%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV243^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:55:40 AM UTC 2026 % Result : Theorem 150.52s 150.83s % Output : Proof 150.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV243^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n017.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 18:20:46 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 150.52/150.83 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 150.52/150.83 --- 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... % 150.52/150.83 --- 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... % 150.52/150.83 --- Run --ho-elim --full-saturate-quant at 18s... % 150.52/150.83 % SZS status Theorem % 150.52/150.83 % SZS output start Proof % 150.52/150.83 ( % 150.52/150.83 (declare-sort tptp.a 0) % 150.52/150.83 (declare-const tptp.cK (-> (-> tptp.a Bool) tptp.a Bool)) % 150.52/150.83 (define @t1 () (@var "Xx" tptp.a)) % 150.52/150.83 (define @t2 () (@var "S" (-> tptp.a Bool))) % 150.52/150.83 (define @t3 () (_ @t2 @t1)) % 150.52/150.83 (define @t4 () (@var "Xx0" tptp.a)) % 150.52/150.83 (define @t5 () (_ tptp.cK @t2)) % 150.52/150.83 (define @t6 () (_ @t5 @t4)) % 150.52/150.83 (define @t7 () (_ @t2 @t4)) % 150.52/150.83 (define @t8 () (@list @t4)) % 150.52/150.83 (define @t9 () (forall @t8 (=> @t7 @t6))) % 150.52/150.83 (define @t10 () (and @t9 @t3)) % 150.52/150.83 (define @t11 () (@list @t2)) % 150.52/150.83 (define @t12 () (exists @t11 @t10)) % 150.52/150.83 (define @t13 () (@var "Xx1" tptp.a)) % 150.52/150.83 (define @t14 () (_ @t5 @t13)) % 150.52/150.83 (define @t15 () (_ @t2 @t13)) % 150.52/150.83 (define @t16 () (@list @t13)) % 150.52/150.83 (define @t17 () (forall @t16 (=> @t15 @t14))) % 150.52/150.83 (define @t18 () (and @t17 @t7)) % 150.52/150.83 (define @t19 () (exists @t11 @t18)) % 150.52/150.83 (define @t20 () (lambda @t8 @t19)) % 150.52/150.83 (define @t21 () (= (_ (_ tptp.cK @t20) @t1) @t12)) % 150.52/150.83 (define @t22 () (@list @t1)) % 150.52/150.83 (define @t23 () (forall @t22 @t21)) % 150.52/150.83 (define @t24 () (@var "Y" (-> tptp.a Bool))) % 150.52/150.83 (define @t25 () (_ (_ tptp.cK @t24) @t1)) % 150.52/150.83 (define @t26 () (@var "X" (-> tptp.a Bool))) % 150.52/150.83 (define @t27 () (_ (_ tptp.cK @t26) @t1)) % 150.52/150.83 (define @t28 () (forall @t22 (=> @t27 @t25))) % 150.52/150.83 (define @t29 () (_ @t24 @t1)) % 150.52/150.83 (define @t30 () (_ @t26 @t1)) % 150.52/150.83 (define @t31 () (forall @t22 (=> @t30 @t29))) % 150.52/150.83 (define @t32 () (=> @t31 @t28)) % 150.52/150.83 (define @t33 () (@list @t24 @t26)) % 150.52/150.83 (define @t34 () (forall @t33 @t32)) % 150.52/150.83 (define @t35 () (=> @t34 @t23)) % 150.52/150.83 (define @t36 () (not @t35)) % 150.52/150.83 (define @t37 () (@const 0 (@ho-elim-sort (-> tptp.a Bool)))) % 150.52/150.83 (define @t38 () (@const 1 (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a Bool)))) % 150.52/150.83 (define @t39 () (@const 2 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a Bool)) (@ho-elim-sort (-> tptp.a Bool)) (@ho-elim-sort (-> tptp.a Bool))))) % 150.52/150.83 (define @t40 () (_ @t39 @t38 @t37)) % 150.52/150.83 (define @t41 () (@const 3 (-> (@ho-elim-sort (-> tptp.a Bool)) tptp.a Bool))) % 150.52/150.83 (define @t42 () (_ @t41 @t40 @t1)) % 150.52/150.83 (define @t43 () (_ @t41 @t37 @t1)) % 150.52/150.83 (define @t44 () (forall @t22 (or (not @t43) @t42))) % 150.52/150.83 (define @t45 () (@quantifiers_skolemize @t44 0)) % 150.52/150.83 (define @t46 () (_ @t41 @t37 @t45)) % 150.52/150.83 (define @t47 () (_ @t41 @t40 @t45)) % 150.52/150.83 (define @t48 () (not @t46)) % 150.52/150.83 (define @t49 () (or @t48 @t47)) % 150.52/150.83 (define @t50 () (@var "BOUND_VARIABLE_7557" tptp.a)) % 150.52/150.83 (define @t51 () (@var "BOUND_VARIABLE_7582" (@ho-elim-sort (-> tptp.a Bool)))) % 150.52/150.83 (define @t52 () (_ @t39 @t38 @t51)) % 150.52/150.83 (define @t53 () (not (forall @t16 (or (not (_ @t41 @t51 @t13)) (_ @t41 @t52 @t13))))) % 150.52/150.83 (define @t54 () (@list @t51)) % 150.52/150.83 (define @t55 () (not (forall @t54 (or @t53 (not (_ @t41 @t51 @t50)))))) % 150.52/150.83 (define @t56 () (_ @t41 @t37 @t50)) % 150.52/150.83 (define @t57 () (@list @t50)) % 150.52/150.83 (define @t58 () (forall @t57 (= @t55 @t56))) % 150.52/150.83 (define @t59 () (@const 4 (-> tptp.a Bool))) % 150.52/150.83 (define @t60 () (tptp.cK @t2 @t13)) % 150.52/150.83 (define @t61 () (_ @t2 @t13)) % 150.52/150.83 (define @t62 () (not @t61)) % 150.52/150.83 (define @t63 () (or @t62 @t60)) % 150.52/150.83 (define @t64 () (forall @t16 @t63)) % 150.52/150.83 (define @t65 () (not @t64)) % 150.52/150.83 (define @t66 () (forall @t57 (= (not (forall @t11 (or @t65 (not (_ @t2 @t50))))) (_ @t59 @t50)))) % 150.52/150.83 (define @t67 () (@list @t45)) % 150.52/150.83 (define @t68 () (forall @t54 (or @t53 (not (_ @t41 @t51 @t45))))) % 150.52/150.83 (define @t69 () (not @t68)) % 150.52/150.83 (define @t70 () (= @t46 @t69)) % 150.52/150.83 (define @t71 () (@quantifiers_skolemize @t68 0)) % 150.52/150.83 (define @t72 () (_ @t41 @t71 @t45)) % 150.52/150.83 (define @t73 () (not @t72)) % 150.52/150.83 (define @t74 () (_ @t39 @t38 @t71)) % 150.52/150.83 (define @t75 () (forall @t16 (or (not (_ @t41 @t71 @t13)) (_ @t41 @t74 @t13)))) % 150.52/150.83 (define @t76 () (not @t75)) % 150.52/150.83 (define @t77 () (or @t76 @t73)) % 150.52/150.83 (define @t78 () (not @t77)) % 150.52/150.83 (define @t79 () (_ @t41 @t74 @t45)) % 150.52/150.83 (define @t80 () (or @t73 @t79)) % 150.52/150.83 (define @t81 () (not (forall @t8 (or (not (_ @t41 @t51 @t4)) (_ @t41 @t52 @t4))))) % 150.52/150.83 (define @t82 () (not (forall @t54 (or @t81 (not (_ @t41 @t51 @t1)))))) % 150.52/150.83 (define @t83 () (forall @t22 (= @t82 @t42))) % 150.52/150.83 (define @t84 () (@var "BOUND_VARIABLE_7476" tptp.a)) % 150.52/150.83 (define @t85 () (@var "BOUND_VARIABLE_7599" (@ho-elim-sort (-> tptp.a Bool)))) % 150.52/150.83 (define @t86 () (@var "BOUND_VARIABLE_7603" (@ho-elim-sort (-> tptp.a Bool)))) % 150.52/150.83 (define @t87 () (forall (@list @t85 @t86 @t84) (or (not (forall @t22 (or (not (_ @t41 @t86 @t1)) (_ @t41 @t85 @t1)))) (not (_ @t41 (_ @t39 @t38 @t86) @t84)) (_ @t41 (_ @t39 @t38 @t85) @t84)))) % 150.52/150.83 (define @t88 () (=> @t87 @t83)) % 150.52/150.83 (define @t89 () (not @t88)) % 150.52/150.83 (define @t90 () (_ @t2 @t1)) % 150.52/150.83 (define @t91 () (tptp.cK @t2 @t4)) % 150.52/150.83 (define @t92 () (_ @t2 @t4)) % 150.52/150.83 (define @t93 () (not @t92)) % 150.52/150.83 (define @t94 () (forall @t8 (or @t93 @t91))) % 150.52/150.83 (define @t95 () (not @t94)) % 150.52/150.83 (define @t96 () (not (forall @t11 (or @t95 (not @t90))))) % 150.52/150.83 (define @t97 () (tptp.cK @t24 @t84)) % 150.52/150.83 (define @t98 () (not (tptp.cK @t26 @t84))) % 150.52/150.83 (define @t99 () (_ @t24 @t1)) % 150.52/150.83 (define @t100 () (_ @t26 @t1)) % 150.52/150.83 (define @t101 () (forall @t22 (or (not @t100) @t99))) % 150.52/150.83 (define @t102 () (not @t101)) % 150.52/150.83 (define @t103 () (or @t102 @t98 @t97)) % 150.52/150.83 (define @t104 () (@list @t24 @t26 @t84)) % 150.52/150.83 (define @t105 () (forall @t104 @t103)) % 150.52/150.83 (define @t106 () (not (=> @t105 (forall @t22 (= @t96 (tptp.cK @t59 @t1)))))) % 150.52/150.83 (define @t107 () (or @t65 @t93)) % 150.52/150.83 (define @t108 () (forall @t11 @t107)) % 150.52/150.83 (define @t109 () (not @t108)) % 150.52/150.83 (define @t110 () (lambda @t8 @t109)) % 150.52/150.83 (define @t111 () (tptp.cK @t110 @t1)) % 150.52/150.83 (define @t112 () (not @t7)) % 150.52/150.83 (define @t113 () (not @t15)) % 150.52/150.83 (define @t114 () (or @t113 @t14)) % 150.52/150.83 (define @t115 () (forall @t16 @t114)) % 150.52/150.83 (define @t116 () (lambda @t8 (not (forall @t11 (or (not @t115) @t112))))) % 150.52/150.83 (define @t117 () (_ (_ tptp.cK @t110) @t1)) % 150.52/150.83 (define @t118 () (= @t117 @t96)) % 150.52/150.83 (define @t119 () (not @t3)) % 150.52/150.83 (define @t120 () (or @t95 @t119)) % 150.52/150.83 (define @t121 () (and @t94 @t3)) % 150.52/150.83 (define @t122 () (forall @t11 (not @t121))) % 150.52/150.83 (define @t123 () (not @t122)) % 150.52/150.83 (define @t124 () (or @t112 @t6)) % 150.52/150.83 (define @t125 () (or @t65 @t112)) % 150.52/150.83 (define @t126 () (and @t64 @t7)) % 150.52/150.83 (define @t127 () (forall @t11 (not @t126))) % 150.52/150.83 (define @t128 () (not @t127)) % 150.52/150.83 (define @t129 () (or @t98 @t97)) % 150.52/150.83 (define @t130 () (or @t102 @t129)) % 150.52/150.83 (define @t131 () (forall @t104 @t130)) % 150.52/150.83 (define @t132 () (@list @t84)) % 150.52/150.83 (define @t133 () (forall @t132 @t130)) % 150.52/150.83 (define @t134 () (forall @t132 @t129)) % 150.52/150.83 (define @t135 () (or @t102 @t134)) % 150.52/150.83 (define @t136 () (tptp.cK @t24 @t1)) % 150.52/150.83 (define @t137 () (tptp.cK @t26 @t1)) % 150.52/150.83 (define @t138 () (forall @t22 (or (not @t137) @t136))) % 150.52/150.83 (define @t139 () (not @t27)) % 150.52/150.83 (define @t140 () (or @t139 @t25)) % 150.52/150.83 (define @t141 () (not @t30)) % 150.52/150.83 (define @t142 () (or @t141 @t29)) % 150.52/150.83 (define @t143 () (not @t79)) % 150.52/150.83 (define @t144 () (forall @t22 (or (not (_ @t41 @t71 @t1)) @t43))) % 150.52/150.83 (define @t145 () (not @t144)) % 150.52/150.83 (define @t146 () (or @t145 @t143 @t47)) % 150.52/150.83 (define @t147 () (@quantifiers_skolemize @t144 0)) % 150.52/150.83 (define @t148 () (_ @t41 @t37 @t147)) % 150.52/150.83 (define @t149 () (_ @t41 @t71 @t147)) % 150.52/150.83 (define @t150 () (not @t149)) % 150.52/150.83 (define @t151 () (or @t150 @t148)) % 150.52/150.83 (define @t152 () (not @t151)) % 150.52/150.83 (define @t153 () (or @t76 @t150)) % 150.52/150.83 (define @t154 () (forall @t54 (or @t53 (not (_ @t41 @t51 @t147))))) % 150.52/150.83 (define @t155 () (not @t154)) % 150.52/150.83 (define @t156 () (= @t148 @t155)) % 150.52/150.83 (define @t157 () (not @t156)) % 150.52/150.83 (define @t158 () (not @t49)) % 150.52/150.83 (define @t159 () (not @t44)) % 150.52/150.83 (define @t160 () (@list false)) % 150.52/150.83 (define @t161 () (@quantifiers_skolemize (forall @t22 (= @t42 @t82)) 0)) % 150.52/150.83 (define @t162 () (@list @t161)) % 150.52/150.83 (define @t163 () (_ @t41 @t40 @t161)) % 150.52/150.83 (define @t164 () (_ @t41 @t37 @t161)) % 150.52/150.83 (define @t165 () (not @t164)) % 150.52/150.83 (define @t166 () (or @t165 @t163)) % 150.52/150.83 (define @t167 () (not (_ @t41 @t51 @t161))) % 150.52/150.83 (define @t168 () (forall @t54 (or @t81 @t167))) % 150.52/150.83 (define @t169 () (not @t163)) % 150.52/150.83 (define @t170 () (not @t168)) % 150.52/150.83 (define @t171 () (= @t163 @t170)) % 150.52/150.83 (define @t172 () (_ @t39 @t38 @t40)) % 150.52/150.83 (define @t173 () (forall @t8 (or (not (_ @t41 @t40 @t4)) (_ @t41 @t172 @t4)))) % 150.52/150.83 (define @t174 () (@quantifiers_skolemize @t173 0)) % 150.52/150.83 (define @t175 () (_ @t41 @t40 @t174)) % 150.52/150.83 (define @t176 () (_ @t41 @t172 @t174)) % 150.52/150.83 (define @t177 () (not @t175)) % 150.52/150.83 (define @t178 () (or @t177 @t176)) % 150.52/150.83 (define @t179 () (or @t159 @t177 @t176)) % 150.52/150.83 (define @t180 () (not @t178)) % 150.52/150.83 (define @t181 () (not @t173)) % 150.52/150.83 (define @t182 () (or @t181 @t169)) % 150.52/150.83 (define @t183 () (@var "BOUND_VARIABLE_10851" (@ho-elim-sort (-> tptp.a Bool)))) % 150.52/150.83 (define @t184 () (@var "BOUND_VARIABLE_10852" tptp.a)) % 150.52/150.83 (define @t185 () (@list @t183 @t184)) % 150.52/150.83 (define @t186 () (forall @t54 (or @t53 @t167))) % 150.52/150.83 (define @t187 () (not @t186)) % 150.52/150.83 (define @t188 () (= @t164 @t187)) % 150.52/150.83 (define @t189 () (not @t188)) % 150.52/150.83 (assume @p1 @t36) % 150.52/150.83 (assume @p2 true) % 150.52/150.83 (step @p3 :rule bool-double-not-elim :args (@t46)) % 150.52/150.83 (step @p4 :rule refl :args (@t49)) % 150.52/150.83 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t49 (not @t48)))) % 150.52/150.83 (step @p6 :rule cnf_or_neg :args (@t49 0)) % 150.52/150.83 (step @p7 :rule eq_resolve :premises (@p6 @p5)) % 150.52/150.83 (step @p8 :rule reordering :premises (@p7) :args ((or @t46 @t49))) % 150.52/150.83 (step @p9 :rule cnf_or_neg :args (@t49 1)) % 150.52/150.83 (step @p10 :rule eq-symm :args (@t55 @t56)) % 150.52/150.83 (step @p11 :rule cong :premises (@p10) :args (@t58)) % 150.52/150.83 ; WARNING: add trust step for TRUST % 150.52/150.83 ; trust TRUST PREPROCESS_HO_ELIM % 150.52/150.83 (step @p12 :rule trust :premises () :args ((= @t66 @t58))) % 150.52/150.83 (step @p13 :rule trans :premises (@p12 @p11)) % 150.52/150.83 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 150.52/150.83 (step @p14 :rule trust :premises () :args (@t66)) % 150.52/150.83 (step @p15 :rule eq_resolve :premises (@p14 @p13)) % 150.52/150.83 (step @p16 :rule instantiate :premises (@p15) :args (@t67)) % 150.52/150.83 (step @p17 :rule cnf_equiv_pos1 :args (@t70)) % 150.52/150.83 (step @p18 :rule reordering :premises (@p17) :args ((or @t48 @t69 (not @t70)))) % 150.52/150.83 (step @p19 :rule refl :args (@t78)) % 150.52/150.83 (step @p20 :rule bool-double-not-elim :args (@t68)) % 150.52/150.83 (step @p21 :rule nary_cong :premises (@p20 @p19) :args ((or (not @t69) @t78))) % 150.52/150.83 (assume-push @p315 @t69) % 150.52/150.83 (step @p23 :rule skolemize :premises (@p315)) % 150.52/150.83 (step-pop @p316 :rule scope :premises (@p23)) % 150.52/150.83 (step @p24 :rule process_scope :premises (@p316) :args (@t78)) % 150.52/150.83 (step @p26 :rule implies_elim :premises (@p24)) % 150.52/150.83 (step @p27 :rule eq_resolve :premises (@p26 @p21)) % 150.52/150.83 (step @p28 :rule bool-double-not-elim :args (@t75)) % 150.52/150.83 (step @p29 :rule refl :args (@t77)) % 150.52/150.83 (step @p30 :rule nary_cong :premises (@p29 @p28) :args ((or @t77 (not @t76)))) % 150.52/150.83 (step @p31 :rule cnf_or_neg :args (@t77 0)) % 150.52/150.83 (step @p32 :rule eq_resolve :premises (@p31 @p30)) % 150.52/150.83 (step @p33 :rule reordering :premises (@p32) :args ((or @t75 @t77))) % 150.52/150.83 (step @p34 :rule bool-double-not-elim :args (@t72)) % 150.52/150.83 (step @p35 :rule nary_cong :premises (@p29 @p34) :args ((or @t77 (not @t73)))) % 150.52/150.83 (step @p36 :rule cnf_or_neg :args (@t77 1)) % 150.52/150.83 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 150.52/150.83 (step @p38 :rule reordering :premises (@p37) :args ((or @t72 @t77))) % 150.52/150.83 (assume-push @p317 @t75) % 150.52/150.83 (step @p40 :rule instantiate :premises (@p317) :args (@t67)) % 150.52/150.83 (step-pop @p318 :rule scope :premises (@p40)) % 150.52/150.83 (step @p41 :rule process_scope :premises (@p318) :args (@t80)) % 150.52/150.83 (step @p43 :rule implies_elim :premises (@p41)) % 150.52/150.83 (step @p44 :rule cnf_or_pos :args (@t80)) % 150.52/150.83 (step @p45 :rule reordering :premises (@p44) :args ((or @t73 @t79 (not @t80)))) % 150.52/150.83 (step @p46 :rule eq-symm :args (@t82 @t42)) % 150.52/150.83 (step @p47 :rule cong :premises (@p46) :args (@t83)) % 150.52/150.83 (step @p48 :rule refl :args (@t87)) % 150.52/150.83 (step @p49 :rule cong :premises (@p48 @p47) :args (@t88)) % 150.52/150.83 (step @p50 :rule cong :premises (@p49) :args (@t89)) % 150.52/150.83 ; trust TRUST PREPROCESS_HO_ELIM % 150.52/150.83 (step @p51 :rule trust :premises () :args ((= @t106 @t89))) % 150.52/150.83 ; trust TRUST PREPROCESS_HO_ELIM % 150.52/150.83 (step @p52 :rule trust :premises () :args ((= (not (=> @t105 (forall @t22 (= @t96 @t111)))) @t106))) % 150.52/150.83 (step @p53 :rule eq-symm :args (@t111 @t96)) % 150.52/150.83 (step @p54 :rule cong :premises (@p53) :args ((forall @t22 (= @t111 @t96)))) % 150.52/150.83 (step @p55 :rule refl :args (@t96)) % 150.52/150.83 (step @p56 :rule refl :args ((tptp.cK @t116 @t1))) % 150.52/150.83 (step @p57 :rule refl :args (@t1)) % 150.52/150.83 (step @p58 :rule refl :args (@t92)) % 150.52/150.83 (step @p59 :rule cong :premises (@p58) :args (@t93)) % 150.52/150.83 (step @p60 :rule refl :args (@t60)) % 150.52/150.83 (step @p61 :rule refl :args (@t61)) % 150.52/150.83 (step @p62 :rule cong :premises (@p61) :args (@t62)) % 150.52/150.83 (step @p63 :rule nary_cong :premises (@p62 @p60) :args (@t63)) % 150.52/150.83 (step @p64 :rule cong :premises (@p63) :args (@t64)) % 150.52/150.83 (step @p65 :rule cong :premises (@p64) :args (@t65)) % 150.52/150.83 (step @p66 :rule nary_cong :premises (@p65 @p59) :args (@t107)) % 150.52/150.83 (step @p67 :rule cong :premises (@p66) :args (@t108)) % 150.52/150.83 (step @p68 :rule cong :premises (@p67) :args (@t109)) % 150.52/150.83 (step @p69 :rule cong :premises (@p68) :args (@t110)) % 150.52/150.83 (step @p70 :rule cong :premises (@p69 @p57) :args (@t111)) % 150.52/150.83 (step @p71 :rule trans :premises (@p70 @p56)) % 150.52/150.83 (step @p72 :rule refl :args (tptp.cK)) % 150.52/150.83 (step @p73 :rule ho_cong :premises (@p72 @p69)) % 150.52/150.83 (step @p74 :rule ho_cong :premises (@p73 @p57)) % 150.52/150.83 (step @p75 :rule cong :premises (@p74 @p71) :args ((= @t117 @t111))) % 150.52/150.83 (step @p76 :rule symm :premises (@p75)) % 150.52/150.83 (step @p77 :rule refl :args ((_ (_ tptp.cK @t116) @t1))) % 150.52/150.83 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 150.52/150.83 (step @p79 :rule cong :premises (@p78 @p55) :args (@t118)) % 150.52/150.83 (step @p80 :rule cong :premises (@p79) :args ((forall @t22 @t118))) % 150.52/150.83 (step @p81 :rule trans :premises (@p80 @p54)) % 150.52/150.83 (step @p82 :rule refl :args (@t90)) % 150.52/150.83 (step @p83 :rule refl :args (@t3)) % 150.52/150.83 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t3 @t90))) % 150.52/150.83 (step @p85 :rule symm :premises (@p84)) % 150.52/150.83 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 150.52/150.83 (step @p87 :rule cong :premises (@p86) :args (@t119)) % 150.52/150.83 (step @p88 :rule refl :args (@t95)) % 150.52/150.83 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t120)) % 150.52/150.83 (step @p90 :rule cong :premises (@p89) :args ((forall @t11 @t120))) % 150.52/150.83 (step @p91 :rule bool-and-de-morgan :args (@t94 @t3 true)) % 150.52/150.83 (step @p92 :rule cong :premises (@p91) :args (@t122)) % 150.52/150.83 (step @p93 :rule trans :premises (@p92 @p90)) % 150.52/150.83 (step @p94 :rule cong :premises (@p93) :args (@t123)) % 150.52/150.83 (step @p95 :rule exists-elim :args ((= (exists @t11 @t121) @t123))) % 150.52/150.83 (step @p96 :rule trans :premises (@p95 @p94)) % 150.52/150.83 (step @p97 :rule refl :args (@t3)) % 150.52/150.83 (step @p98 :rule refl :args (@t91)) % 150.52/150.83 (step @p99 :rule refl :args (@t6)) % 150.52/150.83 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t6 @t91))) % 150.52/150.83 (step @p101 :rule symm :premises (@p100)) % 150.52/150.83 (step @p102 :rule eq_resolve :premises (@p99 @p101)) % 150.52/150.83 (step @p103 :rule refl :args (@t7)) % 150.52/150.83 (step @p104 :rule cong :premises (@p103 @p58) :args ((= @t7 @t92))) % 150.52/150.83 (step @p105 :rule symm :premises (@p104)) % 150.52/150.83 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 150.52/150.83 (step @p107 :rule cong :premises (@p106) :args (@t112)) % 150.52/150.83 (step @p108 :rule nary_cong :premises (@p107 @p102) :args (@t124)) % 150.52/150.83 (step @p109 :rule cong :premises (@p108) :args ((forall @t8 @t124))) % 150.52/150.83 (step @p110 :rule bool-impl-elim :args (@t7 @t6)) % 150.52/150.83 (step @p111 :rule cong :premises (@p110) :args (@t9)) % 150.52/150.83 (step @p112 :rule trans :premises (@p111 @p109)) % 150.52/150.83 (step @p113 :rule nary_cong :premises (@p112 @p97) :args (@t10)) % 150.52/150.83 (step @p114 :rule cong :premises (@p113) :args (@t12)) % 150.52/150.83 (step @p115 :rule trans :premises (@p114 @p96)) % 150.52/150.83 (step @p116 :rule refl :args (@t1)) % 150.52/150.83 (step @p117 :rule refl :args (@t65)) % 150.52/150.83 (step @p118 :rule nary_cong :premises (@p117 @p107) :args (@t125)) % 150.52/150.83 (step @p119 :rule cong :premises (@p118) :args ((forall @t11 @t125))) % 150.52/150.83 (step @p120 :rule bool-and-de-morgan :args (@t64 @t7 true)) % 150.52/150.83 (step @p121 :rule cong :premises (@p120) :args (@t127)) % 150.52/150.83 (step @p122 :rule trans :premises (@p121 @p119)) % 150.52/150.83 (step @p123 :rule cong :premises (@p122) :args (@t128)) % 150.52/150.83 (step @p124 :rule exists-elim :args ((= (exists @t11 @t126) @t128))) % 150.52/150.83 (step @p125 :rule trans :premises (@p124 @p123)) % 150.52/150.83 (step @p126 :rule refl :args (@t7)) % 150.52/150.83 (step @p127 :rule refl :args (@t14)) % 150.52/150.83 (step @p128 :rule cong :premises (@p127 @p60) :args ((= @t14 @t60))) % 150.52/150.83 (step @p129 :rule symm :premises (@p128)) % 150.52/150.83 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 150.52/150.83 (step @p131 :rule refl :args (@t15)) % 150.52/150.83 (step @p132 :rule cong :premises (@p131 @p61) :args ((= @t15 @t61))) % 150.52/150.83 (step @p133 :rule symm :premises (@p132)) % 150.52/150.83 (step @p134 :rule eq_resolve :premises (@p131 @p133)) % 150.52/150.83 (step @p135 :rule cong :premises (@p134) :args (@t113)) % 150.52/150.83 (step @p136 :rule nary_cong :premises (@p135 @p130) :args (@t114)) % 150.52/150.83 (step @p137 :rule cong :premises (@p136) :args (@t115)) % 150.52/150.83 (step @p138 :rule bool-impl-elim :args (@t15 @t14)) % 150.52/150.83 (step @p139 :rule cong :premises (@p138) :args (@t17)) % 150.52/150.83 (step @p140 :rule trans :premises (@p139 @p137)) % 150.52/150.83 (step @p141 :rule nary_cong :premises (@p140 @p126) :args (@t18)) % 150.52/150.83 (step @p142 :rule cong :premises (@p141) :args (@t19)) % 150.52/150.83 (step @p143 :rule trans :premises (@p142 @p125)) % 150.52/150.83 (step @p144 :rule cong :premises (@p143) :args (@t20)) % 150.52/150.83 (step @p145 :rule refl :args (tptp.cK)) % 150.52/150.83 (step @p146 :rule ho_cong :premises (@p145 @p144)) % 150.52/150.83 (step @p147 :rule ho_cong :premises (@p146 @p116)) % 150.52/150.83 (step @p148 :rule cong :premises (@p147 @p115) :args (@t21)) % 150.52/150.83 (step @p149 :rule cong :premises (@p148) :args (@t23)) % 150.52/150.83 (step @p150 :rule trans :premises (@p149 @p81)) % 150.52/150.83 (step @p151 :rule aci_norm :args ((= @t130 @t103))) % 150.52/150.83 (step @p152 :rule cong :premises (@p151) :args (@t131)) % 150.52/150.83 (step @p153 :rule quant-merge-prenex :args ((= (forall @t33 @t133) @t131))) % 150.52/150.83 (step @p154 :rule alpha_equiv :args (@t134 (@list @t84) (@list @t1))) % 150.52/150.83 (step @p155 :rule refl :args (@t102)) % 150.52/150.83 (step @p156 :rule nary_cong :premises (@p155 @p154) :args (@t135)) % 150.52/150.83 (step @p157 :rule quant-miniscope-or :args ((= @t133 @t135))) % 150.52/150.83 (step @p158 :rule trans :premises (@p157 @p156)) % 150.52/150.83 (step @p159 :rule symm :premises (@p158)) % 150.52/150.83 (step @p160 :rule cong :premises (@p159) :args ((forall @t33 (or @t102 @t138)))) % 150.52/150.83 (step @p161 :rule trans :premises (@p160 @p153)) % 150.52/150.83 (step @p162 :rule trans :premises (@p161 @p152)) % 150.52/150.83 (step @p163 :rule bool-impl-elim :args (@t101 @t138)) % 150.52/150.83 (step @p164 :rule cong :premises (@p163) :args ((forall @t33 (=> @t101 @t138)))) % 150.52/150.83 (step @p165 :rule trans :premises (@p164 @p162)) % 150.52/150.83 (step @p166 :rule refl :args (@t136)) % 150.52/150.83 (step @p167 :rule refl :args (@t25)) % 150.52/150.83 (step @p168 :rule cong :premises (@p167 @p166) :args ((= @t25 @t136))) % 150.52/150.83 (step @p169 :rule symm :premises (@p168)) % 150.52/150.83 (step @p170 :rule eq_resolve :premises (@p167 @p169)) % 150.52/150.83 (step @p171 :rule refl :args (@t137)) % 150.52/150.83 (step @p172 :rule refl :args (@t27)) % 150.52/150.83 (step @p173 :rule cong :premises (@p172 @p171) :args ((= @t27 @t137))) % 150.52/150.83 (step @p174 :rule symm :premises (@p173)) % 150.52/150.83 (step @p175 :rule eq_resolve :premises (@p172 @p174)) % 150.52/150.83 (step @p176 :rule cong :premises (@p175) :args (@t139)) % 150.52/150.83 (step @p177 :rule nary_cong :premises (@p176 @p170) :args (@t140)) % 150.52/150.83 (step @p178 :rule cong :premises (@p177) :args ((forall @t22 @t140))) % 150.52/150.83 (step @p179 :rule bool-impl-elim :args (@t27 @t25)) % 150.52/150.83 (step @p180 :rule cong :premises (@p179) :args (@t28)) % 150.52/150.83 (step @p181 :rule trans :premises (@p180 @p178)) % 150.52/150.83 (step @p182 :rule refl :args (@t99)) % 150.52/150.83 (step @p183 :rule refl :args (@t29)) % 150.52/150.83 (step @p184 :rule cong :premises (@p183 @p182) :args ((= @t29 @t99))) % 150.52/150.83 (step @p185 :rule symm :premises (@p184)) % 150.52/150.83 (step @p186 :rule eq_resolve :premises (@p183 @p185)) % 150.52/150.83 (step @p187 :rule refl :args (@t100)) % 150.52/150.83 (step @p188 :rule refl :args (@t30)) % 150.52/150.83 (step @p189 :rule cong :premises (@p188 @p187) :args ((= @t30 @t100))) % 150.52/150.83 (step @p190 :rule symm :premises (@p189)) % 150.52/150.83 (step @p191 :rule eq_resolve :premises (@p188 @p190)) % 150.52/150.83 (step @p192 :rule cong :premises (@p191) :args (@t141)) % 150.52/150.83 (step @p193 :rule nary_cong :premises (@p192 @p186) :args (@t142)) % 150.52/150.83 (step @p194 :rule cong :premises (@p193) :args ((forall @t22 @t142))) % 150.52/150.83 (step @p195 :rule bool-impl-elim :args (@t30 @t29)) % 150.52/150.83 (step @p196 :rule cong :premises (@p195) :args (@t31)) % 150.52/150.83 (step @p197 :rule trans :premises (@p196 @p194)) % 150.52/150.83 (step @p198 :rule cong :premises (@p197 @p181) :args (@t32)) % 150.52/150.83 (step @p199 :rule cong :premises (@p198) :args (@t34)) % 150.52/150.83 (step @p200 :rule trans :premises (@p199 @p165)) % 150.52/150.83 (step @p201 :rule cong :premises (@p200 @p150) :args (@t35)) % 150.52/150.83 (step @p202 :rule cong :premises (@p201) :args (@t36)) % 150.52/150.83 (step @p203 :rule trans :premises (@p202 @p52 @p51 @p50)) % 150.52/150.83 (step @p204 :rule eq_resolve :premises (@p1 @p203)) % 150.52/150.83 (step @p205 :rule not_implies_elim1 :premises (@p204)) % 150.52/150.83 (step @p206 :rule instantiate :premises (@p205) :args ((@list @t37 @t71 @t45))) % 150.52/150.83 (step @p207 :rule cnf_or_pos :args (@t146)) % 150.52/150.83 (step @p208 :rule reordering :premises (@p207) :args ((or @t47 @t143 @t145 (not @t146)))) % 150.52/150.83 (step @p209 :rule refl :args (@t152)) % 150.52/150.83 (step @p210 :rule bool-double-not-elim :args (@t144)) % 150.52/150.83 (step @p211 :rule nary_cong :premises (@p210 @p209) :args ((or (not @t145) @t152))) % 150.52/150.83 (assume-push @p319 @t145) % 150.52/150.83 (step @p213 :rule skolemize :premises (@p319)) % 150.52/150.83 (step-pop @p320 :rule scope :premises (@p213)) % 150.52/150.83 (step @p214 :rule process_scope :premises (@p320) :args (@t152)) % 150.52/150.83 (step @p216 :rule implies_elim :premises (@p214)) % 150.52/150.83 (step @p217 :rule eq_resolve :premises (@p216 @p211)) % 150.52/150.83 (step @p218 :rule bool-double-not-elim :args (@t149)) % 150.52/150.83 (step @p219 :rule refl :args (@t151)) % 150.52/150.83 (step @p220 :rule nary_cong :premises (@p219 @p218) :args ((or @t151 (not @t150)))) % 150.52/150.83 (step @p221 :rule cnf_or_neg :args (@t151 0)) % 150.52/150.83 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 150.52/150.83 (step @p223 :rule reordering :premises (@p222) :args ((or @t149 @t151))) % 150.52/150.83 (step @p224 :rule cnf_or_neg :args (@t151 1)) % 150.52/150.83 (step @p225 :rule cnf_or_pos :args (@t153)) % 150.52/150.83 (step @p226 :rule reordering :premises (@p225) :args ((or @t76 @t150 (not @t153)))) % 150.52/150.83 (step @p227 :rule instantiate :premises (@p15) :args ((@list @t147))) % 150.52/150.83 (step @p228 :rule bool-double-not-elim :args (@t154)) % 150.52/150.83 (step @p229 :rule refl :args (@t148)) % 150.52/150.83 (step @p230 :rule refl :args (@t157)) % 150.52/150.83 (step @p231 :rule nary_cong :premises (@p230 @p229 @p228) :args ((or @t157 @t148 (not @t155)))) % 150.52/150.83 (step @p232 :rule cnf_equiv_pos2 :args (@t156)) % 150.52/150.83 (step @p233 :rule eq_resolve :premises (@p232 @p231)) % 150.52/150.83 (step @p234 :rule reordering :premises (@p233) :args ((or @t148 @t154 @t157))) % 150.52/150.83 (assume-push @p321 @t154) % 150.52/150.83 (step @p236 :rule instantiate :premises (@p321) :args ((@list @t71))) % 150.52/150.83 (step-pop @p322 :rule scope :premises (@p236)) % 150.52/150.83 (step @p237 :rule process_scope :premises (@p322) :args (@t153)) % 150.52/150.83 (step @p239 :rule implies_elim :premises (@p237)) % 150.52/150.83 (step @p240 :rule chain_m_resolution :premises (@p239 @p234 @p227 @p226 @p224 @p223 @p217 @p208 @p206 @p45 @p43 @p38 @p33 @p27 @p18 @p16 @p9 @p8) :args (@t49 (@list false false true true false true true false false false false false true true false true false) (@list @t154 @t156 @t153 @t148 @t149 @t151 @t144 @t146 @t79 @t80 @t72 @t75 @t77 @t68 @t70 @t47 @t46))) % 150.52/150.83 (step @p241 :rule refl :args (@t158)) % 150.52/150.83 (step @p242 :rule bool-double-not-elim :args (@t44)) % 150.52/150.83 (step @p243 :rule nary_cong :premises (@p242 @p241) :args ((or (not @t159) @t158))) % 150.52/150.83 (assume-push @p323 @t159) % 150.52/150.83 (step @p245 :rule skolemize :premises (@p323)) % 150.52/150.83 (step-pop @p324 :rule scope :premises (@p245)) % 150.52/150.83 (step @p246 :rule process_scope :premises (@p324) :args (@t158)) % 150.52/150.83 (step @p248 :rule implies_elim :premises (@p246)) % 150.52/150.83 (step @p249 :rule eq_resolve :premises (@p248 @p243)) % 150.52/150.83 (step @p250 :rule chain_m_resolution :premises (@p249 @p240) :args (@t44 @t160 (@list @t49))) % 150.52/150.83 (assume-push @p325 @t44) % 150.52/150.83 (step @p252 :rule instantiate :premises (@p325) :args (@t162)) % 150.52/150.83 (step-pop @p326 :rule scope :premises (@p252)) % 150.52/150.83 (step @p253 :rule process_scope :premises (@p326) :args (@t166)) % 150.52/150.83 (step @p255 :rule implies_elim :premises (@p253)) % 150.52/150.83 (step @p256 :rule chain_m_resolution :premises (@p255 @p250) :args (@t166 @t160 (@list @t44))) % 150.52/150.83 (step @p257 :rule not_implies_elim2 :premises (@p204)) % 150.52/150.83 (step @p258 :rule skolemize :premises (@p257)) % 150.52/150.83 (step @p259 :rule bool-double-not-elim :args (@t168)) % 150.52/150.83 (step @p260 :rule refl :args (@t169)) % 150.52/150.83 (step @p261 :rule refl :args (@t171)) % 150.52/150.83 (step @p262 :rule nary_cong :premises (@p261 @p260 @p259) :args ((or @t171 @t169 (not @t170)))) % 150.52/150.83 (step @p263 :rule cnf_equiv_neg2 :args (@t171)) % 150.52/150.83 (step @p264 :rule eq_resolve :premises (@p263 @p262)) % 150.52/150.83 (step @p265 :rule reordering :premises (@p264) :args ((or @t168 @t171 @t169))) % 150.52/150.83 (step @p266 :rule bool-double-not-elim :args (@t175)) % 150.52/150.83 (step @p267 :rule refl :args (@t178)) % 150.52/150.83 (step @p268 :rule nary_cong :premises (@p267 @p266) :args ((or @t178 (not @t177)))) % 150.52/150.83 (step @p269 :rule cnf_or_neg :args (@t178 0)) % 150.52/150.83 (step @p270 :rule eq_resolve :premises (@p269 @p268)) % 150.52/150.83 (step @p271 :rule reordering :premises (@p270) :args ((or @t175 @t178))) % 150.52/150.83 (step @p272 :rule cnf_or_neg :args (@t178 1)) % 150.52/150.83 (step @p273 :rule instantiate :premises (@p205) :args ((@list @t40 @t37 @t174))) % 150.52/150.83 (step @p274 :rule cnf_or_pos :args (@t179)) % 150.52/150.83 (step @p275 :rule reordering :premises (@p274) :args ((or @t177 @t176 @t159 (not @t179)))) % 150.52/150.83 (step @p276 :rule chain_m_resolution :premises (@p275 @p273 @p250 @p272 @p271) :args (@t178 (@list false false true false) (@list @t179 @t44 @t176 @t175))) % 150.52/150.83 (step @p277 :rule refl :args (@t180)) % 150.52/150.83 (step @p278 :rule bool-double-not-elim :args (@t173)) % 150.52/150.83 (step @p279 :rule nary_cong :premises (@p278 @p277) :args ((or (not @t181) @t180))) % 150.52/150.83 (assume-push @p327 @t181) % 150.52/150.83 (step @p281 :rule skolemize :premises (@p327)) % 150.52/150.83 (step-pop @p328 :rule scope :premises (@p281)) % 150.52/150.83 (step @p282 :rule process_scope :premises (@p328) :args (@t180)) % 150.52/150.83 (step @p284 :rule implies_elim :premises (@p282)) % 150.52/150.83 (step @p285 :rule eq_resolve :premises (@p284 @p279)) % 150.52/150.83 (step @p286 :rule chain_m_resolution :premises (@p285 @p276) :args (@t173 @t160 (@list @t178))) % 150.52/150.83 (step @p287 :rule cnf_or_pos :args (@t182)) % 150.52/150.83 (step @p288 :rule reordering :premises (@p287) :args ((or @t169 @t181 (not @t182)))) % 150.52/150.83 (assume-push @p329 @t168) % 150.52/150.83 (step @p290 :rule instantiate :premises (@p329) :args ((@list @t40))) % 150.52/150.83 (step-pop @p330 :rule scope :premises (@p290)) % 150.52/150.83 (step @p291 :rule process_scope :premises (@p330) :args (@t182)) % 150.52/150.83 (step @p293 :rule implies_elim :premises (@p291)) % 150.52/150.83 (step @p294 :rule chain_m_resolution :premises (@p293 @p288 @p286 @p265 @p258) :args (@t169 (@list true false false true) (@list @t182 @t173 @t168 @t171))) % 150.52/150.83 (step @p295 :rule cnf_or_pos :args (@t166)) % 150.52/150.83 (step @p296 :rule reordering :premises (@p295) :args ((or @t163 @t165 (not @t166)))) % 150.52/150.83 (step @p297 :rule chain_m_resolution :premises (@p296 @p294 @p256) :args (@t165 (@list true false) (@list @t163 @t166))) % 150.52/150.83 (step @p298 :rule cnf_equiv_neg1 :args (@t171)) % 150.52/150.83 (step @p299 :rule reordering :premises (@p298) :args ((or @t163 @t170 @t171))) % 150.52/150.83 (step @p300 :rule chain_m_resolution :premises (@p299 @p294 @p258) :args (@t170 (@list true true) (@list @t163 @t171))) % 150.52/150.83 (step @p301 :rule alpha_equiv :args ((forall (@list @t183) (or (not (forall (@list @t184) (or (not (_ @t41 @t183 @t184)) (_ @t41 (_ @t39 @t38 @t183) @t184)))) (not (_ @t41 @t183 @t161)))) @t185 (@list @t51 @t13))) % 150.52/150.83 (step @p302 :rule alpha_equiv :args (@t168 (@list @t51 @t4) @t185)) % 150.52/150.83 (step @p303 :rule trans :premises (@p302 @p301)) % 150.52/150.83 (step @p304 :rule equiv_elim2 :premises (@p303)) % 150.52/150.83 (step @p305 :rule chain_m_resolution :premises (@p304 @p300) :args (@t187 (@list true) (@list @t168))) % 150.52/150.83 (step @p306 :rule instantiate :premises (@p15) :args (@t162)) % 150.52/150.83 (step @p307 :rule bool-double-not-elim :args (@t186)) % 150.52/150.83 (step @p308 :rule refl :args (@t164)) % 150.52/150.83 (step @p309 :rule refl :args (@t189)) % 150.52/150.83 (step @p310 :rule nary_cong :premises (@p309 @p308 @p307) :args ((or @t189 @t164 (not @t187)))) % 150.52/150.83 (step @p311 :rule cnf_equiv_pos2 :args (@t188)) % 150.52/150.83 (step @p312 :rule eq_resolve :premises (@p311 @p310)) % 150.52/150.83 (step @p313 :rule reordering :premises (@p312) :args ((or @t164 @t186 @t189))) % 150.52/150.83 (step @p314 false :rule chain_m_resolution :premises (@p313 @p306 @p305 @p297) :args (false (@list false true true) (@list @t188 @t186 @t164))) % 150.52/150.83 ) % 150.52/150.83 % SZS output end Proof % 150.52/150.83 % cvc5 exiting %------------------------------------------------------------------------------