%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO332^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 09:12:26 AM UTC 2026 % Result : Theorem 1.42s 1.69s % Output : Proof 1.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO332^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n019.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 00:03:49 EDT 2026 % 0.16/0.34 % CPUTime : % 0.26/0.49 %----Proving TH0 % 1.42/1.69 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.42/1.69 % SZS status Theorem % 1.42/1.69 % SZS output start Proof % 1.42/1.69 ( % 1.42/1.69 (declare-sort tptp.b 0) % 1.42/1.69 (declare-sort tptp.a 0) % 1.42/1.69 (define @t1 () (@var "X" (-> tptp.a Bool))) % 1.42/1.69 (define @t2 () (@var "Xf" (-> (-> tptp.a Bool) tptp.a))) % 1.42/1.69 (define @t3 () (_ @t2 @t1)) % 1.42/1.69 (define @t4 () (_ @t1 @t3)) % 1.42/1.69 (define @t5 () (@var "Xs" (-> (-> tptp.a Bool) Bool))) % 1.42/1.69 (define @t6 () (_ @t5 @t1)) % 1.42/1.69 (define @t7 () (@list @t1)) % 1.42/1.69 (define @t8 () (forall @t7 (=> @t6 @t4))) % 1.42/1.69 (define @t9 () (@list @t2)) % 1.42/1.69 (define @t10 () (exists @t9 @t8)) % 1.42/1.69 (define @t11 () (@var "Xt" tptp.a)) % 1.42/1.69 (define @t12 () (_ @t1 @t11)) % 1.42/1.69 (define @t13 () (@list @t11)) % 1.42/1.69 (define @t14 () (exists @t13 @t12)) % 1.42/1.69 (define @t15 () (=> @t6 @t14)) % 1.42/1.69 (define @t16 () (forall @t7 @t15)) % 1.42/1.69 (define @t17 () (=> @t16 @t10)) % 1.42/1.69 (define @t18 () (@list @t5)) % 1.42/1.69 (define @t19 () (forall @t18 @t17)) % 1.42/1.69 (define @t20 () (@var "Xx" (-> tptp.a Bool))) % 1.42/1.69 (define @t21 () (@var "Xg" (-> (-> tptp.a Bool) tptp.a))) % 1.42/1.69 (define @t22 () (_ @t21 @t20)) % 1.42/1.69 (define @t23 () (@var "Xr" (-> (-> tptp.a Bool) tptp.a Bool))) % 1.42/1.69 (define @t24 () (_ @t23 @t20)) % 1.42/1.69 (define @t25 () (_ @t24 @t22)) % 1.42/1.69 (define @t26 () (@var "Xy" tptp.a)) % 1.42/1.69 (define @t27 () (_ @t24 @t26)) % 1.42/1.69 (define @t28 () (@list @t26)) % 1.42/1.69 (define @t29 () (exists @t28 @t27)) % 1.42/1.69 (define @t30 () (=> @t29 @t25)) % 1.42/1.69 (define @t31 () (@list @t20)) % 1.42/1.69 (define @t32 () (forall @t31 @t30)) % 1.42/1.69 (define @t33 () (@list @t21)) % 1.42/1.69 (define @t34 () (exists @t33 @t32)) % 1.42/1.69 (define @t35 () (@list @t23)) % 1.42/1.69 (define @t36 () (forall @t35 @t34)) % 1.42/1.69 (define @t37 () (=> @t36 @t19)) % 1.42/1.69 (define @t38 () (@var "Xx" tptp.a)) % 1.42/1.69 (define @t39 () (@var "Xg" (-> tptp.a tptp.b))) % 1.42/1.69 (define @t40 () (_ @t39 @t38)) % 1.42/1.69 (define @t41 () (@var "Xr" (-> tptp.a tptp.b Bool))) % 1.42/1.69 (define @t42 () (_ @t41 @t38)) % 1.42/1.69 (define @t43 () (_ @t42 @t40)) % 1.42/1.69 (define @t44 () (@var "Xy" tptp.b)) % 1.42/1.69 (define @t45 () (_ @t42 @t44)) % 1.42/1.69 (define @t46 () (@list @t44)) % 1.42/1.69 (define @t47 () (exists @t46 @t45)) % 1.42/1.69 (define @t48 () (=> @t47 @t43)) % 1.42/1.69 (define @t49 () (@list @t38)) % 1.42/1.69 (define @t50 () (forall @t49 @t48)) % 1.42/1.69 (define @t51 () (@list @t39)) % 1.42/1.69 (define @t52 () (exists @t51 @t50)) % 1.42/1.69 (define @t53 () (@list @t41)) % 1.42/1.69 (define @t54 () (forall @t53 @t52)) % 1.42/1.69 (define @t55 () (@var "X" (-> tptp.b Bool))) % 1.42/1.69 (define @t56 () (@var "Xf" (-> (-> tptp.b Bool) tptp.b))) % 1.42/1.69 (define @t57 () (_ @t56 @t55)) % 1.42/1.69 (define @t58 () (_ @t55 @t57)) % 1.42/1.69 (define @t59 () (@var "Xs" (-> (-> tptp.b Bool) Bool))) % 1.42/1.69 (define @t60 () (_ @t59 @t55)) % 1.42/1.69 (define @t61 () (@list @t55)) % 1.42/1.69 (define @t62 () (forall @t61 (=> @t60 @t58))) % 1.42/1.69 (define @t63 () (@list @t56)) % 1.42/1.69 (define @t64 () (exists @t63 @t62)) % 1.42/1.69 (define @t65 () (_ @t55 @t44)) % 1.42/1.69 (define @t66 () (exists @t46 @t65)) % 1.42/1.69 (define @t67 () (=> @t60 @t66)) % 1.42/1.69 (define @t68 () (forall @t61 @t67)) % 1.42/1.69 (define @t69 () (=> @t68 @t64)) % 1.42/1.69 (define @t70 () (@list @t59)) % 1.42/1.69 (define @t71 () (forall @t70 @t69)) % 1.42/1.69 (define @t72 () (=> @t71 @t54)) % 1.42/1.69 (define @t73 () (and @t72 @t37)) % 1.42/1.69 (define @t74 () (not @t73)) % 1.42/1.69 (define @t75 () (@const 0 (-> tptp.a tptp.b))) % 1.42/1.69 (define @t76 () (_ @t75 @t38)) % 1.42/1.69 (define @t77 () (_ @t39 @t38)) % 1.42/1.69 (define @t78 () (_ @t41 @t38 @t77)) % 1.42/1.69 (define @t79 () (@var "BOUND_VARIABLE_7541" tptp.b)) % 1.42/1.69 (define @t80 () (not (_ @t41 @t38 @t79))) % 1.42/1.69 (define @t81 () (or @t80 @t78)) % 1.42/1.69 (define @t82 () (@list @t38 @t79)) % 1.42/1.69 (define @t83 () (forall @t82 @t81)) % 1.42/1.69 (define @t84 () (not (forall @t51 (not @t83)))) % 1.42/1.69 (define @t85 () (forall @t53 @t84)) % 1.42/1.69 (define @t86 () (@quantifiers_skolemize @t85 0)) % 1.42/1.69 (define @t87 () (not (_ @t86 @t38 @t79))) % 1.42/1.69 (define @t88 () (forall @t82 (or @t87 (_ @t86 @t38 @t76)))) % 1.42/1.69 (define @t89 () (@quantifiers_skolemize @t88 1)) % 1.42/1.69 (define @t90 () (@quantifiers_skolemize @t88 0)) % 1.42/1.69 (define @t91 () (_ @t86 @t90 @t89)) % 1.42/1.69 (define @t92 () (_ @t86 @t90 (_ @t75 @t90))) % 1.42/1.69 (define @t93 () (not @t91)) % 1.42/1.69 (define @t94 () (or @t93 @t92)) % 1.42/1.69 (define @t95 () (@var "BOUND_VARIABLE_58209" tptp.a)) % 1.42/1.69 (define @t96 () (_ @t75 @t95)) % 1.42/1.69 (define @t97 () (@var "x" tptp.b)) % 1.42/1.69 (define @t98 () (@list @t97)) % 1.42/1.69 (define @t99 () (@list @t95)) % 1.42/1.69 (define @t100 () (forall @t98 (not (_ @t86 @t90 @t97)))) % 1.42/1.69 (define @t101 () (or @t100 @t92)) % 1.42/1.69 (define @t102 () (not @t94)) % 1.42/1.69 (define @t103 () (not @t88)) % 1.42/1.69 (define @t104 () (@list false)) % 1.42/1.69 (define @t105 () (lambda @t99 @t96)) % 1.42/1.69 (define @t106 () (_ @t105 @t38)) % 1.42/1.69 (define @t107 () (_ @t86 @t38 @t106)) % 1.42/1.69 (define @t108 () (or @t87 @t107)) % 1.42/1.69 (define @t109 () (forall @t82 @t108)) % 1.42/1.69 (define @t110 () (not @t109)) % 1.42/1.69 (define @t111 () (forall @t51 (not (forall @t82 (or @t87 (_ @t86 @t38 @t77)))))) % 1.42/1.69 (define @t112 () (not @t111)) % 1.42/1.69 (define @t113 () (not @t85)) % 1.42/1.69 (define @t114 () (not @t112)) % 1.42/1.69 (define @t115 () (@list true)) % 1.42/1.69 (define @t116 () (_ @t56 @t55)) % 1.42/1.69 (define @t117 () (_ @t55 @t116)) % 1.42/1.69 (define @t118 () (_ @t59 @t55)) % 1.42/1.69 (define @t119 () (not @t118)) % 1.42/1.69 (define @t120 () (forall @t61 (or @t119 @t117))) % 1.42/1.69 (define @t121 () (not (forall @t63 (not @t120)))) % 1.42/1.69 (define @t122 () (_ @t55 @t44)) % 1.42/1.69 (define @t123 () (not (forall @t46 (not @t122)))) % 1.42/1.69 (define @t124 () (forall @t61 (or @t119 @t123))) % 1.42/1.69 (define @t125 () (=> (forall @t70 (or (not @t124) @t121)) @t85)) % 1.42/1.69 (define @t126 () (_ @t1 @t11)) % 1.42/1.69 (define @t127 () (not (forall @t13 (not @t126)))) % 1.42/1.69 (define @t128 () (_ @t5 @t1)) % 1.42/1.69 (define @t129 () (not @t128)) % 1.42/1.69 (define @t130 () (forall @t7 (or @t129 @t127))) % 1.42/1.69 (define @t131 () (_ @t2 @t1)) % 1.42/1.69 (define @t132 () (_ @t1 @t131)) % 1.42/1.69 (define @t133 () (forall @t7 (or @t129 @t132))) % 1.42/1.69 (define @t134 () (not (forall @t9 (not @t133)))) % 1.42/1.69 (define @t135 () (not @t6)) % 1.42/1.69 (define @t136 () (or @t135 @t4)) % 1.42/1.69 (define @t137 () (or @t135 @t127)) % 1.42/1.69 (define @t138 () (not @t12)) % 1.42/1.69 (define @t139 () (forall @t13 @t138)) % 1.42/1.69 (define @t140 () (not @t139)) % 1.42/1.69 (define @t141 () (_ @t21 @t20)) % 1.42/1.69 (define @t142 () (_ @t23 @t20 @t141)) % 1.42/1.69 (define @t143 () (@var "BOUND_VARIABLE_7570" tptp.a)) % 1.42/1.69 (define @t144 () (not (_ @t23 @t20 @t143))) % 1.42/1.69 (define @t145 () (or @t144 @t142)) % 1.42/1.69 (define @t146 () (forall (@list @t20 @t143) @t145)) % 1.42/1.69 (define @t147 () (not (forall @t33 (not @t146)))) % 1.42/1.69 (define @t148 () (@list @t143)) % 1.42/1.69 (define @t149 () (forall @t148 @t145)) % 1.42/1.69 (define @t150 () (forall @t148 @t144)) % 1.42/1.69 (define @t151 () (or @t150 @t142)) % 1.42/1.69 (define @t152 () (_ @t23 @t20 @t26)) % 1.42/1.69 (define @t153 () (forall @t28 (not @t152))) % 1.42/1.69 (define @t154 () (or @t153 @t25)) % 1.42/1.69 (define @t155 () (not @t153)) % 1.42/1.69 (define @t156 () (not @t27)) % 1.42/1.69 (define @t157 () (forall @t28 @t156)) % 1.42/1.69 (define @t158 () (not @t157)) % 1.42/1.69 (define @t159 () (@list @t79)) % 1.42/1.69 (define @t160 () (forall @t159 @t81)) % 1.42/1.69 (define @t161 () (forall @t159 @t80)) % 1.42/1.69 (define @t162 () (or @t161 @t78)) % 1.42/1.69 (define @t163 () (_ @t41 @t38 @t44)) % 1.42/1.69 (define @t164 () (forall @t46 (not @t163))) % 1.42/1.69 (define @t165 () (or @t164 @t43)) % 1.42/1.69 (define @t166 () (not @t164)) % 1.42/1.69 (define @t167 () (not @t45)) % 1.42/1.69 (define @t168 () (forall @t46 @t167)) % 1.42/1.69 (define @t169 () (not @t168)) % 1.42/1.69 (define @t170 () (not @t60)) % 1.42/1.69 (define @t171 () (or @t170 @t58)) % 1.42/1.69 (define @t172 () (or @t170 @t123)) % 1.42/1.69 (define @t173 () (not @t65)) % 1.42/1.69 (define @t174 () (forall @t46 @t173)) % 1.42/1.69 (define @t175 () (not @t174)) % 1.42/1.69 (define @t176 () (forall @t18 (or (not @t130) @t134))) % 1.42/1.69 (define @t177 () (=> (forall @t35 @t147) @t176)) % 1.42/1.69 (define @t178 () (not @t176)) % 1.42/1.69 (define @t179 () (@quantifiers_skolemize @t176 0)) % 1.42/1.69 (define @t180 () (not (_ @t179 @t1))) % 1.42/1.69 (define @t181 () (forall @t9 (not (forall @t7 (or @t180 @t132))))) % 1.42/1.69 (define @t182 () (not @t181)) % 1.42/1.69 (define @t183 () (forall @t7 (or @t180 @t127))) % 1.42/1.69 (define @t184 () (not @t183)) % 1.42/1.69 (define @t185 () (or @t184 @t182)) % 1.42/1.69 (define @t186 () (not @t185)) % 1.42/1.69 (define @t187 () (@list @t185)) % 1.42/1.69 (define @t188 () (@const 1 (-> (-> tptp.a Bool) tptp.a))) % 1.42/1.69 (define @t189 () (_ @t188 @t1)) % 1.42/1.69 (define @t190 () (forall @t7 (or @t180 (_ @t1 @t189)))) % 1.42/1.69 (define @t191 () (@quantifiers_skolemize @t190 0)) % 1.42/1.69 (define @t192 () (@list @t191)) % 1.42/1.69 (define @t193 () (forall @t13 (not (_ @t191 @t11)))) % 1.42/1.69 (define @t194 () (not @t193)) % 1.42/1.69 (define @t195 () (_ @t179 @t191)) % 1.42/1.69 (define @t196 () (not @t195)) % 1.42/1.69 (define @t197 () (or @t196 @t194)) % 1.42/1.69 (define @t198 () (@var "BOUND_VARIABLE_205028" (-> tptp.a Bool))) % 1.42/1.69 (define @t199 () (_ @t188 @t198)) % 1.42/1.69 (define @t200 () (@list @t198)) % 1.42/1.69 (define @t201 () (lambda @t200 @t199)) % 1.42/1.69 (define @t202 () (_ @t201 @t1)) % 1.42/1.69 (define @t203 () (_ @t1 @t202)) % 1.42/1.69 (define @t204 () (or @t180 @t203)) % 1.42/1.69 (define @t205 () (forall @t7 @t204)) % 1.42/1.69 (define @t206 () (not @t205)) % 1.42/1.69 (define @t207 () (not @t190)) % 1.42/1.69 (define @t208 () (_ @t191 (_ @t188 @t191))) % 1.42/1.69 (define @t209 () (or @t196 @t208)) % 1.42/1.69 (define @t210 () (not @t209)) % 1.42/1.69 (define @t211 () (@list @t209)) % 1.42/1.69 (define @t212 () (@var "x" tptp.a)) % 1.42/1.69 (define @t213 () (@list @t212)) % 1.42/1.69 (define @t214 () (forall @t213 (not (_ @t191 @t212)))) % 1.42/1.69 (define @t215 () (or @t214 @t208)) % 1.42/1.69 (assume @p1 @t74) % 1.42/1.69 (assume @p2 true) % 1.42/1.69 (step @p3 :rule bool-double-not-elim :args (@t91)) % 1.42/1.69 (step @p4 :rule refl :args (@t94)) % 1.42/1.69 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t94 (not @t93)))) % 1.42/1.69 (step @p6 :rule cnf_or_neg :args (@t94 0)) % 1.42/1.69 (step @p7 :rule eq_resolve :premises (@p6 @p5)) % 1.42/1.69 (step @p8 :rule reordering :premises (@p7) :args ((or @t91 @t94))) % 1.42/1.69 (step @p9 :rule cnf_or_neg :args (@t94 1)) % 1.42/1.69 ; WARNING: add trust step for TRUST % 1.42/1.69 ; trust TRUST THEORY_LEMMA % 1.42/1.69 (step @p10 :rule trust :premises () :args ((forall @t99 (or (forall @t98 (not (_ @t86 @t95 @t97))) (_ @t86 @t95 @t96))))) % 1.42/1.69 (step @p11 :rule instantiate :premises (@p10) :args ((@list @t90))) % 1.42/1.69 (step @p12 :rule cnf_or_pos :args (@t101)) % 1.42/1.69 (step @p13 :rule reordering :premises (@p12) :args ((or @t92 @t100 (not @t101)))) % 1.42/1.69 (assume-push @p363 @t100) % 1.42/1.69 (step @p15 :rule instantiate :premises (@p363) :args ((@list @t89))) % 1.42/1.69 (step-pop @p364 :rule scope :premises (@p15)) % 1.42/1.69 (step @p16 :rule process_scope :premises (@p364) :args (@t93)) % 1.42/1.69 (step @p18 :rule implies_elim :premises (@p16)) % 1.42/1.69 (step @p19 :rule reordering :premises (@p18) :args ((or @t93 (not @t100)))) % 1.42/1.69 (step @p20 :rule chain_m_resolution :premises (@p19 @p13 @p11 @p9 @p8) :args (@t94 (@list false false true false) (@list @t100 @t101 @t92 @t91))) % 1.42/1.69 (step @p21 :rule refl :args (@t102)) % 1.42/1.69 (step @p22 :rule bool-double-not-elim :args (@t88)) % 1.42/1.69 (step @p23 :rule nary_cong :premises (@p22 @p21) :args ((or (not @t103) @t102))) % 1.42/1.69 (assume-push @p365 @t103) % 1.42/1.69 (step @p25 :rule skolemize :premises (@p365)) % 1.42/1.69 (step-pop @p366 :rule scope :premises (@p25)) % 1.42/1.69 (step @p26 :rule process_scope :premises (@p366) :args (@t102)) % 1.42/1.69 (step @p28 :rule implies_elim :premises (@p26)) % 1.42/1.69 (step @p29 :rule eq_resolve :premises (@p28 @p23)) % 1.42/1.69 (step @p30 :rule chain_m_resolution :premises (@p29 @p20) :args (@t88 @t104 (@list @t94))) % 1.42/1.69 (step @p31 :rule beta-reduce :args ((= @t106 @t76))) % 1.42/1.69 (step @p32 :rule refl :args (@t38)) % 1.42/1.69 (step @p33 :rule cong :premises (@p32 @p31) :args (@t107)) % 1.42/1.69 (step @p34 :rule refl :args (@t87)) % 1.42/1.69 (step @p35 :rule nary_cong :premises (@p34 @p33) :args (@t108)) % 1.42/1.69 (step @p36 :rule cong :premises (@p35) :args (@t109)) % 1.42/1.69 (step @p37 :rule cong :premises (@p36) :args (@t110)) % 1.42/1.69 (step @p38 :rule refl :args (@t111)) % 1.42/1.69 (step @p39 :rule cong :premises (@p38 @p37) :args ((=> @t111 @t110))) % 1.42/1.69 (assume-push @p367 @t111) % 1.42/1.69 (step @p41 :rule instantiate :premises (@p367) :args ((@list @t105))) % 1.42/1.69 (step-pop @p368 :rule scope :premises (@p41)) % 1.42/1.69 (step @p42 :rule process_scope :premises (@p368) :args (@t110)) % 1.42/1.69 (step @p44 :rule eq_resolve :premises (@p42 @p39)) % 1.42/1.69 (step @p45 :rule implies_elim :premises (@p44)) % 1.42/1.69 (step @p46 :rule chain_m_resolution :premises (@p45 @p30) :args (@t112 @t104 (@list @t88))) % 1.42/1.69 (step @p47 :rule bool-double-not-elim :args (@t85)) % 1.42/1.69 (step @p48 :rule nary_cong :premises (@p47 @p38) :args ((or (not @t113) @t111))) % 1.42/1.69 (step @p49 :rule bool-double-not-elim :args (@t111)) % 1.42/1.69 (step @p50 :rule refl :args (@t113)) % 1.42/1.69 (step @p51 :rule cong :premises (@p50 @p49) :args ((=> @t113 @t114))) % 1.42/1.69 (assume-push @p369 @t113) % 1.42/1.69 (step @p53 :rule skolemize :premises (@p369)) % 1.42/1.69 (step-pop @p370 :rule scope :premises (@p53)) % 1.42/1.69 (step @p54 :rule process_scope :premises (@p370) :args (@t114)) % 1.42/1.69 (step @p56 :rule eq_resolve :premises (@p54 @p51)) % 1.42/1.69 (step @p57 :rule implies_elim :premises (@p56)) % 1.42/1.69 (step @p58 :rule eq_resolve :premises (@p57 @p48)) % 1.42/1.69 (step @p59 :rule chain_m_resolution :premises (@p58 @p46) :args (@t85 @t115 (@list @t111))) % 1.42/1.69 (step @p60 :rule cnf_implies_neg2 :args (@t125)) % 1.42/1.69 (step @p61 :rule chain_m_resolution :premises (@p60 @p59) :args (@t125 @t104 (@list @t85))) % 1.42/1.69 (step @p62 :rule bool-impl-elim :args (@t130 @t134)) % 1.42/1.69 (step @p63 :rule cong :premises (@p62) :args ((forall @t18 (=> @t130 @t134)))) % 1.42/1.69 (step @p64 :rule exists-elim :args ((= (exists @t9 @t133) @t134))) 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(@t71)) % 1.42/1.69 (step @p280 :rule trans :premises (@p279 @p227)) % 1.42/1.69 (step @p281 :rule cong :premises (@p280 @p225) :args (@t72)) % 1.42/1.69 (step @p282 :rule nary_cong :premises (@p281 @p171) :args (@t73)) % 1.42/1.69 (step @p283 :rule cong :premises (@p282) :args (@t74)) % 1.42/1.69 (step @p284 :rule eq_resolve :premises (@p1 @p283)) % 1.42/1.69 (step @p285 :rule not_and :premises (@p284)) % 1.42/1.69 (step @p286 :rule chain_m_resolution :premises (@p285 @p61) :args ((not @t177) @t104 (@list @t125))) % 1.42/1.69 (step @p287 :rule cnf_implies_neg2 :args (@t177)) % 1.42/1.69 (step @p288 :rule chain_m_resolution :premises (@p287 @p286) :args (@t178 @t115 (@list @t177))) % 1.42/1.69 (step @p289 :rule refl :args (@t186)) % 1.42/1.69 (step @p290 :rule bool-double-not-elim :args (@t176)) % 1.42/1.69 (step @p291 :rule nary_cong :premises (@p290 @p289) :args ((or (not @t178) @t186))) % 1.42/1.69 (assume-push @p371 @t178) % 1.42/1.69 (step @p293 :rule skolemize :premises (@p371)) % 1.42/1.69 (step-pop @p372 :rule scope :premises (@p293)) % 1.42/1.69 (step @p294 :rule process_scope :premises (@p372) :args (@t186)) % 1.42/1.69 (step @p296 :rule implies_elim :premises (@p294)) % 1.42/1.69 (step @p297 :rule eq_resolve :premises (@p296 @p291)) % 1.42/1.69 (step @p298 :rule chain_m_resolution :premises (@p297 @p288) :args (@t186 @t115 (@list @t176))) % 1.42/1.69 (step @p299 :rule bool-double-not-elim :args (@t183)) % 1.42/1.69 (step @p300 :rule refl :args (@t185)) % 1.42/1.69 (step @p301 :rule nary_cong :premises (@p300 @p299) :args ((or @t185 (not @t184)))) % 1.42/1.69 (step @p302 :rule cnf_or_neg :args (@t185 0)) % 1.42/1.69 (step @p303 :rule eq_resolve :premises (@p302 @p301)) % 1.42/1.69 (step @p304 :rule reordering :premises (@p303) :args ((or @t183 @t185))) % 1.42/1.69 (step @p305 :rule chain_m_resolution :premises (@p304 @p298) :args (@t183 @t115 @t187)) % 1.42/1.69 (assume-push @p373 @t183) % 1.42/1.69 (step @p307 :rule instantiate :premises (@p373) :args (@t192)) % 1.42/1.69 (step-pop @p374 :rule scope :premises (@p307)) % 1.42/1.69 (step @p308 :rule process_scope :premises (@p374) :args (@t197)) % 1.42/1.69 (step @p310 :rule implies_elim :premises (@p308)) % 1.42/1.69 (step @p311 :rule chain_m_resolution :premises (@p310 @p305) :args (@t197 @t104 (@list @t183))) % 1.42/1.69 (step @p312 :rule bool-double-not-elim :args (@t181)) % 1.42/1.69 (step @p313 :rule nary_cong :premises (@p300 @p312) :args ((or @t185 (not @t182)))) % 1.42/1.69 (step @p314 :rule cnf_or_neg :args (@t185 1)) % 1.42/1.69 (step @p315 :rule eq_resolve :premises (@p314 @p313)) % 1.42/1.69 (step @p316 :rule reordering :premises (@p315) :args ((or @t181 @t185))) % 1.42/1.69 (step @p317 :rule chain_m_resolution :premises (@p316 @p298) :args (@t181 @t115 @t187)) % 1.42/1.69 (step @p318 :rule beta-reduce :args ((= @t202 @t189))) % 1.42/1.69 (step @p319 :rule cong :premises (@p318) :args (@t203)) % 1.42/1.69 (step @p320 :rule refl :args (@t180)) % 1.42/1.69 (step @p321 :rule nary_cong :premises (@p320 @p319) :args (@t204)) % 1.42/1.69 (step @p322 :rule cong :premises (@p321) :args (@t205)) % 1.42/1.69 (step @p323 :rule cong :premises (@p322) :args (@t206)) % 1.42/1.69 (step @p324 :rule refl :args (@t181)) % 1.42/1.69 (step @p325 :rule cong :premises (@p324 @p323) :args ((=> @t181 @t206))) % 1.42/1.69 (assume-push @p375 @t181) % 1.42/1.69 (step @p327 :rule instantiate :premises (@p375) :args ((@list @t201))) % 1.42/1.69 (step-pop @p376 :rule scope :premises (@p327)) % 1.42/1.69 (step @p328 :rule process_scope :premises (@p376) :args (@t206)) % 1.42/1.69 (step @p330 :rule eq_resolve :premises (@p328 @p325)) % 1.42/1.69 (step @p331 :rule implies_elim :premises (@p330)) % 1.42/1.69 (step @p332 :rule chain_m_resolution :premises (@p331 @p317) :args (@t207 @t104 (@list @t181))) % 1.42/1.69 (step @p333 :rule refl :args (@t210)) % 1.42/1.69 (step @p334 :rule bool-double-not-elim :args (@t190)) % 1.42/1.69 (step @p335 :rule nary_cong :premises (@p334 @p333) :args ((or (not @t207) @t210))) % 1.42/1.69 (assume-push @p377 @t207) % 1.42/1.69 (step @p337 :rule skolemize :premises (@p377)) % 1.42/1.69 (step-pop @p378 :rule scope :premises (@p337)) % 1.42/1.69 (step @p338 :rule process_scope :premises (@p378) :args (@t210)) % 1.42/1.69 (step @p340 :rule implies_elim :premises (@p338)) % 1.42/1.69 (step @p341 :rule eq_resolve :premises (@p340 @p335)) % 1.42/1.69 (step @p342 :rule chain_m_resolution :premises (@p341 @p332) :args (@t210 @t115 (@list @t190))) % 1.42/1.69 (step @p343 :rule bool-double-not-elim :args (@t195)) % 1.42/1.69 (step @p344 :rule refl :args (@t209)) % 1.42/1.69 (step @p345 :rule nary_cong :premises (@p344 @p343) :args ((or @t209 (not @t196)))) % 1.42/1.69 (step @p346 :rule cnf_or_neg :args (@t209 0)) % 1.42/1.69 (step @p347 :rule eq_resolve :premises (@p346 @p345)) % 1.42/1.69 (step @p348 :rule reordering :premises (@p347) :args ((or @t195 @t209))) % 1.42/1.69 (step @p349 :rule chain_m_resolution :premises (@p348 @p342) :args (@t195 @t115 @t211)) % 1.42/1.69 (step @p350 :rule cnf_or_pos :args (@t197)) % 1.42/1.69 (step @p351 :rule reordering :premises (@p350) :args ((or @t196 @t194 (not @t197)))) % 1.42/1.69 (step @p352 :rule chain_m_resolution :premises (@p351 @p349 @p311) :args (@t194 (@list false false) (@list @t195 @t197))) % 1.42/1.69 ; trust TRUST THEORY_LEMMA % 1.42/1.69 (step @p353 :rule trust :premises () :args ((forall @t200 (or (forall @t213 (not (_ @t198 @t212))) (_ @t198 @t199))))) % 1.42/1.69 (step @p354 :rule instantiate :premises (@p353) :args (@t192)) % 1.42/1.69 (step @p355 :rule cnf_or_neg :args (@t209 1)) % 1.42/1.69 (step @p356 :rule chain_m_resolution :premises (@p355 @p342) :args ((not @t208) @t115 @t211)) % 1.42/1.69 (step @p357 :rule cnf_or_pos :args (@t215)) % 1.42/1.69 (step @p358 :rule reordering :premises (@p357) :args ((or @t208 @t214 (not @t215)))) % 1.42/1.69 (step @p359 :rule chain_m_resolution :premises (@p358 @p356 @p354) :args (@t214 (@list true false) (@list @t208 @t215))) % 1.42/1.69 (step @p360 :rule alpha_equiv :args (@t193 (@list @t11) (@list @t212))) % 1.42/1.69 (step @p361 :rule equiv_elim2 :premises (@p360)) % 1.42/1.69 (step @p362 false :rule chain_m_resolution :premises (@p361 @p359 @p352) :args (false (@list false true) (@list @t214 @t193))) % 1.42/1.69 ) % 1.42/1.69 % SZS output end Proof % 1.42/1.69 % cvc5 exiting %------------------------------------------------------------------------------