%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO543^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 09:13:05 AM UTC 2026 % Result : Theorem 150.68s 150.94s % Output : Proof 150.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO543^1 : TPTP v9.2.1. Released v5.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.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 00:20:07 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TH0 % 150.68/150.94 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 150.68/150.94 --- 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... % 150.68/150.94 --- 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... % 150.68/150.94 --- Run --ho-elim --full-saturate-quant at 18s... % 150.68/150.94 % SZS status Theorem % 150.68/150.94 % SZS output start Proof % 150.68/150.94 ( % 150.68/150.94 (declare-sort $$unsorted 0) % 150.68/150.94 (declare-const tptp.epsii (-> (-> (-> $$unsorted $$unsorted) Bool) $$unsorted $$unsorted)) % 150.68/150.94 (define tptp.if () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Z" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "B" Bool))) (let ((_let_5 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_4 _let_5 _let_2 _let_1) (_ (_ tptp.epsii (lambda (@list _let_3) (or (and _let_4 (= _let_3 _let_5)) (and (not _let_4) (= _let_3 _let_2))))) _let_1)))))))) % 150.68/150.94 (define @t1 () (@var "P" (-> (-> $$unsorted $$unsorted) Bool))) % 150.68/150.94 (define @t2 () (_ tptp.epsii @t1)) % 150.68/150.94 (define @t3 () (_ @t1 @t2)) % 150.68/150.94 (define @t4 () (@var "X" (-> $$unsorted $$unsorted))) % 150.68/150.94 (define @t5 () (_ @t1 @t4)) % 150.68/150.94 (define @t6 () (@list @t4)) % 150.68/150.94 (define @t7 () (exists @t6 @t5)) % 150.68/150.94 (define @t8 () (=> @t7 @t3)) % 150.68/150.94 (define @t9 () (@list @t1)) % 150.68/150.94 (define @t10 () (forall @t9 @t8)) % 150.68/150.94 (define @t11 () (@var "B" Bool)) % 150.68/150.94 (define @t12 () (= (_ (_ (_ tptp.if @t11) @t4) @t4) @t4)) % 150.68/150.94 (define @t13 () (@list @t11 @t4)) % 150.68/150.94 (define @t14 () (forall @t13 @t12)) % 150.68/150.94 (define @t15 () (not @t14)) % 150.68/150.94 (define @t16 () (@var "__flatten_var_0" $$unsorted)) % 150.68/150.94 (define @t17 () (@var "Y" (-> $$unsorted $$unsorted))) % 150.68/150.94 (define @t18 () (@var "Z" (-> $$unsorted $$unsorted))) % 150.68/150.94 (define @t19 () (not @t11)) % 150.68/150.94 (define @t20 () (and @t19 (= @t18 @t17))) % 150.68/150.94 (define @t21 () (and @t11 (= @t18 @t4))) % 150.68/150.94 (define @t22 () (or @t21 @t20)) % 150.68/150.94 (define @t23 () (@list @t18)) % 150.68/150.94 (define @t24 () (lambda @t23 @t22)) % 150.68/150.94 (define @t25 () (@list @t11 @t4 @t17 @t16)) % 150.68/150.94 (define @t26 () (lambda @t25 (_ (_ tptp.epsii @t24) @t16))) % 150.68/150.94 (define @t27 () (@var "BOUND_VARIABLE_7659" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 150.68/150.94 (define @t28 () (@var "BOUND_VARIABLE_7658" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 150.68/150.94 (define @t29 () (@var "BOUND_VARIABLE_7568" Bool)) % 150.68/150.94 (define @t30 () (not @t29)) % 150.68/150.94 (define @t31 () (= @t27 @t28)) % 150.68/150.94 (define @t32 () (and @t30 @t31)) % 150.68/150.94 (define @t33 () (and @t29 @t31)) % 150.68/150.94 (define @t34 () (or @t33 @t32)) % 150.68/150.94 (define @t35 () (@const 0 (@ho-elim-sort (-> Bool (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)))) % 150.68/150.94 (define @t36 () (@const 1 (-> (@ho-elim-sort (-> Bool (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) Bool (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool))))) % 150.68/150.94 (define @t37 () (@const 2 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool))))) % 150.68/150.94 (define @t38 () (@const 3 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool))) % 150.68/150.94 (define @t39 () (_ @t38 (_ @t37 (_ @t36 @t35 @t29) @t27) @t28)) % 150.68/150.94 (define @t40 () (@list @t29 @t27 @t28)) % 150.68/150.94 (define @t41 () (forall @t40 (= @t34 @t39))) % 150.68/150.94 (define @t42 () (@var "BOUND_VARIABLE_7570" (-> $$unsorted $$unsorted))) % 150.68/150.94 (define @t43 () (@var "BOUND_VARIABLE_7569" (-> $$unsorted $$unsorted))) % 150.68/150.94 (define @t44 () (@const 4 (-> Bool (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted) Bool))) % 150.68/150.94 (define @t45 () (= @t43 @t42)) % 150.68/150.94 (define @t46 () (forall (@list @t29 @t43 @t42) (= (or (and @t29 @t45) (and @t30 @t45)) (_ @t44 @t29 @t43 @t42)))) % 150.68/150.94 (define @t47 () (@var "BOUND_VARIABLE_7608" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 150.68/150.94 (define @t48 () (@const 5 (@ho-elim-sort (-> Bool (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted)))) % 150.68/150.94 (define @t49 () (@const 6 (-> (@ho-elim-sort (-> Bool (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted)) Bool (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted))))) % 150.68/150.94 (define @t50 () (@const 7 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted))))) % 150.68/150.94 (define @t51 () (forall (@list @t11 @t47) (= @t47 (_ @t50 (_ @t49 @t48 @t11) @t47)))) % 150.68/150.94 (define @t52 () (@quantifiers_skolemize @t51 0)) % 150.68/150.94 (define @t53 () (@purify @t52)) % 150.68/150.94 (define @t54 () (not @t53)) % 150.68/150.94 (define @t55 () (@quantifiers_skolemize @t51 1)) % 150.68/150.94 (define @t56 () (= @t55 @t55)) % 150.68/150.94 (define @t57 () (and @t54 @t56)) % 150.68/150.94 (define @t58 () (and @t53 @t56)) % 150.68/150.94 (define @t59 () (or @t58 @t57)) % 150.68/150.94 (define @t60 () (_ @t37 (_ @t36 @t35 @t53) @t55)) % 150.68/150.94 (define @t61 () (_ @t38 @t60 @t55)) % 150.68/150.94 (define @t62 () (= @t61 @t59)) % 150.68/150.94 (define @t63 () (= @t28 @t27)) % 150.68/150.94 (define @t64 () (forall @t40 (= @t39 (or (and @t29 @t63) (and @t30 @t63))))) % 150.68/150.94 (define @t65 () (or @t53 @t54)) % 150.68/150.94 (define @t66 () (= @t61 @t65)) % 150.68/150.94 (define @t67 () (@list false)) % 150.68/150.94 (define @t68 () (@list @t64)) % 150.68/150.94 (define @t69 () (@var "BOUND_VARIABLE_7587" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)))) % 150.68/150.94 (define @t70 () (@const 8 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) $$unsorted $$unsorted)))) % 150.68/150.94 (define @t71 () (@const 9 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) $$unsorted $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) (@ho-elim-sort (-> $$unsorted $$unsorted))))) % 150.68/150.94 (define @t72 () (@var "BOUND_VARIABLE_7598" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 150.68/150.94 (define @t73 () (_ @t1 @t2)) % 150.68/150.94 (define @t74 () (@var "BOUND_VARIABLE_7479" (-> $$unsorted $$unsorted))) % 150.68/150.94 (define @t75 () (not (_ @t1 @t74))) % 150.68/150.94 (define @t76 () (or @t75 @t73)) % 150.68/150.94 (define @t77 () (forall (@list @t1 @t74) @t76)) % 150.68/150.94 (define @t78 () (@list @t74)) % 150.68/150.94 (define @t79 () (forall @t78 @t76)) % 150.68/150.94 (define @t80 () (forall @t78 @t75)) % 150.68/150.94 (define @t81 () (or @t80 @t73)) % 150.68/150.94 (define @t82 () (_ @t1 @t4)) % 150.68/150.94 (define @t83 () (forall @t6 (not @t82))) % 150.68/150.94 (define @t84 () (or @t83 @t3)) % 150.68/150.94 (define @t85 () (not @t83)) % 150.68/150.94 (define @t86 () (not @t5)) % 150.68/150.94 (define @t87 () (forall @t6 @t86)) % 150.68/150.94 (define @t88 () (not @t87)) % 150.68/150.94 (define @t89 () (_ @t71 @t70 @t60)) % 150.68/150.94 (define @t90 () (= @t89 @t55)) % 150.68/150.94 (define @t91 () (and @t54 @t90)) % 150.68/150.94 (define @t92 () (and @t53 @t90)) % 150.68/150.94 (define @t93 () (or @t92 @t91)) % 150.68/150.94 (define @t94 () (_ @t38 @t60 @t89)) % 150.68/150.94 (define @t95 () (= @t94 @t93)) % 150.68/150.94 (define @t96 () (= @t55 @t89)) % 150.68/150.94 (define @t97 () (and @t54 @t96)) % 150.68/150.94 (define @t98 () (and @t53 @t96)) % 150.68/150.94 (define @t99 () (or @t98 @t97)) % 150.68/150.94 (define @t100 () (= @t94 @t99)) % 150.68/150.94 (define @t101 () (@var "BOUND_VARIABLE_7540" $$unsorted)) % 150.68/150.94 (define @t102 () (@var "BOUND_VARIABLE_7627" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 150.68/150.94 (define @t103 () (@var "BOUND_VARIABLE_7538" Bool)) % 150.68/150.94 (define @t104 () (@const 10 (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted))) % 150.68/150.94 (define @t105 () (_ @t104 (_ @t50 (_ @t49 @t48 @t103) @t102) @t101)) % 150.68/150.94 (define @t106 () (_ @t104 (_ @t71 @t70 (_ @t37 (_ @t36 @t35 @t103) @t102)) @t101)) % 150.68/150.94 (define @t107 () (@list @t103 @t102 @t101)) % 150.68/150.94 (define @t108 () (forall @t107 (= @t105 @t106))) % 150.68/150.94 (define @t109 () (@var "BOUND_VARIABLE_7539" (-> $$unsorted $$unsorted))) % 150.68/150.94 (define @t110 () (@const 11 (-> Bool (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 150.68/150.94 (define @t111 () (forall (@list @t103 @t109 @t101) (= (_ @t110 @t103 @t109 @t101) (tptp.epsii (_ (_ @t44 @t103) @t109) @t101)))) % 150.68/150.94 (define @t112 () (@var "z" $$unsorted)) % 150.68/150.94 (define @t113 () (_ @t50 (_ @t49 @t48 @t53) @t55)) % 150.68/150.94 (define @t114 () (@list @t112)) % 150.68/150.94 (define @t115 () (forall @t114 (= (_ @t104 @t55 @t112) (_ @t104 @t113 @t112)))) % 150.68/150.94 (define @t116 () (@quantifiers_skolemize @t115 0)) % 150.68/150.94 (define @t117 () (_ @t104 @t89 @t116)) % 150.68/150.94 (define @t118 () (_ @t104 @t113 @t116)) % 150.68/150.94 (define @t119 () (forall @t107 (= @t106 @t105))) % 150.68/150.94 (define @t120 () (= @t117 @t118)) % 150.68/150.94 (define @t121 () (@list @t53 @t55 @t116)) % 150.68/150.94 (define @t122 () (= @t118 @t117)) % 150.68/150.94 (define @t123 () (@var "y" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 150.68/150.94 (define @t124 () (@var "x" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 150.68/150.94 (define @t125 () (not @t51)) % 150.68/150.94 (define @t126 () (not (forall @t13 (= @t4 (_ (_ @t110 @t11) @t4))))) % 150.68/150.94 (define @t127 () (= @t4 @t18)) % 150.68/150.94 (define @t128 () (and @t11 @t127)) % 150.68/150.94 (define @t129 () (lambda @t23 (or @t128 (and @t19 @t127)))) % 150.68/150.94 (define @t130 () (tptp.epsii @t129 @t16)) % 150.68/150.94 (define @t131 () (@list @t16)) % 150.68/150.94 (define @t132 () (_ (_ tptp.epsii @t129) @t16)) % 150.68/150.94 (define @t133 () (lambda @t131 @t132)) % 150.68/150.94 (define @t134 () (= @t4 @t133)) % 150.68/150.94 (define @t135 () (_ (_ tptp.epsii (lambda @t23 (or @t128 (and @t19 (= @t17 @t18))))) @t16)) % 150.68/150.94 (define @t136 () (lambda (@list @t17 @t16) @t135)) % 150.68/150.94 (define @t137 () (lambda (@list @t4 @t17 @t16) @t135)) % 150.68/150.94 (define @t138 () (_ (lambda @t25 @t135) @t11)) % 150.68/150.94 (define @t139 () (= (_ (_ @t138 @t4) @t4) @t4)) % 150.68/150.94 (define @t140 () (forall @t13 @t139)) % 150.68/150.94 (define @t141 () (= @t55 @t113)) % 150.68/150.94 (define @t142 () (not @t141)) % 150.68/150.94 (define @t143 () (_ @t49 @t48 @t52)) % 150.68/150.94 (define @t144 () (_ @t50 @t143 @t55)) % 150.68/150.94 (define @t145 () (= @t55 @t144)) % 150.68/150.94 (define @t146 () (not @t145)) % 150.68/150.94 (define @t147 () (@list true)) % 150.68/150.94 (define @t148 () (not @t115)) % 150.68/150.94 (define @t149 () (or @t148 @t141)) % 150.68/150.94 (define @t150 () (@list true false)) % 150.68/150.94 (define @t151 () (_ @t104 @t55 @t116)) % 150.68/150.94 (define @t152 () (= @t151 @t118)) % 150.68/150.94 (define @t153 () (and @t122 @t96)) % 150.68/150.94 (define @t154 () (not @t96)) % 150.68/150.94 (define @t155 () (not @t97)) % 150.68/150.94 (define @t156 () (@list @t96)) % 150.68/150.94 (define @t157 () (not @t98)) % 150.68/150.94 (define @t158 () (not @t99)) % 150.68/150.94 (define @t159 () (@list true true)) % 150.68/150.94 (define @t160 () (not @t94)) % 150.68/150.94 (define @t161 () (not @t61)) % 150.68/150.94 (define @t162 () (or @t161 @t94)) % 150.68/150.94 (define @t163 () (not @t65)) % 150.68/150.94 (assume @p1 @t10) % 150.68/150.94 (assume @p2 @t15) % 150.68/150.94 (assume @p3 true) % 150.68/150.94 (step @p4 (= tptp.if @t26) :rule refl :args (@t26)) % 150.68/150.94 (step @p5 :rule eq-symm :args (@t27 @t28)) % 150.68/150.94 (step @p6 :rule refl :args (@t30)) % 150.68/150.94 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t32)) % 150.68/150.94 (step @p8 :rule refl :args (@t29)) % 150.68/150.94 (step @p9 :rule nary_cong :premises (@p8 @p5) :args (@t33)) % 150.68/150.94 (step @p10 :rule nary_cong :premises (@p9 @p7) :args (@t34)) % 150.68/150.94 (step @p11 :rule refl :args (@t39)) % 150.68/150.94 (step @p12 :rule cong :premises (@p11 @p10) :args ((= @t39 @t34))) % 150.68/150.94 (step @p13 :rule eq-symm :args (@t34 @t39)) % 150.68/150.94 (step @p14 :rule trans :premises (@p13 @p12)) % 150.68/150.94 (step @p15 :rule cong :premises (@p14) :args (@t41)) % 150.68/150.94 ; WARNING: add trust step for TRUST % 150.68/150.94 ; trust TRUST PREPROCESS_HO_ELIM % 150.68/150.94 (step @p16 :rule trust :premises () :args ((= @t46 @t41))) % 150.68/150.94 (step @p17 :rule trans :premises (@p16 @p15)) % 150.68/150.94 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 150.68/150.94 (step @p18 :rule trust :premises () :args (@t46)) % 150.68/150.94 (step @p19 :rule eq_resolve :premises (@p18 @p17)) % 150.68/150.94 (step @p20 :rule aci_norm :args ((= (and @t54 true) @t54))) % 150.68/150.94 (step @p21 :rule eq-refl :args (@t55)) % 150.68/150.94 (step @p22 :rule refl :args (@t54)) % 150.68/150.94 (step @p23 :rule nary_cong :premises (@p22 @p21) :args (@t57)) % 150.68/150.94 (step @p24 :rule trans :premises (@p23 @p20)) % 150.68/150.94 (step @p25 :rule aci_norm :args ((= (and @t53 true) @t53))) % 150.68/150.94 (step @p26 :rule refl :args (@t53)) % 150.68/150.94 (step @p27 :rule nary_cong :premises (@p26 @p21) :args (@t58)) % 150.68/150.94 (step @p28 :rule trans :premises (@p27 @p25)) % 150.68/150.94 (step @p29 :rule nary_cong :premises (@p28 @p24) :args (@t59)) % 150.68/150.94 (step @p30 :rule refl :args (@t61)) % 150.68/150.94 (step @p31 :rule cong :premises (@p30 @p29) :args (@t62)) % 150.68/150.94 (step @p32 :rule refl :args (@t64)) % 150.68/150.94 (step @p33 :rule cong :premises (@p32 @p31) :args ((=> @t64 @t62))) % 150.68/150.94 (assume-push @p240 @t64) % 150.68/150.94 (step @p35 :rule instantiate :premises (@p19) :args ((@list @t53 @t55 @t55))) % 150.68/150.94 (step-pop @p241 :rule scope :premises (@p35)) % 150.68/150.94 (step @p36 :rule process_scope :premises (@p241) :args (@t62)) % 150.68/150.94 (step @p38 :rule eq_resolve :premises (@p36 @p33)) % 150.68/150.94 (step @p39 :rule implies_elim :premises (@p38)) % 150.68/150.94 (step @p40 :rule chain_m_resolution :premises (@p39 @p19) :args (@t66 @t67 @t68)) % 150.68/150.94 ; trust TRUST PREPROCESS_HO_ELIM % 150.68/150.94 (step @p41 :rule trust :premises () :args ((= @t77 (forall (@list @t69 @t72) (or (not (_ @t38 @t69 @t72)) (_ @t38 @t69 (_ @t71 @t70 @t69))))))) % 150.68/150.94 (step @p42 :rule quant-merge-prenex :args ((= (forall @t9 @t79) @t77))) % 150.68/150.94 (step @p43 :rule refl :args (@t73)) % 150.68/150.94 (step @p44 :rule alpha_equiv :args (@t80 (@list @t74) (@list @t4))) % 150.68/150.94 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t81)) % 150.68/150.95 (step @p46 :rule quant-miniscope-or :args ((= @t79 @t81))) % 150.68/150.95 (step @p47 :rule trans :premises (@p46 @p45)) % 150.68/150.95 (step @p48 :rule symm :premises (@p47)) % 150.68/150.95 (step @p49 :rule cong :premises (@p48) :args ((forall @t9 (or @t83 @t73)))) % 150.68/150.95 (step @p50 :rule trans :premises (@p49 @p42)) % 150.68/150.95 (step @p51 :rule refl :args (@t73)) % 150.68/150.95 (step @p52 :rule refl :args (@t3)) % 150.68/150.95 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t3 @t73))) % 150.68/150.95 (step @p54 :rule symm :premises (@p53)) % 150.68/150.95 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 150.68/150.95 (step @p56 :rule refl :args (@t83)) % 150.68/150.95 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t84)) % 150.68/150.95 (step @p58 :rule cong :premises (@p57) :args ((forall @t9 @t84))) % 150.68/150.95 (step @p59 :rule trans :premises (@p58 @p50)) % 150.68/150.95 (step @p60 :rule bool-double-not-elim :args (@t83)) % 150.68/150.95 (step @p61 :rule nary_cong :premises (@p60 @p52) :args ((or (not @t85) @t3))) % 150.68/150.95 (step @p62 :rule bool-impl-elim :args (@t85 @t3)) % 150.68/150.95 (step @p63 :rule trans :premises (@p62 @p61)) % 150.68/150.95 (step @p64 :rule cong :premises (@p63) :args ((forall @t9 (=> @t85 @t3)))) % 150.68/150.95 (step @p65 :rule trans :premises (@p64 @p59)) % 150.68/150.95 (step @p66 :rule refl :args (@t3)) % 150.68/150.95 (step @p67 :rule refl :args (@t82)) % 150.68/150.95 (step @p68 :rule refl :args (@t5)) % 150.68/150.95 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t5 @t82))) % 150.68/150.95 (step @p70 :rule symm :premises (@p69)) % 150.68/150.95 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 150.68/150.95 (step @p72 :rule cong :premises (@p71) :args (@t86)) % 150.68/150.95 (step @p73 :rule cong :premises (@p72) :args (@t87)) % 150.68/150.95 (step @p74 :rule cong :premises (@p73) :args (@t88)) % 150.68/150.95 (step @p75 :rule exists-elim :args ((= @t7 @t88))) % 150.68/150.95 (step @p76 :rule trans :premises (@p75 @p74)) % 150.68/150.95 (step @p77 :rule cong :premises (@p76 @p66) :args (@t8)) % 150.68/150.95 (step @p78 :rule cong :premises (@p77) :args (@t10)) % 150.68/150.95 (step @p79 :rule trans :premises (@p78 @p65)) % 150.68/150.95 (step @p80 :rule trans :premises (@p79 @p41)) % 150.68/150.95 (step @p81 :rule eq_resolve :premises (@p1 @p80)) % 150.68/150.95 (step @p82 :rule instantiate :premises (@p81) :args ((@list @t60 @t55))) % 150.68/150.95 (step @p83 :rule eq-symm :args (@t89 @t55)) % 150.68/150.95 (step @p84 :rule nary_cong :premises (@p22 @p83) :args (@t91)) % 150.68/150.95 (step @p85 :rule nary_cong :premises (@p26 @p83) :args (@t92)) % 150.68/150.95 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t93)) % 150.68/150.95 (step @p87 :rule refl :args (@t94)) % 150.68/150.95 (step @p88 :rule cong :premises (@p87 @p86) :args (@t95)) % 150.68/150.95 (step @p89 :rule cong :premises (@p32 @p88) :args ((=> @t64 @t95))) % 150.68/150.95 (assume-push @p242 @t64) % 150.68/150.95 (step @p91 :rule instantiate :premises (@p19) :args ((@list @t53 @t55 @t89))) % 150.68/150.95 (step-pop @p243 :rule scope :premises (@p91)) % 150.68/150.95 (step @p92 :rule process_scope :premises (@p243) :args (@t95)) % 150.68/150.95 (step @p94 :rule eq_resolve :premises (@p92 @p89)) % 150.68/150.95 (step @p95 :rule implies_elim :premises (@p94)) % 150.68/150.95 (step @p96 :rule chain_m_resolution :premises (@p95 @p19) :args (@t100 @t67 @t68)) % 150.68/150.95 (step @p97 :rule eq-symm :args (@t105 @t106)) % 150.68/150.95 (step @p98 :rule cong :premises (@p97) :args (@t108)) % 150.68/150.95 ; trust TRUST PREPROCESS_HO_ELIM % 150.68/150.95 (step @p99 :rule trust :premises () :args ((= @t111 @t108))) % 150.68/150.95 (step @p100 :rule trans :premises (@p99 @p98)) % 150.68/150.95 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 150.68/150.95 (step @p101 :rule trust :premises () :args (@t111)) % 150.68/150.95 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 150.68/150.95 (step @p103 :rule eq-symm :args (@t117 @t118)) % 150.68/150.95 (step @p104 :rule refl :args (@t119)) % 150.68/150.95 (step @p105 :rule cong :premises (@p104 @p103) :args ((=> @t119 @t120))) % 150.68/150.95 (assume-push @p244 @t119) % 150.68/150.95 (step @p107 :rule instantiate :premises (@p102) :args (@t121)) % 150.68/150.95 (step-pop @p245 :rule scope :premises (@p107)) % 150.68/150.95 (step @p108 :rule process_scope :premises (@p245) :args (@t120)) % 150.68/150.95 (step @p110 :rule eq_resolve :premises (@p108 @p105)) % 150.68/150.95 (step @p111 :rule implies_elim :premises (@p110)) % 150.68/150.95 (step @p112 :rule chain_m_resolution :premises (@p111 @p102) :args (@t122 @t67 (@list @t119))) % 150.68/150.95 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 150.68/150.95 (step @p113 :rule trust :premises () :args ((forall (@list @t124 @t123) (or (not (forall @t114 (= (_ @t104 @t124 @t112) (_ @t104 @t123 @t112)))) (= @t124 @t123))))) % 150.68/150.95 (step @p114 :rule instantiate :premises (@p113) :args ((@list @t55 @t113))) % 150.68/150.95 ; trust TRUST PREPROCESS_HO_ELIM % 150.68/150.95 (step @p115 :rule trust :premises () :args ((= @t126 @t125))) % 150.68/150.95 ; trust TRUST PREPROCESS_HO_ELIM % 150.68/150.95 (step @p116 :rule trust :premises () :args ((= (not (forall @t13 (= @t4 (lambda @t131 @t130)))) @t126))) % 150.68/150.95 (step @p117 :rule refl :args (@t130)) % 150.68/150.95 (step @p118 :rule refl :args (@t132)) % 150.68/150.95 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t132 @t130))) % 150.68/150.95 (step @p120 :rule symm :premises (@p119)) % 150.68/150.95 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 150.68/150.95 (step @p122 :rule cong :premises (@p121) :args (@t133)) % 150.68/150.95 (step @p123 :rule refl :args (@t4)) % 150.68/150.95 (step @p124 :rule cong :premises (@p123 @p122) :args (@t134)) % 150.68/150.95 (step @p125 :rule cong :premises (@p124) :args ((forall @t13 @t134))) % 150.68/150.95 (step @p126 :rule eq-symm :args (@t133 @t4)) % 150.68/150.95 (step @p127 :rule refl :args (@t4)) % 150.68/150.95 (step @p128 :rule beta-reduce :args ((= (_ @t136 @t4) @t133))) % 150.68/150.95 (step @p129 :rule beta-reduce :args ((= (_ @t137 @t4) @t136))) % 150.68/150.95 (step @p130 :rule beta-reduce :args ((= @t138 @t137))) % 150.68/150.95 (step @p131 :rule ho_cong :premises (@p130 @p127)) % 150.68/150.95 (step @p132 :rule trans :premises (@p131 @p129)) % 150.68/150.95 (step @p133 :rule ho_cong :premises (@p132 @p127)) % 150.68/150.95 (step @p134 :rule trans :premises (@p133 @p128)) % 150.68/150.95 (step @p135 :rule cong :premises (@p134 @p127) :args (@t139)) % 150.68/150.95 (step @p136 :rule trans :premises (@p135 @p126)) % 150.68/150.95 (step @p137 :rule cong :premises (@p136) :args (@t140)) % 150.68/150.95 (step @p138 :rule trans :premises (@p137 @p125)) % 150.68/150.95 (step @p139 :rule cong :premises (@p138) :args ((not @t140))) % 150.68/150.95 (step @p140 :rule refl :args (@t11)) % 150.68/150.95 (step @p141 :rule refl :args (@t16)) % 150.68/150.95 (step @p142 :rule eq-symm :args (@t18 @t17)) % 150.68/150.95 (step @p143 :rule refl :args (@t19)) % 150.68/150.95 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t20)) % 150.68/150.95 (step @p145 :rule eq-symm :args (@t18 @t4)) % 150.68/150.95 (step @p146 :rule nary_cong :premises (@p140 @p145) :args (@t21)) % 150.68/150.95 (step @p147 :rule nary_cong :premises (@p146 @p144) :args (@t22)) % 150.68/150.95 (step @p148 :rule cong :premises (@p147) :args (@t24)) % 150.68/150.95 (step @p149 :rule refl :args (tptp.epsii)) % 150.68/150.95 (step @p150 :rule ho_cong :premises (@p149 @p148)) % 150.68/150.95 (step @p151 :rule ho_cong :premises (@p150 @p141)) % 150.68/150.95 (step @p152 :rule cong :premises (@p151) :args (@t26)) % 150.68/150.95 (step @p153 :rule trans :premises (@p4 @p152)) % 150.68/150.95 (step @p154 :rule ho_cong :premises (@p153 @p140)) % 150.68/150.95 (step @p155 :rule ho_cong :premises (@p154 @p127)) % 150.68/150.95 (step @p156 :rule ho_cong :premises (@p155 @p127)) % 150.68/150.95 (step @p157 :rule cong :premises (@p156 @p127) :args (@t12)) % 150.68/150.95 (step @p158 :rule cong :premises (@p157) :args (@t14)) % 150.68/150.95 (step @p159 :rule cong :premises (@p158) :args (@t15)) % 150.68/150.95 (step @p160 :rule trans :premises (@p159 @p139)) % 150.68/150.95 (step @p161 :rule trans :premises (@p160 @p116 @p115)) % 150.68/150.95 (step @p162 :rule eq_resolve :premises (@p2 @p161)) % 150.68/150.95 (step @p163 :rule refl :args (@t142)) % 150.68/150.95 (step @p164 :rule bool-double-not-elim :args (@t51)) % 150.68/150.95 (step @p165 :rule nary_cong :premises (@p164 @p163) :args ((or (not @t125) @t142))) % 150.68/150.95 (step @p166 :rule refl :args (@t55)) % 150.68/150.95 (step @p167 :rule eq-refl :args (@t52)) % 150.68/150.95 (step @p168 :rule skolem_intro :args (@t53)) % 150.68/150.95 (step @p169 :rule refl :args (@t52)) % 150.68/150.95 (step @p170 :rule cong :premises (@p169 @p168) :args ((= @t52 @t53))) % 150.68/150.95 (step @p171 :rule trans :premises (@p170 @p167)) % 150.68/150.95 (step @p172 :rule true_elim :premises (@p171)) % 150.68/150.95 (step @p173 :rule refl :args (@t48)) % 150.68/150.95 (step @p174 :rule cong :premises (@p173 @p172) :args (@t143)) % 150.68/150.95 (step @p175 :rule cong :premises (@p174 @p166) :args (@t144)) % 150.68/150.95 (step @p176 :rule cong :premises (@p166 @p175) :args (@t145)) % 150.68/150.95 (step @p177 :rule cong :premises (@p176) :args (@t146)) % 150.68/150.95 (step @p178 :rule refl :args (@t125)) % 150.68/150.95 (step @p179 :rule cong :premises (@p178 @p177) :args ((=> @t125 @t146))) % 150.68/150.95 (assume-push @p246 @t125) % 150.68/150.95 (step @p181 :rule skolemize :premises (@p162)) % 150.68/150.95 (step-pop @p247 :rule scope :premises (@p181)) % 150.68/150.95 (step @p182 :rule process_scope :premises (@p247) :args (@t146)) % 150.68/150.95 (step @p184 :rule eq_resolve :premises (@p182 @p179)) % 150.68/150.95 (step @p185 :rule implies_elim :premises (@p184)) % 150.68/150.95 (step @p186 :rule eq_resolve :premises (@p185 @p165)) % 150.68/150.95 (step @p187 :rule chain_m_resolution :premises (@p186 @p162) :args (@t142 @t147 (@list @t51))) % 150.68/150.95 (step @p188 :rule cnf_or_pos :args (@t149)) % 150.68/150.95 (step @p189 :rule reordering :premises (@p188) :args ((or @t141 @t148 (not @t149)))) % 150.68/150.95 (step @p190 :rule chain_m_resolution :premises (@p189 @p187 @p114) :args (@t148 @t150 (@list @t141 @t149))) % 150.68/150.95 (step @p191 :rule skolemize :premises (@p190)) % 150.68/150.95 (assume-push @p248 @t122) % 150.68/150.95 (assume-push @p249 @t96) % 150.68/150.95 (assume-push @p250 @t122) % 150.68/150.95 (assume-push @p251 @t96) % 150.68/150.95 (step @p107 :rule instantiate :premises (@p102) :args (@t121)) % 150.68/150.95 (step @p196 :rule refl :args (@t116)) % 150.68/150.95 (step @p197 :rule cong :premises (@p249 @p196) :args (@t151)) % 150.68/150.95 (step @p198 :rule trans :premises (@p197 @p107)) % 150.68/150.95 (step-pop @p252 :rule scope :premises (@p198)) % 150.68/150.95 (step-pop @p253 :rule scope :premises (@p252)) % 150.68/150.95 (step @p199 :rule process_scope :premises (@p253) :args (@t152)) % 150.68/150.95 (step @p202 :rule and_intro :premises (@p112 @p249)) % 150.68/150.95 (step @p203 :rule modus_ponens :premises (@p202 @p199)) % 150.68/150.95 (step-pop @p254 :rule scope :premises (@p203)) % 150.68/150.95 (step-pop @p255 :rule scope :premises (@p254)) % 150.68/150.95 (step @p204 :rule process_scope :premises (@p255) :args (@t152)) % 150.68/150.95 (step @p207 :rule implies_elim :premises (@p204)) % 150.68/150.95 (step @p208 :rule cnf_and_neg :args (@t153)) % 150.68/150.95 (step @p209 :rule resolution :premises (@p208 @p207) :args (true @t153)) % 150.68/150.95 (step @p210 :rule reordering :premises (@p209) :args ((or @t152 (not @t122) @t154))) % 150.68/150.95 (step @p211 :rule chain_m_resolution :premises (@p210 @p191 @p112) :args (@t154 @t150 (@list @t152 @t122))) % 150.68/150.95 (step @p212 :rule cnf_and_pos :args (@t97 1)) % 150.68/150.95 (step @p213 :rule reordering :premises (@p212) :args ((or @t96 @t155))) % 150.68/150.95 (step @p214 :rule chain_m_resolution :premises (@p213 @p211) :args (@t155 @t147 @t156)) % 150.68/150.95 (step @p215 :rule cnf_and_pos :args (@t98 1)) % 150.68/150.95 (step @p216 :rule reordering :premises (@p215) :args ((or @t96 @t157))) % 150.68/150.95 (step @p217 :rule chain_m_resolution :premises (@p216 @p211) :args (@t157 @t147 @t156)) % 150.68/150.95 (step @p218 :rule cnf_or_pos :args (@t99)) % 150.68/150.95 (step @p219 :rule reordering :premises (@p218) :args ((or @t98 @t97 @t158))) % 150.68/150.95 (step @p220 :rule chain_m_resolution :premises (@p219 @p217 @p214) :args (@t158 @t159 (@list @t98 @t97))) % 150.68/150.95 (step @p221 :rule cnf_equiv_pos1 :args (@t100)) % 150.68/150.95 (step @p222 :rule reordering :premises (@p221) :args ((or @t160 @t99 (not @t100)))) % 150.68/150.95 (step @p223 :rule chain_m_resolution :premises (@p222 @p220 @p96) :args (@t160 @t150 (@list @t99 @t100))) % 150.68/150.95 (step @p224 :rule cnf_or_pos :args (@t162)) % 150.68/150.95 (step @p225 :rule reordering :premises (@p224) :args ((or @t161 @t94 (not @t162)))) % 150.68/150.95 (step @p226 :rule chain_m_resolution :premises (@p225 @p223 @p82) :args (@t161 @t150 (@list @t94 @t162))) % 150.68/150.95 (step @p227 :rule cnf_equiv_pos2 :args (@t66)) % 150.68/150.95 (step @p228 :rule reordering :premises (@p227) :args ((or @t61 @t163 (not @t66)))) % 150.68/150.95 (step @p229 :rule chain_m_resolution :premises (@p228 @p226 @p40) :args (@t163 @t150 (@list @t61 @t66))) % 150.68/150.95 (step @p230 :rule cnf_or_neg :args (@t65 0)) % 150.68/150.95 (step @p231 :rule reordering :premises (@p230) :args ((or @t54 @t65))) % 150.68/150.95 (step @p232 :rule chain_m_resolution :premises (@p231 @p229) :args (@t54 @t147 (@list @t65))) % 150.68/150.95 (step @p233 :rule bool-double-not-elim :args (@t53)) % 150.68/150.95 (step @p234 :rule refl :args (@t65)) % 150.68/150.95 (step @p235 :rule nary_cong :premises (@p234 @p233) :args ((or @t65 (not @t54)))) % 150.68/150.95 (step @p236 :rule cnf_or_neg :args (@t65 1)) % 150.68/150.95 (step @p237 :rule eq_resolve :premises (@p236 @p235)) % 150.68/150.95 (step @p238 :rule reordering :premises (@p237) :args ((or @t53 @t65))) % 150.68/150.95 (step @p239 false :rule chain_m_resolution :premises (@p238 @p232 @p229) :args (false @t159 (@list @t53 @t65))) % 150.68/150.95 ) % 150.68/150.95 % SZS output end Proof % 150.68/150.95 % cvc5 exiting %------------------------------------------------------------------------------