%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM415^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n024.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 08:39:20 AM UTC 2026 % Result : Theorem 0.15s 0.38s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : NUM415^1 : TPTP v9.2.1. Released v3.6.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.08/0.26 % Computer : n024.cluster.edu % 0.08/0.26 % Model : x86_64 x86_64 % 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.26 % Memory : 8042.1875MB % 0.08/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.26 % CPULimit : 300 % 0.08/0.26 % WCLimit : 300 % 0.08/0.26 % DateTime : Tue Jun 2 06:17:00 EDT 2026 % 0.08/0.26 % CPUTime : % 0.15/0.34 %----Proving TH0 % 0.15/0.38 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.15/0.38 % SZS status Theorem % 0.15/0.38 % SZS output start Proof % 0.15/0.38 ( % 0.15/0.38 (declare-sort $$unsorted 0) % 0.15/0.38 (define tptp.zero () (let ((_let_1 (@var "Y" $$unsorted))) (lambda (@list (@var "X" (-> $$unsorted $$unsorted)) _let_1) _let_1))) % 0.15/0.38 (define tptp.one () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.15/0.38 (define tptp.two () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 _let_1)))))) % 0.15/0.38 (define tptp.three () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))) % 0.15/0.38 (define tptp.four () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1)))))))) % 0.15/0.38 (define tptp.five () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))) % 0.15/0.38 (define tptp.six () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.15/0.38 (define tptp.seven () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))) % 0.15/0.38 (define tptp.eight () (let ((_let_1 (@var "Y" $$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)))))))))))) % 0.15/0.38 (define tptp.nine () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_1) (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 (_ _let_2 _let_1))))))))))))) % 0.15/0.38 (define tptp.ten () (let ((_let_1 (@var "Y" $$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)))))))))))))) % 0.15/0.38 (define tptp.succ () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted)))) (lambda (@list _let_3 _let_2 _let_1) (_ _let_2 (_ (_ _let_3 _let_2) _let_1))))))) % 0.15/0.38 (define tptp.plus () (let ((_let_1 (@var "Y" $$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)))))))) % 0.15/0.38 (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 $$unsorted)))) (lambda (@list _let_4 _let_3 _let_2 _let_1) (_ (_ _let_4 (_ _let_3 _let_2)) _let_1))))))) % 0.15/0.38 (define @t1 () (_ tptp.mult tptp.two)) % 0.15/0.38 (define @t2 () (= (_ @t1 (_ (_ tptp.plus tptp.three) tptp.seven)) (_ (_ tptp.mult (_ @t1 tptp.five)) (_ (_ tptp.plus tptp.one) tptp.one)))) % 0.15/0.38 (define @t3 () (not @t2)) % 0.15/0.38 (define @t4 () (@var "Y" $$unsorted)) % 0.15/0.38 (define @t5 () (@var "X" (-> $$unsorted $$unsorted))) % 0.15/0.38 (define @t6 () (@list @t5 @t4)) % 0.15/0.38 (define @t7 () (lambda @t6 @t4)) % 0.15/0.38 (define @t8 () (_ @t5 @t4)) % 0.15/0.38 (define @t9 () (lambda @t6 @t8)) % 0.15/0.38 (define @t10 () (_ @t5 @t8)) % 0.15/0.38 (define @t11 () (lambda @t6 @t10)) % 0.15/0.38 (define @t12 () (_ @t5 @t10)) % 0.15/0.38 (define @t13 () (lambda @t6 @t12)) % 0.15/0.38 (define @t14 () (_ @t5 @t12)) % 0.15/0.38 (define @t15 () (lambda @t6 @t14)) % 0.15/0.38 (define @t16 () (_ @t5 @t14)) % 0.15/0.38 (define @t17 () (lambda @t6 @t16)) % 0.15/0.38 (define @t18 () (_ @t5 @t16)) % 0.15/0.38 (define @t19 () (lambda @t6 @t18)) % 0.15/0.38 (define @t20 () (_ @t5 @t18)) % 0.15/0.38 (define @t21 () (lambda @t6 @t20)) % 0.15/0.38 (define @t22 () (_ @t5 @t20)) % 0.15/0.38 (define @t23 () (lambda @t6 @t22)) % 0.15/0.38 (define @t24 () (_ @t5 @t22)) % 0.15/0.38 (define @t25 () (lambda @t6 @t24)) % 0.15/0.38 (define @t26 () (_ @t5 @t24)) % 0.15/0.38 (define @t27 () (lambda @t6 @t26)) % 0.15/0.38 (define @t28 () (@var "N" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 0.15/0.38 (define @t29 () (_ @t28 @t5)) % 0.15/0.38 (define @t30 () (_ @t29 @t4)) % 0.15/0.38 (define @t31 () (_ @t5 @t30)) % 0.15/0.38 (define @t32 () (@list @t28 @t5 @t4)) % 0.15/0.38 (define @t33 () (lambda @t32 @t31)) % 0.15/0.38 (define @t34 () (@var "M" (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 0.15/0.38 (define @t35 () (@list @t34 @t28 @t5 @t4)) % 0.15/0.38 (define @t36 () (lambda @t35 (_ (_ @t34 @t5) @t30))) % 0.15/0.38 (define @t37 () (lambda @t35 (_ (_ @t34 @t29) @t4))) % 0.15/0.38 (define @t38 () (_ @t5 (_ @t5 @t26))) % 0.15/0.38 (define @t39 () (_ @t5 (_ @t5 @t38))) % 0.15/0.38 (define @t40 () (_ @t5 (_ @t5 @t39))) % 0.15/0.38 (define @t41 () (_ @t5 (_ @t5 @t40))) % 0.15/0.38 (define @t42 () (_ @t5 (_ @t5 @t41))) % 0.15/0.38 (define @t43 () (@list @t4)) % 0.15/0.38 (define @t44 () (lambda @t43 @t10)) % 0.15/0.38 (define @t45 () (_ @t11 @t5)) % 0.15/0.38 (define @t46 () (lambda @t6 (_ @t45 (_ @t45 (_ @t45 (_ @t45 (_ @t45 (_ @t45 (_ @t45 (_ @t45 (_ @t45 (_ @t45 @t4)))))))))))) % 0.15/0.38 (define @t47 () (_ @t29 @t30)) % 0.15/0.38 (define @t48 () (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 (_ @t29 @t47))))))))) % 0.15/0.38 (define @t49 () (lambda @t43 @t8)) % 0.15/0.38 (define @t50 () (_ @t9 @t5)) % 0.15/0.38 (define @t51 () (lambda @t6 (_ @t5 (_ @t50 @t4)))) % 0.15/0.38 (define @t52 () (lambda @t32 (_ @t50 @t30))) % 0.15/0.38 (define @t53 () (_ @t36 @t9)) % 0.15/0.38 (define @t54 () (lambda @t43 @t48)) % 0.15/0.38 (define @t55 () (_ @t27 @t29)) % 0.15/0.38 (define @t56 () (lambda @t32 (_ @t55 @t4))) % 0.15/0.38 (define @t57 () (lambda @t43 @t16)) % 0.15/0.38 (define @t58 () (_ @t17 @t5)) % 0.15/0.38 (define @t59 () (lambda @t6 (_ @t58 (_ @t58 @t4)))) % 0.15/0.38 (define @t60 () (lambda @t32 @t47)) % 0.15/0.38 (define @t61 () (lambda @t43 @t47)) % 0.15/0.38 (define @t62 () (_ @t11 @t29)) % 0.15/0.38 (define @t63 () (lambda @t32 (_ @t62 @t4))) % 0.15/0.38 (define @t64 () (_ @t37 @t11)) % 0.15/0.38 (define @t65 () (lambda @t43 @t26)) % 0.15/0.38 (define @t66 () (_ @t27 @t5)) % 0.15/0.38 (define @t67 () (lambda @t6 (_ @t66 (_ @t66 @t4)))) % 0.15/0.38 (define @t68 () (lambda @t43 @t20)) % 0.15/0.38 (define @t69 () (_ @t21 @t5)) % 0.15/0.38 (define @t70 () (lambda @t6 (_ @t5 (_ @t5 (_ @t5 (_ @t69 @t4)))))) % 0.15/0.38 (define @t71 () (_ @t5 (_ @t5 @t31))) % 0.15/0.38 (define @t72 () (lambda @t43 @t12)) % 0.15/0.38 (define @t73 () (_ @t13 @t5)) % 0.15/0.38 (define @t74 () (lambda @t32 (_ @t73 @t30))) % 0.15/0.38 (define @t75 () (_ @t36 @t13)) % 0.15/0.38 (define @t76 () (= (_ @t64 (_ @t75 @t21)) (_ (_ @t37 (_ @t64 @t17)) (_ @t53 @t9)))) % 0.15/0.38 (assume @p1 @t3) % 0.15/0.38 (assume @p2 true) % 0.15/0.38 (step @p3 (= tptp.zero @t7) :rule refl :args (@t7)) % 0.15/0.38 (step @p4 (= tptp.one @t9) :rule refl :args (@t9)) % 0.15/0.38 (step @p5 (= tptp.two @t11) :rule refl :args (@t11)) % 0.15/0.38 (step @p6 (= tptp.three @t13) :rule refl :args (@t13)) % 0.15/0.38 (step @p7 (= tptp.four @t15) :rule refl :args (@t15)) % 0.15/0.38 (step @p8 (= tptp.five @t17) :rule refl :args (@t17)) % 0.15/0.38 (step @p9 (= tptp.six @t19) :rule refl :args (@t19)) % 0.15/0.38 (step @p10 (= tptp.seven @t21) :rule refl :args (@t21)) % 0.15/0.38 (step @p11 (= tptp.eight @t23) :rule refl :args (@t23)) % 0.15/0.38 (step @p12 (= tptp.nine @t25) :rule refl :args (@t25)) % 0.15/0.38 (step @p13 (= tptp.ten @t27) :rule refl :args (@t27)) % 0.15/0.38 (step @p14 (= tptp.succ @t33) :rule refl :args (@t33)) % 0.15/0.38 (step @p15 (= tptp.plus @t36) :rule refl :args (@t36)) % 0.15/0.38 (step @p16 (= tptp.mult @t37) :rule refl :args (@t37)) % 0.15/0.38 (step @p17 :rule evaluate :args ((not true))) % 0.15/0.38 (step @p18 :rule eq-refl :args ((lambda @t6 @t42))) % 0.15/0.38 (step @p19 :rule beta-reduce :args ((= (_ @t44 @t41) @t42))) % 0.15/0.38 (step @p20 :rule beta-reduce :args ((= (_ @t44 @t40) @t41))) % 0.15/0.38 (step @p21 :rule beta-reduce :args ((= (_ @t44 @t39) @t40))) % 0.15/0.38 (step @p22 :rule beta-reduce :args ((= (_ @t44 @t38) @t39))) % 0.15/0.38 (step @p23 :rule beta-reduce :args ((= (_ @t44 @t26) @t38))) % 0.15/0.38 (step @p24 :rule beta-reduce :args ((= (_ @t44 @t22) @t26))) % 0.15/0.38 (step @p25 :rule beta-reduce :args ((= (_ @t44 @t18) @t22))) % 0.15/0.38 (step @p26 :rule beta-reduce :args ((= (_ @t44 @t14) @t18))) % 0.15/0.38 (step @p27 :rule beta-reduce :args ((= (_ @t44 @t10) @t14))) % 0.15/0.38 (step @p28 :rule beta-reduce :args ((= (_ @t44 @t4) @t10))) % 0.15/0.38 (step @p29 :rule refl :args (@t4)) % 0.15/0.38 (step @p30 :rule beta-reduce :args ((= @t45 @t44))) % 0.15/0.38 (step @p31 :rule ho_cong :premises (@p30 @p29)) % 0.15/0.38 (step @p32 :rule trans :premises (@p31 @p28)) % 0.15/0.38 (step @p33 :rule ho_cong :premises (@p30 @p32)) % 0.15/0.38 (step @p34 :rule trans :premises (@p33 @p27)) % 0.15/0.38 (step @p35 :rule ho_cong :premises (@p30 @p34)) % 0.15/0.38 (step @p36 :rule trans :premises (@p35 @p26)) % 0.15/0.38 (step @p37 :rule ho_cong :premises (@p30 @p36)) % 0.15/0.38 (step @p38 :rule trans :premises (@p37 @p25)) % 0.15/0.38 (step @p39 :rule ho_cong :premises (@p30 @p38)) % 0.15/0.38 (step @p40 :rule trans :premises (@p39 @p24)) % 0.15/0.38 (step @p41 :rule ho_cong :premises (@p30 @p40)) % 0.15/0.38 (step @p42 :rule trans :premises (@p41 @p23)) % 0.15/0.38 (step @p43 :rule ho_cong :premises (@p30 @p42)) % 0.15/0.38 (step @p44 :rule trans :premises (@p43 @p22)) % 0.15/0.38 (step @p45 :rule ho_cong :premises (@p30 @p44)) % 0.15/0.38 (step @p46 :rule trans :premises (@p45 @p21)) % 0.15/0.38 (step @p47 :rule ho_cong :premises (@p30 @p46)) % 0.15/0.38 (step @p48 :rule trans :premises (@p47 @p20)) % 0.15/0.38 (step @p49 :rule ho_cong :premises (@p30 @p48)) % 0.15/0.38 (step @p50 :rule trans :premises (@p49 @p19)) % 0.15/0.38 (step @p51 :rule cong :premises (@p50) :args (@t46)) % 0.15/0.38 (step @p52 :rule beta-reduce :args ((= (_ (lambda @t32 @t48) @t11) @t46))) % 0.15/0.38 (step @p53 :rule trans :premises (@p52 @p51)) % 0.15/0.38 (step @p54 :rule beta-reduce :args ((= (_ @t49 @t4) @t8))) % 0.15/0.38 (step @p55 :rule beta-reduce :args ((= @t50 @t49))) % 0.15/0.38 (step @p56 :rule ho_cong :premises (@p55 @p29)) % 0.15/0.38 (step @p57 :rule trans :premises (@p56 @p54)) % 0.15/0.38 (step @p58 :rule refl :args (@t5)) % 0.15/0.38 (step @p59 :rule ho_cong :premises (@p58 @p57)) % 0.15/0.38 (step @p60 :rule cong :premises (@p59) :args (@t51)) % 0.15/0.38 (step @p61 :rule beta-reduce :args ((= (_ @t33 @t9) @t51))) % 0.15/0.38 (step @p62 :rule trans :premises (@p61 @p60)) % 0.15/0.38 (step @p63 :rule refl :args (@t9)) % 0.15/0.38 (step @p64 :rule beta-reduce :args ((= (_ @t49 @t30) @t31))) % 0.15/0.38 (step @p65 :rule refl :args (@t30)) % 0.15/0.38 (step @p66 :rule ho_cong :premises (@p55 @p65)) % 0.15/0.38 (step @p67 :rule trans :premises (@p66 @p64)) % 0.15/0.38 (step @p68 :rule cong :premises (@p67) :args (@t52)) % 0.15/0.38 (step @p69 :rule beta-reduce :args ((= @t53 @t52))) % 0.15/0.38 (step @p70 :rule trans :premises (@p69 @p68)) % 0.15/0.38 (step @p71 :rule ho_cong :premises (@p70 @p63)) % 0.15/0.38 (step @p72 :rule trans :premises (@p71 @p62)) % 0.15/0.38 (step @p73 :rule beta-reduce :args ((= (_ @t54 @t4) @t48))) % 0.15/0.38 (step @p74 :rule beta-reduce :args ((= @t55 @t54))) % 0.15/0.38 (step @p75 :rule ho_cong :premises (@p74 @p29)) % 0.15/0.38 (step @p76 :rule trans :premises (@p75 @p73)) % 0.15/0.38 (step @p77 :rule cong :premises (@p76) :args (@t56)) % 0.15/0.38 (step @p78 :rule beta-reduce :args ((= (_ @t37 @t27) @t56))) % 0.15/0.38 (step @p79 :rule trans :premises (@p78 @p77)) % 0.15/0.38 (step @p80 :rule beta-reduce :args ((= (_ @t57 @t16) @t26))) % 0.15/0.38 (step @p81 :rule beta-reduce :args ((= (_ @t57 @t4) @t16))) % 0.15/0.38 (step @p82 :rule beta-reduce :args ((= @t58 @t57))) % 0.15/0.38 (step @p83 :rule ho_cong :premises (@p82 @p29)) % 0.15/0.38 (step @p84 :rule trans :premises (@p83 @p81)) % 0.15/0.38 (step @p85 :rule ho_cong :premises (@p82 @p84)) % 0.15/0.38 (step @p86 :rule trans :premises (@p85 @p80)) % 0.15/0.38 (step @p87 :rule cong :premises (@p86) :args (@t59)) % 0.15/0.38 (step @p88 :rule beta-reduce :args ((= (_ @t60 @t17) @t59))) % 0.15/0.38 (step @p89 :rule trans :premises (@p88 @p87)) % 0.15/0.38 (step @p90 :rule refl :args (@t17)) % 0.15/0.38 (step @p91 :rule beta-reduce :args ((= (_ @t61 @t4) @t47))) % 0.15/0.38 (step @p92 :rule beta-reduce :args ((= @t62 @t61))) % 0.15/0.38 (step @p93 :rule ho_cong :premises (@p92 @p29)) % 0.15/0.38 (step @p94 :rule trans :premises (@p93 @p91)) % 0.15/0.38 (step @p95 :rule cong :premises (@p94) :args (@t63)) % 0.15/0.38 (step @p96 :rule beta-reduce :args ((= @t64 @t63))) % 0.15/0.38 (step @p97 :rule trans :premises (@p96 @p95)) % 0.15/0.38 (step @p98 :rule ho_cong :premises (@p97 @p90)) % 0.15/0.38 (step @p99 :rule trans :premises (@p98 @p89)) % 0.15/0.38 (step @p100 :rule refl :args (@t37)) % 0.15/0.38 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.15/0.38 (step @p102 :rule trans :premises (@p101 @p79)) % 0.15/0.38 (step @p103 :rule ho_cong :premises (@p102 @p72)) % 0.15/0.38 (step @p104 :rule trans :premises (@p103 @p53)) % 0.15/0.38 (step @p105 :rule beta-reduce :args ((= (_ @t65 @t26) @t42))) % 0.15/0.38 (step @p106 :rule beta-reduce :args ((= (_ @t65 @t4) @t26))) % 0.15/0.38 (step @p107 :rule beta-reduce :args ((= @t66 @t65))) % 0.15/0.38 (step @p108 :rule ho_cong :premises (@p107 @p29)) % 0.15/0.38 (step @p109 :rule trans :premises (@p108 @p106)) % 0.15/0.38 (step @p110 :rule ho_cong :premises (@p107 @p109)) % 0.15/0.38 (step @p111 :rule trans :premises (@p110 @p105)) % 0.15/0.38 (step @p112 :rule cong :premises (@p111) :args (@t67)) % 0.15/0.38 (step @p113 :rule beta-reduce :args ((= (_ @t60 @t27) @t67))) % 0.15/0.38 (step @p114 :rule trans :premises (@p113 @p112)) % 0.15/0.38 (step @p115 :rule beta-reduce :args ((= (_ @t68 @t4) @t20))) % 0.15/0.38 (step @p116 :rule beta-reduce :args ((= @t69 @t68))) % 0.15/0.38 (step @p117 :rule ho_cong :premises (@p116 @p29)) % 0.15/0.38 (step @p118 :rule trans :premises (@p117 @p115)) % 0.15/0.38 (step @p119 :rule ho_cong :premises (@p58 @p118)) % 0.15/0.38 (step @p120 :rule ho_cong :premises (@p58 @p119)) % 0.15/0.38 (step @p121 :rule ho_cong :premises (@p58 @p120)) % 0.15/0.38 (step @p122 :rule cong :premises (@p121) :args (@t70)) % 0.15/0.38 (step @p123 :rule beta-reduce :args ((= (_ (lambda @t32 @t71) @t21) @t70))) % 0.15/0.38 (step @p124 :rule trans :premises (@p123 @p122)) % 0.15/0.38 (step @p125 :rule refl :args (@t21)) % 0.15/0.38 (step @p126 :rule beta-reduce :args ((= (_ @t72 @t30) @t71))) % 0.15/0.38 (step @p127 :rule beta-reduce :args ((= @t73 @t72))) % 0.15/0.38 (step @p128 :rule ho_cong :premises (@p127 @p65)) % 0.15/0.38 (step @p129 :rule trans :premises (@p128 @p126)) % 0.15/0.38 (step @p130 :rule cong :premises (@p129) :args (@t74)) % 0.15/0.38 (step @p131 :rule beta-reduce :args ((= @t75 @t74))) % 0.15/0.38 (step @p132 :rule trans :premises (@p131 @p130)) % 0.15/0.38 (step @p133 :rule ho_cong :premises (@p132 @p125)) % 0.15/0.38 (step @p134 :rule trans :premises (@p133 @p124)) % 0.15/0.38 (step @p135 :rule ho_cong :premises (@p97 @p134)) % 0.15/0.38 (step @p136 :rule trans :premises (@p135 @p114)) % 0.15/0.38 (step @p137 :rule cong :premises (@p136 @p104) :args (@t76)) % 0.15/0.38 (step @p138 :rule trans :premises (@p137 @p18)) % 0.15/0.38 (step @p139 :rule cong :premises (@p138) :args ((not @t76))) % 0.15/0.38 (step @p140 :rule trans :premises (@p139 @p17)) % 0.15/0.38 (step @p141 :rule ho_cong :premises (@p15 @p4)) % 0.15/0.38 (step @p142 :rule ho_cong :premises (@p141 @p4)) % 0.15/0.38 (step @p143 :rule ho_cong :premises (@p16 @p5)) % 0.15/0.38 (step @p144 :rule ho_cong :premises (@p143 @p8)) % 0.15/0.38 (step @p145 :rule ho_cong :premises (@p16 @p144)) % 0.15/0.38 (step @p146 :rule ho_cong :premises (@p145 @p142)) % 0.15/0.38 (step @p147 :rule ho_cong :premises (@p15 @p6)) % 0.15/0.38 (step @p148 :rule ho_cong :premises (@p147 @p10)) % 0.15/0.38 (step @p149 :rule ho_cong :premises (@p143 @p148)) % 0.15/0.38 (step @p150 :rule cong :premises (@p149 @p146) :args (@t2)) % 0.15/0.38 (step @p151 :rule cong :premises (@p150) :args (@t3)) % 0.15/0.38 (step @p152 :rule trans :premises (@p151 @p140)) % 0.15/0.38 (step @p153 false :rule eq_resolve :premises (@p1 @p152)) % 0.15/0.38 ) % 0.15/0.38 % SZS output end Proof % 0.15/0.38 % cvc5 exiting %------------------------------------------------------------------------------