%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV427^2 : TPTP v9.2.1. 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 : n015.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 09:01:30 AM UTC 2026 % Result : Theorem 0.96s 1.14s % Output : Proof 0.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWV427^2 : TPTP v9.2.1. Released v3.6.0. % 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n015.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 20:17:04 EDT 2026 % 0.15/0.33 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.96/1.14 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.96/1.14 % SZS status Theorem % 0.96/1.14 % SZS output start Proof % 0.96/1.14 ( % 0.96/1.14 (declare-sort $$unsorted 0) % 0.96/1.14 (declare-sort tptp.individuals 0) % 0.96/1.14 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.96/1.14 (declare-const tptp.a (-> $$unsorted Bool)) % 0.96/1.14 (declare-const tptp.s (-> $$unsorted Bool)) % 0.96/1.14 (declare-const tptp.icl_true (-> $$unsorted Bool)) % 0.96/1.14 (declare-const tptp.icl_false (-> $$unsorted Bool)) % 0.96/1.14 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.96/1.14 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.96/1.14 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.96/1.14 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.96/1.14 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.96/1.14 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.96/1.14 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.96/1.14 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.96/1.14 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.96/1.14 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.96/1.14 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.96/1.14 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.96/1.14 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.96/1.14 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.96/1.14 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.96/1.14 (define tptp.icl_atom () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) _let_2) _let_1))))) % 0.96/1.14 (define tptp.icl_princ () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.96/1.14 (define tptp.icl_and () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.96/1.14 (define tptp.icl_or () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor _let_3) _let_2) _let_1)))))) % 0.96/1.14 (define tptp.icl_impl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.96/1.14 (define tptp.icl_says () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "S" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mor _let_3) _let_2)) _let_1)))))) % 0.96/1.14 (define tptp.iclval () (let ((_let_1 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_1) (_ tptp.mvalid _let_1)))) % 0.96/1.14 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.96/1.14 (define @t2 () (_ tptp.mbox tptp.rel)) % 0.96/1.14 (define @t3 () (@list @t1)) % 0.96/1.14 (define @t4 () (forall @t3 (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t2 @t1)) @t1)))) % 0.96/1.14 (define @t5 () (@var "B" (-> $$unsorted Bool))) % 0.96/1.14 (define @t6 () (_ @t2 @t5)) % 0.96/1.14 (define @t7 () (_ tptp.icl_says (_ tptp.icl_princ tptp.a))) % 0.96/1.14 (define @t8 () (_ @t7 (_ tptp.icl_atom tptp.s))) % 0.96/1.14 (define @t9 () (not (_ tptp.iclval (_ (_ tptp.icl_impl (_ @t7 @t8)) @t8)))) % 0.96/1.14 (define @t10 () (@var "X" $$unsorted)) % 0.96/1.14 (define @t11 () (@list @t10)) % 0.96/1.14 (define @t12 () (lambda @t11 false)) % 0.96/1.14 (define @t13 () (lambda @t11 true)) % 0.96/1.14 (define @t14 () (@var "U" $$unsorted)) % 0.96/1.14 (define @t15 () (@var "X" (-> $$unsorted Bool))) % 0.96/1.14 (define @t16 () (_ @t15 @t14)) % 0.96/1.14 (define @t17 () (lambda (@list @t15 @t14) (not @t16))) % 0.96/1.14 (define @t18 () (@var "Y" (-> $$unsorted Bool))) % 0.96/1.14 (define @t19 () (_ @t18 @t14)) % 0.96/1.14 (define @t20 () (@list @t15 @t18 @t14)) % 0.96/1.14 (define @t21 () (lambda @t20 (or @t16 @t19))) % 0.96/1.14 (define @t22 () (lambda @t20 (and @t16 @t19))) % 0.96/1.14 (define @t23 () (@var "__flatten_var_0" $$unsorted)) % 0.96/1.14 (define @t24 () (@var "V" (-> $$unsorted Bool))) % 0.96/1.14 (define @t25 () (@var "U" (-> $$unsorted Bool))) % 0.96/1.14 (define @t26 () (@list @t25 @t24 @t23)) % 0.96/1.14 (define @t27 () (lambda @t26 (_ (_ (_ tptp.mor (_ tptp.mnot @t25)) @t24) @t23))) % 0.96/1.14 (define @t28 () (lambda @t26 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t25) @t24)) (_ (_ tptp.mimpl @t24) @t25)) @t23))) % 0.96/1.14 (define @t29 () (@var "Y" $$unsorted)) % 0.96/1.14 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.96/1.14 (define @t31 () (_ @t30 @t29)) % 0.96/1.14 (define @t32 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.96/1.14 (define @t33 () (_ (_ @t32 @t10) @t29)) % 0.96/1.14 (define @t34 () (@list @t29)) % 0.96/1.14 (define @t35 () (forall @t34 (=> @t33 @t31))) % 0.96/1.14 (define @t36 () (@list @t32 @t30 @t10)) % 0.96/1.14 (define @t37 () (lambda @t36 @t35)) % 0.96/1.14 (define @t38 () (lambda @t36 (exists @t34 (and @t33 @t31)))) % 0.96/1.14 (define @t39 () (@var "W" $$unsorted)) % 0.96/1.14 (define @t40 () (@var "X" tptp.individuals)) % 0.96/1.14 (define @t41 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.96/1.14 (define @t42 () (_ (_ @t41 @t40) @t39)) % 0.96/1.14 (define @t43 () (@list @t40)) % 0.96/1.14 (define @t44 () (@list @t41 @t39)) % 0.96/1.14 (define @t45 () (lambda @t44 (forall @t43 @t42))) % 0.96/1.14 (define @t46 () (lambda @t44 (exists @t43 @t42))) % 0.96/1.14 (define @t47 () (_ @t30 @t39)) % 0.96/1.14 (define @t48 () (@list @t39)) % 0.96/1.14 (define @t49 () (forall @t48 @t47)) % 0.96/1.14 (define @t50 () (@list @t30)) % 0.96/1.14 (define @t51 () (lambda @t50 @t49)) % 0.96/1.14 (define @t52 () (lambda @t50 (exists @t48 @t47))) % 0.96/1.14 (define @t53 () (not @t47)) % 0.96/1.14 (define @t54 () (lambda @t50 (exists @t48 @t53))) % 0.96/1.14 (define @t55 () (lambda @t50 (forall @t48 @t53))) % 0.96/1.14 (define @t56 () (@list @t30 @t23)) % 0.96/1.14 (define @t57 () (lambda @t56 (_ (_ @t2 @t30) @t23))) % 0.96/1.14 (define @t58 () (lambda @t56 (_ @t30 @t23))) % 0.96/1.14 (define @t59 () (@list @t1 @t5 @t23)) % 0.96/1.14 (define @t60 () (lambda @t59 (_ (_ (_ tptp.mand @t1) @t5) @t23))) % 0.96/1.14 (define @t61 () (_ tptp.mor @t1)) % 0.96/1.14 (define @t62 () (lambda @t59 (_ (_ @t61 @t5) @t23))) % 0.96/1.14 (define @t63 () (lambda @t59 (_ (_ @t2 (_ (_ tptp.mimpl @t1) @t5)) @t23))) % 0.96/1.14 (define @t64 () (@var "S" (-> $$unsorted Bool))) % 0.96/1.14 (define @t65 () (@list @t1 @t64 @t23)) % 0.96/1.14 (define @t66 () (lambda @t65 (_ (_ @t2 (_ @t61 @t64)) @t23))) % 0.96/1.14 (define @t67 () (@list @t15)) % 0.96/1.14 (define @t68 () (lambda @t67 (_ tptp.mvalid @t15))) % 0.96/1.14 (define @t69 () (@var "BOUND_VARIABLE_8289" $$unsorted)) % 0.96/1.14 (define @t70 () (tptp.s @t69)) % 0.96/1.14 (define @t71 () (@var "BOUND_VARIABLE_8287" $$unsorted)) % 0.96/1.14 (define @t72 () (not (tptp.rel @t71 @t69))) % 0.96/1.14 (define @t73 () (tptp.a @t71)) % 0.96/1.14 (define @t74 () (not (tptp.rel @t29 @t71))) % 0.96/1.14 (define @t75 () (@var "BOUND_VARIABLE_8239" $$unsorted)) % 0.96/1.14 (define @t76 () (tptp.s @t75)) % 0.96/1.14 (define @t77 () (@var "BOUND_VARIABLE_8237" $$unsorted)) % 0.96/1.14 (define @t78 () (not (tptp.rel @t77 @t75))) % 0.96/1.14 (define @t79 () (tptp.a @t77)) % 0.96/1.14 (define @t80 () (@var "BOUND_VARIABLE_8260" $$unsorted)) % 0.96/1.14 (define @t81 () (not (tptp.rel @t80 @t77))) % 0.96/1.14 (define @t82 () (tptp.a @t80)) % 0.96/1.14 (define @t83 () (@list @t80 @t77 @t75)) % 0.96/1.14 (define @t84 () (forall @t83 (or (not (tptp.rel @t29 @t80)) @t82 @t81 @t79 @t78 @t76))) % 0.96/1.14 (define @t85 () (not @t84)) % 0.96/1.14 (define @t86 () (not (tptp.rel @t39 @t29))) % 0.96/1.14 (define @t87 () (or @t86 @t85 @t74 @t73 @t72 @t70)) % 0.96/1.14 (define @t88 () (forall (@list @t39 @t29 @t71 @t69) @t87)) % 0.96/1.14 (define @t89 () (@list @t29 @t71 @t69)) % 0.96/1.14 (define @t90 () (forall @t89 @t87)) % 0.96/1.14 (define @t91 () (not (tptp.rel @t23 @t29))) % 0.96/1.14 (define @t92 () (or @t91 @t85 @t74 @t73 @t72 @t70)) % 0.96/1.14 (define @t93 () (@list @t23)) % 0.96/1.14 (define @t94 () (lambda @t93 (forall @t89 @t92))) % 0.96/1.14 (define @t95 () (_ @t94 @t39)) % 0.96/1.14 (define @t96 () (forall @t48 @t95)) % 0.96/1.14 (define @t97 () (forall @t48 (_ @t15 @t39))) % 0.96/1.14 (define @t98 () (lambda @t67 @t97)) % 0.96/1.14 (define @t99 () (or @t74 @t73 @t72 @t70)) % 0.96/1.14 (define @t100 () (or @t91 @t85 @t99)) % 0.96/1.14 (define @t101 () (forall @t89 @t100)) % 0.96/1.14 (define @t102 () (@list @t71 @t69)) % 0.96/1.14 (define @t103 () (forall @t102 @t100)) % 0.96/1.14 (define @t104 () (forall @t102 @t99)) % 0.96/1.14 (define @t105 () (@var "BOUND_VARIABLE_8202" $$unsorted)) % 0.96/1.14 (define @t106 () (@var "BOUND_VARIABLE_8219" $$unsorted)) % 0.96/1.14 (define @t107 () (@list @t106 @t105)) % 0.96/1.14 (define @t108 () (or @t91 @t85 @t104)) % 0.96/1.14 (define @t109 () (tptp.s @t105)) % 0.96/1.14 (define @t110 () (not (tptp.rel @t106 @t105))) % 0.96/1.14 (define @t111 () (tptp.a @t106)) % 0.96/1.14 (define @t112 () (@list @t106 @t105)) % 0.96/1.14 (define @t113 () (forall @t112 (or (not (tptp.rel @t29 @t106)) @t111 @t110 @t109))) % 0.96/1.14 (define @t114 () (not (tptp.rel @t29 @t105))) % 0.96/1.14 (define @t115 () (tptp.a @t29)) % 0.96/1.14 (define @t116 () (or @t91 @t115 @t114 @t109)) % 0.96/1.14 (define @t117 () (@list @t29 @t105)) % 0.96/1.14 (define @t118 () (forall @t117 @t116)) % 0.96/1.14 (define @t119 () (@list @t29)) % 0.96/1.14 (define @t120 () (lambda @t93 @t118)) % 0.96/1.14 (define @t121 () (_ @t120 @t29)) % 0.96/1.14 (define @t122 () (or @t91 @t85 @t121)) % 0.96/1.14 (define @t123 () (forall @t34 @t122)) % 0.96/1.14 (define @t124 () (lambda @t93 @t123)) % 0.96/1.14 (define @t125 () (_ @t5 @t29)) % 0.96/1.14 (define @t126 () (@list @t5 @t23)) % 0.96/1.14 (define @t127 () (or @t114 @t109)) % 0.96/1.14 (define @t128 () (or @t91 @t115 @t127)) % 0.96/1.14 (define @t129 () (forall @t117 @t128)) % 0.96/1.14 (define @t130 () (@list @t105)) % 0.96/1.14 (define @t131 () (forall @t130 @t128)) % 0.96/1.14 (define @t132 () (forall @t130 @t127)) % 0.96/1.14 (define @t133 () (@var "BOUND_VARIABLE_8186" $$unsorted)) % 0.96/1.14 (define @t134 () (@list @t133)) % 0.96/1.14 (define @t135 () (or @t91 @t115 @t132)) % 0.96/1.14 (define @t136 () (tptp.s @t133)) % 0.96/1.14 (define @t137 () (@list @t133)) % 0.96/1.14 (define @t138 () (forall @t137 (or (not (tptp.rel @t29 @t133)) @t136))) % 0.96/1.14 (define @t139 () (forall @t34 (or @t91 (tptp.s @t29)))) % 0.96/1.14 (define @t140 () (lambda @t93 @t139)) % 0.96/1.14 (define @t141 () (or @t91 @t115 (_ @t140 @t29))) % 0.96/1.14 (define @t142 () (forall @t34 @t141)) % 0.96/1.14 (define @t143 () (lambda @t93 @t142)) % 0.96/1.14 (define @t144 () (_ @t64 @t29)) % 0.96/1.14 (define @t145 () (@list @t64 @t23)) % 0.96/1.14 (define @t146 () (lambda @t145 (forall @t34 (or @t91 @t115 @t144)))) % 0.96/1.14 (define @t147 () (_ @t30 @t29)) % 0.96/1.14 (define @t148 () (forall @t34 (or @t91 @t147))) % 0.96/1.14 (define @t149 () (_ (lambda @t56 @t148) tptp.s)) % 0.96/1.14 (define @t150 () (_ tptp.a @t29)) % 0.96/1.14 (define @t151 () (or @t91 @t150 @t144)) % 0.96/1.14 (define @t152 () (lambda @t93 (_ tptp.a @t23))) % 0.96/1.14 (define @t153 () (_ @t152 @t29)) % 0.96/1.14 (define @t154 () (or @t91 @t153 @t144)) % 0.96/1.14 (define @t155 () (forall @t34 @t154)) % 0.96/1.14 (define @t156 () (lambda @t145 @t155)) % 0.96/1.14 (define @t157 () (_ @t1 @t29)) % 0.96/1.14 (define @t158 () (forall @t34 (or @t91 @t157 @t144))) % 0.96/1.14 (define @t159 () (lambda @t65 @t158)) % 0.96/1.14 (define @t160 () (_ @t58 tptp.a)) % 0.96/1.14 (define @t161 () (not (tptp.rel @t29 @t77))) % 0.96/1.14 (define @t162 () (or @t91 @t115 @t161 @t79 @t78 @t76)) % 0.96/1.14 (define @t163 () (@list @t29 @t77 @t75)) % 0.96/1.14 (define @t164 () (forall @t163 @t162)) % 0.96/1.14 (define @t165 () (lambda @t93 @t164)) % 0.96/1.14 (define @t166 () (not (_ @t165 @t29))) % 0.96/1.14 (define @t167 () (or @t91 @t166 @t125)) % 0.96/1.14 (define @t168 () (forall @t34 @t167)) % 0.96/1.14 (define @t169 () (lambda @t126 @t168)) % 0.96/1.14 (define @t170 () (not @t157)) % 0.96/1.14 (define @t171 () (forall @t34 (or @t91 @t170 @t125))) % 0.96/1.14 (define @t172 () (lambda @t59 @t171)) % 0.96/1.14 (define @t173 () (or @t161 @t79 @t78 @t76)) % 0.96/1.14 (define @t174 () (or @t91 @t115 @t173)) % 0.96/1.14 (define @t175 () (forall @t163 @t174)) % 0.96/1.14 (define @t176 () (@list @t77 @t75)) % 0.96/1.14 (define @t177 () (forall @t176 @t174)) % 0.96/1.14 (define @t178 () (forall @t176 @t173)) % 0.96/1.14 (define @t179 () (or @t91 @t115 @t178)) % 0.96/1.14 (define @t180 () (or @t91 @t115 @t121)) % 0.96/1.14 (define @t181 () (forall @t34 @t180)) % 0.96/1.14 (define @t182 () (lambda @t93 @t181)) % 0.96/1.14 (define @t183 () (_ @t159 @t160)) % 0.96/1.14 (define @t184 () (_ @t183 @t149)) % 0.96/1.14 (define @t185 () (not (tptp.rel @t10 @t29))) % 0.96/1.14 (define @t186 () (forall @t34 (or @t185 @t147))) % 0.96/1.14 (define @t187 () (lambda @t11 @t186)) % 0.96/1.14 (define @t188 () (lambda (@list @t30 @t10) @t186)) % 0.96/1.14 (define @t189 () (_ @t32 @t10 @t29)) % 0.96/1.14 (define @t190 () (_ (lambda @t36 (forall @t34 (or (not @t189) @t147))) tptp.rel)) % 0.96/1.14 (define @t191 () (not @t33)) % 0.96/1.14 (define @t192 () (or @t191 @t31)) % 0.96/1.14 (define @t193 () (_ @t64 @t29)) % 0.96/1.14 (define @t194 () (_ @t1 @t29)) % 0.96/1.14 (define @t195 () (or @t185 @t194 @t193)) % 0.96/1.14 (define @t196 () (or @t194 @t193)) % 0.96/1.14 (define @t197 () (_ @t1 @t14)) % 0.96/1.14 (define @t198 () (@list @t14)) % 0.96/1.14 (define @t199 () (lambda @t198 (or @t197 (_ @t64 @t14)))) % 0.96/1.14 (define @t200 () (_ @t199 @t29)) % 0.96/1.14 (define @t201 () (or @t185 @t200)) % 0.96/1.14 (define @t202 () (forall @t34 @t201)) % 0.96/1.14 (define @t203 () (lambda @t11 @t202)) % 0.96/1.14 (define @t204 () (@list @t18 @t14)) % 0.96/1.14 (define @t205 () (lambda @t204 (or @t197 @t19))) % 0.96/1.14 (define @t206 () (_ @t5 @t29)) % 0.96/1.14 (define @t207 () (not @t194)) % 0.96/1.14 (define @t208 () (or @t185 @t207 @t206)) % 0.96/1.14 (define @t209 () (or @t207 @t206)) % 0.96/1.14 (define @t210 () (_ @t1 @t23)) % 0.96/1.14 (define @t211 () (not @t210)) % 0.96/1.14 (define @t212 () (lambda @t93 (or @t211 (_ @t5 @t23)))) % 0.96/1.14 (define @t213 () (_ @t212 @t29)) % 0.96/1.14 (define @t214 () (or @t185 @t213)) % 0.96/1.14 (define @t215 () (forall @t34 @t214)) % 0.96/1.14 (define @t216 () (lambda @t11 @t215)) % 0.96/1.14 (define @t217 () (_ @t24 @t23)) % 0.96/1.14 (define @t218 () (@list @t24 @t23)) % 0.96/1.14 (define @t219 () (lambda @t218 (or @t211 @t217))) % 0.96/1.14 (define @t220 () (or (not (_ @t25 @t23)) @t217)) % 0.96/1.14 (define @t221 () (lambda @t26 @t220)) % 0.96/1.14 (define @t222 () (not (_ @t25 @t14))) % 0.96/1.14 (define @t223 () (lambda @t198 (or @t222 (_ @t24 @t14)))) % 0.96/1.14 (define @t224 () (lambda @t198 @t222)) % 0.96/1.14 (define @t225 () (_ @t224 @t14)) % 0.96/1.14 (define @t226 () (or @t225 @t19)) % 0.96/1.14 (define @t227 () (lambda @t204 @t226)) % 0.96/1.14 (define @t228 () (_ @t30 @t39)) % 0.96/1.14 (define @t229 () (lambda @t50 (forall @t48 @t228))) % 0.96/1.14 (define @t230 () (@quantifiers_skolemize @t88 2)) % 0.96/1.14 (define @t231 () (@quantifiers_skolemize @t88 1)) % 0.96/1.14 (define @t232 () (tptp.rel @t231 @t230)) % 0.96/1.14 (define @t233 () (@quantifiers_skolemize @t88 3)) % 0.96/1.14 (define @t234 () (tptp.s @t233)) % 0.96/1.14 (define @t235 () (tptp.rel @t230 @t233)) % 0.96/1.14 (define @t236 () (not @t235)) % 0.96/1.14 (define @t237 () (tptp.a @t230)) % 0.96/1.14 (define @t238 () (not @t232)) % 0.96/1.14 (define @t239 () (forall @t83 (or (not (tptp.rel @t231 @t80)) @t82 @t81 @t79 @t78 @t76))) % 0.96/1.14 (define @t240 () (not @t239)) % 0.96/1.14 (define @t241 () (or (not (tptp.rel (@quantifiers_skolemize @t88 0) @t231)) @t240 @t238 @t237 @t236 @t234)) % 0.96/1.14 (define @t242 () (@list true)) % 0.96/1.14 (define @t243 () (@list @t241)) % 0.96/1.14 (define @t244 () (_ @t1 @t39)) % 0.96/1.14 (define @t245 () (not (forall @t34 (or @t86 @t157)))) % 0.96/1.14 (define @t246 () (or @t245 @t244)) % 0.96/1.14 (define @t247 () (forall (@list @t1 @t39) @t246)) % 0.96/1.14 (define @t248 () (_ @t1 @t39)) % 0.96/1.14 (define @t249 () (or @t245 @t248)) % 0.96/1.14 (define @t250 () (forall @t34 (or @t91 @t157))) % 0.96/1.14 (define @t251 () (not @t250)) % 0.96/1.14 (define @t252 () (lambda @t93 (or @t251 @t210))) % 0.96/1.14 (define @t253 () (_ @t252 @t39)) % 0.96/1.14 (define @t254 () (forall @t48 @t253)) % 0.96/1.14 (define @t255 () (lambda @t11 (forall @t34 (or @t185 @t157)))) % 0.96/1.14 (define @t256 () (_ @t255 @t23)) % 0.96/1.14 (define @t257 () (not @t256)) % 0.96/1.14 (define @t258 () (or @t257 @t217)) % 0.96/1.14 (define @t259 () (lambda @t218 @t258)) % 0.96/1.14 (define @t260 () (tptp.rel @t230 @t230)) % 0.96/1.14 (define @t261 () (_ tptp.rel @t230)) % 0.96/1.14 (define @t262 () (_ @t261 @t230)) % 0.96/1.14 (define @t263 () (_ @t261 @t230)) % 0.96/1.14 (define @t264 () (tptp.rel @t230 @t29)) % 0.96/1.14 (define @t265 () (not @t264)) % 0.96/1.14 (define @t266 () (_ @t261 @t29)) % 0.96/1.14 (define @t267 () (or @t265 @t266)) % 0.96/1.14 (define @t268 () (_ @t261 @t29)) % 0.96/1.14 (define @t269 () (or @t265 @t268)) % 0.96/1.14 (define @t270 () (forall @t34 @t269)) % 0.96/1.14 (define @t271 () (not @t270)) % 0.96/1.14 (define @t272 () (or @t271 @t263)) % 0.96/1.14 (define @t273 () (not @t260)) % 0.96/1.14 (define @t274 () (or @t238 @t237 @t273 @t237 @t236 @t234)) % 0.96/1.14 (assume @p1 (= tptp.icl_true tptp.mtrue)) % 0.96/1.14 (assume @p2 (= tptp.icl_false tptp.mfalse)) % 0.96/1.14 (assume @p3 @t4) % 0.96/1.14 (assume @p4 (forall (@list @t5) (_ tptp.mvalid (_ (_ tptp.mimpl @t6) (_ @t2 @t6))))) % 0.96/1.14 (assume @p5 @t9) % 0.96/1.14 (assume @p6 true) % 0.96/1.14 (step @p7 (= tptp.mfalse @t12) :rule refl :args (@t12)) % 0.96/1.14 (step @p8 (= tptp.mtrue @t13) :rule refl :args (@t13)) % 0.96/1.14 (step @p9 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.96/1.14 (step @p10 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.96/1.14 (step @p11 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.96/1.14 (step @p12 (= tptp.mimpl @t27) :rule refl :args (@t27)) % 0.96/1.14 (step @p13 (= tptp.miff @t28) :rule refl :args (@t28)) % 0.96/1.14 (step @p14 (= tptp.mbox @t37) :rule refl :args (@t37)) % 0.96/1.14 (step @p15 (= tptp.mdia @t38) :rule refl :args (@t38)) % 0.96/1.14 (step @p16 (= tptp.mall @t45) :rule refl :args (@t45)) % 0.96/1.14 (step @p17 (= tptp.mexists @t46) :rule refl :args (@t46)) % 0.96/1.14 (step @p18 (= tptp.mvalid @t51) :rule refl :args (@t51)) % 0.96/1.14 (step @p19 (= tptp.msatisfiable @t52) :rule refl :args (@t52)) % 0.96/1.14 (step @p20 (= tptp.mcountersatisfiable @t54) :rule refl :args (@t54)) % 0.96/1.14 (step @p21 (= tptp.minvalid @t55) :rule refl :args (@t55)) % 0.96/1.14 (step @p22 (= tptp.icl_atom @t57) :rule refl :args (@t57)) % 0.96/1.14 (step @p23 (= tptp.icl_princ @t58) :rule refl :args (@t58)) % 0.96/1.14 (step @p24 (= tptp.icl_and @t60) :rule refl :args (@t60)) % 0.96/1.14 (step @p25 (= tptp.icl_or @t62) :rule refl :args (@t62)) % 0.96/1.14 (step @p26 (= tptp.icl_impl @t63) :rule refl :args (@t63)) % 0.96/1.14 (step @p27 (= tptp.icl_says @t66) :rule refl :args (@t66)) % 0.96/1.14 (step @p28 (= tptp.iclval @t68) :rule refl :args (@t68)) % 0.96/1.14 (step @p29 :rule quant-merge-prenex :args ((= (forall @t48 @t90) @t88))) % 0.96/1.14 (step @p30 :rule beta-reduce :args ((= @t95 @t90))) % 0.96/1.14 (step @p31 :rule cong :premises (@p30) :args (@t96)) % 0.96/1.14 (step @p32 :rule trans :premises (@p31 @p29)) % 0.96/1.14 (step @p33 :rule beta-reduce :args ((= (_ @t98 @t94) @t96))) % 0.96/1.14 (step @p34 :rule trans :premises (@p33 @p32)) % 0.96/1.14 (step @p35 :rule aci_norm :args ((= @t100 @t92))) % 0.96/1.14 (step @p36 :rule cong :premises (@p35) :args (@t101)) % 0.96/1.14 (step @p37 :rule quant-merge-prenex :args ((= (forall @t34 @t103) @t101))) % 0.96/1.14 (step @p38 :rule alpha_equiv :args (@t104 (@list @t71 @t69) @t107)) % 0.96/1.14 (step @p39 :rule refl :args (@t85)) % 0.96/1.14 (step @p40 :rule refl :args (@t91)) % 0.96/1.14 (step @p41 :rule nary_cong :premises (@p40 @p39 @p38) :args (@t108)) % 0.96/1.14 (step @p42 :rule quant-miniscope-or :args ((= @t103 @t108))) % 0.96/1.14 (step @p43 :rule trans :premises (@p42 @p41)) % 0.96/1.14 (step @p44 :rule symm :premises (@p43)) % 0.96/1.14 (step @p45 :rule cong :premises (@p44) :args ((forall @t34 (or @t91 @t85 @t113)))) % 0.96/1.14 (step @p46 :rule trans :premises (@p45 @p37)) % 0.96/1.14 (step @p47 :rule trans :premises (@p46 @p36)) % 0.96/1.14 (step @p48 :rule beta-reduce :args ((= (_ (lambda @t93 (forall @t112 (or (not (tptp.rel @t23 @t106)) @t111 @t110 @t109))) @t29) @t113))) % 0.96/1.14 (step @p49 :rule refl :args (@t29)) % 0.96/1.14 (step @p50 :rule alpha_equiv :args (@t118 @t119 (@list @t106))) % 0.96/1.14 (step @p51 :rule cong :premises (@p50) :args (@t120)) % 0.96/1.14 (step @p52 :rule ho_cong :premises (@p51 @p49)) % 0.96/1.14 (step @p53 :rule trans :premises (@p52 @p48)) % 0.96/1.14 (step @p54 :rule refl :args (@t85)) % 0.96/1.14 (step @p55 :rule refl :args (@t91)) % 0.96/1.14 (step @p56 :rule nary_cong :premises (@p55 @p54 @p53) :args (@t122)) % 0.96/1.14 (step @p57 :rule cong :premises (@p56) :args (@t123)) % 0.96/1.14 (step @p58 :rule trans :premises (@p57 @p47)) % 0.96/1.14 (step @p59 :rule cong :premises (@p58) :args (@t124)) % 0.96/1.14 (step @p60 :rule beta-reduce :args ((= (_ (lambda @t126 (forall @t34 (or @t91 @t85 @t125))) @t120) @t124))) % 0.96/1.14 (step @p61 :rule trans :premises (@p60 @p59)) % 0.96/1.14 (step @p62 :rule aci_norm :args ((= @t128 @t116))) % 0.96/1.14 (step @p63 :rule cong :premises (@p62) :args (@t129)) % 0.96/1.14 (step @p64 :rule quant-merge-prenex :args ((= (forall @t34 @t131) @t129))) % 0.96/1.14 (step @p65 :rule alpha_equiv :args (@t132 (@list @t105) @t134)) % 0.96/1.14 (step @p66 :rule refl :args (@t115)) % 0.96/1.14 (step @p67 :rule nary_cong :premises (@p40 @p66 @p65) :args (@t135)) % 0.96/1.14 (step @p68 :rule quant-miniscope-or :args ((= @t131 @t135))) % 0.96/1.14 (step @p69 :rule trans :premises (@p68 @p67)) % 0.96/1.14 (step @p70 :rule symm :premises (@p69)) % 0.96/1.14 (step @p71 :rule cong :premises (@p70) :args ((forall @t34 (or @t91 @t115 @t138)))) % 0.96/1.14 (step @p72 :rule trans :premises (@p71 @p64)) % 0.96/1.14 (step @p73 :rule trans :premises (@p72 @p63)) % 0.96/1.14 (step @p74 :rule beta-reduce :args ((= (_ (lambda @t93 (forall @t137 (or (not (tptp.rel @t23 @t133)) @t136))) @t29) @t138))) % 0.96/1.14 (step @p75 :rule alpha_equiv :args (@t139 @t119 @t134)) % 0.96/1.14 (step @p76 :rule cong :premises (@p75) :args (@t140)) % 0.96/1.14 (step @p77 :rule ho_cong :premises (@p76 @p49)) % 0.96/1.14 (step @p78 :rule trans :premises (@p77 @p74)) % 0.96/1.14 (step @p79 :rule refl :args (@t115)) % 0.96/1.14 (step @p80 :rule nary_cong :premises (@p55 @p79 @p78) :args (@t141)) % 0.96/1.14 (step @p81 :rule cong :premises (@p80) :args (@t142)) % 0.96/1.14 (step @p82 :rule trans :premises (@p81 @p73)) % 0.96/1.14 (step @p83 :rule cong :premises (@p82) :args (@t143)) % 0.96/1.14 (step @p84 :rule beta-reduce :args ((= (_ @t146 @t140) @t143))) % 0.96/1.14 (step @p85 :rule trans :premises (@p84 @p83)) % 0.96/1.14 (step @p86 :rule beta-reduce :args ((= @t149 @t140))) % 0.96/1.14 (step @p87 :rule refl :args (@t144)) % 0.96/1.14 (step @p88 :rule refl :args (@t115)) % 0.96/1.14 (step @p89 :rule refl :args (@t150)) % 0.96/1.14 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t150 @t115))) % 0.96/1.14 (step @p91 :rule symm :premises (@p90)) % 0.96/1.14 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 0.96/1.14 (step @p93 :rule nary_cong :premises (@p40 @p92 @p87) :args (@t151)) % 0.96/1.14 (step @p94 :rule cong :premises (@p93) :args ((forall @t34 @t151))) % 0.96/1.14 (step @p95 :rule refl :args (@t144)) % 0.96/1.14 (step @p96 :rule beta-reduce :args ((= @t153 @t150))) % 0.96/1.14 (step @p97 :rule nary_cong :premises (@p55 @p96 @p95) :args (@t154)) % 0.96/1.14 (step @p98 :rule cong :premises (@p97) :args (@t155)) % 0.96/1.14 (step @p99 :rule trans :premises (@p98 @p94)) % 0.96/1.14 (step @p100 :rule cong :premises (@p99) :args (@t156)) % 0.96/1.14 (step @p101 :rule beta-reduce :args ((= (_ @t159 @t152) @t156))) % 0.96/1.14 (step @p102 :rule trans :premises (@p101 @p100)) % 0.96/1.14 (step @p103 :rule beta-reduce :args ((= @t160 @t152))) % 0.96/1.14 (step @p104 :rule refl :args (@t159)) % 0.96/1.14 (step @p105 :rule ho_cong :premises (@p104 @p103)) % 0.96/1.14 (step @p106 :rule trans :premises (@p105 @p102)) % 0.96/1.14 (step @p107 :rule ho_cong :premises (@p106 @p86)) % 0.96/1.14 (step @p108 :rule trans :premises (@p107 @p85)) % 0.96/1.14 (step @p109 :rule refl :args (@t125)) % 0.96/1.14 (step @p110 :rule beta-reduce :args ((= (_ (lambda @t93 (forall @t83 (or (not (tptp.rel @t23 @t80)) @t82 @t81 @t79 @t78 @t76))) @t29) @t84))) % 0.96/1.14 (step @p111 :rule alpha_equiv :args (@t164 @t119 (@list @t80))) % 0.96/1.14 (step @p112 :rule cong :premises (@p111) :args (@t165)) % 0.96/1.14 (step @p113 :rule ho_cong :premises (@p112 @p49)) % 0.96/1.14 (step @p114 :rule trans :premises (@p113 @p110)) % 0.96/1.14 (step @p115 :rule cong :premises (@p114) :args (@t166)) % 0.96/1.14 (step @p116 :rule nary_cong 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:premises (@p178 @p220)) % 0.96/1.14 (step @p371 :rule ho_cong :premises (@p282 @p370)) % 0.96/1.14 (step @p372 :rule ho_cong :premises (@p371 @p220)) % 0.96/1.14 (step @p373 :rule ho_cong :premises (@p301 @p372)) % 0.96/1.14 (step @p374 :rule cong :premises (@p373) :args (@t4)) % 0.96/1.14 (step @p375 :rule trans :premises (@p374 @p369)) % 0.96/1.14 (step @p376 :rule eq_resolve :premises (@p3 @p375)) % 0.96/1.14 (step @p377 :rule refl :args (@t260)) % 0.96/1.14 (step @p378 :rule refl :args (@t262)) % 0.96/1.14 (step @p379 :rule cong :premises (@p378 @p377) :args ((= @t262 @t260))) % 0.96/1.14 (step @p380 :rule symm :premises (@p379)) % 0.96/1.14 (step @p381 :rule eq_resolve :premises (@p378 @p380)) % 0.96/1.14 (step @p382 :rule refl :args (@t247)) % 0.96/1.14 (step @p383 :rule cong :premises (@p382 @p381) :args ((=> @t247 @t262))) % 0.96/1.14 (step @p384 :rule aci_norm :args ((= (or false @t262) @t262))) % 0.96/1.14 (step @p385 :rule refl :args (@t263)) % 0.96/1.14 (step @p386 :rule evaluate :args ((not true))) % 0.96/1.14 (step @p387 :rule quant-unused-vars :args ((= (forall @t34 true) true))) % 0.96/1.14 (step @p388 :rule bool-or-taut2 :args (false @t264 false false)) % 0.96/1.14 (step @p389 :rule cong :premises (@p388) :args ((forall @t34 (or @t265 @t264)))) % 0.96/1.14 (step @p390 :rule trans :premises (@p389 @p387)) % 0.96/1.14 (step @p391 :rule refl :args (@t264)) % 0.96/1.14 (step @p392 :rule refl :args (@t266)) % 0.96/1.14 (step @p393 :rule cong :premises (@p392 @p391) :args ((= @t266 @t264))) % 0.96/1.14 (step @p394 :rule symm :premises (@p393)) % 0.96/1.14 (step @p395 :rule eq_resolve :premises (@p392 @p394)) % 0.96/1.14 (step @p396 :rule refl :args (@t265)) % 0.96/1.14 (step @p397 :rule nary_cong :premises (@p396 @p395) :args (@t267)) % 0.96/1.14 (step @p398 :rule cong :premises (@p397) :args ((forall @t34 @t267))) % 0.96/1.14 (step @p399 :rule trans :premises (@p398 @p390)) % 0.96/1.14 (step @p400 :rule refl :args (@t268)) % 0.96/1.14 (step @p401 :rule refl :args (@t265)) % 0.96/1.14 (step @p402 :rule nary_cong :premises (@p401 @p400) :args (@t269)) % 0.96/1.14 (step @p403 :rule cong :premises (@p402) :args (@t270)) % 0.96/1.14 (step @p404 :rule trans :premises (@p403 @p399)) % 0.96/1.14 (step @p405 :rule cong :premises (@p404) :args (@t271)) % 0.96/1.14 (step @p406 :rule trans :premises (@p405 @p386)) % 0.96/1.14 (step @p407 :rule nary_cong :premises (@p406 @p385) :args (@t272)) % 0.96/1.14 (step @p408 :rule trans :premises (@p407 @p384)) % 0.96/1.14 (step @p409 :rule cong :premises (@p382 @p408) :args ((=> @t247 @t272))) % 0.96/1.14 (assume-push @p422 @t247) % 0.96/1.14 (step @p411 :rule instantiate :premises (@p376) :args ((@list @t261 @t230))) % 0.96/1.14 (step-pop @p423 :rule scope :premises (@p411)) % 0.96/1.14 (step @p412 :rule process_scope :premises (@p423) :args (@t272)) % 0.96/1.14 (step @p414 :rule eq_resolve :premises (@p412 @p409)) % 0.96/1.14 (step @p415 :rule eq_resolve :premises (@p414 @p383)) % 0.96/1.14 (step @p416 :rule implies_elim :premises (@p415)) % 0.96/1.14 (step @p417 :rule chain_m_resolution :premises (@p416 @p376) :args (@t260 (@list false) (@list @t247))) % 0.96/1.14 (step @p418 :rule cnf_or_pos :args (@t274)) % 0.96/1.14 (step @p419 :rule factoring :premises (@p418)) % 0.96/1.14 (step @p420 :rule reordering :premises (@p419) :args ((or @t238 @t237 @t236 @t234 @t273 (not @t274)))) % 0.96/1.14 (step @p421 false :rule chain_m_resolution :premises (@p420 @p417 @p334 @p327 @p325 @p319 @p317) :args (false (@list false false true false true false) (@list @t260 @t274 @t234 @t235 @t237 @t232))) % 0.96/1.14 ) % 0.96/1.14 % SZS output end Proof % 0.96/1.14 % cvc5 exiting %------------------------------------------------------------------------------