%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO902^8 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n022.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 09:13:45 AM UTC 2026 % Result : Theorem 0.44s 0.69s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO902^8 : TPTP v9.2.1. Released v8.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n022.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 : Wed Jun 3 01:09:08 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.49 %----Proving TH0 % 0.44/0.69 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.69 % SZS status Theorem % 0.44/0.69 % SZS output start Proof % 0.44/0.69 ( % 0.44/0.69 (declare-sort tptp.mworld 0) % 0.44/0.69 (declare-const tptp.mactual tptp.mworld) % 0.44/0.69 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.44/0.69 (declare-const tptp.p (-> tptp.mworld Bool)) % 0.44/0.69 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.44/0.69 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.44/0.69 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.69 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.69 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.69 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.69 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.44/0.69 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.44/0.69 (define @t1 () (@var "W" tptp.mworld)) % 0.44/0.69 (define @t2 () (_ tptp.mrel @t1)) % 0.44/0.69 (define @t3 () (_ @t2 @t1)) % 0.44/0.69 (define @t4 () (@list @t1)) % 0.44/0.69 (define @t5 () (forall @t4 @t3)) % 0.44/0.69 (define @t6 () (_ tptp.mdia tptp.p)) % 0.44/0.69 (define @t7 () (not (_ tptp.mlocal (_ (_ tptp.mimplies (_ tptp.mdia (_ tptp.mbox @t6))) (_ tptp.mdia @t6))))) % 0.44/0.69 (define @t8 () (@var "Phi" (-> tptp.mworld Bool))) % 0.44/0.69 (define @t9 () (lambda (@list @t8) (_ @t8 tptp.mactual))) % 0.44/0.69 (define @t10 () (@var "A" (-> tptp.mworld Bool))) % 0.44/0.69 (define @t11 () (_ @t10 @t1)) % 0.44/0.69 (define @t12 () (lambda (@list @t10 @t1) (not @t11))) % 0.44/0.69 (define @t13 () (@var "B" (-> tptp.mworld Bool))) % 0.44/0.69 (define @t14 () (_ @t13 @t1)) % 0.44/0.69 (define @t15 () (@list @t10 @t13 @t1)) % 0.44/0.69 (define @t16 () (lambda @t15 (and @t11 @t14))) % 0.44/0.69 (define @t17 () (lambda @t15 (or @t11 @t14))) % 0.44/0.69 (define @t18 () (lambda @t15 (=> @t11 @t14))) % 0.44/0.69 (define @t19 () (lambda @t15 (= @t11 @t14))) % 0.44/0.69 (define @t20 () (@var "V" tptp.mworld)) % 0.44/0.69 (define @t21 () (_ @t8 @t20)) % 0.44/0.69 (define @t22 () (_ @t2 @t20)) % 0.44/0.69 (define @t23 () (@list @t20)) % 0.44/0.69 (define @t24 () (forall @t23 (=> @t22 @t21))) % 0.44/0.69 (define @t25 () (@list @t8 @t1)) % 0.44/0.69 (define @t26 () (lambda @t25 @t24)) % 0.44/0.69 (define @t27 () (and @t22 @t21)) % 0.44/0.69 (define @t28 () (exists @t23 @t27)) % 0.44/0.69 (define @t29 () (lambda @t25 @t28)) % 0.44/0.69 (define @t30 () (@var "BOUND_VARIABLE_7624" tptp.mworld)) % 0.44/0.69 (define @t31 () (not (tptp.p @t30))) % 0.44/0.69 (define @t32 () (not (tptp.mrel @t20 @t30))) % 0.44/0.69 (define @t33 () (not (tptp.mrel tptp.mactual @t20))) % 0.44/0.69 (define @t34 () (@list @t20 @t30)) % 0.44/0.69 (define @t35 () (forall @t34 (or @t33 @t32 @t31))) % 0.44/0.69 (define @t36 () (@var "BOUND_VARIABLE_7558" tptp.mworld)) % 0.44/0.69 (define @t37 () (not (tptp.p @t36))) % 0.44/0.69 (define @t38 () (@var "BOUND_VARIABLE_7585" tptp.mworld)) % 0.44/0.69 (define @t39 () (@list @t36)) % 0.44/0.69 (define @t40 () (not (forall @t39 (or (not (tptp.mrel @t38 @t36)) @t37)))) % 0.44/0.69 (define @t41 () (@list @t38)) % 0.44/0.69 (define @t42 () (forall @t41 (or (not (tptp.mrel @t20 @t38)) @t40))) % 0.44/0.69 (define @t43 () (not @t42)) % 0.44/0.69 (define @t44 () (forall @t23 (or @t33 @t43))) % 0.44/0.69 (define @t45 () (tptp.mrel @t1 @t20)) % 0.44/0.69 (define @t46 () (not @t45)) % 0.44/0.69 (define @t47 () (or @t46 @t32 @t31)) % 0.44/0.69 (define @t48 () (not (forall @t34 @t47))) % 0.44/0.69 (define @t49 () (not (forall @t23 (or @t46 @t43)))) % 0.44/0.69 (define @t50 () (lambda @t4 (=> @t49 @t48))) % 0.44/0.69 (define @t51 () (_ @t50 tptp.mactual)) % 0.44/0.69 (define @t52 () (lambda @t4 @t48)) % 0.44/0.69 (define @t53 () (_ @t52 @t1)) % 0.44/0.69 (define @t54 () (=> @t49 @t53)) % 0.44/0.69 (define @t55 () (lambda @t4 @t54)) % 0.44/0.69 (define @t56 () (@list @t13 @t1)) % 0.44/0.69 (define @t57 () (or @t32 @t31)) % 0.44/0.69 (define @t58 () (or @t46 @t57)) % 0.44/0.69 (define @t59 () (forall @t34 @t58)) % 0.44/0.69 (define @t60 () (@list @t30)) % 0.44/0.69 (define @t61 () (forall @t60 @t58)) % 0.44/0.69 (define @t62 () (forall @t60 @t57)) % 0.44/0.69 (define @t63 () (@list @t36)) % 0.44/0.69 (define @t64 () (or @t46 @t62)) % 0.44/0.69 (define @t65 () (forall @t39 (or (not (tptp.mrel @t20 @t36)) @t37))) % 0.44/0.69 (define @t66 () (not @t65)) % 0.44/0.69 (define @t67 () (forall @t23 (or @t46 (not (tptp.p @t20))))) % 0.44/0.69 (define @t68 () (@list @t20)) % 0.44/0.69 (define @t69 () (not @t67)) % 0.44/0.69 (define @t70 () (lambda @t4 @t69)) % 0.44/0.69 (define @t71 () (_ @t70 @t20)) % 0.44/0.69 (define @t72 () (not @t71)) % 0.44/0.69 (define @t73 () (or @t46 @t72)) % 0.44/0.69 (define @t74 () (forall @t23 @t73)) % 0.44/0.69 (define @t75 () (not @t74)) % 0.44/0.69 (define @t76 () (lambda @t4 @t75)) % 0.44/0.69 (define @t77 () (_ @t8 @t20)) % 0.44/0.69 (define @t78 () (lambda @t25 (not (forall @t23 (or @t46 (not @t77)))))) % 0.44/0.69 (define @t79 () (_ @t78 tptp.p)) % 0.44/0.69 (define @t80 () (lambda @t4 @t49)) % 0.44/0.69 (define @t81 () (_ @t80 @t1)) % 0.44/0.69 (define @t82 () (=> @t81 @t14)) % 0.44/0.69 (define @t83 () (lambda @t56 @t82)) % 0.44/0.69 (define @t84 () (forall @t23 (or @t46 @t66))) % 0.44/0.69 (define @t85 () (lambda @t4 @t84)) % 0.44/0.69 (define @t86 () (not (_ @t85 @t20))) % 0.44/0.69 (define @t87 () (or @t46 @t86)) % 0.44/0.69 (define @t88 () (forall @t23 @t87)) % 0.44/0.69 (define @t89 () (not @t88)) % 0.44/0.69 (define @t90 () (lambda @t4 @t89)) % 0.44/0.69 (define @t91 () (or @t46 @t71)) % 0.44/0.69 (define @t92 () (forall @t23 @t91)) % 0.44/0.69 (define @t93 () (lambda @t4 @t92)) % 0.44/0.69 (define @t94 () (lambda @t25 (forall @t23 (or @t46 @t77)))) % 0.44/0.69 (define @t95 () (not @t21)) % 0.44/0.69 (define @t96 () (not @t22)) % 0.44/0.69 (define @t97 () (or @t96 @t95)) % 0.44/0.69 (define @t98 () (forall @t23 (not @t27))) % 0.44/0.69 (define @t99 () (not @t98)) % 0.44/0.69 (define @t100 () (or @t96 @t21)) % 0.44/0.69 (define @t101 () (@quantifiers_skolemize @t44 0)) % 0.44/0.69 (define @t102 () (forall @t41 (or (not (tptp.mrel @t101 @t38)) @t40))) % 0.44/0.69 (define @t103 () (not @t102)) % 0.44/0.69 (define @t104 () (tptp.mrel tptp.mactual @t101)) % 0.44/0.69 (define @t105 () (not @t104)) % 0.44/0.69 (define @t106 () (or @t105 @t103)) % 0.44/0.69 (define @t107 () (@list true)) % 0.44/0.69 (define @t108 () (@list @t106)) % 0.44/0.69 (define @t109 () (@list @t101)) % 0.44/0.69 (define @t110 () (tptp.mrel @t1 @t1)) % 0.44/0.69 (define @t111 () (forall @t39 (or (not (tptp.mrel @t101 @t36)) @t37))) % 0.44/0.69 (define @t112 () (not @t111)) % 0.44/0.69 (define @t113 () (tptp.mrel @t101 @t101)) % 0.44/0.69 (define @t114 () (not @t113)) % 0.44/0.69 (define @t115 () (or @t114 @t112)) % 0.44/0.69 (define @t116 () (@quantifiers_skolemize @t111 0)) % 0.44/0.69 (define @t117 () (tptp.p @t116)) % 0.44/0.69 (define @t118 () (not @t117)) % 0.44/0.69 (define @t119 () (tptp.mrel @t101 @t116)) % 0.44/0.69 (define @t120 () (not @t119)) % 0.44/0.69 (define @t121 () (or @t120 @t118)) % 0.44/0.69 (define @t122 () (@list @t121)) % 0.44/0.69 (define @t123 () (or @t105 @t120 @t118)) % 0.44/0.69 (define @t124 () (not @t123)) % 0.44/0.69 (assume @p1 @t5) % 0.44/0.69 (assume @p2 @t7) % 0.44/0.69 (assume @p3 true) % 0.44/0.69 (step @p4 (= tptp.mlocal @t9) :rule refl :args (@t9)) % 0.44/0.69 (step @p5 (= tptp.mnot @t12) :rule refl :args (@t12)) % 0.44/0.69 (step @p6 (= tptp.mand @t16) :rule refl :args (@t16)) % 0.44/0.69 (step @p7 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.44/0.69 (step @p8 (= tptp.mimplies @t18) :rule refl :args (@t18)) % 0.44/0.69 (step @p9 (= tptp.mequiv @t19) :rule refl :args (@t19)) % 0.44/0.69 (step @p10 (= tptp.mbox @t26) :rule refl :args (@t26)) % 0.44/0.69 (step @p11 (= tptp.mdia @t29) :rule refl :args (@t29)) % 0.44/0.69 (step @p12 :rule beta-reduce :args ((= @t51 (=> (not @t44) (not @t35))))) % 0.44/0.69 (step @p13 :rule beta-reduce :args ((= (_ @t9 @t50) @t51))) % 0.44/0.69 (step @p14 :rule trans :premises (@p13 @p12)) % 0.44/0.69 (step @p15 :rule beta-reduce :args ((= @t53 @t48))) % 0.44/0.69 (step @p16 :rule refl :args (@t49)) % 0.44/0.69 (step @p17 :rule cong :premises (@p16 @p15) :args (@t54)) % 0.44/0.69 (step @p18 :rule cong :premises (@p17) :args (@t55)) % 0.44/0.69 (step @p19 :rule beta-reduce :args ((= (_ (lambda @t56 (=> @t49 @t14)) @t52) @t55))) % 0.44/0.69 (step @p20 :rule trans :premises (@p19 @p18)) % 0.44/0.69 (step @p21 :rule aci_norm :args ((= @t58 @t47))) % 0.44/0.69 (step @p22 :rule cong :premises (@p21) :args (@t59)) % 0.44/0.69 (step @p23 :rule quant-merge-prenex :args ((= (forall @t23 @t61) @t59))) % 0.44/0.69 (step @p24 :rule alpha_equiv :args (@t62 (@list @t30) @t63)) % 0.44/0.69 (step @p25 :rule refl :args (@t46)) % 0.44/0.69 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t64)) % 0.44/0.69 (step @p27 :rule quant-miniscope-or :args ((= @t61 @t64))) % 0.44/0.69 (step @p28 :rule trans :premises (@p27 @p26)) % 0.44/0.69 (step @p29 :rule symm :premises (@p28)) % 0.44/0.69 (step @p30 :rule cong :premises (@p29) :args ((forall @t23 (or @t46 @t65)))) % 0.44/0.69 (step @p31 :rule trans :premises (@p30 @p23)) % 0.44/0.69 (step @p32 :rule trans :premises (@p31 @p22)) % 0.44/0.69 (step @p33 :rule bool-double-not-elim :args (@t65)) % 0.44/0.69 (step @p34 :rule beta-reduce :args ((= (_ (lambda @t4 (not (forall @t39 (or (not (tptp.mrel @t1 @t36)) @t37)))) @t20) @t66))) % 0.44/0.69 (step @p35 :rule refl :args (@t20)) % 0.44/0.69 (step @p36 :rule alpha_equiv :args (@t67 @t68 @t63)) % 0.44/0.69 (step @p37 :rule cong :premises (@p36) :args (@t69)) % 0.44/0.69 (step @p38 :rule cong :premises (@p37) :args (@t70)) % 0.44/0.69 (step @p39 :rule ho_cong :premises (@p38 @p35)) % 0.44/0.69 (step @p40 :rule trans :premises (@p39 @p34)) % 0.44/0.69 (step @p41 :rule cong :premises (@p40) :args (@t72)) % 0.44/0.69 (step @p42 :rule trans :premises (@p41 @p33)) % 0.44/0.69 (step @p43 :rule refl :args (@t46)) % 0.44/0.69 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t73)) % 0.44/0.69 (step @p45 :rule cong :premises (@p44) :args (@t74)) % 0.44/0.69 (step @p46 :rule trans :premises (@p45 @p32)) % 0.44/0.69 (step @p47 :rule cong :premises (@p46) :args (@t75)) % 0.44/0.69 (step @p48 :rule cong :premises (@p47) :args (@t76)) % 0.44/0.69 (step @p49 :rule beta-reduce :args ((= (_ @t78 @t70) @t76))) % 0.44/0.69 (step @p50 :rule trans :premises (@p49 @p48)) % 0.44/0.69 (step @p51 :rule beta-reduce :args ((= @t79 @t70))) % 0.44/0.69 (step @p52 :rule refl :args (@t78)) % 0.44/0.69 (step @p53 :rule ho_cong :premises (@p52 @p51)) % 0.44/0.69 (step @p54 :rule trans :premises (@p53 @p50)) % 0.44/0.69 (step @p55 :rule refl :args (@t14)) % 0.44/0.69 (step @p56 :rule beta-reduce :args ((= @t81 @t49))) % 0.44/0.69 (step @p57 :rule cong :premises (@p56 @p55) :args (@t82)) % 0.44/0.69 (step @p58 :rule cong :premises (@p57) :args (@t83)) % 0.44/0.69 (step @p59 :rule beta-reduce :args ((= (_ @t18 @t80) @t83))) % 0.44/0.69 (step @p60 :rule trans :premises (@p59 @p58)) % 0.44/0.69 (step @p61 :rule beta-reduce :args ((= (_ (lambda @t4 (forall @t41 (or (not (tptp.mrel @t1 @t38)) @t40))) @t20) @t42))) % 0.44/0.69 (step @p62 :rule alpha_equiv :args (@t84 @t68 (@list @t38))) % 0.44/0.69 (step @p63 :rule cong :premises (@p62) :args (@t85)) % 0.44/0.69 (step @p64 :rule ho_cong :premises (@p63 @p35)) % 0.44/0.69 (step @p65 :rule trans :premises (@p64 @p61)) % 0.44/0.69 (step @p66 :rule cong :premises (@p65) :args (@t86)) % 0.44/0.69 (step @p67 :rule nary_cong :premises (@p43 @p66) :args (@t87)) % 0.44/0.69 (step @p68 :rule cong :premises (@p67) :args (@t88)) % 0.44/0.69 (step @p69 :rule cong :premises (@p68) :args (@t89)) % 0.44/0.69 (step @p70 :rule cong :premises (@p69) :args (@t90)) % 0.44/0.69 (step @p71 :rule beta-reduce :args ((= (_ @t78 @t85) @t90))) % 0.44/0.69 (step @p72 :rule trans :premises (@p71 @p70)) % 0.44/0.69 (step @p73 :rule nary_cong :premises (@p43 @p40) :args (@t91)) % 0.44/0.69 (step @p74 :rule cong :premises (@p73) :args (@t92)) % 0.44/0.69 (step @p75 :rule cong :premises (@p74) :args (@t93)) % 0.44/0.69 (step @p76 :rule beta-reduce :args ((= (_ @t94 @t70) @t93))) % 0.44/0.69 (step @p77 :rule trans :premises (@p76 @p75)) % 0.44/0.69 (step @p78 :rule refl :args (@t94)) % 0.44/0.69 (step @p79 :rule ho_cong :premises (@p78 @p51)) % 0.44/0.69 (step @p80 :rule trans :premises (@p79 @p77)) % 0.44/0.69 (step @p81 :rule ho_cong :premises (@p52 @p80)) % 0.44/0.69 (step @p82 :rule trans :premises (@p81 @p72)) % 0.44/0.69 (step @p83 :rule refl :args (@t18)) % 0.44/0.69 (step @p84 :rule ho_cong :premises (@p83 @p82)) % 0.44/0.69 (step @p85 :rule trans :premises (@p84 @p60)) % 0.44/0.69 (step @p86 :rule ho_cong :premises (@p85 @p54)) % 0.44/0.69 (step @p87 :rule trans :premises (@p86 @p20)) % 0.44/0.69 (step @p88 :rule refl :args (@t9)) % 0.44/0.69 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.44/0.69 (step @p90 :rule trans :premises (@p89 @p14)) % 0.44/0.69 (step @p91 :rule cong :premises (@p90) :args ((not (_ @t9 (_ (_ @t18 (_ @t78 (_ @t94 @t79))) (_ @t78 @t79)))))) % 0.44/0.69 (step @p92 :rule refl :args (tptp.p)) % 0.44/0.69 (step @p93 :rule refl :args (@t77)) % 0.44/0.69 (step @p94 :rule refl :args (@t21)) % 0.44/0.69 (step @p95 :rule cong :premises (@p94 @p93) :args ((= @t21 @t77))) % 0.44/0.69 (step @p96 :rule symm :premises (@p95)) % 0.44/0.69 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 0.44/0.69 (step @p98 :rule cong :premises (@p97) :args (@t95)) % 0.44/0.69 (step @p99 :rule refl :args (@t45)) % 0.44/0.69 (step @p100 :rule refl :args (@t22)) % 0.44/0.69 (step @p101 :rule cong :premises (@p100 @p99) :args ((= @t22 @t45))) % 0.44/0.69 (step @p102 :rule symm :premises (@p101)) % 0.44/0.69 (step @p103 :rule eq_resolve :premises (@p100 @p102)) % 0.44/0.69 (step @p104 :rule cong :premises (@p103) :args (@t96)) % 0.44/0.69 (step @p105 :rule nary_cong :premises (@p104 @p98) :args (@t97)) % 0.44/0.69 (step @p106 :rule cong :premises (@p105) :args ((forall @t23 @t97))) % 0.44/0.69 (step @p107 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.44/0.69 (step @p108 :rule cong :premises (@p107) :args (@t98)) % 0.44/0.69 (step @p109 :rule trans :premises (@p108 @p106)) % 0.44/0.69 (step @p110 :rule cong :premises (@p109) :args (@t99)) % 0.44/0.69 (step @p111 :rule exists-elim :args ((= @t28 @t99))) % 0.44/0.69 (step @p112 :rule trans :premises (@p111 @p110)) % 0.44/0.69 (step @p113 :rule cong :premises (@p112) :args (@t29)) % 0.44/0.69 (step @p114 :rule trans :premises (@p11 @p113)) % 0.44/0.69 (step @p115 :rule ho_cong :premises (@p114 @p92)) % 0.44/0.69 (step @p116 :rule ho_cong :premises (@p114 @p115)) % 0.44/0.69 (step @p117 :rule nary_cong :premises (@p104 @p97) :args (@t100)) % 0.44/0.69 (step @p118 :rule cong :premises (@p117) :args ((forall @t23 @t100))) % 0.44/0.69 (step @p119 :rule bool-impl-elim :args (@t22 @t21)) % 0.44/0.69 (step @p120 :rule cong :premises (@p119) :args (@t24)) % 0.44/0.69 (step @p121 :rule trans :premises (@p120 @p118)) % 0.44/0.69 (step @p122 :rule cong :premises (@p121) :args (@t26)) % 0.44/0.69 (step @p123 :rule trans :premises (@p10 @p122)) % 0.44/0.69 (step @p124 :rule ho_cong :premises (@p123 @p115)) % 0.44/0.69 (step @p125 :rule ho_cong :premises (@p114 @p124)) % 0.44/0.69 (step @p126 :rule ho_cong :premises (@p8 @p125)) % 0.44/0.69 (step @p127 :rule ho_cong :premises (@p126 @p116)) % 0.44/0.69 (step @p128 :rule ho_cong :premises (@p4 @p127)) % 0.44/0.69 (step @p129 :rule cong :premises (@p128) :args (@t7)) % 0.44/0.69 (step @p130 :rule trans :premises (@p129 @p91)) % 0.44/0.69 (step @p131 :rule eq_resolve :premises (@p2 @p130)) % 0.44/0.69 (step @p132 :rule not_implies_elim2 :premises (@p131)) % 0.44/0.69 (step @p133 :rule not_not_elim :premises (@p132)) % 0.44/0.69 (step @p134 :rule not_implies_elim1 :premises (@p131)) % 0.44/0.69 (step @p135 :rule skolemize :premises (@p134)) % 0.44/0.69 (step @p136 :rule bool-double-not-elim :args (@t102)) % 0.44/0.69 (step @p137 :rule refl :args (@t106)) % 0.44/0.69 (step @p138 :rule nary_cong :premises (@p137 @p136) :args ((or @t106 (not @t103)))) % 0.44/0.69 (step @p139 :rule cnf_or_neg :args (@t106 1)) % 0.44/0.69 (step @p140 :rule eq_resolve :premises (@p139 @p138)) % 0.44/0.69 (step @p141 :rule reordering :premises (@p140) :args ((or @t102 @t106))) % 0.44/0.69 (step @p142 :rule chain_m_resolution :premises (@p141 @p135) :args (@t102 @t107 @t108)) % 0.44/0.69 (step @p143 :rule instantiate :premises (@p142) :args (@t109)) % 0.44/0.69 (step @p144 :rule refl :args (@t110)) % 0.44/0.69 (step @p145 :rule refl :args (@t3)) % 0.44/0.69 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t3 @t110))) % 0.44/0.69 (step @p147 :rule symm :premises (@p146)) % 0.44/0.69 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.44/0.69 (step @p149 :rule cong :premises (@p148) :args (@t5)) % 0.44/0.69 (step @p150 :rule eq_resolve :premises (@p1 @p149)) % 0.44/0.69 (step @p151 :rule instantiate :premises (@p150) :args (@t109)) % 0.44/0.69 (step @p152 :rule cnf_or_pos :args (@t115)) % 0.44/0.69 (step @p153 :rule reordering :premises (@p152) :args ((or @t114 @t112 (not @t115)))) % 0.44/0.69 (step @p154 :rule chain_m_resolution :premises (@p153 @p151 @p143) :args (@t112 (@list false false) (@list @t113 @t115))) % 0.44/0.69 (step @p155 :rule skolemize :premises (@p154)) % 0.44/0.69 (step @p156 :rule bool-double-not-elim :args (@t117)) % 0.44/0.69 (step @p157 :rule refl :args (@t121)) % 0.44/0.69 (step @p158 :rule nary_cong :premises (@p157 @p156) :args ((or @t121 (not @t118)))) % 0.44/0.69 (step @p159 :rule cnf_or_neg :args (@t121 1)) % 0.44/0.69 (step @p160 :rule eq_resolve :premises (@p159 @p158)) % 0.44/0.69 (step @p161 :rule reordering :premises (@p160) :args ((or @t117 @t121))) % 0.44/0.69 (step @p162 :rule chain_m_resolution :premises (@p161 @p155) :args (@t117 @t107 @t122)) % 0.44/0.69 (step @p163 :rule bool-double-not-elim :args (@t119)) % 0.44/0.69 (step @p164 :rule nary_cong :premises (@p157 @p163) :args ((or @t121 (not @t120)))) % 0.44/0.69 (step @p165 :rule cnf_or_neg :args (@t121 0)) % 0.44/0.69 (step @p166 :rule eq_resolve :premises (@p165 @p164)) % 0.44/0.69 (step @p167 :rule reordering :premises (@p166) :args ((or @t119 @t121))) % 0.44/0.69 (step @p168 :rule chain_m_resolution :premises (@p167 @p155) :args (@t119 @t107 @t122)) % 0.44/0.69 (step @p169 :rule bool-double-not-elim :args (@t104)) % 0.44/0.69 (step @p170 :rule nary_cong :premises (@p137 @p169) :args ((or @t106 (not @t105)))) % 0.44/0.69 (step @p171 :rule cnf_or_neg :args (@t106 0)) % 0.44/0.69 (step @p172 :rule eq_resolve :premises (@p171 @p170)) % 0.44/0.69 (step @p173 :rule reordering :premises (@p172) :args ((or @t104 @t106))) % 0.44/0.69 (step @p174 :rule chain_m_resolution :premises (@p173 @p135) :args (@t104 @t107 @t108)) % 0.44/0.69 (step @p175 :rule cnf_or_pos :args (@t123)) % 0.44/0.69 (step @p176 :rule reordering :premises (@p175) :args ((or @t105 @t120 @t118 @t124))) % 0.44/0.69 (step @p177 :rule chain_m_resolution :premises (@p176 @p174 @p168 @p162) :args (@t124 (@list false false false) (@list @t104 @t119 @t117))) % 0.44/0.69 (assume-push @p184 @t35) % 0.44/0.69 (step @p179 :rule instantiate :premises (@p133) :args ((@list @t101 @t116))) % 0.44/0.69 (step-pop @p185 :rule scope :premises (@p179)) % 0.44/0.69 (step @p180 :rule process_scope :premises (@p185) :args (@t123)) % 0.44/0.69 (step @p182 :rule implies_elim :premises (@p180)) % 0.44/0.69 (step @p183 false :rule chain_m_resolution :premises (@p182 @p177 @p133) :args (false (@list true false) (@list @t123 @t35))) % 0.44/0.69 ) % 0.44/0.69 % SZS output end Proof % 0.44/0.69 % cvc5 exiting %------------------------------------------------------------------------------