%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM799^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:40:43 AM UTC 2026 % Result : Theorem 28.49s 28.78s % Output : Proof 28.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM799^1 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n001.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 12:25:50 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 28.49/28.78 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 28.49/28.78 % SZS status Theorem % 28.49/28.78 % SZS output start Proof % 28.49/28.78 ( % 28.49/28.78 (declare-sort $$unsorted 0) % 28.49/28.78 (define tptp.zero () (let ((_let_1 (@var "Y" $$unsorted))) (lambda (@list (@var "X" (-> $$unsorted $$unsorted)) _let_1) _let_1))) % 28.49/28.78 (define tptp.one () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 28.49/28.78 (define tptp.two () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 _let_1)))))) % 28.49/28.78 (define tptp.three () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))) % 28.49/28.78 (define tptp.four () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))) % 28.49/28.78 (define tptp.five () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))) % 28.49/28.78 (define tptp.six () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))))) % 28.49/28.78 (define tptp.seven () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))) % 28.49/28.78 (define tptp.eight () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))))))) % 28.49/28.78 (define tptp.nine () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))))) % 28.49/28.78 (define tptp.ten () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))))))))) % 28.49/28.78 (define tptp.succ () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_3 _let_2 _let_1) (_ _let_2 (_ (_ _let_3 _let_2) _let_1))))))) % 28.49/28.78 (define tptp.plus () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (let ((_let_4 (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (_ (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 28.49/28.78 (define tptp.mult () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (let ((_let_4 (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (_ (_ _let_4 (_ _let_3 _let_2)) _let_1))))))) % 28.49/28.78 (define @t1 () (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 28.49/28.78 (define @t2 () (= (_ (_ tptp.mult @t1) tptp.four) (_ (_ tptp.plus tptp.five) tptp.seven))) % 28.49/28.78 (define @t3 () (@list @t1)) % 28.49/28.78 (define @t4 () (exists @t3 @t2)) % 28.49/28.78 (define @t5 () (not @t4)) % 28.49/28.78 (define @t6 () (@var "Y" $$unsorted)) % 28.49/28.78 (define @t7 () (@var "X" (-> $$unsorted $$unsorted))) % 28.49/28.78 (define @t8 () (@list @t7 @t6)) % 28.49/28.78 (define @t9 () (lambda @t8 @t6)) % 28.49/28.78 (define @t10 () (_ @t7 @t6)) % 28.49/28.78 (define @t11 () (lambda @t8 @t10)) % 28.49/28.78 (define @t12 () (_ @t7 @t10)) % 28.49/28.78 (define @t13 () (lambda @t8 @t12)) % 28.49/28.78 (define @t14 () (_ @t7 @t12)) % 28.49/28.78 (define @t15 () (lambda @t8 @t14)) % 28.49/28.78 (define @t16 () (_ @t7 @t14)) % 28.49/28.78 (define @t17 () (lambda @t8 @t16)) % 28.49/28.78 (define @t18 () (_ @t7 @t16)) % 28.49/28.78 (define @t19 () (lambda @t8 @t18)) % 28.49/28.78 (define @t20 () (_ @t7 @t18)) % 28.49/28.78 (define @t21 () (lambda @t8 @t20)) % 28.49/28.78 (define @t22 () (_ @t7 @t20)) % 28.49/28.78 (define @t23 () (lambda @t8 @t22)) % 28.49/28.78 (define @t24 () (_ @t7 @t22)) % 28.49/28.78 (define @t25 () (lambda @t8 @t24)) % 28.49/28.78 (define @t26 () (_ @t7 @t24)) % 28.49/28.78 (define @t27 () (lambda @t8 @t26)) % 28.49/28.78 (define @t28 () (_ @t7 @t26)) % 28.49/28.78 (define @t29 () (lambda @t8 @t28)) % 28.49/28.78 (define @t30 () (_ @t1 @t7)) % 28.49/28.78 (define @t31 () (_ @t30 @t6)) % 28.49/28.78 (define @t32 () (_ @t7 @t31)) % 28.49/28.78 (define @t33 () (@list @t1 @t7 @t6)) % 28.49/28.78 (define @t34 () (lambda @t33 @t32)) % 28.49/28.78 (define @t35 () (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 28.49/28.78 (define @t36 () (@list @t35 @t1 @t7 @t6)) % 28.49/28.78 (define @t37 () (lambda @t36 (_ (_ @t35 @t7) @t31))) % 28.49/28.78 (define @t38 () (lambda @t36 (_ (_ @t35 @t30) @t6))) % 28.49/28.78 (define @t39 () (_ @t7 @t6)) % 28.49/28.78 (define @t40 () (_ @t7 @t39)) % 28.49/28.78 (define @t41 () (_ @t7 @t40)) % 28.49/28.78 (define @t42 () (_ @t7 @t41)) % 28.49/28.78 (define @t43 () (_ @t7 @t42)) % 28.49/28.78 (define @t44 () (_ @t7 @t43)) % 28.49/28.78 (define @t45 () (_ @t7 @t44)) % 28.49/28.78 (define @t46 () (_ @t7 @t45)) % 28.49/28.78 (define @t47 () (_ @t7 @t46)) % 28.49/28.78 (define @t48 () (_ @t7 @t47)) % 28.49/28.78 (define @t49 () (_ @t7 @t48)) % 28.49/28.78 (define @t50 () (_ @t7 @t49)) % 28.49/28.78 (define @t51 () (lambda @t8 @t50)) % 28.49/28.78 (define @t52 () (@var "BOUND_VARIABLE_7563" $$unsorted)) % 28.49/28.78 (define @t53 () (_ @t7 @t52)) % 28.49/28.78 (define @t54 () (_ @t7 @t53)) % 28.49/28.78 (define @t55 () (_ @t7 @t54)) % 28.49/28.78 (define @t56 () (_ @t7 @t55)) % 28.49/28.78 (define @t57 () (@list @t52)) % 28.49/28.78 (define @t58 () (lambda @t57 @t56)) % 28.49/28.78 (define @t59 () (_ @t1 @t58 @t6)) % 28.49/28.78 (define @t60 () (forall @t3 (not (= (lambda @t8 @t59) @t51)))) % 28.49/28.78 (define @t61 () (_ @t7 @t28)) % 28.49/28.78 (define @t62 () (_ @t7 @t61)) % 28.49/28.78 (define @t63 () (lambda @t8 @t62)) % 28.49/28.78 (define @t64 () (_ @t7 @t52)) % 28.49/28.78 (define @t65 () (_ @t7 @t64)) % 28.49/28.78 (define @t66 () (_ @t7 @t65)) % 28.49/28.78 (define @t67 () (_ @t7 @t66)) % 28.49/28.78 (define @t68 () (lambda @t57 @t67)) % 28.49/28.78 (define @t69 () (_ (_ @t1 @t68) @t6)) % 28.49/28.78 (define @t70 () (lambda @t8 @t69)) % 28.49/28.78 (define @t71 () (= @t70 @t63)) % 28.49/28.78 (define @t72 () (not @t71)) % 28.49/28.78 (define @t73 () (forall @t3 @t72)) % 28.49/28.78 (define @t74 () (not @t73)) % 28.49/28.79 (define @t75 () (@list @t6)) % 28.49/28.79 (define @t76 () (lambda @t75 @t22)) % 28.49/28.79 (define @t77 () (_ @t23 @t7)) % 28.49/28.79 (define @t78 () (lambda @t8 (_ @t7 (_ @t7 (_ @t7 (_ @t7 (_ @t7 (_ @t77 @t6)))))))) % 28.49/28.79 (define @t79 () (_ @t7 (_ @t7 (_ @t7 (_ @t7 @t32))))) % 28.49/28.79 (define @t80 () (lambda @t75 @t18)) % 28.49/28.79 (define @t81 () (_ @t19 @t7)) % 28.49/28.79 (define @t82 () (lambda @t33 (_ @t81 @t31))) % 28.49/28.79 (define @t83 () (_ @t37 @t19)) % 28.49/28.79 (define @t84 () (lambda @t75 @t16)) % 28.49/28.79 (define @t85 () (_ @t17 @t7)) % 28.49/28.79 (define @t86 () (lambda @t8 (_ (_ @t1 @t85) @t6))) % 28.49/28.79 (define @t87 () (@var "BOUND_VARIABLE_7537" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 28.49/28.79 (define @t88 () (_ @t87 @t7)) % 28.49/28.79 (define @t89 () (lambda (@list @t87 @t7 @t6) (_ (_ @t1 @t88) @t6))) % 28.49/28.79 (define @t90 () (= (_ (_ @t38 @t1) @t17) (_ @t83 @t23))) % 28.49/28.79 (define @t91 () (exists @t3 @t90)) % 28.49/28.79 (define @t92 () (_ @t58 @t6)) % 28.49/28.79 (define @t93 () (_ @t58 @t92)) % 28.49/28.79 (define @t94 () (_ @t58 @t93)) % 28.49/28.79 (define @t95 () (@var "BOUND_VARIABLE_92345" $$unsorted)) % 28.49/28.79 (define @t96 () (@var "BOUND_VARIABLE_92344" (-> $$unsorted $$unsorted))) % 28.49/28.79 (define @t97 () (lambda (@list @t96 @t95) (_ @t96 (_ @t96 (_ @t96 @t95))))) % 28.49/28.79 (define @t98 () (_ @t97 @t58 @t6)) % 28.49/28.79 (define @t99 () (lambda @t8 @t98)) % 28.49/28.79 (define @t100 () (= @t99 @t51)) % 28.49/28.79 (define @t101 () (not @t100)) % 28.49/28.79 (assume @p1 @t5) % 28.49/28.79 (assume @p2 true) % 28.49/28.79 (step @p3 (= tptp.zero @t9) :rule refl :args (@t9)) % 28.49/28.79 (step @p4 (= tptp.one @t11) :rule refl :args (@t11)) % 28.49/28.79 (step @p5 (= tptp.two @t13) :rule refl :args (@t13)) % 28.49/28.79 (step @p6 (= tptp.three @t15) :rule refl :args (@t15)) % 28.49/28.79 (step @p7 (= tptp.four @t17) :rule refl :args (@t17)) % 28.49/28.79 (step @p8 (= tptp.five @t19) :rule refl :args (@t19)) % 28.49/28.79 (step @p9 (= tptp.six @t21) :rule refl :args (@t21)) % 28.49/28.79 (step @p10 (= tptp.seven @t23) :rule refl :args (@t23)) % 28.49/28.79 (step @p11 (= tptp.eight @t25) :rule refl :args (@t25)) % 28.49/28.79 (step @p12 (= tptp.nine @t27) :rule refl :args (@t27)) % 28.49/28.79 (step @p13 (= tptp.ten @t29) :rule refl :args (@t29)) % 28.49/28.79 (step @p14 (= tptp.succ @t34) :rule refl :args (@t34)) % 28.49/28.79 (step @p15 (= tptp.plus @t37) :rule refl :args (@t37)) % 28.49/28.79 (step @p16 (= tptp.mult @t38) :rule refl :args (@t38)) % 28.49/28.79 (step @p17 :rule bool-double-not-elim :args (@t60)) % 28.49/28.79 (step @p18 :rule refl :args ((_ @t7 @t61))) % 28.49/28.79 (step @p19 :rule refl :args ((_ @t7 @t28))) % 28.49/28.79 (step @p20 :rule refl :args ((_ @t7 @t26))) % 28.49/28.79 (step @p21 :rule refl :args ((_ @t7 @t24))) % 28.49/28.79 (step @p22 :rule refl :args ((_ @t7 @t22))) % 28.49/28.79 (step @p23 :rule refl :args ((_ @t7 @t20))) % 28.49/28.79 (step @p24 :rule refl :args ((_ @t7 @t18))) % 28.49/28.79 (step @p25 :rule refl :args ((_ @t7 @t16))) % 28.49/28.79 (step @p26 :rule refl :args ((_ @t7 @t14))) % 28.49/28.79 (step @p27 :rule refl :args ((_ @t7 @t12))) % 28.49/28.79 (step @p28 :rule refl :args ((_ @t7 @t10))) % 28.49/28.79 (step @p29 :rule refl :args (@t39)) % 28.49/28.79 (step @p30 :rule cong :premises (@p29) :args (@t40)) % 28.49/28.79 (step @p31 :rule trans :premises (@p30 @p28)) % 28.49/28.79 (step @p32 :rule cong :premises (@p31) :args (@t41)) % 28.49/28.79 (step @p33 :rule trans :premises (@p32 @p27)) % 28.49/28.79 (step @p34 :rule cong :premises (@p33) :args (@t42)) % 28.49/28.79 (step @p35 :rule trans :premises (@p34 @p26)) % 28.49/28.79 (step @p36 :rule cong :premises (@p35) :args (@t43)) % 28.49/28.79 (step @p37 :rule trans :premises (@p36 @p25)) % 28.49/28.79 (step @p38 :rule cong :premises (@p37) :args (@t44)) % 28.49/28.79 (step @p39 :rule trans :premises (@p38 @p24)) % 28.49/28.79 (step @p40 :rule cong :premises (@p39) :args (@t45)) % 28.49/28.79 (step @p41 :rule trans :premises (@p40 @p23)) % 28.49/28.79 (step @p42 :rule cong :premises (@p41) :args (@t46)) % 28.49/28.79 (step @p43 :rule trans :premises (@p42 @p22)) % 28.49/28.79 (step @p44 :rule cong :premises (@p43) :args (@t47)) % 28.49/28.79 (step @p45 :rule trans :premises (@p44 @p21)) % 28.49/28.79 (step @p46 :rule cong :premises (@p45) :args (@t48)) % 28.49/28.79 (step @p47 :rule trans :premises (@p46 @p20)) % 28.49/28.79 (step @p48 :rule cong :premises (@p47) :args (@t49)) % 28.49/28.79 (step @p49 :rule trans :premises (@p48 @p19)) % 28.49/28.79 (step @p50 :rule cong :premises (@p49) :args (@t50)) % 28.49/28.79 (step @p51 :rule trans :premises (@p50 @p18)) % 28.49/28.79 (step @p52 :rule refl :args (@t7)) % 28.49/28.79 (step @p53 :rule ho_cong :premises (@p52 @p49)) % 28.49/28.79 (step @p54 :rule cong :premises (@p53 @p51) :args ((= (_ @t7 @t49) @t50))) % 28.49/28.79 (step @p55 :rule symm :premises (@p54)) % 28.49/28.79 (step @p56 :rule refl :args (@t62)) % 28.49/28.79 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 28.49/28.79 (step @p58 :rule ho_cong :premises (@p52 @p47)) % 28.49/28.79 (step @p59 :rule cong :premises (@p58 @p49) :args ((= (_ @t7 @t48) @t49))) % 28.49/28.79 (step @p60 :rule symm :premises (@p59)) % 28.49/28.79 (step @p61 :rule refl :args (@t61)) % 28.49/28.79 (step @p62 :rule eq_resolve :premises (@p61 @p60)) % 28.49/28.79 (step @p63 :rule ho_cong :premises (@p52 @p45)) % 28.49/28.79 (step @p64 :rule cong :premises (@p63 @p47) :args ((= (_ @t7 @t47) @t48))) % 28.49/28.79 (step @p65 :rule symm :premises (@p64)) % 28.49/28.79 (step @p66 :rule refl :args (@t28)) % 28.49/28.79 (step @p67 :rule eq_resolve :premises (@p66 @p65)) % 28.49/28.79 (step @p68 :rule ho_cong :premises (@p52 @p43)) % 28.49/28.79 (step @p69 :rule cong :premises (@p68 @p45) :args ((= (_ @t7 @t46) @t47))) % 28.49/28.79 (step @p70 :rule symm :premises (@p69)) % 28.49/28.79 (step @p71 :rule refl :args (@t26)) % 28.49/28.79 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 28.49/28.79 (step @p73 :rule ho_cong :premises (@p52 @p41)) % 28.49/28.79 (step @p74 :rule cong :premises (@p73 @p43) :args ((= (_ @t7 @t45) @t46))) % 28.49/28.79 (step @p75 :rule symm :premises (@p74)) % 28.49/28.79 (step @p76 :rule refl :args (@t24)) % 28.49/28.79 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 28.49/28.79 (step @p78 :rule ho_cong :premises (@p52 @p39)) % 28.49/28.79 (step @p79 :rule cong :premises (@p78 @p41) :args ((= (_ @t7 @t44) @t45))) % 28.49/28.79 (step @p80 :rule symm :premises (@p79)) % 28.49/28.79 (step @p81 :rule refl :args (@t22)) % 28.49/28.79 (step @p82 :rule eq_resolve :premises (@p81 @p80)) % 28.49/28.79 (step @p83 :rule ho_cong :premises (@p52 @p37)) % 28.49/28.79 (step @p84 :rule cong :premises (@p83 @p39) :args ((= (_ @t7 @t43) @t44))) % 28.49/28.79 (step @p85 :rule symm :premises (@p84)) % 28.49/28.79 (step @p86 :rule refl :args (@t20)) % 28.49/28.79 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 28.49/28.79 (step @p88 :rule ho_cong :premises (@p52 @p35)) % 28.49/28.79 (step @p89 :rule cong :premises (@p88 @p37) :args ((= (_ @t7 @t42) @t43))) % 28.49/28.79 (step @p90 :rule symm :premises (@p89)) % 28.49/28.79 (step @p91 :rule refl :args (@t18)) % 28.49/28.79 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 28.49/28.79 (step @p93 :rule ho_cong :premises (@p52 @p33)) % 28.49/28.79 (step @p94 :rule cong :premises (@p93 @p35) :args ((= (_ @t7 @t41) @t42))) % 28.49/28.79 (step @p95 :rule symm :premises (@p94)) % 28.49/28.79 (step @p96 :rule refl :args (@t16)) % 28.49/28.79 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 28.49/28.79 (step @p98 :rule ho_cong :premises (@p52 @p31)) % 28.49/28.79 (step @p99 :rule cong :premises (@p98 @p33) :args ((= (_ @t7 @t40) @t41))) % 28.49/28.79 (step @p100 :rule symm :premises (@p99)) % 28.49/28.79 (step @p101 :rule refl :args (@t14)) % 28.49/28.79 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 28.49/28.79 (step @p103 :rule ho_cong :premises (@p52 @p29)) % 28.49/28.79 (step @p104 :rule cong :premises (@p103 @p31) :args ((= (_ @t7 @t39) @t40))) % 28.49/28.79 (step @p105 :rule symm :premises (@p104)) % 28.49/28.79 (step @p106 :rule refl :args (@t12)) % 28.49/28.79 (step @p107 :rule eq_resolve :premises (@p106 @p105)) % 28.49/28.79 (step @p108 :rule refl :args (@t10)) % 28.49/28.79 (step @p109 :rule cong :premises (@p108 @p29) :args ((= @t10 @t39))) % 28.49/28.79 (step @p110 :rule symm :premises (@p109)) % 28.49/28.79 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 28.49/28.79 (step @p112 :rule ho_cong :premises (@p52 @p111)) % 28.49/28.79 (step @p113 :rule trans :premises (@p112 @p107)) % 28.49/28.79 (step @p114 :rule ho_cong :premises (@p52 @p113)) % 28.49/28.79 (step @p115 :rule trans :premises (@p114 @p102)) % 28.49/28.79 (step @p116 :rule ho_cong :premises (@p52 @p115)) % 28.49/28.79 (step @p117 :rule trans :premises (@p116 @p97)) % 28.49/28.79 (step @p118 :rule ho_cong :premises (@p52 @p117)) % 28.49/28.79 (step @p119 :rule trans :premises (@p118 @p92)) % 28.49/28.79 (step @p120 :rule ho_cong :premises (@p52 @p119)) % 28.49/28.79 (step @p121 :rule trans :premises (@p120 @p87)) % 28.49/28.79 (step @p122 :rule ho_cong :premises (@p52 @p121)) % 28.49/28.79 (step @p123 :rule trans :premises (@p122 @p82)) % 28.49/28.79 (step @p124 :rule ho_cong :premises (@p52 @p123)) % 28.49/28.79 (step @p125 :rule trans :premises (@p124 @p77)) % 28.49/28.79 (step @p126 :rule ho_cong :premises (@p52 @p125)) % 28.49/28.79 (step @p127 :rule trans :premises (@p126 @p72)) % 28.49/28.79 (step @p128 :rule ho_cong :premises (@p52 @p127)) % 28.49/28.79 (step @p129 :rule trans :premises (@p128 @p67)) % 28.49/28.79 (step @p130 :rule ho_cong :premises (@p52 @p129)) % 28.49/28.79 (step @p131 :rule trans :premises (@p130 @p62)) % 28.49/28.79 (step @p132 :rule ho_cong :premises (@p52 @p131)) % 28.49/28.79 (step @p133 :rule trans :premises (@p132 @p57)) % 28.49/28.79 (step @p134 :rule cong :premises (@p133) :args (@t63)) % 28.49/28.79 (step @p135 :rule refl :args ((_ @t1 @t68 @t6))) % 28.49/28.79 (step @p136 :rule refl :args (@t6)) % 28.49/28.79 (step @p137 :rule refl :args ((_ @t7 @t66))) % 28.49/28.79 (step @p138 :rule refl :args ((_ @t7 @t65))) % 28.49/28.79 (step @p139 :rule refl :args ((_ @t7 @t64))) % 28.49/28.79 (step @p140 :rule refl :args (@t53)) % 28.49/28.79 (step @p141 :rule cong :premises (@p140) :args (@t54)) % 28.49/28.79 (step @p142 :rule trans :premises (@p141 @p139)) % 28.49/28.79 (step @p143 :rule cong :premises (@p142) :args (@t55)) % 28.49/28.79 (step @p144 :rule trans :premises (@p143 @p138)) % 28.49/28.79 (step @p145 :rule cong :premises (@p144) :args (@t56)) % 28.49/28.79 (step @p146 :rule trans :premises (@p145 @p137)) % 28.49/28.79 (step @p147 :rule cong :premises (@p146) :args (@t58)) % 28.49/28.79 (step @p148 :rule cong :premises (@p147 @p136) :args (@t59)) % 28.49/28.79 (step @p149 :rule trans :premises (@p148 @p135)) % 28.49/28.79 (step @p150 :rule refl :args (@t1)) % 28.49/28.79 (step @p151 :rule ho_cong :premises (@p150 @p147)) % 28.49/28.79 (step @p152 :rule ho_cong :premises (@p151 @p136)) % 28.49/28.79 (step @p153 :rule cong :premises (@p152 @p149) :args ((= (_ (_ @t1 @t58) @t6) @t59))) % 28.49/28.79 (step @p154 :rule symm :premises (@p153)) % 28.49/28.79 (step @p155 :rule refl :args (@t69)) % 28.49/28.79 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 28.49/28.79 (step @p157 :rule ho_cong :premises (@p52 @p144)) % 28.49/28.79 (step @p158 :rule cong :premises (@p157 @p146) :args ((= (_ @t7 @t55) @t56))) % 28.49/28.79 (step @p159 :rule symm :premises (@p158)) % 28.49/28.79 (step @p160 :rule refl :args (@t67)) % 28.49/28.79 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 28.49/28.79 (step @p162 :rule ho_cong :premises (@p52 @p142)) % 28.49/28.79 (step @p163 :rule cong :premises (@p162 @p144) :args ((= (_ @t7 @t54) @t55))) % 28.49/28.79 (step @p164 :rule symm :premises (@p163)) % 28.49/28.79 (step @p165 :rule refl :args (@t66)) % 28.49/28.79 (step @p166 :rule eq_resolve :premises (@p165 @p164)) % 28.49/28.79 (step @p167 :rule ho_cong :premises (@p52 @p140)) % 28.49/28.79 (step @p168 :rule cong :premises (@p167 @p142) :args ((= (_ @t7 @t53) @t54))) % 28.49/28.79 (step @p169 :rule symm :premises (@p168)) % 28.49/28.79 (step @p170 :rule refl :args (@t65)) % 28.49/28.79 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 28.49/28.79 (step @p172 :rule refl :args (@t64)) % 28.49/28.79 (step @p173 :rule cong :premises (@p172 @p140) :args ((= @t64 @t53))) % 28.49/28.79 (step @p174 :rule symm :premises (@p173)) % 28.49/28.79 (step @p175 :rule eq_resolve :premises (@p172 @p174)) % 28.49/28.79 (step @p176 :rule ho_cong :premises (@p52 @p175)) % 28.49/28.79 (step @p177 :rule trans :premises (@p176 @p171)) % 28.49/28.79 (step @p178 :rule ho_cong :premises (@p52 @p177)) % 28.49/28.79 (step @p179 :rule trans :premises (@p178 @p166)) % 28.49/28.79 (step @p180 :rule ho_cong :premises (@p52 @p179)) % 28.49/28.79 (step @p181 :rule trans :premises (@p180 @p161)) % 28.49/28.79 (step @p182 :rule cong :premises (@p181) :args (@t68)) % 28.49/28.79 (step @p183 :rule ho_cong :premises (@p150 @p182)) % 28.49/28.79 (step @p184 :rule ho_cong :premises (@p183 @p136)) % 28.49/28.79 (step @p185 :rule trans :premises (@p184 @p156)) % 28.49/28.79 (step @p186 :rule cong :premises (@p185) :args (@t70)) % 28.49/28.79 (step @p187 :rule cong :premises (@p186 @p134) :args (@t71)) % 28.49/28.79 (step @p188 :rule cong :premises (@p187) :args (@t72)) % 28.49/28.79 (step @p189 :rule cong :premises (@p188) :args (@t73)) % 28.49/28.79 (step @p190 :rule cong :premises (@p189) :args (@t74)) % 28.49/28.79 (step @p191 :rule exists-elim :args ((= (exists @t3 @t71) @t74))) % 28.49/28.79 (step @p192 :rule trans :premises (@p191 @p190)) % 28.49/28.79 (step @p193 :rule beta-reduce :args ((= (_ @t76 @t6) @t22))) % 28.49/28.79 (step @p194 :rule refl :args (@t6)) % 28.49/28.79 (step @p195 :rule beta-reduce :args ((= @t77 @t76))) % 28.49/28.79 (step @p196 :rule ho_cong :premises (@p195 @p194)) % 28.49/28.79 (step @p197 :rule trans :premises (@p196 @p193)) % 28.49/28.79 (step @p198 :rule refl :args (@t7)) % 28.49/28.79 (step @p199 :rule ho_cong :premises (@p198 @p197)) % 28.49/28.79 (step @p200 :rule ho_cong :premises (@p198 @p199)) % 28.49/28.79 (step @p201 :rule ho_cong :premises (@p198 @p200)) % 28.49/28.79 (step @p202 :rule ho_cong :premises (@p198 @p201)) % 28.49/28.79 (step @p203 :rule ho_cong :premises (@p198 @p202)) % 28.49/28.79 (step @p204 :rule cong :premises (@p203) :args (@t78)) % 28.49/28.79 (step @p205 :rule beta-reduce :args ((= (_ (lambda @t33 @t79) @t23) @t78))) % 28.49/28.79 (step @p206 :rule trans :premises (@p205 @p204)) % 28.49/28.79 (step @p207 :rule refl :args (@t23)) % 28.49/28.79 (step @p208 :rule beta-reduce :args ((= (_ @t80 @t31) @t79))) % 28.49/28.79 (step @p209 :rule refl :args (@t31)) % 28.49/28.79 (step @p210 :rule beta-reduce :args ((= @t81 @t80))) % 28.49/28.79 (step @p211 :rule ho_cong :premises (@p210 @p209)) % 28.49/28.79 (step @p212 :rule trans :premises (@p211 @p208)) % 28.49/28.79 (step @p213 :rule cong :premises (@p212) :args (@t82)) % 28.49/28.79 (step @p214 :rule beta-reduce :args ((= @t83 @t82))) % 28.49/28.79 (step @p215 :rule trans :premises (@p214 @p213)) % 28.49/28.79 (step @p216 :rule ho_cong :premises (@p215 @p207)) % 28.49/28.79 (step @p217 :rule trans :premises (@p216 @p206)) % 28.49/28.79 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 28.49/28.79 ; trust TRUST_THEORY_REWRITE % 28.49/28.79 (step @p218 :rule trust :premises () :args ((= (lambda @t8 (_ (_ @t1 @t84) @t6)) @t70))) % 28.49/28.79 (step @p219 :rule beta-reduce :args ((= @t85 @t84))) % 28.49/28.79 (step @p220 :rule refl :args (@t1)) % 28.49/28.79 (step @p221 :rule ho_cong :premises (@p220 @p219)) % 28.49/28.79 (step @p222 :rule ho_cong :premises (@p221 @p194)) % 28.49/28.79 (step @p223 :rule cong :premises (@p222) :args (@t86)) % 28.49/28.79 (step @p224 :rule trans :premises (@p223 @p218)) % 28.49/28.79 (step @p225 :rule beta-reduce :args ((= (_ @t89 @t17) @t86))) % 28.49/28.79 (step @p226 :rule trans :premises (@p225 @p224)) % 28.49/28.79 (step @p227 :rule refl :args (@t17)) % 28.49/28.79 (step @p228 :rule beta-reduce :args ((= (_ (lambda (@list @t35 @t87 @t7 @t6) (_ (_ @t35 @t88) @t6)) @t1) @t89))) % 28.49/28.79 (step @p229 :rule alpha_equiv :args (@t38 (@list @t1) (@list @t87))) % 28.49/28.79 (step @p230 :rule ho_cong :premises (@p229 @p150)) % 28.49/28.79 (step @p231 :rule trans :premises (@p230 @p228)) % 28.49/28.79 (step @p232 :rule ho_cong :premises (@p231 @p227)) % 28.49/28.79 (step @p233 :rule trans :premises (@p232 @p226)) % 28.49/28.79 (step @p234 :rule cong :premises (@p233 @p217) :args (@t90)) % 28.49/28.79 (step @p235 :rule cong :premises (@p234) :args (@t91)) % 28.49/28.79 (step @p236 :rule trans :premises (@p235 @p192)) % 28.49/28.79 (step @p237 :rule cong :premises (@p236) :args ((not @t91))) % 28.49/28.79 (step @p238 :rule trans :premises (@p237 @p17)) % 28.49/28.79 (step @p239 :rule ho_cong :premises (@p15 @p8)) % 28.49/28.79 (step @p240 :rule ho_cong :premises (@p239 @p10)) % 28.49/28.79 (step @p241 :rule ho_cong :premises (@p16 @p220)) % 28.49/28.79 (step @p242 :rule ho_cong :premises (@p241 @p7)) % 28.49/28.79 (step @p243 :rule cong :premises (@p242 @p240) :args (@t2)) % 28.49/28.79 (step @p244 :rule cong :premises (@p243) :args (@t4)) % 28.49/28.79 (step @p245 :rule cong :premises (@p244) :args (@t5)) % 28.49/28.79 (step @p246 :rule trans :premises (@p245 @p238)) % 28.49/28.79 (step @p247 :rule eq_resolve :premises (@p1 @p246)) % 28.49/28.79 (step @p248 :rule bool-impl-false1 :args (@t60)) % 28.49/28.79 (step @p249 :rule evaluate :args ((not true))) % 28.49/28.79 (step @p250 :rule eq-refl :args (@t51)) % 28.49/28.79 (step @p251 :rule refl :args (@t51)) % 28.49/28.79 (step @p252 :rule beta-reduce :args ((= (_ @t58 @t46) @t50))) % 28.49/28.79 (step @p253 :rule beta-reduce :args ((= (_ @t58 @t42) @t46))) % 28.49/28.79 (step @p254 :rule beta-reduce :args ((= @t92 @t42))) % 28.49/28.79 (step @p255 :rule cong :premises (@p254) :args (@t93)) % 28.49/28.79 (step @p256 :rule trans :premises (@p255 @p253)) % 28.49/28.79 (step @p257 :rule cong :premises (@p256) :args (@t94)) % 28.49/28.79 (step @p258 :rule trans :premises (@p257 @p252)) % 28.61/28.80 (step @p259 :rule beta-reduce :args ((= @t98 @t94))) % 28.61/28.80 (step @p260 :rule trans :premises (@p259 @p258)) % 28.61/28.80 (step @p261 :rule cong :premises (@p260) :args (@t99)) % 28.61/28.80 (step @p262 :rule cong :premises (@p261 @p251) :args (@t100)) % 28.61/28.80 (step @p263 :rule trans :premises (@p262 @p250)) % 28.61/28.80 (step @p264 :rule cong :premises (@p263) :args (@t101)) % 28.61/28.80 (step @p265 :rule trans :premises (@p264 @p249)) % 28.61/28.80 (step @p266 :rule refl :args (@t60)) % 28.61/28.80 (step @p267 :rule cong :premises (@p266 @p265) :args ((=> @t60 @t101))) % 28.61/28.80 (step @p268 :rule trans :premises (@p267 @p248)) % 28.61/28.80 (assume-push @p275 @t60) % 28.61/28.80 (step @p270 :rule instantiate :premises (@p247) :args ((@list @t97))) % 28.61/28.80 (step-pop @p276 :rule scope :premises (@p270)) % 28.61/28.80 (step @p271 :rule process_scope :premises (@p276) :args (@t101)) % 28.61/28.80 (step @p273 :rule eq_resolve :premises (@p271 @p268)) % 28.61/28.80 (step @p274 false :rule chain_m_resolution :premises (@p273 @p247) :args (false (@list false) (@list @t60))) % 28.61/28.80 ) % 28.61/28.80 % SZS output end Proof % 28.61/28.80 % cvc5 exiting %------------------------------------------------------------------------------