%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET724^4 : 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 : n017.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 08:48:31 AM UTC 2026 % Result : Theorem 0.91s 1.17s % Output : Proof 0.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET724^4 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n017.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 16:09:01 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.91/1.17 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.91/1.17 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 0.91/1.17 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 0.91/1.17 % SZS status Theorem % 0.91/1.17 % SZS output start Proof % 0.91/1.17 ( % 0.91/1.17 (declare-sort $$unsorted 0) % 0.91/1.17 (define tptp.fun_image () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_4 _let_3) (exists (@list _let_1) (and (_ _let_4 _let_1) (= _let_3 (_ _let_2 _let_1)))))))))) % 0.91/1.17 (define tptp.fun_composition () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "G" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_3 _let_1) (_ _let_3 (_ _let_2 _let_1))))))) % 0.91/1.17 (define tptp.fun_inv_image () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "B" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_4 _let_1) (exists (@list _let_3) (and (_ _let_4 _let_3) (= _let_3 (_ _let_2 _let_1)))))))))) % 0.91/1.17 (define tptp.fun_injective () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "F" (-> $$unsorted $$unsorted)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (= (_ _let_3 _let_2) (_ _let_3 _let_1)) (= _let_2 _let_1)))))))) % 0.91/1.17 (define tptp.fun_surjective () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (lambda (@list _let_2) (forall (@list _let_3) (exists (@list _let_1) (= _let_3 (_ _let_2 _let_1))))))))) % 0.91/1.17 (define tptp.fun_bijective () (let ((_let_1 (@var "F" (-> $$unsorted $$unsorted)))) (lambda (@list _let_1) (and (_ tptp.fun_injective _let_1) (_ tptp.fun_surjective _let_1))))) % 0.91/1.17 (define tptp.fun_decreasing () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "SMALLER" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_4) (forall (@list _let_1 _let_3) (=> (_ (_ _let_4 _let_1) _let_3) (_ (_ _let_4 (_ _let_2 _let_3)) (_ _let_2 _let_1)))))))))) % 0.91/1.17 (define tptp.fun_increasing () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "SMALLER" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_4) (forall (@list _let_3 _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ (_ _let_4 (_ _let_2 _let_3)) (_ _let_2 _let_1)))))))))) % 0.91/1.17 (define @t1 () (@var "H" (-> $$unsorted $$unsorted))) % 0.91/1.17 (define @t2 () (@var "G" (-> $$unsorted $$unsorted))) % 0.91/1.17 (define @t3 () (= @t2 @t1)) % 0.91/1.17 (define @t4 () (@var "F" (-> $$unsorted $$unsorted))) % 0.91/1.17 (define @t5 () (_ tptp.fun_surjective @t4)) % 0.91/1.17 (define @t6 () (_ tptp.fun_composition @t4)) % 0.91/1.17 (define @t7 () (= (_ @t6 @t2) (_ @t6 @t1))) % 0.91/1.17 (define @t8 () (and @t7 @t5)) % 0.91/1.17 (define @t9 () (=> @t8 @t3)) % 0.91/1.17 (define @t10 () (@list @t4 @t2 @t1)) % 0.91/1.17 (define @t11 () (forall @t10 @t9)) % 0.91/1.17 (define @t12 () (not @t11)) % 0.91/1.17 (define @t13 () (@var "X" $$unsorted)) % 0.91/1.17 (define @t14 () (_ @t4 @t13)) % 0.91/1.17 (define @t15 () (@var "Y" $$unsorted)) % 0.91/1.17 (define @t16 () (= @t15 @t14)) % 0.91/1.17 (define @t17 () (@var "A" (-> $$unsorted Bool))) % 0.91/1.17 (define @t18 () (@list @t13)) % 0.91/1.17 (define @t19 () (lambda (@list @t4 @t17 @t15) (exists @t18 (and (_ @t17 @t13) @t16)))) % 0.91/1.17 (define @t20 () (_ @t2 @t14)) % 0.91/1.17 (define @t21 () (lambda (@list @t4 @t2 @t13) @t20)) % 0.91/1.17 (define @t22 () (@var "B" (-> $$unsorted Bool))) % 0.91/1.17 (define @t23 () (@list @t15)) % 0.91/1.17 (define @t24 () (lambda (@list @t4 @t22 @t13) (exists @t23 (and (_ @t22 @t15) @t16)))) % 0.91/1.17 (define @t25 () (_ @t4 @t15)) % 0.91/1.17 (define @t26 () (@list @t13 @t15)) % 0.91/1.17 (define @t27 () (@list @t4)) % 0.91/1.17 (define @t28 () (lambda @t27 (forall @t26 (=> (= @t14 @t25) (= @t13 @t15))))) % 0.91/1.17 (define @t29 () (exists @t18 @t16)) % 0.91/1.17 (define @t30 () (forall @t23 @t29)) % 0.91/1.17 (define @t31 () (lambda @t27 @t30)) % 0.91/1.17 (define @t32 () (lambda @t27 (and (_ tptp.fun_injective @t4) @t5))) % 0.91/1.17 (define @t33 () (@var "SMALLER" (-> $$unsorted $$unsorted Bool))) % 0.91/1.17 (define @t34 () (_ (_ @t33 @t13) @t15)) % 0.91/1.17 (define @t35 () (@list @t4 @t33)) % 0.91/1.17 (define @t36 () (lambda @t35 (forall @t26 (=> @t34 (_ (_ @t33 @t25) @t14))))) % 0.91/1.17 (define @t37 () (lambda @t35 (forall @t26 (=> @t34 (_ (_ @t33 @t14) @t25))))) % 0.91/1.17 (define @t38 () (_ @t4 @t13)) % 0.91/1.17 (define @t39 () (forall @t23 (not (forall @t18 (not (= @t15 @t38)))))) % 0.91/1.17 (define @t40 () (not @t39)) % 0.91/1.17 (define @t41 () (_ @t1 @t38)) % 0.91/1.17 (define @t42 () (_ @t1 @t14)) % 0.91/1.17 (define @t43 () (lambda @t18 @t42)) % 0.91/1.17 (define @t44 () (_ @t2 @t38)) % 0.91/1.17 (define @t45 () (lambda @t18 @t20)) % 0.91/1.17 (define @t46 () (= @t45 @t43)) % 0.91/1.17 (define @t47 () (not @t46)) % 0.91/1.17 (define @t48 () (or @t47 @t40 @t3)) % 0.91/1.17 (define @t49 () (and @t46 @t39)) % 0.91/1.17 (define @t50 () (_ (lambda @t27 @t39) @t4)) % 0.91/1.17 (define @t51 () (lambda (@list @t2 @t13) @t20)) % 0.91/1.17 (define @t52 () (_ @t21 @t4)) % 0.91/1.17 (define @t53 () (= (_ @t52 @t2) (_ @t52 @t1))) % 0.91/1.17 (define @t54 () (and @t53 @t50)) % 0.91/1.17 (define @t55 () (=> @t54 @t3)) % 0.91/1.17 (define @t56 () (forall @t10 @t55)) % 0.91/1.17 (define @t57 () (not @t16)) % 0.91/1.17 (define @t58 () (forall @t18 @t57)) % 0.91/1.17 (define @t59 () (not @t58)) % 0.91/1.17 (define @t60 () (forall @t10 (or (not (= (lambda @t18 @t44) (lambda @t18 @t41))) @t40 @t3))) % 0.91/1.17 (define @t61 () (@quantifiers_skolemize @t60 2)) % 0.91/1.17 (define @t62 () (@quantifiers_skolemize @t60 1)) % 0.91/1.17 (define @t63 () (= @t62 @t61)) % 0.91/1.17 (define @t64 () (@quantifiers_skolemize @t60 0)) % 0.91/1.17 (define @t65 () (_ @t64 @t13)) % 0.91/1.17 (define @t66 () (forall @t23 (not (forall @t18 (not (= @t15 @t65)))))) % 0.91/1.17 (define @t67 () (not @t66)) % 0.91/1.17 (define @t68 () (_ @t62 @t65)) % 0.91/1.17 (define @t69 () (lambda @t18 @t68)) % 0.91/1.17 (define @t70 () (@purify @t69)) % 0.91/1.17 (define @t71 () (_ @t61 @t65)) % 0.91/1.17 (define @t72 () (lambda @t18 @t71)) % 0.91/1.17 (define @t73 () (@purify @t72)) % 0.91/1.17 (define @t74 () (= @t73 @t70)) % 0.91/1.17 (define @t75 () (not @t74)) % 0.91/1.17 (define @t76 () (or @t75 @t67 @t63)) % 0.91/1.17 (define @t77 () (not @t76)) % 0.91/1.17 (define @t78 () (not @t60)) % 0.91/1.17 (define @t79 () (= @t69 @t72)) % 0.91/1.17 (define @t80 () (not @t79)) % 0.91/1.17 (define @t81 () (or @t80 @t67 @t63)) % 0.91/1.17 (define @t82 () (not @t81)) % 0.91/1.17 (define @t83 () (@list true)) % 0.91/1.17 (define @t84 () (@list @t76)) % 0.91/1.17 (define @t85 () (forall @t18 (= @t71 @t68))) % 0.91/1.17 (define @t86 () (=> @t74 @t85)) % 0.91/1.17 (define @t87 () (forall @t18 (= @t68 @t71))) % 0.91/1.17 (define @t88 () (@list false)) % 0.91/1.17 (define @t89 () (@const 0 $$unsorted)) % 0.91/1.17 (define @t90 () (not (= (_ @t62 @t89) (_ @t61 @t89)))) % 0.91/1.17 (define @t91 () (not (= @t89 @t65))) % 0.91/1.17 (define @t92 () (forall @t18 @t91)) % 0.91/1.17 (define @t93 () (not @t92)) % 0.91/1.17 (define @t94 () (forall @t18 (not (= @t65 @t89)))) % 0.91/1.17 (define @t95 () (not @t94)) % 0.91/1.17 (define @t96 () (@quantifiers_skolemize @t94 0)) % 0.91/1.17 (define @t97 () (_ @t64 @t96)) % 0.91/1.17 (define @t98 () (= @t89 @t97)) % 0.91/1.17 (define @t99 () (= @t97 @t89)) % 0.91/1.17 (define @t100 () (not (not @t99))) % 0.91/1.17 (define @t101 () (_ @t61 @t97)) % 0.91/1.17 (define @t102 () (_ @t62 @t97)) % 0.91/1.17 (define @t103 () (= @t102 @t101)) % 0.91/1.17 (assume @p1 @t12) % 0.91/1.17 (assume @p2 true) % 0.91/1.17 (step @p3 (= tptp.fun_image @t19) :rule refl :args (@t19)) % 0.91/1.17 (step @p4 (= tptp.fun_composition @t21) :rule refl :args (@t21)) % 0.91/1.17 (step @p5 (= tptp.fun_inv_image @t24) :rule refl :args (@t24)) % 0.91/1.17 (step @p6 (= tptp.fun_injective @t28) :rule refl :args (@t28)) % 0.91/1.17 (step @p7 (= tptp.fun_surjective @t31) :rule refl :args (@t31)) % 0.91/1.17 (step @p8 (= tptp.fun_bijective @t32) :rule refl :args (@t32)) % 0.91/1.17 (step @p9 (= tptp.fun_decreasing @t36) :rule refl :args (@t36)) % 0.91/1.17 (step @p10 (= tptp.fun_increasing @t37) :rule refl :args (@t37)) % 0.91/1.17 (step @p11 :rule refl :args (@t3)) % 0.91/1.17 (step @p12 :rule refl :args (@t40)) % 0.91/1.17 (step @p13 :rule refl :args ((_ @t1 @t14))) % 0.91/1.17 (step @p14 :rule refl :args (@t38)) % 0.91/1.17 (step @p15 :rule cong :premises (@p14) :args (@t41)) % 0.91/1.17 (step @p16 :rule trans :premises (@p15 @p13)) % 0.91/1.17 (step @p17 :rule refl :args (@t1)) % 0.91/1.17 (step @p18 :rule ho_cong :premises (@p17 @p14)) % 0.91/1.17 (step @p19 :rule cong :premises (@p18 @p16) :args ((= (_ @t1 @t38) @t41))) % 0.91/1.17 (step @p20 :rule symm :premises (@p19)) % 0.91/1.17 (step @p21 :rule refl :args (@t42)) % 0.91/1.17 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 0.91/1.17 (step @p23 :rule refl :args (@t14)) % 0.91/1.17 (step @p24 :rule cong :premises (@p23 @p14) :args ((= @t14 @t38))) % 0.91/1.17 (step @p25 :rule symm :premises (@p24)) % 0.91/1.17 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.91/1.17 (step @p27 :rule ho_cong :premises (@p17 @p26)) % 0.91/1.17 (step @p28 :rule trans :premises (@p27 @p22)) % 0.91/1.17 (step @p29 :rule cong :premises (@p28) :args (@t43)) % 0.91/1.17 (step @p30 :rule refl :args ((_ @t2 @t14))) % 0.91/1.17 (step @p31 :rule cong :premises (@p14) :args (@t44)) % 0.91/1.17 (step @p32 :rule trans :premises (@p31 @p30)) % 0.91/1.17 (step @p33 :rule refl :args (@t2)) % 0.91/1.17 (step @p34 :rule ho_cong :premises (@p33 @p14)) % 0.91/1.17 (step @p35 :rule cong :premises (@p34 @p32) :args ((= (_ @t2 @t38) @t44))) % 0.91/1.17 (step @p36 :rule symm :premises (@p35)) % 0.91/1.17 (step @p37 :rule refl :args (@t20)) % 0.91/1.17 (step @p38 :rule eq_resolve :premises (@p37 @p36)) % 0.91/1.17 (step @p39 :rule ho_cong :premises (@p33 @p26)) % 0.91/1.17 (step @p40 :rule trans :premises (@p39 @p38)) % 0.91/1.17 (step @p41 :rule cong :premises (@p40) :args (@t45)) % 0.91/1.17 (step @p42 :rule cong :premises (@p41 @p29) :args (@t46)) % 0.91/1.17 (step @p43 :rule cong :premises (@p42) :args (@t47)) % 0.91/1.17 (step @p44 :rule nary_cong :premises (@p43 @p12 @p11) :args (@t48)) % 0.91/1.17 (step @p45 :rule cong :premises (@p44) :args ((forall @t10 @t48))) % 0.91/1.17 (step @p46 :rule aci_norm :args ((= (or (or @t47 @t40) @t3) @t48))) % 0.91/1.17 (step @p47 :rule bool-and-de-morgan :args (@t46 @t39 true)) % 0.91/1.17 (step @p48 :rule nary_cong :premises (@p47 @p11) :args ((or (not @t49) @t3))) % 0.91/1.17 (step @p49 :rule trans :premises (@p48 @p46)) % 0.91/1.17 (step @p50 :rule bool-impl-elim :args (@t49 @t3)) % 0.91/1.17 (step @p51 :rule trans :premises (@p50 @p49)) % 0.91/1.17 (step @p52 :rule cong :premises (@p51) :args ((forall @t10 (=> @t49 @t3)))) % 0.91/1.17 (step @p53 :rule trans :premises (@p52 @p45)) % 0.91/1.17 (step @p54 :rule refl :args (@t3)) % 0.91/1.17 (step @p55 :rule beta-reduce :args ((= @t50 @t39))) % 0.91/1.17 (step @p56 :rule beta-reduce :args ((= (_ @t51 @t1) @t43))) % 0.91/1.17 (step @p57 :rule refl :args (@t1)) % 0.91/1.17 (step @p58 :rule beta-reduce :args ((= @t52 @t51))) % 0.91/1.17 (step @p59 :rule ho_cong :premises (@p58 @p57)) % 0.91/1.17 (step @p60 :rule trans :premises (@p59 @p56)) % 0.91/1.17 (step @p61 :rule beta-reduce :args ((= (_ @t51 @t2) @t45))) % 0.91/1.17 (step @p62 :rule refl :args (@t2)) % 0.91/1.17 (step @p63 :rule ho_cong :premises (@p58 @p62)) % 0.91/1.17 (step @p64 :rule trans :premises (@p63 @p61)) % 0.91/1.17 (step @p65 :rule cong :premises (@p64 @p60) :args (@t53)) % 0.91/1.17 (step @p66 :rule nary_cong :premises (@p65 @p55) :args (@t54)) % 0.91/1.17 (step @p67 :rule cong :premises (@p66 @p54) :args (@t55)) % 0.91/1.17 (step @p68 :rule cong :premises (@p67) :args (@t56)) % 0.91/1.17 (step @p69 :rule trans :premises (@p68 @p53)) % 0.91/1.17 (step @p70 :rule cong :premises (@p69) :args ((not @t56))) % 0.91/1.17 (step @p71 :rule refl :args (@t4)) % 0.91/1.17 (step @p72 :rule refl :args (@t15)) % 0.91/1.17 (step @p73 :rule cong :premises (@p72 @p26) :args (@t16)) % 0.91/1.17 (step @p74 :rule cong :premises (@p73) :args (@t57)) % 0.91/1.17 (step @p75 :rule cong :premises (@p74) :args (@t58)) % 0.91/1.17 (step @p76 :rule cong :premises (@p75) :args (@t59)) % 0.91/1.17 (step @p77 :rule exists-elim :args ((= @t29 @t59))) % 0.91/1.17 (step @p78 :rule trans :premises (@p77 @p76)) % 0.91/1.17 (step @p79 :rule cong :premises (@p78) :args (@t30)) % 0.91/1.17 (step @p80 :rule cong :premises (@p79) :args (@t31)) % 0.91/1.17 (step @p81 :rule trans :premises (@p7 @p80)) % 0.91/1.17 (step @p82 :rule ho_cong :premises (@p81 @p71)) % 0.91/1.17 (step @p83 :rule ho_cong :premises (@p4 @p71)) % 0.91/1.17 (step @p84 :rule ho_cong :premises (@p83 @p57)) % 0.91/1.17 (step @p85 :rule ho_cong :premises (@p83 @p62)) % 0.91/1.17 (step @p86 :rule cong :premises (@p85 @p84) :args (@t7)) % 0.91/1.17 (step @p87 :rule nary_cong :premises (@p86 @p82) :args (@t8)) % 0.91/1.17 (step @p88 :rule cong :premises (@p87 @p54) :args (@t9)) % 0.91/1.17 (step @p89 :rule cong :premises (@p88) :args (@t11)) % 0.91/1.17 (step @p90 :rule cong :premises (@p89) :args (@t12)) % 0.91/1.17 (step @p91 :rule trans :premises (@p90 @p70)) % 0.91/1.17 (step @p92 :rule eq_resolve :premises (@p1 @p91)) % 0.91/1.17 (step @p93 :rule refl :args (@t77)) % 0.91/1.17 (step @p94 :rule bool-double-not-elim :args (@t60)) % 0.91/1.17 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((or (not @t78) @t77))) % 0.91/1.17 (step @p96 :rule refl :args (@t63)) % 0.91/1.17 (step @p97 :rule refl :args (@t67)) % 0.91/1.17 (step @p98 :rule eq-symm :args (@t70 @t73)) % 0.91/1.17 (step @p99 :rule eq-refl :args (@t72)) % 0.91/1.17 (step @p100 :rule skolem_intro :args (@t73)) % 0.91/1.17 (step @p101 :rule refl :args (@t72)) % 0.91/1.17 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t72 @t73))) % 0.91/1.17 (step @p103 :rule trans :premises (@p102 @p99)) % 0.91/1.17 (step @p104 :rule true_elim :premises (@p103)) % 0.91/1.17 (step @p105 :rule eq-refl :args (@t69)) % 0.91/1.17 (step @p106 :rule skolem_intro :args (@t70)) % 0.91/1.17 (step @p107 :rule refl :args (@t69)) % 0.91/1.17 (step @p108 :rule cong :premises (@p107 @p106) :args ((= @t69 @t70))) % 0.91/1.17 (step @p109 :rule trans :premises (@p108 @p105)) % 0.91/1.17 (step @p110 :rule true_elim :premises (@p109)) % 0.91/1.17 (step @p111 :rule cong :premises (@p110 @p104) :args (@t79)) % 0.91/1.17 (step @p112 :rule trans :premises (@p111 @p98)) % 0.91/1.17 (step @p113 :rule cong :premises (@p112) :args (@t80)) % 0.91/1.17 (step @p114 :rule nary_cong :premises (@p113 @p97 @p96) :args (@t81)) % 0.91/1.17 (step @p115 :rule cong :premises (@p114) :args (@t82)) % 0.91/1.17 (step @p116 :rule refl :args (@t78)) % 0.91/1.17 (step @p117 :rule cong :premises (@p116 @p115) :args ((=> @t78 @t82))) % 0.91/1.17 (assume-push @p193 @t78) % 0.91/1.17 (step @p119 :rule skolemize :premises (@p92)) % 0.91/1.17 (step-pop @p194 :rule scope :premises (@p119)) % 0.91/1.17 (step @p120 :rule process_scope :premises (@p194) :args (@t82)) % 0.91/1.17 (step @p122 :rule eq_resolve :premises (@p120 @p117)) % 0.91/1.17 (step @p123 :rule implies_elim :premises (@p122)) % 0.91/1.17 (step @p124 :rule eq_resolve :premises (@p123 @p95)) % 0.91/1.17 (step @p125 :rule chain_m_resolution :premises (@p124 @p92) :args (@t77 @t83 (@list @t60))) % 0.91/1.17 (step @p126 :rule bool-double-not-elim :args (@t74)) % 0.91/1.17 (step @p127 :rule refl :args (@t76)) % 0.91/1.17 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or @t76 (not @t75)))) % 0.91/1.17 (step @p129 :rule cnf_or_neg :args (@t76 0)) % 0.91/1.17 (step @p130 :rule eq_resolve :premises (@p129 @p128)) % 0.91/1.17 (step @p131 :rule reordering :premises (@p130) :args ((or @t74 @t76))) % 0.91/1.17 (step @p132 :rule chain_m_resolution :premises (@p131 @p125) :args (@t74 @t83 @t84)) % 0.91/1.17 (step @p133 :rule eq-symm :args (@t71 @t68)) % 0.91/1.17 (step @p134 :rule cong :premises (@p133) :args (@t85)) % 0.91/1.17 (step @p135 :rule refl :args (@t74)) % 0.91/1.17 (step @p136 :rule cong :premises (@p135 @p134) :args (@t86)) % 0.91/1.17 ; WARNING: add trust step for TRUST % 0.91/1.17 ; trust TRUST THEORY_LEMMA % 0.91/1.17 (step @p137 :rule trust :premises () :args (@t86)) % 0.91/1.17 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 0.91/1.17 (step @p139 :rule implies_elim :premises (@p138)) % 0.91/1.17 (step @p140 :rule chain_m_resolution :premises (@p139 @p132) :args (@t87 @t88 (@list @t74))) % 0.91/1.17 (step @p141 :rule cnf_or_neg :args (@t76 2)) % 0.91/1.17 (step @p142 :rule chain_m_resolution :premises (@p141 @p125) :args ((not @t63) @t83 @t84)) % 0.91/1.17 ; trust TRUST THEORY_LEMMA % 0.91/1.17 (step @p143 :rule trust :premises () :args ((or @t63 @t90))) % 0.91/1.17 (step @p144 :rule chain_m_resolution :premises (@p143 @p142) :args (@t90 @t83 (@list @t63))) % 0.91/1.17 (step @p145 :rule false_intro :premises (@p144)) % 0.91/1.17 (step @p146 :rule bool-double-not-elim :args (@t66)) % 0.91/1.17 (step @p147 :rule nary_cong :premises (@p127 @p146) :args ((or @t76 (not @t67)))) % 0.91/1.17 (step @p148 :rule cnf_or_neg :args (@t76 1)) % 0.91/1.17 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.91/1.17 (step @p150 :rule reordering :premises (@p149) :args ((or @t66 @t76))) % 0.91/1.17 (step @p151 :rule chain_m_resolution :premises (@p150 @p125) :args (@t66 @t83 @t84)) % 0.91/1.17 (step @p152 :rule eq-symm :args (@t89 @t65)) % 0.91/1.17 (step @p153 :rule cong :premises (@p152) :args (@t91)) % 0.91/1.17 (step @p154 :rule cong :premises (@p153) :args (@t92)) % 0.91/1.17 (step @p155 :rule cong :premises (@p154) :args (@t93)) % 0.91/1.17 (step @p156 :rule refl :args (@t66)) % 0.91/1.17 (step @p157 :rule cong :premises (@p156 @p155) :args ((=> @t66 @t93))) % 0.91/1.17 (assume-push @p195 @t66) % 0.91/1.17 (step @p159 :rule instantiate :premises (@p151) :args ((@list @t89))) % 0.91/1.17 (step-pop @p196 :rule scope :premises (@p159)) % 0.91/1.17 (step @p160 :rule process_scope :premises (@p196) :args (@t93)) % 0.91/1.17 (step @p162 :rule eq_resolve :premises (@p160 @p157)) % 0.91/1.17 (step @p163 :rule implies_elim :premises (@p162)) % 0.91/1.17 (step @p164 :rule chain_m_resolution :premises (@p163 @p151) :args (@t95 @t88 (@list @t66))) % 0.91/1.17 (step @p165 :rule refl :args (@t98)) % 0.91/1.17 (step @p166 :rule bool-double-not-elim :args (@t94)) % 0.91/1.17 (step @p167 :rule nary_cong :premises (@p166 @p165) :args ((or (not @t95) @t98))) % 0.91/1.17 (step @p168 :rule eq-symm :args (@t97 @t89)) % 0.91/1.17 (step @p169 :rule bool-double-not-elim :args (@t99)) % 0.91/1.17 (step @p170 :rule trans :premises (@p169 @p168)) % 0.91/1.17 (step @p171 :rule refl :args (@t95)) % 0.91/1.17 (step @p172 :rule cong :premises (@p171 @p170) :args ((=> @t95 @t100))) % 0.91/1.17 (assume-push @p197 @t95) % 0.91/1.17 (step @p174 :rule skolemize :premises (@p164)) % 0.91/1.17 (step-pop @p198 :rule scope :premises (@p174)) % 0.91/1.17 (step @p175 :rule process_scope :premises (@p198) :args (@t100)) % 0.91/1.17 (step @p177 :rule eq_resolve :premises (@p175 @p172)) % 0.91/1.17 (step @p178 :rule implies_elim :premises (@p177)) % 0.91/1.17 (step @p179 :rule eq_resolve :premises (@p178 @p167)) % 0.91/1.17 (step @p180 :rule chain_m_resolution :premises (@p179 @p164) :args (@t98 @t83 (@list @t94))) % 0.91/1.17 (step @p181 :rule symm :premises (@p180)) % 0.91/1.17 (step @p182 :rule cong :premises (@p181) :args (@t101)) % 0.91/1.17 (step @p183 :rule cong :premises (@p181) :args (@t102)) % 0.91/1.17 (step @p184 :rule cong :premises (@p183 @p182) :args (@t103)) % 0.91/1.17 (step @p185 :rule trans :premises (@p184 @p145)) % 0.91/1.17 (step @p186 :rule false_elim :premises (@p185)) % 0.91/1.17 (assume-push @p199 @t87) % 0.91/1.17 (step @p188 :rule instantiate :premises (@p140) :args ((@list @t96))) % 0.91/1.17 (step-pop @p200 :rule scope :premises (@p188)) % 0.91/1.17 (step @p189 :rule process_scope :premises (@p200) :args (@t103)) % 0.91/1.17 (step @p191 :rule implies_elim :premises (@p189)) % 0.91/1.17 (step @p192 false :rule chain_m_resolution :premises (@p191 @p186 @p140) :args (false (@list true false) (@list @t103 @t87))) % 0.91/1.17 ) % 0.91/1.17 % SZS output end Proof % 0.91/1.17 % cvc5 exiting %------------------------------------------------------------------------------