%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL594^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.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 11:23:08 AM UTC 2026 % Result : Theorem 0.41s 0.77s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL594^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.37 % Computer : n002.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Sat Sep 5 08:34:35 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.43 %----Proving TH0 % 0.41/0.77 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.41/0.77 % SZS status Theorem % 0.41/0.77 % SZS output start Proof % 0.41/0.77 ( % 0.41/0.77 (declare-sort $$unsorted 0) % 0.41/0.77 (declare-sort tptp.individuals 0) % 0.41/0.77 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.41/0.77 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.41/0.77 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.41/0.77 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.41/0.77 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.41/0.77 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.41/0.77 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.41/0.77 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.41/0.77 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.41/0.77 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.41/0.77 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.41/0.77 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.41/0.77 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.41/0.77 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.41/0.77 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.41/0.77 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.41/0.77 (define @t2 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.41/0.77 (define @t3 () (@list @t1)) % 0.41/0.77 (define @t4 () (forall @t3 (_ tptp.mvalid (_ (_ tptp.mimpl (_ (_ tptp.mbox @t2) @t1)) @t1)))) % 0.41/0.77 (define @t5 () (@list @t2)) % 0.41/0.77 (define @t6 () (exists @t5 @t4)) % 0.41/0.77 (define @t7 () (not @t6)) % 0.41/0.77 (define @t8 () (@var "X" $$unsorted)) % 0.41/0.77 (define @t9 () (@list @t8)) % 0.41/0.77 (define @t10 () (lambda @t9 false)) % 0.41/0.77 (define @t11 () (lambda @t9 true)) % 0.41/0.77 (define @t12 () (@var "U" $$unsorted)) % 0.41/0.77 (define @t13 () (@var "X" (-> $$unsorted Bool))) % 0.41/0.77 (define @t14 () (_ @t13 @t12)) % 0.41/0.77 (define @t15 () (lambda (@list @t13 @t12) (not @t14))) % 0.41/0.77 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.41/0.77 (define @t17 () (_ @t16 @t12)) % 0.41/0.77 (define @t18 () (@list @t13 @t16 @t12)) % 0.41/0.77 (define @t19 () (lambda @t18 (or @t14 @t17))) % 0.41/0.77 (define @t20 () (lambda @t18 (and @t14 @t17))) % 0.41/0.77 (define @t21 () (@var "__flatten_var_0" $$unsorted)) % 0.41/0.77 (define @t22 () (@var "V" (-> $$unsorted Bool))) % 0.41/0.77 (define @t23 () (@var "U" (-> $$unsorted Bool))) % 0.41/0.77 (define @t24 () (@list @t23 @t22 @t21)) % 0.41/0.77 (define @t25 () (lambda @t24 (_ (_ (_ tptp.mor (_ tptp.mnot @t23)) @t22) @t21))) % 0.41/0.77 (define @t26 () (lambda @t24 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t23) @t22)) (_ (_ tptp.mimpl @t22) @t23)) @t21))) % 0.41/0.77 (define @t27 () (@var "Y" $$unsorted)) % 0.41/0.77 (define @t28 () (@var "P" (-> $$unsorted Bool))) % 0.41/0.77 (define @t29 () (_ @t28 @t27)) % 0.41/0.77 (define @t30 () (_ (_ @t2 @t8) @t27)) % 0.41/0.77 (define @t31 () (@list @t27)) % 0.41/0.77 (define @t32 () (forall @t31 (=> @t30 @t29))) % 0.41/0.77 (define @t33 () (@list @t2 @t28 @t8)) % 0.41/0.77 (define @t34 () (lambda @t33 @t32)) % 0.41/0.77 (define @t35 () (lambda @t33 (exists @t31 (and @t30 @t29)))) % 0.41/0.77 (define @t36 () (@var "W" $$unsorted)) % 0.41/0.77 (define @t37 () (@var "X" tptp.individuals)) % 0.41/0.77 (define @t38 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.41/0.77 (define @t39 () (_ (_ @t38 @t37) @t36)) % 0.41/0.77 (define @t40 () (@list @t37)) % 0.41/0.77 (define @t41 () (@list @t38 @t36)) % 0.41/0.77 (define @t42 () (lambda @t41 (forall @t40 @t39))) % 0.41/0.77 (define @t43 () (lambda @t41 (exists @t40 @t39))) % 0.41/0.77 (define @t44 () (_ @t28 @t36)) % 0.41/0.77 (define @t45 () (@list @t36)) % 0.41/0.77 (define @t46 () (forall @t45 @t44)) % 0.41/0.77 (define @t47 () (@list @t28)) % 0.41/0.77 (define @t48 () (lambda @t47 @t46)) % 0.41/0.77 (define @t49 () (lambda @t47 (exists @t45 @t44))) % 0.41/0.77 (define @t50 () (not @t44)) % 0.41/0.77 (define @t51 () (lambda @t47 (exists @t45 @t50))) % 0.41/0.77 (define @t52 () (lambda @t47 (forall @t45 @t50))) % 0.41/0.77 (define @t53 () (_ @t1 @t36)) % 0.41/0.77 (define @t54 () (_ @t1 @t27)) % 0.41/0.77 (define @t55 () (not (forall @t31 (or (not (_ @t2 @t36 @t27)) @t54)))) % 0.41/0.77 (define @t56 () (or @t55 @t53)) % 0.41/0.77 (define @t57 () (@list @t1 @t36)) % 0.41/0.77 (define @t58 () (forall @t57 @t56)) % 0.41/0.77 (define @t59 () (forall @t5 (not @t58))) % 0.41/0.77 (define @t60 () (_ @t1 @t36)) % 0.41/0.77 (define @t61 () (or @t55 @t60)) % 0.41/0.77 (define @t62 () (forall @t31 (or (not (_ @t2 @t21 @t27)) @t54))) % 0.41/0.77 (define @t63 () (not @t62)) % 0.41/0.77 (define @t64 () (lambda (@list @t21) (or @t63 (_ @t1 @t21)))) % 0.41/0.77 (define @t65 () (_ @t64 @t36)) % 0.41/0.77 (define @t66 () (forall @t45 @t65)) % 0.41/0.77 (define @t67 () (_ @t28 @t36)) % 0.41/0.77 (define @t68 () (lambda @t47 (forall @t45 @t67))) % 0.41/0.77 (define @t69 () (_ @t22 @t21)) % 0.41/0.77 (define @t70 () (@list @t22 @t21)) % 0.41/0.77 (define @t71 () (_ @t2 @t8 @t27)) % 0.41/0.77 (define @t72 () (not @t71)) % 0.41/0.77 (define @t73 () (lambda @t9 (forall @t31 (or @t72 @t54)))) % 0.41/0.77 (define @t74 () (_ @t73 @t21)) % 0.41/0.77 (define @t75 () (not @t74)) % 0.41/0.77 (define @t76 () (or @t75 @t69)) % 0.41/0.77 (define @t77 () (lambda @t70 @t76)) % 0.41/0.77 (define @t78 () (or (not (_ @t23 @t21)) @t69)) % 0.41/0.77 (define @t79 () (lambda @t24 @t78)) % 0.41/0.77 (define @t80 () (_ @t28 @t27)) % 0.41/0.77 (define @t81 () (forall @t31 (or @t72 @t80))) % 0.41/0.77 (define @t82 () (lambda (@list @t28 @t8) @t81)) % 0.41/0.77 (define @t83 () (_ (lambda @t33 @t81) @t2)) % 0.41/0.77 (define @t84 () (forall @t3 (_ @t68 (_ (_ @t79 (_ @t83 @t1)) @t1)))) % 0.41/0.77 (define @t85 () (exists @t5 @t84)) % 0.41/0.77 (define @t86 () (not @t30)) % 0.41/0.77 (define @t87 () (or @t86 @t29)) % 0.41/0.77 (define @t88 () (not (_ @t23 @t12))) % 0.41/0.77 (define @t89 () (@list @t12)) % 0.41/0.77 (define @t90 () (lambda @t89 (or @t88 (_ @t22 @t12)))) % 0.41/0.77 (define @t91 () (@list @t16 @t12)) % 0.41/0.77 (define @t92 () (lambda @t89 @t88)) % 0.41/0.77 (define @t93 () (_ @t92 @t12)) % 0.41/0.77 (define @t94 () (or @t93 @t17)) % 0.41/0.77 (define @t95 () (lambda @t91 @t94)) % 0.41/0.77 (define @t96 () (lambda (@list (@var "BOUND_VARIABLE_36481" $$unsorted) (@var "BOUND_VARIABLE_36482" $$unsorted)) true)) % 0.41/0.77 (define @t97 () (_ @t96 @t36 @t27)) % 0.41/0.77 (define @t98 () (not @t97)) % 0.41/0.77 (define @t99 () (or @t98 @t54)) % 0.41/0.77 (define @t100 () (forall @t31 @t99)) % 0.41/0.77 (define @t101 () (not @t100)) % 0.41/0.77 (define @t102 () (or @t101 @t53)) % 0.41/0.77 (define @t103 () (forall @t57 @t102)) % 0.41/0.77 (define @t104 () (not @t103)) % 0.41/0.77 (define @t105 () (forall @t57 (or (not (forall @t31 @t54)) @t53))) % 0.41/0.77 (define @t106 () (@quantifiers_skolemize @t105 0)) % 0.41/0.77 (define @t107 () (forall @t31 (_ @t106 @t27))) % 0.41/0.77 (define @t108 () (@quantifiers_skolemize @t105 1)) % 0.41/0.77 (define @t109 () (_ @t106 @t108)) % 0.41/0.77 (define @t110 () (not @t107)) % 0.41/0.77 (define @t111 () (or @t110 @t109)) % 0.41/0.77 (define @t112 () (@list true)) % 0.41/0.77 (define @t113 () (@list @t111)) % 0.41/0.77 (assume @p1 @t7) % 0.41/0.77 (assume @p2 true) % 0.41/0.77 (step @p3 (= tptp.mfalse @t10) :rule refl :args (@t10)) % 0.41/0.77 (step @p4 (= tptp.mtrue @t11) :rule refl :args (@t11)) % 0.41/0.77 (step @p5 (= tptp.mnot @t15) :rule refl :args (@t15)) % 0.41/0.77 (step @p6 (= tptp.mor @t19) :rule refl :args (@t19)) % 0.41/0.77 (step @p7 (= tptp.mand @t20) :rule refl :args (@t20)) % 0.41/0.77 (step @p8 (= tptp.mimpl @t25) :rule refl :args (@t25)) % 0.41/0.77 (step @p9 (= tptp.miff @t26) :rule refl :args (@t26)) % 0.41/0.77 (step @p10 (= tptp.mbox @t34) :rule refl :args (@t34)) % 0.41/0.77 (step @p11 (= tptp.mdia @t35) :rule refl :args (@t35)) % 0.41/0.77 (step @p12 (= tptp.mall @t42) :rule refl :args (@t42)) % 0.41/0.77 (step @p13 (= tptp.mexists @t43) :rule refl :args (@t43)) % 0.41/0.77 (step @p14 (= tptp.mvalid @t48) :rule refl :args (@t48)) % 0.41/0.77 (step @p15 (= tptp.msatisfiable @t49) :rule refl :args (@t49)) % 0.41/0.77 (step @p16 (= tptp.mcountersatisfiable @t51) :rule refl :args (@t51)) % 0.41/0.77 (step @p17 (= tptp.minvalid @t52) :rule refl :args (@t52)) % 0.41/0.77 (step @p18 :rule bool-double-not-elim :args (@t59)) % 0.41/0.77 (step @p19 :rule exists-elim :args ((= (exists @t5 @t58) (not @t59)))) % 0.41/0.77 (step @p20 :rule quant-merge-prenex :args ((= (forall @t3 (forall @t45 @t56)) @t58))) % 0.41/0.77 (step @p21 :rule refl :args (@t53)) % 0.41/0.77 (step @p22 :rule refl :args (@t60)) % 0.41/0.77 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t60 @t53))) % 0.41/0.77 (step @p24 :rule symm :premises (@p23)) % 0.41/0.77 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.41/0.77 (step @p26 :rule refl :args (@t55)) % 0.41/0.77 (step @p27 :rule nary_cong :premises (@p26 @p25) :args (@t61)) % 0.41/0.77 (step @p28 :rule cong :premises (@p27) :args ((forall @t45 @t61))) % 0.41/0.77 (step @p29 :rule beta-reduce :args ((= @t65 @t61))) % 0.41/0.77 (step @p30 :rule cong :premises (@p29) :args (@t66)) % 0.41/0.77 (step @p31 :rule trans :premises (@p30 @p28)) % 0.41/0.77 (step @p32 :rule beta-reduce :args ((= (_ @t68 @t64) @t66))) % 0.41/0.77 (step @p33 :rule trans :premises (@p32 @p31)) % 0.41/0.77 (step @p34 :rule beta-reduce :args ((= (_ (lambda @t70 (or @t63 @t69)) @t1) @t64))) % 0.41/0.77 (step @p35 :rule refl :args (@t1)) % 0.41/0.77 (step @p36 :rule refl :args (@t69)) % 0.41/0.77 (step @p37 :rule beta-reduce :args ((= @t74 @t62))) % 0.41/0.77 (step @p38 :rule cong :premises (@p37) :args (@t75)) % 0.41/0.77 (step @p39 :rule nary_cong :premises (@p38 @p36) :args (@t76)) % 0.41/0.77 (step @p40 :rule cong :premises (@p39) :args (@t77)) % 0.41/0.77 (step @p41 :rule beta-reduce :args ((= (_ @t79 @t73) @t77))) % 0.41/0.77 (step @p42 :rule trans :premises (@p41 @p40)) % 0.41/0.77 (step @p43 :rule beta-reduce :args ((= (_ @t82 @t1) @t73))) % 0.41/0.77 (step @p44 :rule beta-reduce :args ((= @t83 @t82))) % 0.41/0.77 (step @p45 :rule ho_cong :premises (@p44 @p35)) % 0.41/0.77 (step @p46 :rule trans :premises (@p45 @p43)) % 0.41/0.77 (step @p47 :rule refl :args (@t79)) % 0.41/0.77 (step @p48 :rule ho_cong :premises (@p47 @p46)) % 0.41/0.77 (step @p49 :rule trans :premises (@p48 @p42)) % 0.41/0.77 (step @p50 :rule ho_cong :premises (@p49 @p35)) % 0.41/0.77 (step @p51 :rule trans :premises (@p50 @p34)) % 0.41/0.77 (step @p52 :rule refl :args (@t68)) % 0.41/0.77 (step @p53 :rule ho_cong :premises (@p52 @p51)) % 0.41/0.77 (step @p54 :rule trans :premises (@p53 @p33)) % 0.41/0.77 (step @p55 :rule cong :premises (@p54) :args (@t84)) % 0.41/0.77 (step @p56 :rule trans :premises (@p55 @p20)) % 0.41/0.77 (step @p57 :rule cong :premises (@p56) :args (@t85)) % 0.41/0.77 (step @p58 :rule trans :premises (@p57 @p19)) % 0.41/0.77 (step @p59 :rule cong :premises (@p58) :args ((not @t85))) % 0.41/0.77 (step @p60 :rule trans :premises (@p59 @p18)) % 0.41/0.77 (step @p61 :rule refl :args (@t2)) % 0.41/0.77 (step @p62 :rule refl :args (@t80)) % 0.41/0.77 (step @p63 :rule refl :args (@t29)) % 0.41/0.77 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t29 @t80))) % 0.41/0.77 (step @p65 :rule symm :premises (@p64)) % 0.41/0.77 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.41/0.77 (step @p67 :rule refl :args (@t71)) % 0.41/0.77 (step @p68 :rule refl :args (@t30)) % 0.41/0.77 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t30 @t71))) % 0.41/0.77 (step @p70 :rule symm :premises (@p69)) % 0.41/0.77 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.41/0.77 (step @p72 :rule cong :premises (@p71) :args (@t86)) % 0.41/0.77 (step @p73 :rule nary_cong :premises (@p72 @p66) :args (@t87)) % 0.41/0.77 (step @p74 :rule cong :premises (@p73) :args ((forall @t31 @t87))) % 0.41/0.77 (step @p75 :rule bool-impl-elim :args (@t30 @t29)) % 0.41/0.77 (step @p76 :rule cong :premises (@p75) :args (@t32)) % 0.41/0.77 (step @p77 :rule trans :premises (@p76 @p74)) % 0.41/0.77 (step @p78 :rule cong :premises (@p77) :args (@t34)) % 0.41/0.77 (step @p79 :rule trans :premises (@p10 @p78)) % 0.41/0.77 (step @p80 :rule ho_cong :premises (@p79 @p61)) % 0.41/0.77 (step @p81 :rule ho_cong :premises (@p80 @p35)) % 0.41/0.77 (step @p82 :rule beta-reduce :args ((= (_ @t90 @t21) @t78))) % 0.41/0.77 (step @p83 :rule refl :args (@t21)) % 0.41/0.77 (step @p84 :rule beta-reduce :args ((= (_ (lambda @t91 (or @t88 @t17)) @t22) @t90))) % 0.41/0.77 (step @p85 :rule refl :args (@t22)) % 0.41/0.77 (step @p86 :rule refl :args (@t17)) % 0.41/0.77 (step @p87 :rule beta-reduce :args ((= @t93 @t88))) % 0.41/0.77 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t94)) % 0.41/0.77 (step @p89 :rule cong :premises (@p88) :args (@t95)) % 0.41/0.77 (step @p90 :rule beta-reduce :args ((= (_ @t19 @t92) @t95))) % 0.41/0.77 (step @p91 :rule trans :premises (@p90 @p89)) % 0.41/0.77 (step @p92 :rule beta-reduce :args ((= (_ @t15 @t23) @t92))) % 0.41/0.77 (step @p93 :rule refl :args (@t19)) % 0.41/0.77 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 0.41/0.77 (step @p95 :rule trans :premises (@p94 @p91)) % 0.41/0.77 (step @p96 :rule ho_cong :premises (@p95 @p85)) % 0.41/0.77 (step @p97 :rule trans :premises (@p96 @p84)) % 0.41/0.77 (step @p98 :rule ho_cong :premises (@p97 @p83)) % 0.41/0.77 (step @p99 :rule trans :premises (@p98 @p82)) % 0.41/0.77 (step @p100 :rule refl :args (@t23)) % 0.41/0.77 (step @p101 :rule ho_cong :premises (@p5 @p100)) % 0.41/0.77 (step @p102 :rule ho_cong :premises (@p6 @p101)) % 0.41/0.77 (step @p103 :rule ho_cong :premises (@p102 @p85)) % 0.41/0.77 (step @p104 :rule ho_cong :premises (@p103 @p83)) % 0.41/0.77 (step @p105 :rule trans :premises (@p104 @p99)) % 0.41/0.77 (step @p106 :rule cong :premises (@p105) :args (@t25)) % 0.41/0.77 (step @p107 :rule trans :premises (@p8 @p106)) % 0.41/0.77 (step @p108 :rule ho_cong :premises (@p107 @p81)) % 0.41/0.77 (step @p109 :rule ho_cong :premises (@p108 @p35)) % 0.41/0.77 (step @p110 :rule refl :args (@t67)) % 0.41/0.77 (step @p111 :rule refl :args (@t44)) % 0.41/0.77 (step @p112 :rule cong :premises (@p111 @p110) :args ((= @t44 @t67))) % 0.41/0.77 (step @p113 :rule symm :premises (@p112)) % 0.41/0.77 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.41/0.77 (step @p115 :rule cong :premises (@p114) :args (@t46)) % 0.41/0.77 (step @p116 :rule cong :premises (@p115) :args (@t48)) % 0.41/0.77 (step @p117 :rule trans :premises (@p14 @p116)) % 0.41/0.77 (step @p118 :rule ho_cong :premises (@p117 @p109)) % 0.41/0.77 (step @p119 :rule cong :premises (@p118) :args (@t4)) % 0.41/0.77 (step @p120 :rule cong :premises (@p119) :args (@t6)) % 0.41/0.77 (step @p121 :rule cong :premises (@p120) :args (@t7)) % 0.41/0.77 (step @p122 :rule trans :premises (@p121 @p60)) % 0.41/0.77 (step @p123 :rule eq_resolve :premises (@p1 @p122)) % 0.41/0.77 (step @p124 :rule refl :args (@t53)) % 0.41/0.77 (step @p125 :rule aci_norm :args ((= (or false @t54) @t54))) % 0.41/0.77 (step @p126 :rule refl :args (@t54)) % 0.41/0.77 (step @p127 :rule evaluate :args ((not true))) % 0.41/0.77 (step @p128 :rule beta-reduce :args ((= @t97 true))) % 0.41/0.77 (step @p129 :rule cong :premises (@p128) :args (@t98)) % 0.41/0.77 (step @p130 :rule trans :premises (@p129 @p127)) % 0.41/0.77 (step @p131 :rule nary_cong :premises (@p130 @p126) :args (@t99)) % 0.41/0.77 (step @p132 :rule trans :premises (@p131 @p125)) % 0.41/0.77 (step @p133 :rule cong :premises (@p132) :args (@t100)) % 0.41/0.77 (step @p134 :rule cong :premises (@p133) :args (@t101)) % 0.41/0.77 (step @p135 :rule nary_cong :premises (@p134 @p124) :args (@t102)) % 0.41/0.77 (step @p136 :rule cong :premises (@p135) :args (@t103)) % 0.41/0.77 (step @p137 :rule cong :premises (@p136) :args (@t104)) % 0.41/0.77 (step @p138 :rule refl :args (@t59)) % 0.41/0.77 (step @p139 :rule cong :premises (@p138 @p137) :args ((=> @t59 @t104))) % 0.41/0.77 (assume-push @p163 @t59) % 0.41/0.77 (step @p141 :rule instantiate :premises (@p123) :args ((@list @t96))) % 0.41/0.77 (step-pop @p164 :rule scope :premises (@p141)) % 0.41/0.77 (step @p142 :rule process_scope :premises (@p164) :args (@t104)) % 0.41/0.77 (step @p144 :rule eq_resolve :premises (@p142 @p139)) % 0.41/0.77 (step @p145 :rule implies_elim :premises (@p144)) % 0.41/0.77 (step @p146 :rule chain_m_resolution :premises (@p145 @p123) :args ((not @t105) (@list false) (@list @t59))) % 0.41/0.77 (step @p147 :rule skolemize :premises (@p146)) % 0.41/0.77 (step @p148 :rule bool-double-not-elim :args (@t107)) % 0.41/0.77 (step @p149 :rule refl :args (@t111)) % 0.41/0.77 (step @p150 :rule nary_cong :premises (@p149 @p148) :args ((or @t111 (not @t110)))) % 0.41/0.77 (step @p151 :rule cnf_or_neg :args (@t111 0)) % 0.41/0.77 (step @p152 :rule eq_resolve :premises (@p151 @p150)) % 0.41/0.77 (step @p153 :rule reordering :premises (@p152) :args ((or @t107 @t111))) % 0.41/0.77 (step @p154 :rule chain_m_resolution :premises (@p153 @p147) :args (@t107 @t112 @t113)) % 0.41/0.77 (step @p155 :rule cnf_or_neg :args (@t111 1)) % 0.41/0.77 (step @p156 :rule chain_m_resolution :premises (@p155 @p147) :args ((not @t109) @t112 @t113)) % 0.41/0.77 (assume-push @p165 @t107) % 0.41/0.77 (step @p158 :rule instantiate :premises (@p154) :args ((@list @t108))) % 0.41/0.77 (step-pop @p166 :rule scope :premises (@p158)) % 0.41/0.77 (step @p159 :rule process_scope :premises (@p166) :args (@t109)) % 0.41/0.77 (step @p161 :rule implies_elim :premises (@p159)) % 0.41/0.77 (step @p162 false :rule chain_m_resolution :premises (@p161 @p156 @p154) :args (false (@list true false) (@list @t109 @t107))) % 0.41/0.77 ) % 0.41/0.77 % SZS output end Proof % 0.41/0.77 % cvc5 exiting %------------------------------------------------------------------------------