%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL583^1 : TPTP v9.3.1. 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 : n028.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:06 AM UTC 2026 % Result : Theorem 0.18s 0.50s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL583^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.36 % Computer : n028.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sun Sep 6 02:06:00 UTC 2026 % 0.13/0.36 % CPUTime : % 0.13/0.43 %----Proving TH0 % 0.18/0.50 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.18/0.50 % SZS status Theorem % 0.18/0.50 % SZS output start Proof % 0.18/0.50 ( % 0.18/0.50 (declare-sort $$unsorted 0) % 0.18/0.50 (declare-sort tptp.individuals 0) % 0.18/0.50 (declare-const tptp.s (-> $$unsorted $$unsorted Bool)) % 0.18/0.50 (declare-const tptp.r (-> $$unsorted $$unsorted Bool)) % 0.18/0.50 (declare-const tptp.a (-> $$unsorted Bool)) % 0.18/0.50 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.18/0.50 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.18/0.50 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.18/0.50 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.18/0.50 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.18/0.50 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.18/0.50 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.18/0.50 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.18/0.50 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.18/0.50 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.18/0.50 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.18/0.50 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.50 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.50 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.50 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.50 (define @t1 () (_ (_ tptp.mbox tptp.r) tptp.a)) % 0.18/0.50 (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mbox tptp.s) (_ (_ tptp.mimpl @t1) @t1))))) % 0.18/0.50 (define @t3 () (@var "X" $$unsorted)) % 0.18/0.50 (define @t4 () (@list @t3)) % 0.18/0.50 (define @t5 () (lambda @t4 false)) % 0.18/0.50 (define @t6 () (lambda @t4 true)) % 0.18/0.50 (define @t7 () (@var "U" $$unsorted)) % 0.18/0.50 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.18/0.50 (define @t9 () (_ @t8 @t7)) % 0.18/0.50 (define @t10 () (lambda (@list @t8 @t7) (not @t9))) % 0.18/0.50 (define @t11 () (@var "Y" (-> $$unsorted Bool))) % 0.18/0.50 (define @t12 () (_ @t11 @t7)) % 0.18/0.50 (define @t13 () (@list @t8 @t11 @t7)) % 0.18/0.50 (define @t14 () (lambda @t13 (or @t9 @t12))) % 0.18/0.50 (define @t15 () (lambda @t13 (and @t9 @t12))) % 0.18/0.50 (define @t16 () (@var "__flatten_var_0" $$unsorted)) % 0.18/0.50 (define @t17 () (@var "V" (-> $$unsorted Bool))) % 0.18/0.50 (define @t18 () (@var "U" (-> $$unsorted Bool))) % 0.18/0.50 (define @t19 () (@list @t18 @t17 @t16)) % 0.18/0.50 (define @t20 () (lambda @t19 (_ (_ (_ tptp.mor (_ tptp.mnot @t18)) @t17) @t16))) % 0.18/0.50 (define @t21 () (lambda @t19 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t18) @t17)) (_ (_ tptp.mimpl @t17) @t18)) @t16))) % 0.18/0.50 (define @t22 () (@var "Y" $$unsorted)) % 0.18/0.50 (define @t23 () (@var "P" (-> $$unsorted Bool))) % 0.18/0.50 (define @t24 () (_ @t23 @t22)) % 0.18/0.50 (define @t25 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.18/0.50 (define @t26 () (_ (_ @t25 @t3) @t22)) % 0.18/0.50 (define @t27 () (@list @t22)) % 0.18/0.50 (define @t28 () (forall @t27 (=> @t26 @t24))) % 0.18/0.50 (define @t29 () (@list @t25 @t23 @t3)) % 0.18/0.50 (define @t30 () (lambda @t29 @t28)) % 0.18/0.50 (define @t31 () (lambda @t29 (exists @t27 (and @t26 @t24)))) % 0.18/0.50 (define @t32 () (@var "W" $$unsorted)) % 0.18/0.50 (define @t33 () (@var "X" tptp.individuals)) % 0.18/0.50 (define @t34 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.18/0.50 (define @t35 () (_ (_ @t34 @t33) @t32)) % 0.18/0.50 (define @t36 () (@list @t33)) % 0.18/0.50 (define @t37 () (@list @t34 @t32)) % 0.18/0.50 (define @t38 () (lambda @t37 (forall @t36 @t35))) % 0.18/0.50 (define @t39 () (lambda @t37 (exists @t36 @t35))) % 0.18/0.50 (define @t40 () (_ @t23 @t32)) % 0.18/0.50 (define @t41 () (@list @t32)) % 0.18/0.50 (define @t42 () (forall @t41 @t40)) % 0.18/0.50 (define @t43 () (@list @t23)) % 0.18/0.50 (define @t44 () (lambda @t43 @t42)) % 0.18/0.50 (define @t45 () (lambda @t43 (exists @t41 @t40))) % 0.18/0.50 (define @t46 () (not @t40)) % 0.18/0.50 (define @t47 () (lambda @t43 (exists @t41 @t46))) % 0.18/0.50 (define @t48 () (lambda @t43 (forall @t41 @t46))) % 0.18/0.50 (define @t49 () (@var "BOUND_VARIABLE_7839" $$unsorted)) % 0.18/0.50 (define @t50 () (lambda (@list @t49) true)) % 0.18/0.50 (define @t51 () (_ @t50 @t32)) % 0.18/0.50 (define @t52 () (forall @t41 @t51)) % 0.18/0.50 (define @t53 () (_ @t23 @t32)) % 0.18/0.50 (define @t54 () (lambda @t43 (forall @t41 @t53))) % 0.18/0.50 (define @t55 () (not (tptp.s @t3 @t22))) % 0.18/0.50 (define @t56 () (@var "BOUND_VARIABLE_7811" $$unsorted)) % 0.18/0.50 (define @t57 () (tptp.a @t56)) % 0.18/0.50 (define @t58 () (@list @t56)) % 0.18/0.50 (define @t59 () (forall @t58 (or (not (tptp.r @t22 @t56)) @t57))) % 0.18/0.50 (define @t60 () (not @t59)) % 0.18/0.50 (define @t61 () (or @t55 @t60 @t59)) % 0.18/0.50 (define @t62 () (or @t60 @t59)) % 0.18/0.50 (define @t63 () (forall @t58 (or (not (tptp.r @t16 @t56)) @t57))) % 0.18/0.50 (define @t64 () (@list @t16)) % 0.18/0.50 (define @t65 () (tptp.a @t22)) % 0.18/0.50 (define @t66 () (forall @t27 (or (not (tptp.r @t16 @t22)) @t65))) % 0.18/0.50 (define @t67 () (not @t66)) % 0.18/0.50 (define @t68 () (or @t67 @t66)) % 0.18/0.50 (define @t69 () (lambda @t64 @t68)) % 0.18/0.50 (define @t70 () (or @t55 (_ @t69 @t22))) % 0.18/0.50 (define @t71 () (forall @t27 @t70)) % 0.18/0.50 (define @t72 () (lambda @t4 @t71)) % 0.18/0.50 (define @t73 () (_ @t23 @t22)) % 0.18/0.50 (define @t74 () (@list @t23 @t3)) % 0.18/0.50 (define @t75 () (lambda @t74 (forall @t27 (or @t55 @t73)))) % 0.18/0.50 (define @t76 () (not (tptp.r @t3 @t22))) % 0.18/0.50 (define @t77 () (lambda @t4 (forall @t27 (or @t76 @t65)))) % 0.18/0.50 (define @t78 () (_ @t77 @t16)) % 0.18/0.50 (define @t79 () (or @t67 @t78)) % 0.18/0.50 (define @t80 () (lambda @t64 @t79)) % 0.18/0.50 (define @t81 () (_ @t17 @t16)) % 0.18/0.50 (define @t82 () (@list @t17 @t16)) % 0.18/0.50 (define @t83 () (lambda @t74 (forall @t27 (or @t76 @t73)))) % 0.18/0.50 (define @t84 () (_ @t25 @t3 @t22)) % 0.18/0.50 (define @t85 () (lambda @t29 (forall @t27 (or (not @t84) @t73)))) % 0.18/0.50 (define @t86 () (_ @t85 tptp.r)) % 0.18/0.50 (define @t87 () (not @t78)) % 0.18/0.50 (define @t88 () (or @t87 @t81)) % 0.18/0.50 (define @t89 () (lambda @t82 @t88)) % 0.18/0.50 (define @t90 () (or (not (_ @t18 @t16)) @t81)) % 0.18/0.50 (define @t91 () (lambda @t19 @t90)) % 0.18/0.50 (define @t92 () (_ @t85 tptp.s)) % 0.18/0.50 (define @t93 () (_ @t86 tptp.a)) % 0.18/0.50 (define @t94 () (not @t26)) % 0.18/0.50 (define @t95 () (or @t94 @t24)) % 0.18/0.50 (define @t96 () (not (_ @t18 @t7))) % 0.18/0.50 (define @t97 () (@list @t7)) % 0.18/0.50 (define @t98 () (lambda @t97 (or @t96 (_ @t17 @t7)))) % 0.18/0.50 (define @t99 () (@list @t11 @t7)) % 0.18/0.50 (define @t100 () (lambda @t97 @t96)) % 0.18/0.50 (define @t101 () (_ @t100 @t7)) % 0.18/0.50 (define @t102 () (or @t101 @t12)) % 0.18/0.50 (define @t103 () (lambda @t99 @t102)) % 0.18/0.50 (assume @p1 @t2) % 0.18/0.50 (assume @p2 true) % 0.18/0.50 (step @p3 (= tptp.mfalse @t5) :rule refl :args (@t5)) % 0.18/0.50 (step @p4 (= tptp.mtrue @t6) :rule refl :args (@t6)) % 0.18/0.50 (step @p5 (= tptp.mnot @t10) :rule refl :args (@t10)) % 0.18/0.50 (step @p6 (= tptp.mor @t14) :rule refl :args (@t14)) % 0.18/0.50 (step @p7 (= tptp.mand @t15) :rule refl :args (@t15)) % 0.18/0.50 (step @p8 (= tptp.mimpl @t20) :rule refl :args (@t20)) % 0.18/0.50 (step @p9 (= tptp.miff @t21) :rule refl :args (@t21)) % 0.18/0.50 (step @p10 (= tptp.mbox @t30) :rule refl :args (@t30)) % 0.18/0.50 (step @p11 (= tptp.mdia @t31) :rule refl :args (@t31)) % 0.18/0.50 (step @p12 (= tptp.mall @t38) :rule refl :args (@t38)) % 0.18/0.50 (step @p13 (= tptp.mexists @t39) :rule refl :args (@t39)) % 0.18/0.50 (step @p14 (= tptp.mvalid @t44) :rule refl :args (@t44)) % 0.18/0.50 (step @p15 (= tptp.msatisfiable @t45) :rule refl :args (@t45)) % 0.18/0.50 (step @p16 (= tptp.mcountersatisfiable @t47) :rule refl :args (@t47)) % 0.18/0.50 (step @p17 (= tptp.minvalid @t48) :rule refl :args (@t48)) % 0.18/0.50 (step @p18 :rule evaluate :args ((not true))) % 0.18/0.50 (step @p19 :rule quant-unused-vars :args ((= (forall @t41 true) true))) % 0.18/0.50 (step @p20 :rule beta-reduce :args ((= @t51 true))) % 0.18/0.50 (step @p21 :rule cong :premises (@p20) :args (@t52)) % 0.18/0.50 (step @p22 :rule trans :premises (@p21 @p19)) % 0.18/0.50 (step @p23 :rule beta-reduce :args ((= (_ @t54 @t50) @t52))) % 0.18/0.50 (step @p24 :rule trans :premises (@p23 @p22)) % 0.18/0.50 (step @p25 :rule refl :args (@t50)) % 0.18/0.50 (step @p26 :rule symm :premises (@p25)) % 0.18/0.50 (step @p27 :rule alpha_equiv :args (@t6 (@list @t3) (@list @t49))) % 0.18/0.50 (step @p28 :rule trans :premises (@p27 @p26)) % 0.18/0.50 (step @p29 :rule quant-unused-vars :args ((= (forall @t27 true) true))) % 0.18/0.50 (step @p30 :rule bool-or-taut2 :args ((or @t55) @t59 false false)) % 0.18/0.50 (step @p31 :rule cong :premises (@p30) :args ((forall @t27 @t61))) % 0.18/0.50 (step @p32 :rule trans :premises (@p31 @p29)) % 0.18/0.50 (step @p33 :rule aci_norm :args ((= (or @t55 @t62) @t61))) % 0.18/0.50 (step @p34 :rule beta-reduce :args ((= (_ (lambda @t64 (or (not @t63) @t63)) @t22) @t62))) % 0.18/0.50 (step @p35 :rule refl :args (@t22)) % 0.18/0.50 (step @p36 :rule alpha_equiv :args (@t66 (@list @t22) (@list @t56))) % 0.18/0.50 (step @p37 :rule cong :premises (@p36) :args (@t67)) % 0.18/0.50 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t68)) % 0.18/0.50 (step @p39 :rule cong :premises (@p38) :args (@t69)) % 0.18/0.50 (step @p40 :rule ho_cong :premises (@p39 @p35)) % 0.18/0.50 (step @p41 :rule trans :premises (@p40 @p34)) % 0.18/0.50 (step @p42 :rule refl :args (@t55)) % 0.18/0.50 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t70)) % 0.18/0.50 (step @p44 :rule trans :premises (@p43 @p33)) % 0.18/0.50 (step @p45 :rule cong :premises (@p44) :args (@t71)) % 0.18/0.50 (step @p46 :rule trans :premises (@p45 @p32)) % 0.18/0.50 (step @p47 :rule cong :premises (@p46) :args (@t72)) % 0.18/0.50 (step @p48 :rule trans :premises (@p47 @p28)) % 0.18/0.50 (step @p49 :rule beta-reduce :args ((= (_ @t75 @t69) @t72))) % 0.18/0.50 (step @p50 :rule trans :premises (@p49 @p48)) % 0.18/0.50 (step @p51 :rule beta-reduce :args ((= @t78 @t66))) % 0.18/0.50 (step @p52 :rule refl :args (@t67)) % 0.18/0.50 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t79)) % 0.18/0.50 (step @p54 :rule cong :premises (@p53) :args (@t80)) % 0.18/0.50 (step @p55 :rule beta-reduce :args ((= (_ (lambda @t82 (or @t67 @t81)) @t77) @t80))) % 0.18/0.50 (step @p56 :rule trans :premises (@p55 @p54)) % 0.18/0.50 (step @p57 :rule beta-reduce :args ((= (_ @t83 tptp.a) @t77))) % 0.18/0.50 (step @p58 :rule refl :args (tptp.a)) % 0.18/0.50 (step @p59 :rule beta-reduce :args ((= @t86 @t83))) % 0.18/0.50 (step @p60 :rule ho_cong :premises (@p59 @p58)) % 0.18/0.50 (step @p61 :rule trans :premises (@p60 @p57)) % 0.18/0.50 (step @p62 :rule refl :args (@t81)) % 0.18/0.50 (step @p63 :rule cong :premises (@p51) :args (@t87)) % 0.18/0.50 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t88)) % 0.18/0.50 (step @p65 :rule cong :premises (@p64) :args (@t89)) % 0.18/0.50 (step @p66 :rule beta-reduce :args ((= (_ @t91 @t77) @t89))) % 0.18/0.50 (step @p67 :rule trans :premises (@p66 @p65)) % 0.18/0.50 (step @p68 :rule refl :args (@t91)) % 0.18/0.50 (step @p69 :rule ho_cong :premises (@p68 @p61)) % 0.18/0.50 (step @p70 :rule trans :premises (@p69 @p67)) % 0.18/0.50 (step @p71 :rule ho_cong :premises (@p70 @p61)) % 0.18/0.50 (step @p72 :rule trans :premises (@p71 @p56)) % 0.18/0.50 (step @p73 :rule beta-reduce :args ((= @t92 @t75))) % 0.18/0.50 (step @p74 :rule ho_cong :premises (@p73 @p72)) % 0.18/0.50 (step @p75 :rule trans :premises (@p74 @p50)) % 0.18/0.50 (step @p76 :rule refl :args (@t54)) % 0.18/0.50 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.18/0.50 (step @p78 :rule trans :premises (@p77 @p24)) % 0.18/0.50 (step @p79 :rule cong :premises (@p78) :args ((not (_ @t54 (_ @t92 (_ (_ @t91 @t93) @t93)))))) % 0.18/0.50 (step @p80 :rule trans :premises (@p79 @p18)) % 0.18/0.50 (step @p81 :rule refl :args (tptp.r)) % 0.18/0.50 (step @p82 :rule refl :args (@t73)) % 0.18/0.50 (step @p83 :rule refl :args (@t24)) % 0.18/0.50 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t24 @t73))) % 0.18/0.50 (step @p85 :rule symm :premises (@p84)) % 0.18/0.50 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 0.18/0.50 (step @p87 :rule refl :args (@t84)) % 0.18/0.50 (step @p88 :rule refl :args (@t26)) % 0.18/0.50 (step @p89 :rule cong :premises (@p88 @p87) :args ((= @t26 @t84))) % 0.18/0.50 (step @p90 :rule symm :premises (@p89)) % 0.18/0.50 (step @p91 :rule eq_resolve :premises (@p88 @p90)) % 0.18/0.50 (step @p92 :rule cong :premises (@p91) :args (@t94)) % 0.18/0.50 (step @p93 :rule nary_cong :premises (@p92 @p86) :args (@t95)) % 0.18/0.50 (step @p94 :rule cong :premises (@p93) :args ((forall @t27 @t95))) % 0.18/0.50 (step @p95 :rule bool-impl-elim :args (@t26 @t24)) % 0.18/0.50 (step @p96 :rule cong :premises (@p95) :args (@t28)) % 0.18/0.50 (step @p97 :rule trans :premises (@p96 @p94)) % 0.18/0.50 (step @p98 :rule cong :premises (@p97) :args (@t30)) % 0.18/0.50 (step @p99 :rule trans :premises (@p10 @p98)) % 0.18/0.50 (step @p100 :rule ho_cong :premises (@p99 @p81)) % 0.18/0.50 (step @p101 :rule ho_cong :premises (@p100 @p58)) % 0.18/0.50 (step @p102 :rule beta-reduce :args ((= (_ @t98 @t16) @t90))) % 0.18/0.50 (step @p103 :rule refl :args (@t16)) % 0.18/0.50 (step @p104 :rule beta-reduce :args ((= (_ (lambda @t99 (or @t96 @t12)) @t17) @t98))) % 0.18/0.50 (step @p105 :rule refl :args (@t17)) % 0.18/0.50 (step @p106 :rule refl :args (@t12)) % 0.18/0.50 (step @p107 :rule beta-reduce :args ((= @t101 @t96))) % 0.18/0.50 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t102)) % 0.18/0.50 (step @p109 :rule cong :premises (@p108) :args (@t103)) % 0.18/0.50 (step @p110 :rule beta-reduce :args ((= (_ @t14 @t100) @t103))) % 0.18/0.50 (step @p111 :rule trans :premises (@p110 @p109)) % 0.18/0.50 (step @p112 :rule beta-reduce :args ((= (_ @t10 @t18) @t100))) % 0.18/0.50 (step @p113 :rule refl :args (@t14)) % 0.18/0.50 (step @p114 :rule ho_cong :premises (@p113 @p112)) % 0.18/0.50 (step @p115 :rule trans :premises (@p114 @p111)) % 0.18/0.50 (step @p116 :rule ho_cong :premises (@p115 @p105)) % 0.18/0.50 (step @p117 :rule trans :premises (@p116 @p104)) % 0.18/0.50 (step @p118 :rule ho_cong :premises (@p117 @p103)) % 0.18/0.50 (step @p119 :rule trans :premises (@p118 @p102)) % 0.18/0.50 (step @p120 :rule refl :args (@t18)) % 0.18/0.50 (step @p121 :rule ho_cong :premises (@p5 @p120)) % 0.18/0.50 (step @p122 :rule ho_cong :premises (@p6 @p121)) % 0.18/0.50 (step @p123 :rule ho_cong :premises (@p122 @p105)) % 0.18/0.50 (step @p124 :rule ho_cong :premises (@p123 @p103)) % 0.18/0.50 (step @p125 :rule trans :premises (@p124 @p119)) % 0.18/0.50 (step @p126 :rule cong :premises (@p125) :args (@t20)) % 0.18/0.50 (step @p127 :rule trans :premises (@p8 @p126)) % 0.18/0.50 (step @p128 :rule ho_cong :premises (@p127 @p101)) % 0.18/0.50 (step @p129 :rule ho_cong :premises (@p128 @p101)) % 0.18/0.50 (step @p130 :rule refl :args (tptp.s)) % 0.18/0.50 (step @p131 :rule ho_cong :premises (@p99 @p130)) % 0.18/0.50 (step @p132 :rule ho_cong :premises (@p131 @p129)) % 0.18/0.50 (step @p133 :rule refl :args (@t53)) % 0.18/0.50 (step @p134 :rule refl :args (@t40)) % 0.18/0.50 (step @p135 :rule cong :premises (@p134 @p133) :args ((= @t40 @t53))) % 0.18/0.50 (step @p136 :rule symm :premises (@p135)) % 0.18/0.50 (step @p137 :rule eq_resolve :premises (@p134 @p136)) % 0.18/0.50 (step @p138 :rule cong :premises (@p137) :args (@t42)) % 0.18/0.50 (step @p139 :rule cong :premises (@p138) :args (@t44)) % 0.18/0.50 (step @p140 :rule trans :premises (@p14 @p139)) % 0.18/0.50 (step @p141 :rule ho_cong :premises (@p140 @p132)) % 0.18/0.50 (step @p142 :rule cong :premises (@p141) :args (@t2)) % 0.18/0.50 (step @p143 :rule trans :premises (@p142 @p80)) % 0.18/0.50 (step @p144 false :rule eq_resolve :premises (@p1 @p143)) % 0.18/0.50 ) % 0.18/0.50 % SZS output end Proof % 0.18/0.50 % cvc5 exiting %------------------------------------------------------------------------------