0.02/0.08 % Problem : Vampire---4.8_27656 : TPTP v0.0.0. Released v0.0.0. 0.02/0.09 % Command : do_cvc5 %s %d 0.08/0.29 % Computer : n012.cluster.edu 0.08/0.29 % Model : x86_64 x86_64 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.29 % Memory : 8042.1875MB 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.29 % CPULimit : 1440 0.08/0.29 % WCLimit : 180 0.08/0.29 % DateTime : Mon Jul 3 12:48:37 EDT 2023 0.08/0.29 % CPUTime : 0.13/0.39 %----Proving TH0 42.57/43.00 thf(a_type,type, 42.57/43.00 a: $tType ). 42.57/43.00 42.57/43.00 thf(cTHM250_pme,conjecture, 42.57/43.00 ! [R: a > a > $o,S: a > a > $o] : 42.57/43.00 ( ( ^ [Xx1: a,Xy1: a] : 42.57/43.00 ! [Xp1: a > a > $o] : 42.57/43.00 ( ( ! [Xx: a,Xy: a,Xz: a] : 42.57/43.00 ( ( Xp1 @ Xx @ Xz ) 42.57/43.00 <= ( ( Xp1 @ Xy @ Xz ) 42.57/43.00 & ( Xp1 @ Xx @ Xy ) ) ) 42.57/43.00 & ! [Xx: a,Xy: a] : 42.57/43.00 ( ( ( S @ Xx @ Xy ) 42.57/43.00 | ( R @ Xx @ Xy ) ) 42.57/43.00 => ( Xp1 @ Xx @ Xy ) ) ) 42.57/43.00 => ( Xp1 @ Xx1 @ Xy1 ) ) ) 42.57/43.00 = ( ^ [Xx1: a,Xy1: a] : 42.57/43.00 ! [Xp1: a > a > $o] : 42.57/43.00 ( ( Xp1 @ Xx1 @ Xy1 ) 42.57/43.00 <= ( ! [Xx: a,Xy: a,Xz: a] : 42.57/43.00 ( ( Xp1 @ Xx @ Xz ) 42.57/43.00 <= ( ( Xp1 @ Xx @ Xy ) 42.57/43.00 & ( Xp1 @ Xy @ Xz ) ) ) 42.57/43.00 & ! [Xx: a,Xy: a] : 42.57/43.00 ( ( Xp1 @ Xx @ Xy ) 42.57/43.00 <= ( ! [Xp10: a > a > $o] : 42.57/43.00 ( ( ! [Xx0: a,Xy0: a,Xz: a] : 42.57/43.00 ( ( Xp10 @ Xx0 @ Xz ) 42.57/43.00 <= ( ( Xp10 @ Xx0 @ Xy0 ) 42.57/43.00 & ( Xp10 @ Xy0 @ Xz ) ) ) 42.57/43.00 & ! [Xx0: a,Xy0: a] : 42.57/43.00 ( ( Xp10 @ Xx0 @ Xy0 ) 42.57/43.00 <= ( S @ Xx0 @ Xy0 ) ) ) 42.57/43.00 => ( Xp10 @ Xx @ Xy ) ) 42.57/43.00 | ! [Xp10: a > a > $o] : 42.57/43.00 ( ( ! [Xx0: a,Xy0: a,Xz: a] : 42.57/43.00 ( ( ( Xp10 @ Xx0 @ Xy0 ) 42.57/43.00 & ( Xp10 @ Xy0 @ Xz ) ) 42.57/43.00 => ( Xp10 @ Xx0 @ Xz ) ) 42.57/43.00 & ! [Xx0: a,Xy0: a] : 42.57/43.00 ( ( Xp10 @ Xx0 @ Xy0 ) 42.57/43.00 <= ( R @ Xx0 @ Xy0 ) ) ) 42.57/43.00 => ( Xp10 @ Xx @ Xy ) ) ) ) ) ) ) ) ). 42.57/43.00 42.57/43.00 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.W8j1el57dM/cvc5---1.0.5_27757.p... 42.57/43.00 (declare-sort $$unsorted 0) 42.57/43.00 (declare-sort tptp.a 0) 42.57/43.00 (assert (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool))) (= (lambda ((Xx1 tptp.a) (Xy1 tptp.a)) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx))) (=> (and (@ (@ Xp1 Xy) Xz) (@ _let_1 Xy)) (@ _let_1 Xz)))) (forall ((Xx tptp.a) (Xy tptp.a)) (=> (or (@ (@ S Xx) Xy) (@ (@ R Xx) Xy)) (@ (@ Xp1 Xx) Xy)))) (@ (@ Xp1 Xx1) Xy1)))) (lambda ((Xx1 tptp.a) (Xy1 tptp.a)) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx))) (=> (and (@ _let_1 Xy) (@ (@ Xp1 Xy) Xz)) (@ _let_1 Xz)))) (forall ((Xx tptp.a) (Xy tptp.a)) (=> (or (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz)))) (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (@ (@ S Xx0) Xy0) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy))) (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz)))) (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (@ (@ R Xx0) Xy0) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy)))) (@ (@ Xp1 Xx) Xy)))) (@ (@ Xp1 Xx1) Xy1)))))))) 42.57/43.00 (set-info :filename cvc5---1.0.5_27757) 42.57/43.00 (check-sat-assuming ( true )) 42.57/43.00 ------- get file name : TPTP file name is 42.57/43.00 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27757.smt2... 42.57/43.00 --- Run --ho-elim --full-saturate-quant at 10... 42.57/43.00 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10... 42.57/43.00 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10... 42.57/43.00 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5... 42.57/43.00 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5... 42.57/43.00 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10... 42.57/43.00 % SZS status Theorem for 42.57/43.00 % SZS output start Proof for 42.57/43.00 ( 42.57/43.00 (let ((_let_1 (not (forall ((R (-> tptp.a tptp.a Bool)) (S (-> tptp.a tptp.a Bool))) (= (lambda ((Xx1 tptp.a) (Xy1 tptp.a)) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx))) (=> (and (@ (@ Xp1 Xy) Xz) (@ _let_1 Xy)) (@ _let_1 Xz)))) (forall ((Xx tptp.a) (Xy tptp.a)) (=> (or (@ (@ S Xx) Xy) (@ (@ R Xx) Xy)) (@ (@ Xp1 Xx) Xy)))) (@ (@ Xp1 Xx1) Xy1)))) (lambda ((Xx1 tptp.a) (Xy1 tptp.a)) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx))) (=> (and (@ _let_1 Xy) (@ (@ Xp1 Xy) Xz)) (@ _let_1 Xz)))) (forall ((Xx tptp.a) (Xy tptp.a)) (=> (or (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz)))) (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (@ (@ S Xx0) Xy0) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy))) (forall ((Xp10 (-> tptp.a tptp.a Bool))) (=> (and (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (=> (and (@ _let_1 Xy0) (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz)))) (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (=> (@ (@ R Xx0) Xy0) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy)))) (@ (@ Xp1 Xx) Xy)))) (@ (@ Xp1 Xx1) Xy1))))))))) (let ((_let_2 (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx0) Xy0)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_208 Xx0) Xy0))))) (let ((_let_3 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_208 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106))) (let ((_let_4 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106))) (let ((_let_5 (not _let_4))) (let ((_let_6 (or _let_5 _let_3))) (let ((_let_7 (not _let_2))) (let ((_let_8 (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_208 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_208 Xy0) Xz)) (@ _let_1 Xz))))))) (let ((_let_9 (or _let_8 _let_7 _let_3))) (let ((_let_10 (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106))))) (let ((_let_11 (not _let_9))) (let ((_let_12 (not _let_10))) (let ((_let_13 (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106))))) (let ((_let_14 (not _let_13))) (let ((_let_15 (and _let_14 _let_12))) (let ((_let_16 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106))) (let ((_let_17 (or _let_15 _let_16))) (let ((_let_18 (forall ((Xx tptp.a) (Xy tptp.a)) (or (and (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy)))) (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy))))) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xx) Xy))))) (let ((_let_19 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 k_6 k_7))) (let ((_let_20 (not _let_18))) (let ((_let_21 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xx))) (or (not (@ _let_1 Xy)) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xy) Xz)) (@ _let_1 Xz)))))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_19))) (let ((_let_24 (forall ((Xp1 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx))) (or (not (@ _let_1 Xy)) (not (@ (@ Xp1 Xy) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (or (and (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy)))) (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy))))) (@ (@ Xp1 Xx) Xy)))) (@ (@ Xp1 k_6) k_7))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (lambdaF_4 k_6 k_7))) (let ((_let_27 (= _let_26 _let_24))) (let ((_let_28 (not _let_24))) (let ((_let_29 (forall ((Xx1 tptp.a) (Xy1 tptp.a)) (= (forall ((Xp1 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx))) (or (not (@ _let_1 Xy)) (not (@ (@ Xp1 Xy) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (or (and (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy)))) (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy))))) (@ (@ Xp1 Xx) Xy)))) (@ (@ Xp1 Xx1) Xy1))) (lambdaF_4 Xx1 Xy1))))) (let ((_let_30 ((forall ((Xx1 tptp.a) (Xy1 tptp.a)) (= (lambdaF_4 Xx1 Xy1) (@ (@ (lambda ((Xx1 tptp.a) (Xy1 tptp.a)) (forall ((Xp1 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (or (not (@ (@ Xp1 Xx) Xy)) (not (@ (@ Xp1 Xy) Xz)) (@ (@ Xp1 Xx) Xz)))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (or (and (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (or (not (@ (@ Xp10 Xx0) Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ (@ Xp10 Xx0) Xz)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy)))) (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (or (not (@ (@ Xp10 Xx0) Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ (@ Xp10 Xx0) Xz)))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy))))) (@ (@ Xp1 Xx) Xy)))) (@ (@ Xp1 Xx1) Xy1)))) Xx1) Xy1)))))) (let ((_let_31 (EQ_RESOLVE (MACRO_SR_PRED_INTRO :args _let_30) (REWRITE :args _let_30)))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (k_6 k_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((lambdaF_4 Xx1 Xy1)))) :args (_let_29)))) _let_31 :args (_let_27 false _let_29)))) (let ((_let_33 (lambdaF_5 k_6 k_7))) (let ((_let_34 (= _let_26 _let_33))) (let ((_let_35 (forall ((Xp1 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp1 Xx))) (or (not (@ (@ Xp1 Xy) Xz)) (not (@ _let_1 Xy)) (@ _let_1 Xz))))) (not (forall ((Xx tptp.a) (Xy tptp.a)) (or (and (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx) Xy)) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx) Xy))) (@ (@ Xp1 Xx) Xy)))) (@ (@ Xp1 k_6) k_7))))) (let ((_let_36 (= _let_33 _let_35))) (let ((_let_37 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 k_6 k_7))) (let ((_let_38 (forall ((Xx tptp.a) (Xy tptp.a)) (or (and (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy)))) (not (forall ((Xp10 (-> tptp.a tptp.a Bool))) (or (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ Xp10 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ Xp10 Xy0) Xz)) (@ _let_1 Xz))))) (not (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx0) Xy0)) (@ (@ Xp10 Xx0) Xy0)))) (@ (@ Xp10 Xx) Xy))))) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx) Xy))))) (let ((_let_39 (not _let_38))) (let ((_let_40 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx))) (or (not (@ _let_1 Xy)) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xy) Xz)) (@ _let_1 Xz)))))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_39 _let_37))) (let ((_let_43 (forall ((Xx tptp.a) (Xy tptp.a)) (or (and (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx) Xy)) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx) Xy))) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx) Xy))))) (let ((_let_44 (not _let_43))) (let ((_let_45 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx))) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xy) Xz)) (not (@ _let_1 Xy)) (@ _let_1 Xz)))))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_44 _let_37))) (let ((_let_48 (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx0))) 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(CONG _let_114 (CONG (CONG _let_112 (CONG (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_25) _let_51))) :args _let_90) :args _let_111) _let_110 :args _let_88) :args _let_89))) (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_45 (= Xx Xx0) (= Xz Xz) (= Xy Xy0))) (MACRO_SR_PRED_INTRO :args ((= (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx0))) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xy0) Xz)) (not (@ _let_1 Xy0)) (@ _let_1 Xz)))) _let_49) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_45 (= Xx Xx0) (= Xz Xz) (= Xy Xy0))) (MACRO_SR_PRED_INTRO :args ((= (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx0))) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xy0) Xz)) (not (@ _let_1 Xy0)) (@ _let_1 Xz)))) _let_48) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_45 (= Xx Xx) (= Xz Xz) (= Xy Xy))) (MACRO_SR_PRED_INTRO :args ((= (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xx))) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 Xy) Xz)) (not (@ _let_1 Xy)) (@ _let_1 Xz)))) _let_40) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (CNF_OR_NEG :args (_let_47 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 1)) (CONG _let_109 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_88)) :args ((or _let_43 _let_47))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_47 0)) (CONG _let_109 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_88)) :args ((or _let_45 _let_47))) (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_108)) :args _let_108) (CONG (REFL :args _let_108) (CONG (CONG (REFL :args (_let_46)) (REFL :args (_let_44)) _let_103 :args _let_88) :args _let_90) :args _let_89))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_101) _let_35))) (REFL :args ((not _let_47))) :args _let_88)) (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_106) :args _let_107) :args _let_106) (CONG (REFL :args _let_106) (CONG (REFL :args (_let_41)) _let_105 _let_103 :args _let_88) :args _let_89))) (REORDERING (CNF_EQUIV_POS2 :args _let_102) :args ((or _let_33 _let_101 _let_100))) _let_99 (REORDERING (CNF_EQUIV_POS1 :args _let_95) :args ((or _let_79 _let_24 _let_94))) _let_32 (CNF_EQUIV_NEG2 :args _let_93) _let_92 :args (_let_79 false _let_78 true _let_77 true _let_72 false _let_73 true _let_75 true _let_68 false _let_71 false _let_58 true _let_60 true _let_67 true _let_57 true _let_62 false _let_64 true _let_63 false _let_56 true _let_38 false _let_55 false _let_49 false _let_48 false _let_40 true _let_37 false _let_43 false _let_45 true _let_47 false _let_42 true _let_35 false _let_36 false _let_24 false _let_27 true _let_33 true _let_34)))) (let ((_let_129 (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 k_6) k_7) _let_19))))) (let ((_let_130 (_let_28))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_130)) :args _let_130) (CONG (REFL :args _let_130) (CONG (CONG (REFL :args (_let_22)) (REFL :args (_let_20)) _let_129 :args _let_88) :args _let_90) :args _let_89))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_95) :args ((or _let_26 _let_28 _let_94))) _let_128 _let_32 :args (_let_28 true _let_26 false _let_27)) :args (_let_25 true _let_24)))) (let ((_let_132 (REFL :args (_let_23)))) (let ((_let_133 (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106) _let_16))))) (let ((_let_134 (_let_18))) (let ((_let_135 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106))) (let ((_let_136 (not _let_135))) (let ((_let_137 (and _let_136 _let_5))) (let ((_let_138 (or _let_137 _let_16))) (let ((_let_139 (forall ((Xx tptp.a) (Xy tptp.a)) (or (and (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx) Xy)) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Xx) Xy))) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xx) Xy))))) (let ((_let_140 (not _let_138))) (let ((_let_141 (not _let_139))) (let ((_let_142 (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xx))) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xy) Xz)) (not (@ _let_1 Xy)) (@ _let_1 Xz)))))) (let ((_let_143 (not _let_142))) (let ((_let_144 (or _let_143 _let_141 _let_19))) (let ((_let_145 (_let_141))) (let ((_let_146 (REFL :args _let_145))) (let ((_let_147 (_let_35))) (let ((_let_148 (CONG (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106) _let_4))) :args _let_90))) (let ((_let_149 (CONG (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106) _let_135))) :args _let_90))) (let ((_let_150 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_145)) :args _let_145) (CONG _let_146 (CONG (CONG (CONG _let_149 _let_148 :args _let_111) _let_133 :args _let_88) :args _let_90) :args _let_89))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_141) _let_139))) (REFL :args (_let_140)) :args _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_144)) :args ((or _let_19 _let_143 _let_141 (not _let_144)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 2)) _let_131 :args ((not _let_19) true _let_23)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (TRANS (ALPHA_EQUIV :args (_let_21 (= Xx Xx) (= Xz Xz) (= Xy Xy))) (MACRO_SR_PRED_INTRO :args ((= (forall ((Xx tptp.a) (Xy tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xx))) (or (not (@ _let_1 Xy)) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xy) Xz)) (@ _let_1 Xz)))) _let_142) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_132 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_88)) :args ((or _let_21 _let_23))) _let_131 :args (_let_21 true _let_23)) :args (_let_142 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_147) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 QUANTIFIERS_INST_E_MATCHING)) :args _let_147) (CONG (REFL :args _let_147) (CONG (REFL :args (_let_143)) _let_146 _let_129 :args _let_88) :args _let_89))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_102) :args ((or (not _let_33) _let_35 _let_100))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_93) :args ((or _let_26 _let_33 _let_34))) _let_128 _let_92 :args (_let_33 true _let_26 true _let_34)) _let_99 :args (_let_35 false _let_33 false _let_36)) :args (_let_144 false _let_35)) :args (_let_141 true _let_19 false _let_142 false _let_144)) :args (_let_140 true _let_139)))) (let ((_let_151 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_17)) :args ((or _let_16 _let_15 (not _let_17)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_138 1)) _let_150 :args ((not _let_16) true _let_138)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_134) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106 QUANTIFIERS_INST_E_MATCHING ((not (= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_55 Xx) Xy) true))))) :args _let_134) (CONG (REFL :args _let_134) (CONG (REFL :args (_let_15)) _let_133 :args _let_88) :args _let_89))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 1)) (CONG _let_132 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_18))) :args _let_88)) :args ((or _let_18 _let_23))) _let_131 :args (_let_18 true _let_23)) :args (_let_17 false _let_18)) :args (_let_15 true _let_16 false _let_17)))) (let ((_let_152 (not _let_15))) (let ((_let_153 (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_208 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106) _let_3))))) (let ((_let_154 (_let_12))) (let ((_let_155 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_154)) :args _let_154) (CONG (REFL :args _let_154) (CONG (CONG (REFL :args (_let_8)) (REFL :args (_let_7)) _let_153 :args _let_88) :args _let_90) :args _let_89))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_10))) (REFL :args (_let_11)) :args _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_15 1)) :args ((or _let_12 _let_152))) _let_151 :args (_let_12 false _let_15)) :args (_let_11 true _let_10)))) (let ((_let_156 (not _let_6))) (let ((_let_157 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_207 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106))) (let ((_let_158 (or _let_136 _let_157))) (let ((_let_159 (forall ((Xx0 tptp.a) (Xy0 tptp.a)) (or (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx0) Xy0)) (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_207 Xx0) Xy0))))) (let ((_let_160 (not _let_159))) (let ((_let_161 (not (forall ((Xx0 tptp.a) (Xy0 tptp.a) (Xz tptp.a)) (let ((_let_1 (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_207 Xx0))) (or (not (@ _let_1 Xy0)) (not (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_207 Xy0) Xz)) (@ _let_1 Xz))))))) (let ((_let_162 (or _let_161 _let_160 _let_157))) (let ((_let_163 (not _let_162))) (let ((_let_164 (THEORY_PREPROCESS :args ((= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_207 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106) _let_157))))) (let ((_let_165 (_let_14))) (let ((_let_166 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_165)) :args _let_165) (CONG (REFL :args _let_165) (CONG (CONG (REFL :args (_let_161)) (REFL :args (_let_160)) _let_164 :args _let_88) :args _let_90) :args _let_89))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) (REFL :args (_let_163)) :args _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_15 0)) :args ((or _let_14 _let_152))) _let_151 :args (_let_14 false _let_15)) :args (_let_163 true _let_13)))) (let ((_let_167 (_let_159))) (let ((_let_168 (_let_137))) (let ((_let_169 (_let_2))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_169) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_169) (CONG (REFL :args _let_169) (CONG _let_148 _let_153 :args _let_88) :args _let_89))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_6)) :args ((or _let_5 _let_3 _let_156))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_168) (CONG (REFL :args _let_168) (MACRO_SR_PRED_INTRO :args ((= (not _let_136) _let_135))) (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) :args _let_88)) :args ((or _let_4 _let_135 _let_137))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_158)) :args ((or _let_136 _let_157 (not _let_158)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_162 2)) _let_166 :args ((not _let_157) true _let_162)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (INSTANTIATE (ASSUME :args _let_167) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_105 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_106 QUANTIFIERS_INST_E_MATCHING ((not (= (@ (@ SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Xx0) Xy0) false))))) :args _let_167) (CONG (REFL :args _let_167) (CONG _let_149 _let_164 :args _let_88) :args _let_89))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_162 1)) (CONG (REFL :args (_let_162)) (MACRO_SR_PRED_INTRO :args ((= (not _let_160) _let_159))) :args _let_88)) :args ((or _let_159 _let_162))) _let_166 :args (_let_159 true _let_162)) :args (_let_158 false _let_159)) :args (_let_136 true _let_157 false _let_158)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_138 0)) _let_150 :args ((not _let_137) true _let_138)) :args (_let_4 true _let_135 true _let_137)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_9 2)) _let_155 :args ((not _let_3) true _let_9)) :args (_let_156 false _let_4 true _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_9 1)) (CONG (REFL :args (_let_9)) (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_2))) :args _let_88)) :args ((or _let_2 _let_9))) _let_155 :args (_let_2 true _let_9)) :args (false true _let_6 false _let_2)) :args (_let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 42.57/43.01 ) 42.57/43.01 % SZS output end Proof for 42.57/43.01 % cvc5---1.0.5 exiting 42.57/43.01 % cvc5---1.0.5 exiting 42.57/43.01 EOF