%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV272^5 : TPTP v9.2.1. Bugfixed 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 : 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 08:55:42 AM UTC 2026 % Result : Theorem 151.06s 151.49s % Output : Proof 151.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV272^5 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n017.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 18:22:31 EDT 2026 % 0.15/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 151.06/151.49 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 151.06/151.49 --- 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... % 151.06/151.49 --- 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... % 151.06/151.49 --- Run --ho-elim --full-saturate-quant at 18s... % 151.06/151.49 % SZS status Theorem % 151.06/151.49 % SZS output start Proof % 151.06/151.49 ( % 151.06/151.49 (declare-sort $$unsorted 0) % 151.06/151.49 (define tptp.cSUCC () (let ((_let_1 (@var "Xt" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "Xn" (-> (-> $$unsorted Bool) Bool)))) (lambda (@list _let_4 _let_2) (exists (@list _let_3) (and (_ _let_2 _let_3) (_ _let_4 (lambda (@list _let_1) (and (not (= _let_1 _let_3)) (_ _let_2 _let_1)))))))))))) % 151.06/151.49 (define tptp.cZERO () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (lambda (@list _let_2) (not (exists (@list _let_1) (_ _let_2 _let_1))))))) % 151.06/151.49 (define @t1 () (@var "Xx" (-> (-> $$unsorted Bool) Bool))) % 151.06/151.49 (define @t2 () (@var "S" (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 151.06/151.49 (define @t3 () (_ @t2 @t1)) % 151.06/151.49 (define @t4 () (@var "X" (-> (-> $$unsorted Bool) Bool))) % 151.06/151.49 (define @t5 () (_ tptp.cSUCC @t4)) % 151.06/151.49 (define @t6 () (_ @t2 @t4)) % 151.06/151.49 (define @t7 () (=> @t6 (_ @t2 @t5))) % 151.06/151.49 (define @t8 () (@list @t4)) % 151.06/151.49 (define @t9 () (forall @t8 @t7)) % 151.06/151.49 (define @t10 () (and (_ @t2 tptp.cZERO) @t9)) % 151.06/151.49 (define @t11 () (=> @t10 @t3)) % 151.06/151.49 (define @t12 () (@list @t2)) % 151.06/151.49 (define @t13 () (forall @t12 @t11)) % 151.06/151.49 (define @t14 () (@list @t1)) % 151.06/151.49 (define @t15 () (lambda @t14 @t13)) % 151.06/151.49 (define @t16 () (@var "N" (-> (-> $$unsorted Bool) Bool))) % 151.06/151.49 (define @t17 () (@var "P" (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 151.06/151.49 (define @t18 () (_ @t17 @t16)) % 151.06/151.49 (define @t19 () (_ @t17 @t4)) % 151.06/151.49 (define @t20 () (=> @t19 (_ @t17 @t5))) % 151.06/151.49 (define @t21 () (forall @t8 @t20)) % 151.06/151.49 (define @t22 () (and (_ @t17 tptp.cZERO) @t21)) % 151.06/151.49 (define @t23 () (=> @t22 @t18)) % 151.06/151.49 (define @t24 () (@list @t17)) % 151.06/151.49 (define @t25 () (forall @t24 @t23)) % 151.06/151.49 (define @t26 () (@list @t16)) % 151.06/151.49 (define @t27 () (lambda @t26 @t25)) % 151.06/151.49 (define @t28 () (= @t27 @t15)) % 151.06/151.49 (define @t29 () (not @t28)) % 151.06/151.49 (define @t30 () (@var "Xt" $$unsorted)) % 151.06/151.49 (define @t31 () (@var "Xp" (-> $$unsorted Bool))) % 151.06/151.49 (define @t32 () (_ @t31 @t30)) % 151.06/151.49 (define @t33 () (@var "Xx" $$unsorted)) % 151.06/151.49 (define @t34 () (not (= @t30 @t33))) % 151.06/151.49 (define @t35 () (and @t34 @t32)) % 151.06/151.49 (define @t36 () (@list @t30)) % 151.06/151.49 (define @t37 () (lambda @t36 @t35)) % 151.06/151.49 (define @t38 () (@var "Xn" (-> (-> $$unsorted Bool) Bool))) % 151.06/151.49 (define @t39 () (_ @t31 @t33)) % 151.06/151.49 (define @t40 () (and @t39 (_ @t38 @t37))) % 151.06/151.49 (define @t41 () (@list @t33)) % 151.06/151.49 (define @t42 () (exists @t41 @t40)) % 151.06/151.49 (define @t43 () (@list @t38 @t31)) % 151.06/151.49 (define @t44 () (lambda @t43 @t42)) % 151.06/151.49 (define @t45 () (exists @t41 @t39)) % 151.06/151.49 (define @t46 () (not @t45)) % 151.06/151.49 (define @t47 () (@list @t31)) % 151.06/151.49 (define @t48 () (lambda @t47 @t46)) % 151.06/151.49 (define @t49 () (@var "BOUND_VARIABLE_7733" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 151.06/151.49 (define @t50 () (@const 0 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 151.06/151.49 (define @t51 () (@const 1 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool))) % 151.06/151.49 (define @t52 () (_ @t51 @t50 @t49)) % 151.06/151.49 (define @t53 () (@var "BOUND_VARIABLE_7736" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 151.06/151.49 (define @t54 () (@var "BOUND_VARIABLE_7739" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 151.06/151.49 (define @t55 () (@const 2 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 151.06/151.49 (define @t56 () (@const 3 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) (@ho-elim-sort (-> $$unsorted Bool)) Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool))))) % 151.06/151.49 (define @t57 () (_ @t56 @t55 @t54)) % 151.06/151.49 (define @t58 () (@list @t54)) % 151.06/151.49 (define @t59 () (not (forall @t58 (or (not (_ @t51 @t53 @t54)) (_ @t51 @t53 @t57))))) % 151.06/151.49 (define @t60 () (@const 4 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 151.06/151.49 (define @t61 () (not (_ @t51 @t53 @t60))) % 151.06/151.49 (define @t62 () (@list @t53)) % 151.06/151.49 (define @t63 () (forall @t62 (or @t61 @t59 (_ @t51 @t53 @t49)))) % 151.06/151.49 (define @t64 () (@list @t49)) % 151.06/151.49 (define @t65 () (forall @t64 (= @t52 @t63))) % 151.06/151.49 (define @t66 () (@var "BOUND_VARIABLE_7609" (-> (-> $$unsorted Bool) Bool))) % 151.06/151.49 (define @t67 () (_ (@const 5 (-> (-> (-> $$unsorted Bool) Bool) (-> $$unsorted Bool) Bool)) @t4)) % 151.06/151.49 (define @t68 () (_ @t2 @t4)) % 151.06/151.49 (define @t69 () (not @t68)) % 151.06/151.49 (define @t70 () (@const 6 (-> (-> $$unsorted Bool) Bool))) % 151.06/151.49 (define @t71 () (@const 7 (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 151.06/151.49 (define @t72 () (forall (@list @t66) (= (_ @t71 @t66) (forall @t12 (or (not (_ @t2 @t70)) (not (forall @t8 (or @t69 (_ @t2 @t67)))) (_ @t2 @t66)))))) % 151.06/151.49 (define @t73 () (@var "z" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 151.06/151.49 (define @t74 () (@const 8 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 151.06/151.49 (define @t75 () (@list @t73)) % 151.06/151.49 (define @t76 () (forall @t75 (= (_ @t51 @t50 @t73) (_ @t51 @t74 @t73)))) % 151.06/151.49 (define @t77 () (@quantifiers_skolemize @t76 0)) % 151.06/151.49 (define @t78 () (forall @t62 (or @t61 @t59 (_ @t51 @t53 @t77)))) % 151.06/151.49 (define @t79 () (_ @t51 @t50 @t77)) % 151.06/151.49 (define @t80 () (forall @t64 (= @t63 @t52))) % 151.06/151.49 (define @t81 () (= @t78 @t79)) % 151.06/151.49 (define @t82 () (@list @t77)) % 151.06/151.49 (define @t83 () (= @t79 @t78)) % 151.06/151.49 (define @t84 () (@list false)) % 151.06/151.49 (define @t85 () (@var "y" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 151.06/151.49 (define @t86 () (@var "x" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 151.06/151.49 (define @t87 () (forall (@list @t86 @t85) (or (not (forall @t75 (= (_ @t51 @t86 @t73) (_ @t51 @t85 @t73)))) (= @t86 @t85)))) % 151.06/151.49 (define @t88 () (not @t76)) % 151.06/151.49 (define @t89 () (= @t50 @t74)) % 151.06/151.49 (define @t90 () (or @t88 @t89)) % 151.06/151.49 (define @t91 () (= @t74 @t50)) % 151.06/151.49 (define @t92 () (or @t88 @t91)) % 151.06/151.49 (define @t93 () (not @t89)) % 151.06/151.49 (define @t94 () (@const 9 (-> (-> (-> $$unsorted Bool) Bool) Bool))) % 151.06/151.49 (define @t95 () (not (= @t94 @t71))) % 151.06/151.49 (define @t96 () (_ @t2 @t1)) % 151.06/151.49 (define @t97 () (_ @t31 @t30)) % 151.06/151.49 (define @t98 () (not (= @t33 @t30))) % 151.06/151.49 (define @t99 () (and @t98 @t97)) % 151.06/151.49 (define @t100 () (lambda @t36 @t99)) % 151.06/151.49 (define @t101 () (_ @t4 @t100)) % 151.06/151.49 (define @t102 () (not @t101)) % 151.06/151.49 (define @t103 () (_ @t31 @t33)) % 151.06/151.49 (define @t104 () (not @t103)) % 151.06/151.49 (define @t105 () (or @t104 @t102)) % 151.06/151.49 (define @t106 () (forall @t41 @t105)) % 151.06/151.49 (define @t107 () (not @t106)) % 151.06/151.49 (define @t108 () (lambda @t47 @t107)) % 151.06/151.49 (define @t109 () (_ @t2 @t108)) % 151.06/151.49 (define @t110 () (forall @t8 (or @t69 @t109))) % 151.06/151.49 (define @t111 () (not @t110)) % 151.06/151.49 (define @t112 () (forall @t41 @t104)) % 151.06/151.49 (define @t113 () (lambda @t47 @t112)) % 151.06/151.49 (define @t114 () (_ @t2 @t113)) % 151.06/151.49 (define @t115 () (_ @t17 @t16)) % 151.06/151.49 (define @t116 () (_ @t17 @t108)) % 151.06/151.49 (define @t117 () (_ @t17 @t4)) % 151.06/151.49 (define @t118 () (not @t117)) % 151.06/151.49 (define @t119 () (forall @t8 (or @t118 @t116))) % 151.06/151.49 (define @t120 () (not @t119)) % 151.06/151.49 (define @t121 () (_ @t17 @t113)) % 151.06/151.49 (define @t122 () (not @t39)) % 151.06/151.49 (define @t123 () (forall @t41 @t122)) % 151.06/151.49 (define @t124 () (lambda @t47 @t123)) % 151.06/151.49 (define @t125 () (_ @t2 @t113)) % 151.06/151.49 (define @t126 () (not @t125)) % 151.06/151.49 (define @t127 () (or @t126 @t111 @t3)) % 151.06/151.49 (define @t128 () (and @t125 @t110)) % 151.06/151.49 (define @t129 () (and @t98 @t32)) % 151.06/151.49 (define @t130 () (lambda @t36 @t129)) % 151.06/151.49 (define @t131 () (lambda @t47 (not (forall @t41 (or @t122 (not (_ @t4 @t130))))))) % 151.06/151.49 (define @t132 () (_ @t2 @t108)) % 151.06/151.49 (define @t133 () (not @t6)) % 151.06/151.49 (define @t134 () (or @t133 @t132)) % 151.06/151.49 (define @t135 () (_ @t38 @t100)) % 151.06/151.49 (define @t136 () (_ (lambda @t43 (not (forall @t41 (or @t104 (not @t135))))) @t4)) % 151.06/151.49 (define @t137 () (=> @t6 (_ @t2 @t136))) % 151.06/151.49 (define @t138 () (forall @t8 @t137)) % 151.06/151.49 (define @t139 () (and @t125 @t138)) % 151.06/151.49 (define @t140 () (=> @t139 @t3)) % 151.06/151.49 (define @t141 () (forall @t12 @t140)) % 151.06/151.49 (define @t142 () (lambda @t14 @t141)) % 151.06/151.49 (define @t143 () (_ @t17 @t113)) % 151.06/151.49 (define @t144 () (not @t143)) % 151.06/151.49 (define @t145 () (or @t144 @t120 @t18)) % 151.06/151.49 (define @t146 () (and @t143 @t119)) % 151.06/151.49 (define @t147 () (_ @t17 @t108)) % 151.06/151.49 (define @t148 () (not @t19)) % 151.06/151.49 (define @t149 () (or @t148 @t147)) % 151.06/151.49 (define @t150 () (=> @t19 (_ @t17 @t136))) % 151.06/151.49 (define @t151 () (forall @t8 @t150)) % 151.06/151.49 (define @t152 () (and @t143 @t151)) % 151.06/151.49 (define @t153 () (=> @t152 @t18)) % 151.06/151.49 (define @t154 () (forall @t24 @t153)) % 151.06/151.49 (define @t155 () (lambda @t26 @t154)) % 151.06/151.49 (define @t156 () (= @t155 @t142)) % 151.06/151.49 (define @t157 () (_ @t38 @t130)) % 151.06/151.49 (define @t158 () (not @t157)) % 151.06/151.49 (define @t159 () (or @t122 @t158)) % 151.06/151.49 (define @t160 () (and @t39 @t157)) % 151.06/151.49 (define @t161 () (forall @t41 (not @t160))) % 151.06/151.49 (define @t162 () (not @t161)) % 151.06/151.49 (define @t163 () (not @t123)) % 151.06/151.49 (define @t164 () (@list true false)) % 151.06/151.49 (define @t165 () (_ @t51 @t74 @t77)) % 151.06/151.49 (define @t166 () (= @t79 @t165)) % 151.06/151.49 (define @t167 () (not @t83)) % 151.06/151.49 (define @t168 () (not @t79)) % 151.06/151.49 (define @t169 () (@var "BOUND_VARIABLE_7770" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 151.06/151.49 (define @t170 () (_ @t51 @t74 @t169)) % 151.06/151.49 (define @t171 () (@var "BOUND_VARIABLE_7771" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 151.06/151.49 (define @t172 () (not (forall @t58 (or (not (_ @t51 @t171 @t54)) (_ @t51 @t171 @t57))))) % 151.06/151.49 (define @t173 () (not (_ @t51 @t171 @t60))) % 151.06/151.49 (define @t174 () (@list @t171)) % 151.06/151.49 (define @t175 () (forall @t174 (or @t173 @t172 (_ @t51 @t171 @t169)))) % 151.06/151.49 (define @t176 () (@list @t169)) % 151.06/151.49 (define @t177 () (forall @t176 (= @t170 @t175))) % 151.06/151.49 (define @t178 () (@var "BOUND_VARIABLE_7638" (-> (-> $$unsorted Bool) Bool))) % 151.06/151.49 (define @t179 () (forall (@list @t178) (= (_ @t94 @t178) (forall @t24 (or (not (_ @t17 @t70)) (not (forall @t8 (or @t118 (_ @t17 @t67)))) (_ @t17 @t178)))))) % 151.06/151.49 (define @t180 () (forall @t174 (or @t173 @t172 (_ @t51 @t171 @t77)))) % 151.06/151.49 (define @t181 () (forall @t176 (= @t175 @t170))) % 151.06/151.49 (define @t182 () (= @t180 @t165)) % 151.06/151.49 (define @t183 () (= @t165 @t180)) % 151.06/151.49 (define @t184 () (not @t183)) % 151.06/151.49 (define @t185 () (@var "BOUND_VARIABLE_9610" (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)) Bool)))) % 151.06/151.49 (define @t186 () (@var "BOUND_VARIABLE_9609" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted Bool)) Bool)))) % 151.06/151.49 (define @t187 () (@list @t186 @t185)) % 151.06/151.49 (define @t188 () (not @t78)) % 151.06/151.49 (assume @p1 @t29) % 151.06/151.49 (assume @p2 true) % 151.06/151.49 (step @p3 (= tptp.cSUCC @t44) :rule refl :args (@t44)) % 151.06/151.49 (step @p4 (= tptp.cZERO @t48) :rule refl :args (@t48)) % 151.06/151.49 (step @p5 :rule eq-symm :args (@t52 @t63)) % 151.06/151.49 (step @p6 :rule cong :premises (@p5) :args (@t65)) % 151.06/151.49 ; WARNING: add trust step for TRUST % 151.06/151.49 ; trust TRUST PREPROCESS_HO_ELIM % 151.06/151.49 (step @p7 :rule trust :premises () :args ((= @t72 @t65))) % 151.06/151.49 (step @p8 :rule trans :premises (@p7 @p6)) % 151.06/151.49 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 151.06/151.49 (step @p9 :rule trust :premises () :args (@t72)) % 151.06/151.49 (step @p10 :rule eq_resolve :premises (@p9 @p8)) % 151.06/151.49 (step @p11 :rule eq-symm :args (@t78 @t79)) % 151.06/151.49 (step @p12 :rule refl :args (@t80)) % 151.06/151.49 (step @p13 :rule cong :premises (@p12 @p11) :args ((=> @t80 @t81))) % 151.06/151.49 (assume-push @p292 @t80) % 151.06/151.49 (step @p15 :rule instantiate :premises (@p10) :args (@t82)) % 151.06/151.49 (step-pop @p293 :rule scope :premises (@p15)) % 151.06/151.49 (step @p16 :rule process_scope :premises (@p293) :args (@t81)) % 151.06/151.49 (step @p18 :rule eq_resolve :premises (@p16 @p13)) % 151.06/151.49 (step @p19 :rule implies_elim :premises (@p18)) % 151.06/151.49 (step @p20 :rule chain_m_resolution :premises (@p19 @p10) :args (@t83 @t84 (@list @t80))) % 151.06/151.49 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 151.06/151.49 (step @p21 :rule trust :premises () :args (@t87)) % 151.06/151.49 (step @p22 :rule eq-symm :args (@t50 @t74)) % 151.06/151.49 (step @p23 :rule refl :args (@t88)) % 151.06/151.49 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t90)) % 151.06/151.49 (step @p25 :rule refl :args (@t87)) % 151.06/151.49 (step @p26 :rule cong :premises (@p25 @p24) :args ((=> @t87 @t90))) % 151.06/151.49 (assume-push @p294 @t87) % 151.06/151.49 (step @p28 :rule instantiate :premises (@p21) :args ((@list @t50 @t74))) % 151.06/151.49 (step-pop @p295 :rule scope :premises (@p28)) % 151.06/151.49 (step @p29 :rule process_scope :premises (@p295) :args (@t90)) % 151.06/151.49 (step @p31 :rule eq_resolve :premises (@p29 @p26)) % 151.06/151.49 (step @p32 :rule implies_elim :premises (@p31)) % 151.06/151.49 (step @p33 :rule chain_m_resolution :premises (@p32 @p21) :args (@t92 @t84 (@list @t87))) % 151.06/151.49 (step @p34 :rule cong :premises (@p22) :args (@t93)) % 151.06/151.49 ; trust TRUST PREPROCESS_HO_ELIM % 151.06/151.49 (step @p35 :rule trust :premises () :args ((= (not (= @t71 @t94)) @t93))) % 151.06/151.49 (step @p36 :rule eq-symm :args (@t94 @t71)) % 151.06/151.49 (step @p37 :rule cong :premises (@p36) :args (@t95)) % 151.06/151.49 ; trust TRUST PREPROCESS_HO_ELIM % 151.06/151.49 (step @p38 :rule trust :premises () :args ((= (not (= (lambda @t26 (forall @t24 (or (not @t121) @t120 @t115))) (lambda @t14 (forall @t12 (or (not @t114) @t111 @t96))))) @t95))) % 151.06/151.49 (step @p39 :rule refl :args (@t96)) % 151.06/151.49 (step @p40 :rule refl :args (@t3)) % 151.06/151.49 (step @p41 :rule cong :premises (@p40 @p39) :args ((= @t3 @t96))) % 151.06/151.49 (step @p42 :rule symm :premises (@p41)) % 151.06/151.49 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 151.06/151.49 (step @p44 :rule refl :args (@t111)) % 151.06/151.49 (step @p45 :rule refl :args ((_ @t2 @t124))) % 151.06/151.49 (step @p46 :rule refl :args (@t103)) % 151.06/151.49 (step @p47 :rule cong :premises (@p46) :args (@t104)) % 151.06/151.49 (step @p48 :rule cong :premises (@p47) :args (@t112)) % 151.06/151.49 (step @p49 :rule cong :premises (@p48) :args (@t113)) % 151.06/151.49 (step @p50 :rule cong :premises (@p49) :args (@t114)) % 151.06/151.49 (step @p51 :rule trans :premises (@p50 @p45)) % 151.06/151.49 (step @p52 :rule refl :args (@t2)) % 151.06/151.49 (step @p53 :rule ho_cong :premises (@p52 @p49)) % 151.06/151.49 (step @p54 :rule cong :premises (@p53 @p51) :args ((= @t125 @t114))) % 151.06/151.49 (step @p55 :rule symm :premises (@p54)) % 151.06/151.49 (step @p56 :rule refl :args ((_ @t2 @t124))) % 151.06/151.49 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 151.06/151.49 (step @p58 :rule cong :premises (@p57) :args (@t126)) % 151.06/151.49 (step @p59 :rule nary_cong :premises (@p58 @p44 @p43) :args (@t127)) % 151.06/151.49 (step @p60 :rule cong :premises (@p59) :args ((forall @t12 @t127))) % 151.06/151.49 (step @p61 :rule aci_norm :args ((= (or (or @t126 @t111) @t3) @t127))) % 151.06/151.49 (step @p62 :rule bool-and-de-morgan :args (@t125 @t110 true)) % 151.06/151.49 (step @p63 :rule nary_cong :premises (@p62 @p40) :args ((or (not @t128) @t3))) % 151.06/151.49 (step @p64 :rule trans :premises (@p63 @p61)) % 151.06/151.49 (step @p65 :rule bool-impl-elim :args (@t128 @t3)) % 151.06/151.49 (step @p66 :rule trans :premises (@p65 @p64)) % 151.06/151.49 (step @p67 :rule cong :premises (@p66) :args ((forall @t12 (=> @t128 @t3)))) % 151.06/151.49 (step @p68 :rule trans :premises (@p67 @p60)) % 151.06/151.49 (step @p69 :rule refl :args (@t3)) % 151.06/151.49 (step @p70 :rule refl :args ((_ @t2 @t131))) % 151.06/151.49 (step @p71 :rule refl :args ((_ @t4 @t130))) % 151.06/151.49 (step @p72 :rule refl :args (@t97)) % 151.06/151.49 (step @p73 :rule refl :args (@t98)) % 151.06/151.49 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t99)) % 151.06/151.49 (step @p75 :rule cong :premises (@p74) :args (@t100)) % 151.06/151.49 (step @p76 :rule cong :premises (@p75) :args (@t101)) % 151.06/151.49 (step @p77 :rule trans :premises (@p76 @p71)) % 151.06/151.49 (step @p78 :rule cong :premises (@p77) :args (@t102)) % 151.06/151.49 (step @p79 :rule nary_cong :premises (@p47 @p78) :args (@t105)) % 151.06/151.49 (step @p80 :rule cong :premises (@p79) :args (@t106)) % 151.06/151.49 (step @p81 :rule cong :premises (@p80) :args (@t107)) % 151.06/151.49 (step @p82 :rule cong :premises (@p81) :args (@t108)) % 151.06/151.49 (step @p83 :rule cong :premises (@p82) :args (@t109)) % 151.06/151.49 (step @p84 :rule trans :premises (@p83 @p70)) % 151.06/151.49 (step @p85 :rule ho_cong :premises (@p52 @p82)) % 151.06/151.49 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t132 @t109))) % 151.06/151.49 (step @p87 :rule symm :premises (@p86)) % 151.06/151.49 (step @p88 :rule refl :args ((_ @t2 @t131))) % 151.06/151.49 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 151.06/151.49 (step @p90 :rule refl :args (@t68)) % 151.06/151.49 (step @p91 :rule refl :args (@t6)) % 151.06/151.49 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t6 @t68))) % 151.06/151.49 (step @p93 :rule symm :premises (@p92)) % 151.06/151.49 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 151.06/151.49 (step @p95 :rule cong :premises (@p94) :args (@t133)) % 151.06/151.49 (step @p96 :rule nary_cong :premises (@p95 @p89) :args (@t134)) % 151.06/151.49 (step @p97 :rule cong :premises (@p96) :args ((forall @t8 @t134))) % 151.06/151.49 (step @p98 :rule bool-impl-elim :args (@t6 @t132)) % 151.06/151.49 (step @p99 :rule cong :premises (@p98) :args ((forall @t8 (=> @t6 @t132)))) % 151.06/151.49 (step @p100 :rule trans :premises (@p99 @p97)) % 151.06/151.49 (step @p101 :rule beta-reduce :args ((= @t136 @t108))) % 151.06/151.49 (step @p102 :rule refl :args (@t2)) % 151.06/151.49 (step @p103 :rule ho_cong :premises (@p102 @p101)) % 151.06/151.49 (step @p104 :rule refl :args (@t6)) % 151.06/151.49 (step @p105 :rule cong :premises (@p104 @p103) :args (@t137)) % 151.06/151.49 (step @p106 :rule cong :premises (@p105) :args (@t138)) % 151.06/151.49 (step @p107 :rule trans :premises (@p106 @p100)) % 151.06/151.49 (step @p108 :rule refl :args (@t125)) % 151.06/151.49 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t139)) % 151.06/151.49 (step @p110 :rule cong :premises (@p109 @p69) :args (@t140)) % 151.06/151.49 (step @p111 :rule cong :premises (@p110) :args (@t141)) % 151.06/151.49 (step @p112 :rule trans :premises (@p111 @p68)) % 151.06/151.49 (step @p113 :rule cong :premises (@p112) :args (@t142)) % 151.06/151.49 (step @p114 :rule refl :args (@t115)) % 151.06/151.49 (step @p115 :rule refl :args (@t18)) % 151.06/151.49 (step @p116 :rule cong :premises (@p115 @p114) :args ((= @t18 @t115))) % 151.06/151.49 (step @p117 :rule symm :premises (@p116)) % 151.06/151.49 (step @p118 :rule eq_resolve :premises (@p115 @p117)) % 151.06/151.49 (step @p119 :rule refl :args (@t120)) % 151.06/151.49 (step @p120 :rule refl :args ((_ @t17 @t124))) % 151.06/151.49 (step @p121 :rule cong :premises (@p49) :args (@t121)) % 151.06/151.49 (step @p122 :rule trans :premises (@p121 @p120)) % 151.06/151.49 (step @p123 :rule refl :args (@t17)) % 151.06/151.49 (step @p124 :rule ho_cong :premises (@p123 @p49)) % 151.06/151.49 (step @p125 :rule cong :premises (@p124 @p122) :args ((= @t143 @t121))) % 151.06/151.49 (step @p126 :rule symm :premises (@p125)) % 151.06/151.49 (step @p127 :rule refl :args ((_ @t17 @t124))) % 151.06/151.49 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 151.06/151.49 (step @p129 :rule cong :premises (@p128) :args (@t144)) % 151.06/151.49 (step @p130 :rule nary_cong :premises (@p129 @p119 @p118) :args (@t145)) % 151.06/151.49 (step @p131 :rule cong :premises (@p130) :args ((forall @t24 @t145))) % 151.06/151.49 (step @p132 :rule aci_norm :args ((= (or (or @t144 @t120) @t18) @t145))) % 151.06/151.49 (step @p133 :rule bool-and-de-morgan :args (@t143 @t119 true)) % 151.06/151.49 (step @p134 :rule nary_cong :premises (@p133 @p115) :args ((or (not @t146) @t18))) % 151.06/151.49 (step @p135 :rule trans :premises (@p134 @p132)) % 151.06/151.49 (step @p136 :rule bool-impl-elim :args (@t146 @t18)) % 151.06/151.49 (step @p137 :rule trans :premises (@p136 @p135)) % 151.06/151.49 (step @p138 :rule cong :premises (@p137) :args ((forall @t24 (=> @t146 @t18)))) % 151.06/151.49 (step @p139 :rule trans :premises (@p138 @p131)) % 151.06/151.49 (step @p140 :rule refl :args (@t18)) % 151.06/151.49 (step @p141 :rule refl :args ((_ @t17 @t131))) % 151.06/151.49 (step @p142 :rule cong :premises (@p82) :args (@t116)) % 151.06/151.49 (step @p143 :rule trans :premises (@p142 @p141)) % 151.06/151.49 (step @p144 :rule ho_cong :premises (@p123 @p82)) % 151.06/151.49 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t147 @t116))) % 151.06/151.49 (step @p146 :rule symm :premises (@p145)) % 151.06/151.49 (step @p147 :rule refl :args ((_ @t17 @t131))) % 151.06/151.49 (step @p148 :rule eq_resolve :premises (@p147 @p146)) % 151.06/151.49 (step @p149 :rule refl :args (@t117)) % 151.06/151.49 (step @p150 :rule refl :args (@t19)) % 151.06/151.49 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t19 @t117))) % 151.06/151.49 (step @p152 :rule symm :premises (@p151)) % 151.06/151.49 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 151.06/151.49 (step @p154 :rule cong :premises (@p153) :args (@t148)) % 151.06/151.49 (step @p155 :rule nary_cong :premises (@p154 @p148) :args (@t149)) % 151.06/151.49 (step @p156 :rule cong :premises (@p155) :args ((forall @t8 @t149))) % 151.06/151.49 (step @p157 :rule bool-impl-elim :args (@t19 @t147)) % 151.06/151.49 (step @p158 :rule cong :premises (@p157) :args ((forall @t8 (=> @t19 @t147)))) % 151.06/151.49 (step @p159 :rule trans :premises (@p158 @p156)) % 151.06/151.49 (step @p160 :rule refl :args (@t17)) % 151.06/151.49 (step @p161 :rule ho_cong :premises (@p160 @p101)) % 151.06/151.49 (step @p162 :rule refl :args (@t19)) % 151.06/151.49 (step @p163 :rule cong :premises (@p162 @p161) :args (@t150)) % 151.06/151.49 (step @p164 :rule cong :premises (@p163) :args (@t151)) % 151.06/151.49 (step @p165 :rule trans :premises (@p164 @p159)) % 151.06/151.49 (step @p166 :rule refl :args (@t143)) % 151.06/151.49 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t152)) % 151.06/151.49 (step @p168 :rule cong :premises (@p167 @p140) :args (@t153)) % 151.06/151.49 (step @p169 :rule cong :premises (@p168) :args (@t154)) % 151.06/151.49 (step @p170 :rule trans :premises (@p169 @p139)) % 151.06/151.49 (step @p171 :rule cong :premises (@p170) :args (@t155)) % 151.06/151.49 (step @p172 :rule cong :premises (@p171 @p113) :args (@t156)) % 151.06/151.49 (step @p173 :rule cong :premises (@p172) :args ((not @t156))) % 151.06/151.49 (step @p174 :rule refl :args (@t4)) % 151.06/151.49 (step @p175 :rule refl :args ((_ @t38 @t130))) % 151.06/151.49 (step @p176 :rule cong :premises (@p75) :args (@t135)) % 151.06/151.49 (step @p177 :rule trans :premises (@p176 @p175)) % 151.06/151.49 (step @p178 :rule refl :args (@t38)) % 151.06/151.49 (step @p179 :rule ho_cong :premises (@p178 @p75)) % 151.06/151.49 (step @p180 :rule cong :premises (@p179 @p177) :args ((= (_ @t38 @t100) @t135))) % 151.06/151.49 (step @p181 :rule symm :premises (@p180)) % 151.06/151.49 (step @p182 :rule refl :args (@t157)) % 151.06/151.49 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 151.06/151.49 (step @p184 :rule refl :args (@t32)) % 151.06/151.49 (step @p185 :rule cong :premises (@p184 @p72) :args ((= @t32 @t97))) % 151.06/151.49 (step @p186 :rule symm :premises (@p185)) % 151.06/151.49 (step @p187 :rule eq_resolve :premises (@p184 @p186)) % 151.06/151.49 (step @p188 :rule nary_cong :premises (@p73 @p187) :args (@t129)) % 151.06/151.49 (step @p189 :rule cong :premises (@p188) :args (@t130)) % 151.06/151.49 (step @p190 :rule ho_cong :premises (@p178 @p189)) % 151.06/151.49 (step @p191 :rule trans :premises (@p190 @p183)) % 151.06/151.49 (step @p192 :rule cong :premises (@p191) :args (@t158)) % 151.06/151.49 (step @p193 :rule refl :args (@t39)) % 151.06/151.49 (step @p194 :rule cong :premises (@p193 @p46) :args ((= @t39 @t103))) % 151.06/151.49 (step @p195 :rule symm :premises (@p194)) % 151.06/151.49 (step @p196 :rule eq_resolve :premises (@p193 @p195)) % 151.06/151.49 (step @p197 :rule cong :premises (@p196) :args (@t122)) % 151.06/151.49 (step @p198 :rule nary_cong :premises (@p197 @p192) :args (@t159)) % 151.06/151.49 (step @p199 :rule cong :premises (@p198) :args ((forall @t41 @t159))) % 151.06/151.49 (step @p200 :rule bool-and-de-morgan :args (@t39 @t157 true)) % 151.06/151.49 (step @p201 :rule cong :premises (@p200) :args (@t161)) % 151.06/151.49 (step @p202 :rule trans :premises (@p201 @p199)) % 151.06/151.49 (step @p203 :rule cong :premises (@p202) :args (@t162)) % 151.06/151.49 (step @p204 :rule exists-elim :args ((= (exists @t41 @t160) @t162))) % 151.06/151.49 (step @p205 :rule trans :premises (@p204 @p203)) % 151.06/151.49 (step @p206 :rule refl :args (@t32)) % 151.06/151.49 (step @p207 :rule eq-symm :args (@t30 @t33)) % 151.06/151.49 (step @p208 :rule cong :premises (@p207) :args (@t34)) % 151.06/151.49 (step @p209 :rule nary_cong :premises (@p208 @p206) :args (@t35)) % 151.06/151.49 (step @p210 :rule cong :premises (@p209) :args (@t37)) % 151.06/151.49 (step @p211 :rule refl :args (@t38)) % 151.06/151.49 (step @p212 :rule ho_cong :premises (@p211 @p210)) % 151.06/151.49 (step @p213 :rule refl :args (@t39)) % 151.06/151.49 (step @p214 :rule nary_cong :premises (@p213 @p212) :args (@t40)) % 151.06/151.49 (step @p215 :rule cong :premises (@p214) :args (@t42)) % 151.06/151.49 (step @p216 :rule trans :premises (@p215 @p205)) % 151.06/151.49 (step @p217 :rule cong :premises (@p216) :args (@t44)) % 151.06/151.49 (step @p218 :rule trans :premises (@p3 @p217)) % 151.06/151.49 (step @p219 :rule ho_cong :premises (@p218 @p174)) % 151.06/151.49 (step @p220 :rule ho_cong :premises (@p102 @p219)) % 151.06/151.49 (step @p221 :rule cong :premises (@p104 @p220) :args (@t7)) % 151.06/151.49 (step @p222 :rule cong :premises (@p221) :args (@t9)) % 151.06/151.49 (step @p223 :rule bool-double-not-elim :args (@t112)) % 151.06/151.49 (step @p224 :rule cong :premises (@p197) :args (@t123)) % 151.06/151.49 (step @p225 :rule cong :premises (@p224) :args (@t163)) % 151.06/151.49 (step @p226 :rule exists-elim :args ((= @t45 @t163))) % 151.06/151.49 (step @p227 :rule trans :premises (@p226 @p225)) % 151.06/151.49 (step @p228 :rule cong :premises (@p227) :args (@t46)) % 151.06/151.49 (step @p229 :rule trans :premises (@p228 @p223)) % 151.06/151.49 (step @p230 :rule cong :premises (@p229) :args (@t48)) % 151.06/151.49 (step @p231 :rule trans :premises (@p4 @p230)) % 151.06/151.49 (step @p232 :rule ho_cong :premises (@p102 @p231)) % 151.06/151.49 (step @p233 :rule nary_cong :premises (@p232 @p222) :args (@t10)) % 151.06/151.49 (step @p234 :rule cong :premises (@p233 @p69) :args (@t11)) % 151.06/151.49 (step @p235 :rule cong :premises (@p234) :args (@t13)) % 151.06/151.49 (step @p236 :rule cong :premises (@p235) :args (@t15)) % 151.06/151.49 (step @p237 :rule ho_cong :premises (@p160 @p219)) % 151.06/151.49 (step @p238 :rule cong :premises (@p162 @p237) :args (@t20)) % 151.06/151.49 (step @p239 :rule cong :premises (@p238) :args (@t21)) % 151.06/151.49 (step @p240 :rule ho_cong :premises (@p160 @p231)) % 151.06/151.49 (step @p241 :rule nary_cong :premises (@p240 @p239) :args (@t22)) % 151.06/151.49 (step @p242 :rule cong :premises (@p241 @p140) :args (@t23)) % 151.06/151.49 (step @p243 :rule cong :premises (@p242) :args (@t25)) % 151.06/151.49 (step @p244 :rule cong :premises (@p243) :args (@t27)) % 151.06/151.49 (step @p245 :rule cong :premises (@p244 @p236) :args (@t28)) % 151.06/151.49 (step @p246 :rule cong :premises (@p245) :args (@t29)) % 151.06/151.49 (step @p247 :rule trans :premises (@p246 @p173)) % 151.06/151.49 (step @p248 :rule trans :premises (@p247 @p38 @p37 @p35 @p34)) % 151.06/151.49 (step @p249 :rule eq_resolve :premises (@p1 @p248)) % 151.06/151.49 (step @p250 :rule cnf_or_pos :args (@t92)) % 151.06/151.49 (step @p251 :rule reordering :premises (@p250) :args ((or @t91 @t88 (not @t92)))) % 151.06/151.49 (step @p252 :rule chain_m_resolution :premises (@p251 @p249 @p33) :args (@t88 @t164 (@list @t91 @t92))) % 151.06/151.49 (step @p253 :rule skolemize :premises (@p252)) % 151.06/151.49 (step @p254 :rule cnf_equiv_neg2 :args (@t166)) % 151.06/151.49 (step @p255 :rule cnf_equiv_pos1 :args (@t83)) % 151.06/151.49 (step @p256 :rule reordering :premises (@p255) :args ((or @t168 @t78 @t167))) % 151.06/151.49 (step @p257 :rule eq-symm :args (@t170 @t175)) % 151.06/151.49 (step @p258 :rule cong :premises (@p257) :args (@t177)) % 151.06/151.49 ; trust TRUST PREPROCESS_HO_ELIM % 151.06/151.49 (step @p259 :rule trust :premises () :args ((= @t179 @t177))) % 151.06/151.49 (step @p260 :rule trans :premises (@p259 @p258)) % 151.06/151.49 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 151.06/151.49 (step @p261 :rule trust :premises () :args (@t179)) % 151.06/151.50 (step @p262 :rule eq_resolve :premises (@p261 @p260)) % 151.06/151.50 (step @p263 :rule eq-symm :args (@t180 @t165)) % 151.06/151.50 (step @p264 :rule refl :args (@t181)) % 151.06/151.50 (step @p265 :rule cong :premises (@p264 @p263) :args ((=> @t181 @t182))) % 151.06/151.50 (assume-push @p296 @t181) % 151.06/151.50 (step @p267 :rule instantiate :premises (@p262) :args (@t82)) % 151.06/151.50 (step-pop @p297 :rule scope :premises (@p267)) % 151.06/151.50 (step @p268 :rule process_scope :premises (@p297) :args (@t182)) % 151.06/151.50 (step @p270 :rule eq_resolve :premises (@p268 @p265)) % 151.06/151.50 (step @p271 :rule implies_elim :premises (@p270)) % 151.06/151.50 (step @p272 :rule chain_m_resolution :premises (@p271 @p262) :args (@t183 @t84 (@list @t181))) % 151.06/151.50 (step @p273 :rule cnf_equiv_pos2 :args (@t183)) % 151.06/151.50 (step @p274 :rule reordering :premises (@p273) :args ((or @t165 (not @t180) @t184))) % 151.06/151.50 (step @p275 :rule alpha_equiv :args ((forall (@list @t185) (or (not (_ @t51 @t185 @t60)) (not (forall (@list @t186) (or (not (_ @t51 @t185 @t186)) (_ @t51 @t185 (_ @t56 @t55 @t186))))) (_ @t51 @t185 @t77))) @t187 (@list @t54 @t171))) % 151.06/151.50 (step @p276 :rule alpha_equiv :args (@t78 (@list @t54 @t53) @t187)) % 151.06/151.50 (step @p277 :rule trans :premises (@p276 @p275)) % 151.06/151.50 (step @p278 :rule equiv_elim1 :premises (@p277)) % 151.06/151.50 (step @p279 :rule reordering :premises (@p278) :args ((or @t180 @t188))) % 151.06/151.50 (step @p280 :rule chain_m_resolution :premises (@p279 @p274 @p272 @p256 @p20 @p254 @p253) :args (@t168 (@list true false false false true true) (@list @t180 @t183 @t78 @t83 @t165 @t166))) % 151.06/151.50 (step @p281 :rule cnf_equiv_pos2 :args (@t83)) % 151.06/151.50 (step @p282 :rule reordering :premises (@p281) :args ((or @t79 @t188 @t167))) % 151.06/151.50 (step @p283 :rule chain_m_resolution :premises (@p282 @p280 @p20) :args (@t188 @t164 (@list @t79 @t83))) % 151.06/151.50 (step @p284 :rule cnf_equiv_neg1 :args (@t166)) % 151.06/151.50 (step @p285 :rule reordering :premises (@p284) :args ((or @t79 @t165 @t166))) % 151.06/151.50 (step @p286 :rule chain_m_resolution :premises (@p285 @p280 @p253) :args (@t165 (@list true true) (@list @t79 @t166))) % 151.06/151.50 (step @p287 :rule cnf_equiv_pos1 :args (@t183)) % 151.06/151.50 (step @p288 :rule reordering :premises (@p287) :args ((or (not @t165) @t180 @t184))) % 151.06/151.50 (step @p289 :rule chain_m_resolution :premises (@p288 @p286 @p272) :args (@t180 (@list false false) (@list @t165 @t183))) % 151.06/151.50 (step @p290 :rule equiv_elim2 :premises (@p277)) % 151.06/151.50 (step @p291 false :rule chain_m_resolution :premises (@p290 @p289 @p283) :args (false (@list false true) (@list @t180 @t78))) % 151.06/151.50 ) % 151.06/151.50 % SZS output end Proof % 151.06/151.50 % cvc5 exiting %------------------------------------------------------------------------------