%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL585^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:07 AM UTC 2026 % Result : Theorem 0.19s 0.51s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL585^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.35 % Computer : n018.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Fri Sep 4 17:07:18 UTC 2026 % 0.09/0.35 % CPUTime : % 0.13/0.42 %----Proving TH0 % 0.19/0.51 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.19/0.51 % SZS status Theorem % 0.19/0.51 % SZS output start Proof % 0.19/0.51 ( % 0.19/0.51 (declare-sort $$unsorted 0) % 0.19/0.51 (declare-sort tptp.individuals 0) % 0.19/0.51 (declare-const tptp.a (-> $$unsorted Bool)) % 0.19/0.51 (declare-const tptp.r (-> $$unsorted $$unsorted Bool)) % 0.19/0.51 (declare-const tptp.b (-> $$unsorted Bool)) % 0.19/0.51 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.19/0.51 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.19/0.51 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.19/0.51 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.51 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.51 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.19/0.51 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.19/0.51 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.51 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.51 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.51 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.51 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.51 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.51 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.51 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.51 (define @t1 () (_ tptp.mdia tptp.r)) % 0.19/0.51 (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t1 (_ (_ tptp.mimpl tptp.a) tptp.b))) (_ (_ tptp.mimpl (_ (_ tptp.mbox tptp.r) tptp.a)) (_ @t1 tptp.b)))))) % 0.19/0.51 (define @t3 () (@var "X" $$unsorted)) % 0.19/0.51 (define @t4 () (@list @t3)) % 0.19/0.51 (define @t5 () (lambda @t4 false)) % 0.19/0.51 (define @t6 () (lambda @t4 true)) % 0.19/0.51 (define @t7 () (@var "U" $$unsorted)) % 0.19/0.51 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.19/0.51 (define @t9 () (_ @t8 @t7)) % 0.19/0.51 (define @t10 () (lambda (@list @t8 @t7) (not @t9))) % 0.19/0.51 (define @t11 () (@var "Y" (-> $$unsorted Bool))) % 0.19/0.51 (define @t12 () (_ @t11 @t7)) % 0.19/0.51 (define @t13 () (@list @t8 @t11 @t7)) % 0.19/0.51 (define @t14 () (lambda @t13 (or @t9 @t12))) % 0.19/0.51 (define @t15 () (lambda @t13 (and @t9 @t12))) % 0.19/0.51 (define @t16 () (@var "__flatten_var_0" $$unsorted)) % 0.19/0.51 (define @t17 () (@var "V" (-> $$unsorted Bool))) % 0.19/0.51 (define @t18 () (@var "U" (-> $$unsorted Bool))) % 0.19/0.51 (define @t19 () (@list @t18 @t17 @t16)) % 0.19/0.51 (define @t20 () (lambda @t19 (_ (_ (_ tptp.mor (_ tptp.mnot @t18)) @t17) @t16))) % 0.19/0.51 (define @t21 () (lambda @t19 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t18) @t17)) (_ (_ tptp.mimpl @t17) @t18)) @t16))) % 0.19/0.51 (define @t22 () (@var "Y" $$unsorted)) % 0.19/0.51 (define @t23 () (@var "P" (-> $$unsorted Bool))) % 0.19/0.51 (define @t24 () (_ @t23 @t22)) % 0.19/0.51 (define @t25 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.19/0.51 (define @t26 () (_ (_ @t25 @t3) @t22)) % 0.19/0.51 (define @t27 () (@list @t22)) % 0.19/0.51 (define @t28 () (forall @t27 (=> @t26 @t24))) % 0.19/0.51 (define @t29 () (@list @t25 @t23 @t3)) % 0.19/0.51 (define @t30 () (lambda @t29 @t28)) % 0.19/0.51 (define @t31 () (and @t26 @t24)) % 0.19/0.51 (define @t32 () (exists @t27 @t31)) % 0.19/0.51 (define @t33 () (lambda @t29 @t32)) % 0.19/0.51 (define @t34 () (@var "W" $$unsorted)) % 0.19/0.51 (define @t35 () (@var "X" tptp.individuals)) % 0.19/0.51 (define @t36 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.19/0.51 (define @t37 () (_ (_ @t36 @t35) @t34)) % 0.19/0.51 (define @t38 () (@list @t35)) % 0.19/0.51 (define @t39 () (@list @t36 @t34)) % 0.19/0.51 (define @t40 () (lambda @t39 (forall @t38 @t37))) % 0.19/0.51 (define @t41 () (lambda @t39 (exists @t38 @t37))) % 0.19/0.51 (define @t42 () (_ @t23 @t34)) % 0.19/0.51 (define @t43 () (@list @t34)) % 0.19/0.51 (define @t44 () (forall @t43 @t42)) % 0.19/0.51 (define @t45 () (@list @t23)) % 0.19/0.51 (define @t46 () (lambda @t45 @t44)) % 0.19/0.51 (define @t47 () (lambda @t45 (exists @t43 @t42))) % 0.19/0.51 (define @t48 () (not @t42)) % 0.19/0.51 (define @t49 () (lambda @t45 (exists @t43 @t48))) % 0.19/0.51 (define @t50 () (lambda @t45 (forall @t43 @t48))) % 0.19/0.51 (define @t51 () (@var "BOUND_VARIABLE_7894" $$unsorted)) % 0.19/0.51 (define @t52 () (and (tptp.a @t51) (not (tptp.b @t51)))) % 0.19/0.51 (define @t53 () (not (tptp.r @t34 @t51))) % 0.19/0.51 (define @t54 () (tptp.b @t22)) % 0.19/0.51 (define @t55 () (not @t54)) % 0.19/0.51 (define @t56 () (not (tptp.r @t34 @t22))) % 0.19/0.51 (define @t57 () (not (forall @t27 (or @t56 @t55)))) % 0.19/0.51 (define @t58 () (tptp.a @t22)) % 0.19/0.51 (define @t59 () (not (forall @t27 (or @t56 @t58)))) % 0.19/0.51 (define @t60 () (or @t59 @t57 @t53 @t52)) % 0.19/0.51 (define @t61 () (or @t53 @t52)) % 0.19/0.51 (define @t62 () (or @t61 @t59 @t57)) % 0.19/0.51 (define @t63 () (@list @t34 @t51)) % 0.19/0.51 (define @t64 () (forall @t63 @t62)) % 0.19/0.51 (define @t65 () (@list @t51)) % 0.19/0.51 (define @t66 () (forall @t65 @t62)) % 0.19/0.51 (define @t67 () (forall @t65 @t61)) % 0.19/0.51 (define @t68 () (or @t67 @t59 @t57)) % 0.19/0.51 (define @t69 () (and @t58 @t55)) % 0.19/0.51 (define @t70 () (or (forall @t27 (or @t56 @t69)) @t59 @t57)) % 0.19/0.51 (define @t71 () (not (tptp.r @t16 @t22))) % 0.19/0.51 (define @t72 () (not (forall @t27 (or @t71 @t55)))) % 0.19/0.51 (define @t73 () (forall @t27 (or @t71 @t58))) % 0.19/0.51 (define @t74 () (not @t73)) % 0.19/0.51 (define @t75 () (forall @t27 (or @t71 @t69))) % 0.19/0.51 (define @t76 () (or @t75 @t74 @t72)) % 0.19/0.51 (define @t77 () (@list @t16)) % 0.19/0.51 (define @t78 () (lambda @t77 @t76)) % 0.19/0.51 (define @t79 () (_ @t78 @t34)) % 0.19/0.51 (define @t80 () (forall @t43 @t79)) % 0.19/0.51 (define @t81 () (_ @t23 @t34)) % 0.19/0.51 (define @t82 () (lambda @t45 (forall @t43 @t81))) % 0.19/0.51 (define @t83 () (or @t74 @t72)) % 0.19/0.51 (define @t84 () (lambda @t77 @t83)) % 0.19/0.51 (define @t85 () (_ @t84 @t16)) % 0.19/0.51 (define @t86 () (or @t75 @t85)) % 0.19/0.51 (define @t87 () (lambda @t77 @t86)) % 0.19/0.51 (define @t88 () (_ @t17 @t16)) % 0.19/0.51 (define @t89 () (@list @t17 @t16)) % 0.19/0.51 (define @t90 () (not (tptp.r @t3 @t22))) % 0.19/0.51 (define @t91 () (lambda @t4 (not (forall @t27 (or @t90 @t55))))) % 0.19/0.51 (define @t92 () (_ @t91 @t16)) % 0.19/0.51 (define @t93 () (or @t74 @t92)) % 0.19/0.51 (define @t94 () (lambda @t77 @t93)) % 0.19/0.51 (define @t95 () (_ @t23 @t22)) % 0.19/0.51 (define @t96 () (not @t95)) % 0.19/0.51 (define @t97 () (@list @t23 @t3)) % 0.19/0.51 (define @t98 () (lambda @t97 (not (forall @t27 (or @t90 @t96))))) % 0.19/0.51 (define @t99 () (_ @t25 @t3 @t22)) % 0.19/0.51 (define @t100 () (not @t99)) % 0.19/0.51 (define @t101 () (_ (lambda @t29 (not (forall @t27 (or @t100 @t96)))) tptp.r)) % 0.19/0.51 (define @t102 () (lambda @t4 (forall @t27 (or @t90 @t58)))) % 0.19/0.51 (define @t103 () (_ @t102 @t16)) % 0.19/0.51 (define @t104 () (not @t103)) % 0.19/0.51 (define @t105 () (or @t104 @t88)) % 0.19/0.51 (define @t106 () (lambda @t89 @t105)) % 0.19/0.51 (define @t107 () (or (not (_ @t18 @t16)) @t88)) % 0.19/0.51 (define @t108 () (lambda @t19 @t107)) % 0.19/0.51 (define @t109 () (lambda @t97 (forall @t27 (or @t90 @t95)))) % 0.19/0.51 (define @t110 () (_ (lambda @t29 (forall @t27 (or @t100 @t95))) tptp.r)) % 0.19/0.51 (define @t111 () (lambda @t4 (not (forall @t27 (or @t90 @t69))))) % 0.19/0.51 (define @t112 () (_ @t111 @t16)) % 0.19/0.51 (define @t113 () (not @t112)) % 0.19/0.51 (define @t114 () (or @t113 @t88)) % 0.19/0.51 (define @t115 () (lambda @t89 @t114)) % 0.19/0.51 (define @t116 () (_ tptp.b @t22)) % 0.19/0.51 (define @t117 () (not @t116)) % 0.19/0.51 (define @t118 () (_ tptp.a @t22)) % 0.19/0.51 (define @t119 () (and @t118 @t117)) % 0.19/0.51 (define @t120 () (or @t90 @t119)) % 0.19/0.51 (define @t121 () (not @t118)) % 0.19/0.51 (define @t122 () (or @t121 @t116)) % 0.19/0.51 (define @t123 () (or @t90 (not @t122))) % 0.19/0.51 (define @t124 () (not (_ tptp.a @t16))) % 0.19/0.51 (define @t125 () (lambda @t77 (or @t124 (_ tptp.b @t16)))) % 0.19/0.51 (define @t126 () (_ @t125 @t22)) % 0.19/0.51 (define @t127 () (not @t126)) % 0.19/0.51 (define @t128 () (or @t90 @t127)) % 0.19/0.51 (define @t129 () (forall @t27 @t128)) % 0.19/0.51 (define @t130 () (not @t129)) % 0.19/0.51 (define @t131 () (lambda @t4 @t130)) % 0.19/0.51 (define @t132 () (lambda @t89 (or @t124 @t88))) % 0.19/0.51 (define @t133 () (_ @t108 tptp.a)) % 0.19/0.51 (define @t134 () (not @t24)) % 0.19/0.51 (define @t135 () (not @t26)) % 0.19/0.51 (define @t136 () (or @t135 @t134)) % 0.19/0.51 (define @t137 () (forall @t27 (not @t31))) % 0.19/0.51 (define @t138 () (not @t137)) % 0.19/0.51 (define @t139 () (or @t135 @t24)) % 0.19/0.51 (define @t140 () (not (_ @t18 @t7))) % 0.19/0.51 (define @t141 () (@list @t7)) % 0.19/0.51 (define @t142 () (lambda @t141 (or @t140 (_ @t17 @t7)))) % 0.19/0.51 (define @t143 () (@list @t11 @t7)) % 0.19/0.51 (define @t144 () (lambda @t141 @t140)) % 0.19/0.51 (define @t145 () (_ @t144 @t7)) % 0.19/0.51 (define @t146 () (or @t145 @t12)) % 0.19/0.51 (define @t147 () (lambda @t143 @t146)) % 0.19/0.51 (define @t148 () (forall @t63 @t60)) % 0.19/0.51 (define @t149 () (@quantifiers_skolemize @t148 0)) % 0.19/0.51 (define @t150 () (not (tptp.r @t149 @t22))) % 0.19/0.51 (define @t151 () (forall @t27 (or @t150 @t55))) % 0.19/0.51 (define @t152 () (@quantifiers_skolemize @t148 1)) % 0.19/0.51 (define @t153 () (tptp.b @t152)) % 0.19/0.51 (define @t154 () (not @t153)) % 0.19/0.51 (define @t155 () (tptp.a @t152)) % 0.19/0.51 (define @t156 () (and @t155 @t154)) % 0.19/0.51 (define @t157 () (tptp.r @t149 @t152)) % 0.19/0.51 (define @t158 () (not @t157)) % 0.19/0.51 (define @t159 () (not @t151)) % 0.19/0.51 (define @t160 () (forall @t27 (or @t150 @t58))) % 0.19/0.51 (define @t161 () (not @t160)) % 0.19/0.51 (define @t162 () (or @t161 @t159 @t158 @t156)) % 0.19/0.51 (define @t163 () (@list true)) % 0.19/0.51 (define @t164 () (@list @t162)) % 0.19/0.51 (define @t165 () (@list @t152)) % 0.19/0.51 (define @t166 () (or @t158 @t155)) % 0.19/0.51 (define @t167 () (@list false false)) % 0.19/0.51 (define @t168 () (not @t155)) % 0.19/0.51 (define @t169 () (@list true false)) % 0.19/0.51 (define @t170 () (or @t158 @t154)) % 0.19/0.51 (define @t171 () (not @t170)) % 0.19/0.51 (assume @p1 @t2) % 0.19/0.51 (assume @p2 true) % 0.19/0.51 (step @p3 (= tptp.mfalse @t5) :rule refl :args (@t5)) % 0.19/0.51 (step @p4 (= tptp.mtrue @t6) :rule refl :args (@t6)) % 0.19/0.51 (step @p5 (= tptp.mnot @t10) :rule refl :args (@t10)) % 0.19/0.51 (step @p6 (= tptp.mor @t14) :rule refl :args (@t14)) % 0.19/0.51 (step @p7 (= tptp.mand @t15) :rule refl :args (@t15)) % 0.19/0.51 (step @p8 (= tptp.mimpl @t20) :rule refl :args (@t20)) % 0.19/0.51 (step @p9 (= tptp.miff @t21) :rule refl :args (@t21)) % 0.19/0.51 (step @p10 (= tptp.mbox @t30) :rule refl :args (@t30)) % 0.19/0.51 (step @p11 (= tptp.mdia @t33) :rule refl :args (@t33)) % 0.19/0.51 (step @p12 (= tptp.mall @t40) :rule refl :args (@t40)) % 0.19/0.51 (step @p13 (= tptp.mexists @t41) :rule refl :args (@t41)) % 0.19/0.51 (step @p14 (= tptp.mvalid @t46) :rule refl :args (@t46)) % 0.19/0.51 (step @p15 (= tptp.msatisfiable @t47) :rule refl :args (@t47)) % 0.19/0.51 (step @p16 (= tptp.mcountersatisfiable @t49) :rule refl :args (@t49)) % 0.19/0.51 (step @p17 (= tptp.minvalid @t50) :rule refl :args (@t50)) % 0.19/0.51 (step @p18 :rule aci_norm :args ((= @t62 @t60))) % 0.19/0.51 (step @p19 :rule cong :premises (@p18) :args (@t64)) % 0.19/0.51 (step @p20 :rule quant-merge-prenex :args ((= (forall @t43 @t66) @t64))) % 0.19/0.51 (step @p21 :rule refl :args (@t57)) % 0.19/0.51 (step @p22 :rule refl :args (@t59)) % 0.19/0.51 (step @p23 :rule alpha_equiv :args (@t67 (@list @t51) (@list @t22))) % 0.19/0.51 (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args (@t68)) % 0.19/0.51 (step @p25 :rule quant-miniscope-or :args ((= @t66 @t68))) % 0.19/0.51 (step @p26 :rule trans :premises (@p25 @p24)) % 0.19/0.51 (step @p27 :rule symm :premises (@p26)) % 0.19/0.51 (step @p28 :rule cong :premises (@p27) :args ((forall @t43 @t70))) % 0.19/0.51 (step @p29 :rule trans :premises (@p28 @p20)) % 0.19/0.51 (step @p30 :rule trans :premises (@p29 @p19)) % 0.19/0.51 (step @p31 :rule beta-reduce :args ((= @t79 @t70))) % 0.19/0.51 (step @p32 :rule cong :premises (@p31) :args (@t80)) % 0.19/0.51 (step @p33 :rule trans :premises (@p32 @p30)) % 0.19/0.51 (step @p34 :rule beta-reduce :args ((= (_ @t82 @t78) @t80))) % 0.19/0.51 (step @p35 :rule trans :premises (@p34 @p33)) % 0.19/0.51 (step @p36 :rule aci_norm :args ((= (or @t75 @t83) @t76))) % 0.19/0.51 (step @p37 :rule beta-reduce :args ((= @t85 @t83))) % 0.19/0.51 (step @p38 :rule refl :args (@t75)) % 0.19/0.51 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t86)) % 0.19/0.51 (step @p40 :rule trans :premises (@p39 @p36)) % 0.19/0.51 (step @p41 :rule cong :premises (@p40) :args (@t87)) % 0.19/0.51 (step @p42 :rule beta-reduce :args ((= (_ (lambda @t89 (or @t75 @t88)) @t84) @t87))) % 0.19/0.51 (step @p43 :rule trans :premises (@p42 @p41)) % 0.19/0.51 (step @p44 :rule beta-reduce :args ((= @t92 @t72))) % 0.19/0.51 (step @p45 :rule refl :args (@t74)) % 0.19/0.51 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t93)) % 0.19/0.51 (step @p47 :rule cong :premises (@p46) :args (@t94)) % 0.19/0.51 (step @p48 :rule beta-reduce :args ((= (_ (lambda @t89 (or @t74 @t88)) @t91) @t94))) % 0.19/0.51 (step @p49 :rule trans :premises (@p48 @p47)) % 0.19/0.51 (step @p50 :rule beta-reduce :args ((= (_ @t98 tptp.b) @t91))) % 0.19/0.51 (step @p51 :rule refl :args (tptp.b)) % 0.19/0.51 (step @p52 :rule beta-reduce :args ((= @t101 @t98))) % 0.19/0.51 (step @p53 :rule ho_cong :premises (@p52 @p51)) % 0.19/0.51 (step @p54 :rule trans :premises (@p53 @p50)) % 0.19/0.51 (step @p55 :rule refl :args (@t88)) % 0.19/0.51 (step @p56 :rule beta-reduce :args ((= @t103 @t73))) % 0.19/0.51 (step @p57 :rule cong :premises (@p56) :args (@t104)) % 0.19/0.51 (step @p58 :rule nary_cong :premises (@p57 @p55) :args (@t105)) % 0.19/0.51 (step @p59 :rule cong :premises (@p58) :args (@t106)) % 0.19/0.51 (step @p60 :rule beta-reduce :args ((= (_ @t108 @t102) @t106))) % 0.19/0.51 (step @p61 :rule trans :premises (@p60 @p59)) % 0.19/0.51 (step @p62 :rule beta-reduce :args ((= (_ @t109 tptp.a) @t102))) % 0.19/0.51 (step @p63 :rule refl :args (tptp.a)) % 0.19/0.51 (step @p64 :rule beta-reduce :args ((= @t110 @t109))) % 0.19/0.51 (step @p65 :rule ho_cong :premises (@p64 @p63)) % 0.19/0.51 (step @p66 :rule trans :premises (@p65 @p62)) % 0.19/0.51 (step @p67 :rule refl :args (@t108)) % 0.19/0.51 (step @p68 :rule ho_cong :premises (@p67 @p66)) % 0.19/0.51 (step @p69 :rule trans :premises (@p68 @p61)) % 0.19/0.51 (step @p70 :rule ho_cong :premises (@p69 @p54)) % 0.19/0.51 (step @p71 :rule trans :premises (@p70 @p49)) % 0.19/0.51 (step @p72 :rule bool-double-not-elim :args (@t75)) % 0.19/0.51 (step @p73 :rule beta-reduce :args ((= @t112 (not @t75)))) % 0.19/0.51 (step @p74 :rule cong :premises (@p73) :args (@t113)) % 0.19/0.51 (step @p75 :rule trans :premises (@p74 @p72)) % 0.19/0.51 (step @p76 :rule nary_cong :premises (@p75 @p55) :args (@t114)) % 0.19/0.51 (step @p77 :rule cong :premises (@p76) :args (@t115)) % 0.19/0.51 (step @p78 :rule beta-reduce :args ((= (_ @t108 @t111) @t115))) % 0.19/0.51 (step @p79 :rule trans :premises (@p78 @p77)) % 0.19/0.51 (step @p80 :rule refl :args (@t54)) % 0.19/0.51 (step @p81 :rule refl :args (@t116)) % 0.19/0.51 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t116 @t54))) % 0.19/0.51 (step @p83 :rule symm :premises (@p82)) % 0.19/0.51 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.19/0.51 (step @p85 :rule cong :premises (@p84) :args (@t117)) % 0.19/0.51 (step @p86 :rule refl :args (@t58)) % 0.19/0.51 (step @p87 :rule refl :args (@t118)) % 0.19/0.51 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t118 @t58))) % 0.19/0.51 (step @p89 :rule symm :premises (@p88)) % 0.19/0.51 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 0.19/0.51 (step @p91 :rule nary_cong :premises (@p90 @p85) :args (@t119)) % 0.19/0.51 (step @p92 :rule refl :args (@t90)) % 0.19/0.51 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t120)) % 0.19/0.51 (step @p94 :rule cong :premises (@p93) :args ((forall @t27 @t120))) % 0.19/0.51 (step @p95 :rule refl :args (@t117)) % 0.19/0.51 (step @p96 :rule bool-double-not-elim :args (@t118)) % 0.19/0.51 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((and (not @t121) @t117))) % 0.19/0.51 (step @p98 :rule bool-or-de-morgan :args (@t121 @t116 false)) % 0.19/0.51 (step @p99 :rule trans :premises (@p98 @p97)) % 0.19/0.51 (step @p100 :rule nary_cong :premises (@p92 @p99) :args (@t123)) % 0.19/0.51 (step @p101 :rule cong :premises (@p100) :args ((forall @t27 @t123))) % 0.19/0.51 (step @p102 :rule trans :premises (@p101 @p94)) % 0.19/0.51 (step @p103 :rule beta-reduce :args ((= @t126 @t122))) % 0.19/0.51 (step @p104 :rule cong :premises (@p103) :args (@t127)) % 0.19/0.51 (step @p105 :rule refl :args (@t90)) % 0.19/0.51 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t128)) % 0.19/0.51 (step @p107 :rule cong :premises (@p106) :args (@t129)) % 0.19/0.51 (step @p108 :rule trans :premises (@p107 @p102)) % 0.19/0.51 (step @p109 :rule cong :premises (@p108) :args (@t130)) % 0.19/0.51 (step @p110 :rule cong :premises (@p109) :args (@t131)) % 0.19/0.51 (step @p111 :rule beta-reduce :args ((= (_ @t98 @t125) @t131))) % 0.19/0.51 (step @p112 :rule trans :premises (@p111 @p110)) % 0.19/0.51 (step @p113 :rule beta-reduce :args ((= (_ @t132 tptp.b) @t125))) % 0.19/0.51 (step @p114 :rule beta-reduce :args ((= @t133 @t132))) % 0.19/0.51 (step @p115 :rule ho_cong :premises (@p114 @p51)) % 0.19/0.51 (step @p116 :rule trans :premises (@p115 @p113)) % 0.19/0.51 (step @p117 :rule ho_cong :premises (@p52 @p116)) % 0.19/0.51 (step @p118 :rule trans :premises (@p117 @p112)) % 0.19/0.51 (step @p119 :rule ho_cong :premises (@p67 @p118)) % 0.19/0.51 (step @p120 :rule trans :premises (@p119 @p79)) % 0.19/0.51 (step @p121 :rule ho_cong :premises (@p120 @p71)) % 0.19/0.51 (step @p122 :rule trans :premises (@p121 @p43)) % 0.19/0.51 (step @p123 :rule refl :args (@t82)) % 0.19/0.51 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 0.19/0.51 (step @p125 :rule trans :premises (@p124 @p35)) % 0.19/0.51 (step @p126 :rule cong :premises (@p125) :args ((not (_ @t82 (_ (_ @t108 (_ @t101 (_ @t133 tptp.b))) (_ (_ @t108 (_ @t110 tptp.a)) (_ @t101 tptp.b))))))) % 0.19/0.51 (step @p127 :rule refl :args (tptp.r)) % 0.19/0.51 (step @p128 :rule refl :args (@t95)) % 0.19/0.51 (step @p129 :rule refl :args (@t24)) % 0.19/0.51 (step @p130 :rule cong :premises (@p129 @p128) :args ((= @t24 @t95))) % 0.19/0.51 (step @p131 :rule symm :premises (@p130)) % 0.19/0.51 (step @p132 :rule eq_resolve :premises (@p129 @p131)) % 0.19/0.51 (step @p133 :rule cong :premises (@p132) :args (@t134)) % 0.19/0.51 (step @p134 :rule refl :args (@t99)) % 0.19/0.51 (step @p135 :rule refl :args (@t26)) % 0.19/0.51 (step @p136 :rule cong :premises (@p135 @p134) :args ((= @t26 @t99))) % 0.19/0.51 (step @p137 :rule symm :premises (@p136)) % 0.19/0.51 (step @p138 :rule eq_resolve :premises (@p135 @p137)) % 0.19/0.51 (step @p139 :rule cong :premises (@p138) :args (@t135)) % 0.19/0.51 (step @p140 :rule nary_cong :premises (@p139 @p133) :args (@t136)) % 0.19/0.51 (step @p141 :rule cong :premises (@p140) :args ((forall @t27 @t136))) % 0.19/0.51 (step @p142 :rule bool-and-de-morgan :args (@t26 @t24 true)) % 0.19/0.51 (step @p143 :rule cong :premises (@p142) :args (@t137)) % 0.19/0.51 (step @p144 :rule trans :premises (@p143 @p141)) % 0.19/0.51 (step @p145 :rule cong :premises (@p144) :args (@t138)) % 0.19/0.51 (step @p146 :rule exists-elim :args ((= @t32 @t138))) % 0.19/0.51 (step @p147 :rule trans :premises (@p146 @p145)) % 0.19/0.51 (step @p148 :rule cong :premises (@p147) :args (@t33)) % 0.19/0.51 (step @p149 :rule trans :premises (@p11 @p148)) % 0.19/0.51 (step @p150 :rule ho_cong :premises (@p149 @p127)) % 0.19/0.51 (step @p151 :rule ho_cong :premises (@p150 @p51)) % 0.19/0.51 (step @p152 :rule nary_cong :premises (@p139 @p132) :args (@t139)) % 0.19/0.51 (step @p153 :rule cong :premises (@p152) :args ((forall @t27 @t139))) % 0.19/0.51 (step @p154 :rule bool-impl-elim :args (@t26 @t24)) % 0.19/0.51 (step @p155 :rule cong :premises (@p154) :args (@t28)) % 0.19/0.51 (step @p156 :rule trans :premises (@p155 @p153)) % 0.19/0.51 (step @p157 :rule cong :premises (@p156) :args (@t30)) % 0.19/0.51 (step @p158 :rule trans :premises (@p10 @p157)) % 0.19/0.51 (step @p159 :rule ho_cong :premises (@p158 @p127)) % 0.19/0.51 (step @p160 :rule ho_cong :premises (@p159 @p63)) % 0.19/0.51 (step @p161 :rule beta-reduce :args ((= (_ @t142 @t16) @t107))) % 0.19/0.51 (step @p162 :rule refl :args (@t16)) % 0.19/0.51 (step @p163 :rule beta-reduce :args ((= (_ (lambda @t143 (or @t140 @t12)) @t17) @t142))) % 0.19/0.51 (step @p164 :rule refl :args (@t17)) % 0.19/0.51 (step @p165 :rule refl :args (@t12)) % 0.19/0.51 (step @p166 :rule beta-reduce :args ((= @t145 @t140))) % 0.19/0.51 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t146)) % 0.19/0.51 (step @p168 :rule cong :premises (@p167) :args (@t147)) % 0.19/0.51 (step @p169 :rule beta-reduce :args ((= (_ @t14 @t144) @t147))) % 0.19/0.51 (step @p170 :rule trans :premises (@p169 @p168)) % 0.19/0.51 (step @p171 :rule beta-reduce :args ((= (_ @t10 @t18) @t144))) % 0.19/0.51 (step @p172 :rule refl :args (@t14)) % 0.19/0.51 (step @p173 :rule ho_cong :premises (@p172 @p171)) % 0.19/0.51 (step @p174 :rule trans :premises (@p173 @p170)) % 0.19/0.51 (step @p175 :rule ho_cong :premises (@p174 @p164)) % 0.19/0.51 (step @p176 :rule trans :premises (@p175 @p163)) % 0.19/0.51 (step @p177 :rule ho_cong :premises (@p176 @p162)) % 0.19/0.51 (step @p178 :rule trans :premises (@p177 @p161)) % 0.19/0.51 (step @p179 :rule refl :args (@t18)) % 0.19/0.51 (step @p180 :rule ho_cong :premises (@p5 @p179)) % 0.19/0.51 (step @p181 :rule ho_cong :premises (@p6 @p180)) % 0.19/0.51 (step @p182 :rule ho_cong :premises (@p181 @p164)) % 0.19/0.51 (step @p183 :rule ho_cong :premises (@p182 @p162)) % 0.19/0.51 (step @p184 :rule trans :premises (@p183 @p178)) % 0.19/0.51 (step @p185 :rule cong :premises (@p184) :args (@t20)) % 0.19/0.51 (step @p186 :rule trans :premises (@p8 @p185)) % 0.19/0.51 (step @p187 :rule ho_cong :premises (@p186 @p160)) % 0.19/0.51 (step @p188 :rule ho_cong :premises (@p187 @p151)) % 0.19/0.51 (step @p189 :rule ho_cong :premises (@p186 @p63)) % 0.19/0.51 (step @p190 :rule ho_cong :premises (@p189 @p51)) % 0.19/0.51 (step @p191 :rule ho_cong :premises (@p150 @p190)) % 0.19/0.51 (step @p192 :rule ho_cong :premises (@p186 @p191)) % 0.19/0.51 (step @p193 :rule ho_cong :premises (@p192 @p188)) % 0.19/0.51 (step @p194 :rule refl :args (@t81)) % 0.19/0.51 (step @p195 :rule refl :args (@t42)) % 0.19/0.51 (step @p196 :rule cong :premises (@p195 @p194) :args ((= @t42 @t81))) % 0.19/0.51 (step @p197 :rule symm :premises (@p196)) % 0.19/0.51 (step @p198 :rule eq_resolve :premises (@p195 @p197)) % 0.19/0.51 (step @p199 :rule cong :premises (@p198) :args (@t44)) % 0.19/0.51 (step @p200 :rule cong :premises (@p199) :args (@t46)) % 0.19/0.51 (step @p201 :rule trans :premises (@p14 @p200)) % 0.19/0.51 (step @p202 :rule ho_cong :premises (@p201 @p193)) % 0.19/0.51 (step @p203 :rule cong :premises (@p202) :args (@t2)) % 0.19/0.51 (step @p204 :rule trans :premises (@p203 @p126)) % 0.19/0.51 (step @p205 :rule eq_resolve :premises (@p1 @p204)) % 0.19/0.51 (step @p206 :rule skolemize :premises (@p205)) % 0.19/0.51 (step @p207 :rule bool-double-not-elim :args (@t151)) % 0.19/0.51 (step @p208 :rule refl :args (@t162)) % 0.19/0.51 (step @p209 :rule nary_cong :premises (@p208 @p207) :args ((or @t162 (not @t159)))) % 0.19/0.51 (step @p210 :rule cnf_or_neg :args (@t162 1)) % 0.19/0.51 (step @p211 :rule eq_resolve :premises (@p210 @p209)) % 0.19/0.51 (step @p212 :rule reordering :premises (@p211) :args ((or @t151 @t162))) % 0.19/0.51 (step @p213 :rule chain_m_resolution :premises (@p212 @p206) :args (@t151 @t163 @t164)) % 0.19/0.51 (step @p214 :rule bool-double-not-elim :args (@t160)) % 0.19/0.51 (step @p215 :rule nary_cong :premises (@p208 @p214) :args ((or @t162 (not @t161)))) % 0.19/0.51 (step @p216 :rule cnf_or_neg :args (@t162 0)) % 0.19/0.51 (step @p217 :rule eq_resolve :premises (@p216 @p215)) % 0.19/0.51 (step @p218 :rule reordering :premises (@p217) :args ((or @t160 @t162))) % 0.19/0.51 (step @p219 :rule chain_m_resolution :premises (@p218 @p206) :args (@t160 @t163 @t164)) % 0.19/0.51 (step @p220 :rule instantiate :premises (@p219) :args (@t165)) % 0.19/0.51 (step @p221 :rule bool-double-not-elim :args (@t157)) % 0.19/0.51 (step @p222 :rule nary_cong :premises (@p208 @p221) :args ((or @t162 (not @t158)))) % 0.19/0.51 (step @p223 :rule cnf_or_neg :args (@t162 2)) % 0.19/0.51 (step @p224 :rule eq_resolve :premises (@p223 @p222)) % 0.19/0.51 (step @p225 :rule reordering :premises (@p224) :args ((or @t157 @t162))) % 0.19/0.51 (step @p226 :rule chain_m_resolution :premises (@p225 @p206) :args (@t157 @t163 @t164)) % 0.19/0.51 (step @p227 :rule cnf_or_pos :args (@t166)) % 0.19/0.51 (step @p228 :rule reordering :premises (@p227) :args ((or @t158 @t155 (not @t166)))) % 0.19/0.51 (step @p229 :rule chain_m_resolution :premises (@p228 @p226 @p220) :args (@t155 @t167 (@list @t157 @t166))) % 0.19/0.51 (step @p230 :rule cnf_or_neg :args (@t162 3)) % 0.19/0.51 (step @p231 :rule chain_m_resolution :premises (@p230 @p206) :args ((not @t156) @t163 @t164)) % 0.19/0.51 (step @p232 :rule bool-double-not-elim :args (@t153)) % 0.19/0.51 (step @p233 :rule refl :args (@t168)) % 0.19/0.51 (step @p234 :rule refl :args (@t156)) % 0.19/0.51 (step @p235 :rule nary_cong :premises (@p234 @p233 @p232) :args ((or @t156 @t168 (not @t154)))) % 0.19/0.51 (step @p236 :rule cnf_and_neg :args (@t156)) % 0.19/0.51 (step @p237 :rule eq_resolve :premises (@p236 @p235)) % 0.19/0.51 (step @p238 :rule reordering :premises (@p237) :args ((or @t153 @t156 @t168))) % 0.19/0.51 (step @p239 :rule chain_m_resolution :premises (@p238 @p231 @p229) :args (@t153 @t169 (@list @t156 @t155))) % 0.19/0.51 (step @p240 :rule cnf_or_pos :args (@t170)) % 0.19/0.51 (step @p241 :rule reordering :premises (@p240) :args ((or @t158 @t154 @t171))) % 0.19/0.51 (step @p242 :rule chain_m_resolution :premises (@p241 @p226 @p239) :args (@t171 @t167 (@list @t157 @t153))) % 0.19/0.51 (assume-push @p249 @t151) % 0.19/0.51 (step @p244 :rule instantiate :premises (@p213) :args (@t165)) % 0.19/0.51 (step-pop @p250 :rule scope :premises (@p244)) % 0.19/0.51 (step @p245 :rule process_scope :premises (@p250) :args (@t170)) % 0.19/0.51 (step @p247 :rule implies_elim :premises (@p245)) % 0.19/0.51 (step @p248 false :rule chain_m_resolution :premises (@p247 @p242 @p213) :args (false @t169 (@list @t170 @t151))) % 0.19/0.51 ) % 0.19/0.51 % SZS output end Proof % 0.19/0.51 % cvc5 exiting %------------------------------------------------------------------------------