43.35 ( skv_1, (multiplication skv_1 one), (multiplication skv_1 (multiplication (star skv_1) skv_1)) ) 42.33/43.35 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), zero ) 42.33/43.35 ( (strong_iteration skv_1), skv_1, skv_1 ) 42.33/43.35 ( (strong_iteration skv_1), skv_1, (addition (multiplication skv_1 skv_1) skv_1) ) 42.33/43.35 ( (strong_iteration skv_1), (multiplication (star skv_1) skv_1), (addition skv_1 (strong_iteration skv_1)) ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), zero, skv_1 ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1, zero ) 42.33/43.35 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 (multiplication _let_0 _let_0))), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1) ) 42.33/43.35 ( (multiplication skv_1 skv_1), one, one ) 42.33/43.35 ( (multiplication skv_1 skv_1), one, (multiplication skv_1 (strong_iteration skv_1)) ) 42.33/43.35 ( (multiplication skv_1 skv_1), one, (multiplication (star skv_1) skv_1) ) 42.33/43.35 ( (multiplication skv_1 skv_1), (strong_iteration skv_1), skv_1 ) 42.33/43.35 ( (multiplication skv_1 skv_1), (strong_iteration skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.35 ( (multiplication skv_1 skv_1), (multiplication skv_1 (multiplication (addition skv_1 skv_1) skv_1)), (let ((_let_0 (strong_iteration skv_1))) (multiplication skv_1 (multiplication _let_0 _let_0))) ) 42.33/43.36 ( (multiplication skv_1 skv_1), (let ((_let_0 (multiplication (addition skv_1 skv_1) skv_1))) (multiplication (star _let_0) _let_0)), one ) 42.33/43.36 ( (multiplication skv_1 skv_1), (let ((_let_0 (star skv_1))) (multiplication (star _let_0) _let_0)), one ) 42.33/43.36 ( (star skv_1), one, zero ) 42.33/43.36 ( (star skv_1), zero, skv_1 ) 42.33/43.36 ( (star skv_1), zero, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (star skv_1), skv_1, zero ) 42.33/43.36 ( (star skv_1), (multiplication skv_1 skv_1), skv_1 ) 42.33/43.36 ( (star skv_1), (multiplication skv_1 one), (multiplication (star skv_1) skv_1) ) 42.33/43.36 ( (star skv_1), (multiplication (addition skv_1 skv_1) skv_1), zero ) 42.33/43.36 ( (multiplication skv_1 one), one, (multiplication skv_1 skv_1) ) 42.33/43.36 ( (multiplication skv_1 one), (multiplication (star skv_1) skv_1), one ) 42.33/43.36 ( (multiplication skv_1 one), (multiplication skv_1 (multiplication skv_1 one)), (multiplication skv_1 (multiplication (star skv_1) skv_1)) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, zero ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, zero ) 42.33/43.36 ( (multiplication (star skv_1) skv_1), one, one ) 42.33/43.36 ( (multiplication (star skv_1) skv_1), one, (multiplication skv_1 skv_1) ) 42.33/43.36 ( (multiplication (star skv_1) skv_1), (strong_iteration skv_1), skv_1 ) 42.33/43.36 ( (multiplication (star skv_1) skv_1), (multiplication skv_1 skv_1), one ) 42.33/43.36 ( (multiplication (star skv_1) skv_1), (addition skv_1 (strong_iteration skv_1)), skv_1 ) 42.33/43.36 ( (addition skv_1 (strong_iteration skv_1)), one, (multiplication (star skv_1) skv_1) ) 42.33/43.36 ( (addition skv_1 (strong_iteration skv_1)), skv_1, one ) 42.33/43.36 ( (addition skv_1 (strong_iteration skv_1)), (multiplication (strong_iteration skv_1) skv_1), (multiplication (strong_iteration skv_1) skv_1) ) 42.33/43.36 ( (addition skv_1 (strong_iteration skv_1)), (multiplication (strong_iteration skv_1) skv_1), (multiplication (multiplication skv_1 skv_1) skv_1) ) 42.33/43.36 ( (addition skv_1 (strong_iteration skv_1)), (multiplication (star skv_1) skv_1), one ) 42.33/43.36 ( (addition skv_1 (strong_iteration skv_1)), (multiplication (star skv_1) skv_1), (multiplication skv_1 skv_1) ) 42.33/43.36 ( (addition zero one), skv_1, skv_1 ) 42.33/43.36 ( (addition zero one), (strong_iteration skv_1), skv_1 ) 42.33/43.36 ( (multiplication (strong_iteration skv_1) one), skv_1, one ) 42.33/43.36 ( (multiplication (strong_iteration skv_1) one), skv_1, (strong_iteration skv_1) ) 42.33/43.36 ( (multiplication (strong_iteration skv_1) one), (addition skv_1 one), (strong_iteration skv_1) ) 42.33/43.36 ( (multiplication (strong_iteration skv_1) one), (addition (multiplication skv_1 skv_1) skv_1), skv_1 ) 42.33/43.36 ( (multiplication (strong_iteration skv_1) one), (addition skv_1 (multiplication (strong_iteration skv_1) one)), (strong_iteration skv_1) ) 42.33/43.36 ( (multiplication (strong_iteration skv_1) one), (let ((_let_0 (strong_iteration skv_1))) (multiplication one (multiplication _let_0 _let_0))), (multiplication skv_1 (multiplication (star skv_1) skv_1)) ) 42.33/43.36 ( (multiplication (strong_iteration skv_1) one), (let ((_let_0 (multiplication (addition skv_1 skv_1) skv_1))) (multiplication (star _let_0) _let_0)), one ) 42.33/43.36 ( (addition (addition skv_1 (strong_iteration skv_1)) (multiplication (star skv_1) skv_1)), skv_1, one ) 42.33/43.36 ( (addition (addition skv_1 (strong_iteration skv_1)) (multiplication (star skv_1) skv_1)), (addition zero one), skv_1 ) 42.33/43.36 ( (addition (multiplication skv_1 (multiplication skv_1 (addition skv_1 (strong_iteration skv_1)))) one), one, zero ) 42.33/43.36 ( (addition (multiplication skv_1 (multiplication skv_1 (addition skv_1 (strong_iteration skv_1)))) one), (addition zero one), skv_1 ) 42.33/43.36 ( (addition (multiplication skv_1 (multiplication skv_1 (addition skv_1 (strong_iteration skv_1)))) one), (let ((_let_0 (strong_iteration skv_1))) (multiplication skv_1 (multiplication _let_0 (multiplication _let_0 _let_0)))), (let ((_let_0 (strong_iteration skv_1))) (multiplication skv_1 (multiplication _let_0 _let_0))) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication skv_1 (multiplication _let_0 (multiplication _let_0 _let_0)))), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication one (multiplication _let_0 _let_0))), (multiplication skv_1 (multiplication (star skv_1) skv_1)), (multiplication skv_1 (addition skv_1 (strong_iteration skv_1))) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication one (multiplication _let_0 _let_0))), (multiplication skv_1 (multiplication (star skv_1) (multiplication (addition skv_1 skv_1) skv_1))), (multiplication skv_1 (multiplication (star skv_1) skv_1)) ) 42.33/43.36 ( (multiplication (strong_iteration skv_1) (multiplication skv_1 one)), (addition zero one), skv_1 ) 42.33/43.36 ( (let ((_let_0 (multiplication (addition skv_1 skv_1) skv_1))) (multiplication (star _let_0) _let_0)), one, one ) 42.33/43.36 ( (let ((_let_0 (star skv_1))) (multiplication (star _let_0) _let_0)), one, one ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (addition (multiplication skv_1 (multiplication (star skv_1) skv_1)) (multiplication one (multiplication _let_0 _let_0)))), (multiplication skv_1 (strong_iteration skv_1)), (multiplication skv_1 skv_1) ) 42.33/43.36 ( (multiplication one (strong_iteration skv_21)), one, (multiplication skv_21 (strong_iteration skv_21)) ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted)) (= A (multiplication A one)) ) 42.33/43.36 ( one ) 42.33/43.36 ( zero ) 42.33/43.36 ( skv_1 ) 42.33/43.36 ( (strong_iteration skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (strong_iteration (star skv_1)) ) 42.33/43.36 ( (strong_iteration (multiplication (addition skv_1 skv_1) skv_1)) ) 42.33/43.36 ( (strong_iteration skv_21) ) 42.33/43.36 ( (strong_iteration (strong_iteration skv_21)) ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (leq C (addition (multiplication A C) B))) (leq C (multiplication (strong_iteration A) B))) ) 42.33/43.36 ( one, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1 ) 42.33/43.36 ( one, (strong_iteration skv_21), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( zero, skv_1, zero ) 42.33/43.36 ( zero, (star skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( zero, (multiplication (addition skv_1 skv_1) skv_1), zero ) 42.33/43.36 ( zero, (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( zero, (strong_iteration skv_21), zero ) 42.33/43.36 ( skv_1, one, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( skv_1, one, (star skv_1) ) 42.33/43.36 ( skv_1, one, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( skv_1, zero, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( skv_1, skv_1, zero ) 42.33/43.36 ( skv_1, skv_1, skv_1 ) 42.33/43.36 ( skv_1, (multiplication skv_1 skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( skv_1, (star skv_1), skv_1 ) 42.33/43.36 ( skv_1, (star skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( skv_1, (multiplication (strong_iteration skv_1) skv_1), skv_1 ) 42.33/43.36 ( skv_1, (multiplication skv_1 one), (star skv_1) ) 42.33/43.36 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), zero ) 42.33/43.36 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( skv_1, (multiplication (strong_iteration skv_1) one), (star skv_1) ) 42.33/43.36 ( skv_1, (multiplication skv_1 (addition skv_1 (strong_iteration skv_1))), skv_1 ) 42.33/43.36 ( skv_1, (multiplication skv_1 (multiplication (addition skv_1 skv_1) skv_1)), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (multiplication skv_1 skv_1), (multiplication (strong_iteration skv_1) skv_1), skv_1 ) 42.33/43.36 ( (star skv_1), one, (star skv_1) ) 42.33/43.36 ( (star skv_1), zero, skv_1 ) 42.33/43.36 ( (star skv_1), zero, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (star skv_1), skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (star skv_1), (star skv_1), skv_1 ) 42.33/43.36 ( (star skv_1), (star skv_1), (star skv_1) ) 42.33/43.36 ( (star skv_1), (star skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (star skv_1), (multiplication (addition skv_1 skv_1) skv_1), skv_1 ) 42.33/43.36 ( (star skv_1), (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (star skv_1), (addition skv_1 (strong_iteration skv_1)), skv_1 ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, skv_1 ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, zero ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (strong_iteration skv_1), (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (star skv_1), skv_1 ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (star skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1), zero ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1), skv_1 ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (strong_iteration skv_21), one, one ) 42.33/43.36 ( (strong_iteration skv_21), one, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted)) (= A (addition A zero)) ) 42.33/43.36 ( one ) 42.33/43.36 ( skv_1 ) 42.33/43.36 ( (multiplication zero zero) ) 42.33/43.36 ( (multiplication skv_21 (strong_iteration skv_21)) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_21))) (multiplication _let_0 (strong_iteration _let_0))) ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted)) (= A (addition A A)) ) 42.33/43.36 ( one ) 42.33/43.36 ( skv_1 ) 42.33/43.36 ( (multiplication skv_1 (strong_iteration skv_1)) ) 42.33/43.36 ) 42.33/43.36 (instantiation (let ((_let_0 (strong_iteration A))) (forall ((A $$unsorted)) (= _let_0 (addition (multiplication A _let_0) one)) )) 42.33/43.36 ( one ) 42.33/43.36 ( zero ) 42.33/43.36 ( skv_1 ) 42.33/43.36 ( (strong_iteration skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( skv_21 ) 42.33/43.36 ( (strong_iteration skv_21) ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted) (B $$unsorted)) (= (addition A B) (addition B A)) ) 42.33/43.36 ( one, zero ) 42.33/43.36 ( one, (multiplication (star skv_1) skv_1) ) 42.33/43.36 ( one, skv_21 ) 42.33/43.36 ( one, (strong_iteration skv_21) ) 42.33/43.36 ( zero, one ) 42.33/43.36 ( zero, skv_21 ) 42.33/43.36 ( skv_1, zero ) 42.33/43.36 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( skv_1, (addition (multiplication skv_1 skv_1) skv_1) ) 42.33/43.36 ( skv_1, (addition skv_1 (strong_iteration skv_1)) ) 42.33/43.36 ( skv_1, (addition zero one) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1 ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (multiplication skv_1 (strong_iteration skv_1)), one ) 42.33/43.36 ( (multiplication skv_1 skv_1), one ) 42.33/43.36 ( (multiplication skv_1 skv_1), skv_1 ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (multiplication (star skv_1) skv_1), (addition skv_1 (strong_iteration skv_1)) ) 42.33/43.36 ( (addition skv_1 (strong_iteration skv_1)), (multiplication (star skv_1) skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication skv_1 (multiplication _let_0 _let_0))), (multiplication skv_1 (strong_iteration skv_1)) ) 42.33/43.36 ( skv_21, one ) 42.33/43.36 ( skv_21, zero ) 42.33/43.36 ( (strong_iteration skv_21), one ) 42.33/43.36 ) 42.33/43.36 (instantiation (let ((_let_0 (star A))) (forall ((A $$unsorted)) (= _let_0 (addition one (multiplication _let_0 A))) )) 42.33/43.36 ( zero ) 42.33/43.36 ( skv_1 ) 42.33/43.36 ( (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (strong_iteration skv_21) ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (leq (addition (multiplication C A) B) C)) (leq (multiplication B (star A)) C)) ) 42.33/43.36 ( one, one, skv_1 ) 42.33/43.36 ( one, (strong_iteration skv_21), skv_1 ) 42.33/43.36 ( zero, one, skv_1 ) 42.33/43.36 ( zero, (strong_iteration skv_21), skv_1 ) 42.33/43.36 ( skv_1, zero, (star skv_1) ) 42.33/43.36 ( skv_1, skv_1, skv_1 ) 42.33/43.36 ( skv_1, (multiplication (star skv_1) skv_1), (star skv_1) ) 42.33/43.36 ( skv_1, (addition skv_1 (strong_iteration skv_1)), (star skv_1) ) 42.33/43.36 ( skv_1, (strong_iteration skv_21), zero ) 42.33/43.36 ( (star skv_1), zero, (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, skv_1 ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, skv_1 ) 42.33/43.36 ( (strong_iteration skv_21), one, skv_1 ) 42.33/43.36 ( (strong_iteration skv_21), zero, (strong_iteration skv_21) ) 42.33/43.36 ( (strong_iteration skv_21), (strong_iteration skv_21), skv_1 ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (addition (multiplication A C) (multiplication B C)) (multiplication (addition A B) C)) ) 42.33/43.36 ( one, one, (strong_iteration skv_21) ) 42.33/43.36 ( one, zero, skv_1 ) 42.33/43.36 ( one, zero, (strong_iteration skv_21) ) 42.33/43.36 ( one, skv_1, skv_1 ) 42.33/43.36 ( one, (addition skv_1 skv_1), (strong_iteration skv_21) ) 42.33/43.36 ( one, (strong_iteration skv_21), (strong_iteration skv_21) ) 42.33/43.36 ( zero, one, skv_1 ) 42.33/43.36 ( zero, one, (strong_iteration skv_21) ) 42.33/43.36 ( zero, zero, skv_1 ) 42.33/43.36 ( zero, skv_1, skv_1 ) 42.33/43.36 ( zero, skv_1, (star skv_1) ) 42.33/43.36 ( zero, (star skv_1), skv_1 ) 42.33/43.36 ( zero, (star skv_1), (star skv_1) ) 42.33/43.36 ( zero, (multiplication (addition skv_1 skv_1) skv_1), (star skv_1) ) 42.33/43.36 ( skv_1, zero, (star skv_1) ) 42.33/43.36 ( skv_1, skv_1, skv_1 ) 42.33/43.36 ( skv_1, skv_1, (strong_iteration skv_1) ) 42.33/43.36 ( skv_1, skv_1, (strong_iteration skv_21) ) 42.33/43.36 ( skv_1, (strong_iteration skv_1), skv_1 ) 42.33/43.36 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1 ) 42.33/43.36 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (star skv_1) ) 42.33/43.36 ( skv_1, (star skv_1), skv_1 ) 42.33/43.36 ( skv_1, (star skv_1), (multiplication (star skv_1) skv_1) ) 42.33/43.36 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), zero ) 42.33/43.36 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), (strong_iteration skv_1) ) 42.33/43.36 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( skv_1, (multiplication (addition skv_1 skv_1) skv_1), (star skv_1) ) 42.33/43.36 ( (strong_iteration skv_1), one, skv_1 ) 42.33/43.36 ( (strong_iteration skv_1), skv_1, skv_1 ) 42.33/43.36 ( (strong_iteration skv_1), (strong_iteration skv_1), (strong_iteration skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1, skv_1 ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1, (star skv_1) ) 42.33/43.36 ( (multiplication skv_1 (strong_iteration skv_1)), one, (strong_iteration skv_1) ) 42.33/43.36 ( (multiplication skv_1 (strong_iteration skv_1)), one, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (multiplication skv_1 (strong_iteration skv_1)), skv_1, (strong_iteration skv_1) ) 42.33/43.36 ( (multiplication skv_1 (strong_iteration skv_1)), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1) ) 42.33/43.36 ( (addition skv_1 skv_1), one, (strong_iteration skv_21) ) 42.33/43.36 ( (multiplication skv_1 skv_1), (strong_iteration skv_1), skv_1 ) 42.33/43.36 ( (star skv_1), one, skv_1 ) 42.33/43.36 ( (star skv_1), zero, (star skv_1) ) 42.33/43.36 ( (star skv_1), skv_1, skv_1 ) 42.33/43.36 ( (star skv_1), (strong_iteration skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, zero ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication skv_1 (multiplication _let_0 _let_0))) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1 ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), (multiplication (addition skv_1 skv_1) skv_1), (strong_iteration skv_1) ) 42.33/43.36 ( (addition one skv_1), skv_1, skv_1 ) 42.33/43.36 ( skv_21, one, one ) 42.33/43.36 ( skv_21, one, (strong_iteration skv_21) ) 42.33/43.36 ( (strong_iteration skv_21), (addition skv_1 skv_1), (strong_iteration skv_21) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_21))) (multiplication _let_0 _let_0)), one, skv_1 ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_21))) (multiplication _let_0 _let_0)), (strong_iteration skv_1), skv_1 ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (multiplication (multiplication A B) C) (multiplication A (multiplication B C))) ) 42.33/43.36 ( one, skv_1, skv_1 ) 42.33/43.36 ( one, skv_1, (strong_iteration skv_1) ) 42.33/43.36 ( zero, skv_1, skv_1 ) 42.33/43.36 ( zero, skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( zero, skv_1, (strong_iteration zero) ) 42.33/43.36 ( zero, (strong_iteration skv_21), (strong_iteration zero) ) 42.33/43.36 ( skv_1, zero, skv_1 ) 42.33/43.36 ( skv_1, zero, (strong_iteration skv_21) ) 42.33/43.36 ( skv_1, zero, (multiplication skv_1 (strong_iteration skv_21)) ) 42.33/43.36 ( skv_1, skv_1, skv_1 ) 42.33/43.36 ( skv_1, skv_1, (strong_iteration skv_1) ) 42.33/43.36 ( skv_1, skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( skv_1, skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( skv_1, skv_1, (strong_iteration skv_21) ) 42.33/43.36 ( skv_1, (strong_iteration skv_1), (strong_iteration skv_1) ) 42.33/43.36 ( skv_1, (strong_iteration skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1 ) 42.33/43.36 ( skv_1, (star skv_1), skv_1 ) 42.33/43.36 ( skv_1, (strong_iteration skv_21), (strong_iteration skv_21) ) 42.33/43.36 ( (strong_iteration skv_1), skv_1, skv_1 ) 42.33/43.36 ( (strong_iteration skv_1), (strong_iteration skv_1), skv_1 ) 42.33/43.36 ( (strong_iteration skv_1), (strong_iteration skv_1), (strong_iteration skv_1) ) 42.33/43.36 ( (strong_iteration skv_1), (strong_iteration skv_1), (star skv_1) ) 42.33/43.36 ( (strong_iteration skv_1), (strong_iteration skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), skv_1, (star skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1), skv_1 ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1), (strong_iteration skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (strong_iteration skv_1), (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (star skv_1), skv_1 ) 42.33/43.36 ( (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)), (star skv_1), (star skv_1) ) 42.33/43.36 ( (star skv_1), skv_1, skv_1 ) 42.33/43.36 ( (star skv_1), skv_1, (multiplication (addition skv_1 skv_1) skv_1) ) 42.33/43.36 ( (star skv_1), (star skv_1), skv_1 ) 42.33/43.36 ( (star skv_1), (star skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, (star skv_1) ) 42.33/43.36 ( (addition skv_1 (multiplication (addition skv_1 skv_1) skv_1)), (strong_iteration skv_1), (strong_iteration skv_1) ) 42.33/43.36 ( (addition skv_1 (multiplication (addition skv_1 skv_1) skv_1)), (strong_iteration skv_1), (let ((_let_0 (strong_iteration skv_1))) (multiplication _let_0 _let_0)) ) 42.33/43.36 ( (strong_iteration (multiplication (addition skv_1 skv_1) skv_1)), zero, skv_1 ) 42.33/43.36 ( skv_21, one, (strong_iteration skv_21) ) 42.33/43.36 ( skv_21, (strong_iteration skv_21), one ) 42.33/43.36 ( skv_21, (strong_iteration skv_21), (strong_iteration skv_21) ) 42.33/43.36 ( (strong_iteration skv_21), skv_1, skv_1 ) 42.33/43.36 ( (strong_iteration skv_21), (strong_iteration skv_21), skv_1 ) 42.33/43.36 ( (strong_iteration skv_21), (strong_iteration skv_21), (strong_iteration skv_21) ) 42.33/43.36 ( (strong_iteration skv_21), (let ((_let_0 (strong_iteration skv_21))) (multiplication _let_0 _let_0)), skv_1 ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted)) (= zero (multiplication zero A)) ) 42.33/43.36 ( zero ) 42.33/43.36 ( skv_1 ) 42.33/43.36 ( (star (multiplication (addition skv_1 skv_1) skv_1)) ) 42.33/43.36 ( (star zero) ) 42.33/43.36 ( (strong_iteration zero) ) 42.33/43.36 ( (strong_iteration skv_21) ) 42.33/43.36 ( (multiplication skv_1 (strong_iteration skv_21)) ) 42.33/43.36 ) 42.33/43.36 (instantiation (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (leq (addition (multiplication A C) B) C)) (leq (multiplication (star A) B) C)) ) 42.33/43.36 ( one, one, skv_1 ) 42.33/43.36 ( one, (strong_iteration skv_21), skv_1 ) 42.33/43.36 ( zero, skv_1, skv_1 ) 42.33/43.36 ( skv_1, zero, (star skv_1) ) 42.33/43.36 ( skv_1, skv_1, skv_1 ) 42.33/43.36 ( skv_1, (strong_iteration skv_21), zero ) 42.33/43.36 ( (star skv_1), zero, (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, skv_1 ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), zero, (star skv_1) ) 42.33/43.36 ( (multiplication (addition skv_1 skv_1) skv_1), skv_1, skv_1 ) 42.33/43.36 ( (strong_iteration skv_21), one, skv_1 ) 42.33/43.36 ( (strong_iteration skv_21), zero, (strong_iteration skv_21) ) 42.33/43.36 ( (strong_iteration skv_21), (strong_iteration skv_21), skv_1 ) 42.33/43.36 ) 42.33/43.36 (instantiation (let ((_let_0 (strong_iteration X0))) (forall ((X0 $$unsorted)) (leq (multiplication _let_0 _let_0) _let_0) )) 42.33/43.36 ( zero ) 42.33/43.36 ( skv_21 ) 42.33/43.36 ) 42.33/43.36 % SZS output end Proof for theBenchmark 42.33/43.37 EOF