%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV432^2 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:01:31 AM UTC 2026 % Result : Theorem 0.61s 0.87s % Output : Proof 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV432^2 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n017.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 20:15:31 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.61/0.87 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.61/0.87 % SZS status Theorem % 0.61/0.87 % SZS output start Proof % 0.61/0.87 ( % 0.61/0.87 (declare-sort $$unsorted 0) % 0.61/0.87 (declare-sort tptp.individuals 0) % 0.61/0.87 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.61/0.87 (declare-const tptp.b (-> $$unsorted Bool)) % 0.61/0.87 (declare-const tptp.a (-> $$unsorted Bool)) % 0.61/0.87 (declare-const tptp.icl_true (-> $$unsorted Bool)) % 0.61/0.87 (declare-const tptp.icl_false (-> $$unsorted Bool)) % 0.61/0.87 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.61/0.87 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.61/0.87 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.61/0.87 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.61/0.87 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.61/0.87 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.61/0.87 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.61/0.87 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.61/0.87 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.61/0.87 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.61/0.87 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.61/0.87 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.61/0.87 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.61/0.87 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.61/0.87 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.61/0.87 (define tptp.icl_atom () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) _let_2) _let_1))))) % 0.61/0.87 (define tptp.icl_princ () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.61/0.87 (define tptp.icl_and () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.61/0.87 (define tptp.icl_or () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor _let_3) _let_2) _let_1)))))) % 0.61/0.87 (define tptp.icl_impl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.61/0.87 (define tptp.icl_says () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "S" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mor _let_3) _let_2)) _let_1)))))) % 0.61/0.87 (define tptp.iclval () (let ((_let_1 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_1) (_ tptp.mvalid _let_1)))) % 0.61/0.87 (define tptp.icl_impl_princ () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mbox tptp.rel) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.61/0.87 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.61/0.87 (define @t2 () (_ tptp.mbox tptp.rel)) % 0.61/0.87 (define @t3 () (@list @t1)) % 0.61/0.87 (define @t4 () (forall @t3 (_ tptp.mvalid (_ (_ tptp.mimpl (_ @t2 @t1)) @t1)))) % 0.61/0.87 (define @t5 () (@var "B" (-> $$unsorted Bool))) % 0.61/0.87 (define @t6 () (_ @t2 @t5)) % 0.61/0.87 (define @t7 () (_ tptp.icl_princ tptp.b)) % 0.61/0.87 (define @t8 () (_ (_ tptp.icl_impl_princ (_ tptp.icl_princ tptp.a)) @t7)) % 0.61/0.87 (define @t9 () (not (_ tptp.iclval (_ (_ tptp.icl_impl (_ (_ tptp.icl_says @t7) @t8)) @t8)))) % 0.61/0.87 (define @t10 () (@var "X" $$unsorted)) % 0.61/0.87 (define @t11 () (@list @t10)) % 0.61/0.87 (define @t12 () (lambda @t11 false)) % 0.61/0.87 (define @t13 () (lambda @t11 true)) % 0.61/0.87 (define @t14 () (@var "U" $$unsorted)) % 0.61/0.87 (define @t15 () (@var "X" (-> $$unsorted Bool))) % 0.61/0.87 (define @t16 () (_ @t15 @t14)) % 0.61/0.87 (define @t17 () (lambda (@list @t15 @t14) (not @t16))) % 0.61/0.87 (define @t18 () (@var "Y" (-> $$unsorted Bool))) % 0.61/0.87 (define @t19 () (_ @t18 @t14)) % 0.61/0.87 (define @t20 () (@list @t15 @t18 @t14)) % 0.61/0.87 (define @t21 () (lambda @t20 (or @t16 @t19))) % 0.61/0.87 (define @t22 () (lambda @t20 (and @t16 @t19))) % 0.61/0.87 (define @t23 () (@var "__flatten_var_0" $$unsorted)) % 0.61/0.87 (define @t24 () (@var "V" (-> $$unsorted Bool))) % 0.61/0.87 (define @t25 () (@var "U" (-> $$unsorted Bool))) % 0.61/0.87 (define @t26 () (@list @t25 @t24 @t23)) % 0.61/0.87 (define @t27 () (lambda @t26 (_ (_ (_ tptp.mor (_ tptp.mnot @t25)) @t24) @t23))) % 0.61/0.87 (define @t28 () (lambda @t26 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t25) @t24)) (_ (_ tptp.mimpl @t24) @t25)) @t23))) % 0.61/0.87 (define @t29 () (@var "Y" $$unsorted)) % 0.61/0.87 (define @t30 () (@var "P" (-> $$unsorted Bool))) % 0.61/0.87 (define @t31 () (_ @t30 @t29)) % 0.61/0.87 (define @t32 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.61/0.87 (define @t33 () (_ (_ @t32 @t10) @t29)) % 0.61/0.87 (define @t34 () (@list @t29)) % 0.61/0.87 (define @t35 () (forall @t34 (=> @t33 @t31))) % 0.61/0.87 (define @t36 () (@list @t32 @t30 @t10)) % 0.61/0.87 (define @t37 () (lambda @t36 @t35)) % 0.61/0.87 (define @t38 () (lambda @t36 (exists @t34 (and @t33 @t31)))) % 0.61/0.87 (define @t39 () (@var "W" $$unsorted)) % 0.61/0.87 (define @t40 () (@var "X" tptp.individuals)) % 0.61/0.87 (define @t41 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.61/0.87 (define @t42 () (_ (_ @t41 @t40) @t39)) % 0.61/0.87 (define @t43 () (@list @t40)) % 0.61/0.87 (define @t44 () (@list @t41 @t39)) % 0.61/0.87 (define @t45 () (lambda @t44 (forall @t43 @t42))) % 0.61/0.87 (define @t46 () (lambda @t44 (exists @t43 @t42))) % 0.61/0.87 (define @t47 () (_ @t30 @t39)) % 0.61/0.87 (define @t48 () (@list @t39)) % 0.61/0.87 (define @t49 () (forall @t48 @t47)) % 0.61/0.87 (define @t50 () (@list @t30)) % 0.61/0.87 (define @t51 () (lambda @t50 @t49)) % 0.61/0.87 (define @t52 () (lambda @t50 (exists @t48 @t47))) % 0.61/0.87 (define @t53 () (not @t47)) % 0.61/0.87 (define @t54 () (lambda @t50 (exists @t48 @t53))) % 0.61/0.87 (define @t55 () (lambda @t50 (forall @t48 @t53))) % 0.61/0.87 (define @t56 () (@list @t30 @t23)) % 0.61/0.87 (define @t57 () (lambda @t56 (_ (_ @t2 @t30) @t23))) % 0.61/0.87 (define @t58 () (lambda @t56 (_ @t30 @t23))) % 0.61/0.87 (define @t59 () (@list @t1 @t5 @t23)) % 0.61/0.87 (define @t60 () (lambda @t59 (_ (_ (_ tptp.mand @t1) @t5) @t23))) % 0.61/0.87 (define @t61 () (_ tptp.mor @t1)) % 0.61/0.87 (define @t62 () (lambda @t59 (_ (_ @t61 @t5) @t23))) % 0.61/0.87 (define @t63 () (lambda @t59 (_ (_ @t2 (_ (_ tptp.mimpl @t1) @t5)) @t23))) % 0.61/0.87 (define @t64 () (@var "S" (-> $$unsorted Bool))) % 0.61/0.87 (define @t65 () (@list @t1 @t64 @t23)) % 0.61/0.87 (define @t66 () (lambda @t65 (_ (_ @t2 (_ @t61 @t64)) @t23))) % 0.61/0.87 (define @t67 () (@list @t15)) % 0.61/0.87 (define @t68 () (lambda @t67 (_ tptp.mvalid @t15))) % 0.61/0.87 (define @t69 () (_ @t1 @t39)) % 0.61/0.87 (define @t70 () (_ @t1 @t29)) % 0.61/0.87 (define @t71 () (not (tptp.rel @t39 @t29))) % 0.61/0.87 (define @t72 () (not (forall @t34 (or @t71 @t70)))) % 0.61/0.87 (define @t73 () (or @t72 @t69)) % 0.61/0.87 (define @t74 () (forall (@list @t1 @t39) @t73)) % 0.61/0.87 (define @t75 () (_ @t1 @t39)) % 0.61/0.87 (define @t76 () (or @t72 @t75)) % 0.61/0.87 (define @t77 () (_ @t1 @t23)) % 0.61/0.87 (define @t78 () (not (tptp.rel @t23 @t29))) % 0.61/0.87 (define @t79 () (forall @t34 (or @t78 @t70))) % 0.61/0.87 (define @t80 () (not @t79)) % 0.61/0.87 (define @t81 () (@list @t23)) % 0.61/0.87 (define @t82 () (lambda @t81 (or @t80 @t77))) % 0.61/0.87 (define @t83 () (_ @t82 @t39)) % 0.61/0.87 (define @t84 () (forall @t48 @t83)) % 0.61/0.87 (define @t85 () (_ @t30 @t39)) % 0.61/0.87 (define @t86 () (lambda @t50 (forall @t48 @t85))) % 0.61/0.87 (define @t87 () (_ @t24 @t23)) % 0.61/0.87 (define @t88 () (@list @t24 @t23)) % 0.61/0.87 (define @t89 () (not (tptp.rel @t10 @t29))) % 0.61/0.87 (define @t90 () (lambda @t11 (forall @t34 (or @t89 @t70)))) % 0.61/0.87 (define @t91 () (_ @t90 @t23)) % 0.61/0.87 (define @t92 () (not @t91)) % 0.61/0.87 (define @t93 () (or @t92 @t87)) % 0.61/0.87 (define @t94 () (lambda @t88 @t93)) % 0.61/0.87 (define @t95 () (or (not (_ @t25 @t23)) @t87)) % 0.61/0.87 (define @t96 () (lambda @t26 @t95)) % 0.61/0.87 (define @t97 () (_ @t30 @t29)) % 0.61/0.87 (define @t98 () (lambda (@list @t30 @t10) (forall @t34 (or @t89 @t97)))) % 0.61/0.87 (define @t99 () (_ @t32 @t10 @t29)) % 0.61/0.87 (define @t100 () (_ (lambda @t36 (forall @t34 (or (not @t99) @t97))) tptp.rel)) % 0.61/0.87 (define @t101 () (not @t33)) % 0.61/0.87 (define @t102 () (or @t101 @t31)) % 0.61/0.87 (define @t103 () (not (_ @t25 @t14))) % 0.61/0.87 (define @t104 () (@list @t14)) % 0.61/0.87 (define @t105 () (lambda @t104 (or @t103 (_ @t24 @t14)))) % 0.61/0.87 (define @t106 () (@list @t18 @t14)) % 0.61/0.87 (define @t107 () (lambda @t104 @t103)) % 0.61/0.87 (define @t108 () (_ @t107 @t14)) % 0.61/0.87 (define @t109 () (or @t108 @t19)) % 0.61/0.87 (define @t110 () (lambda @t106 @t109)) % 0.61/0.87 (define @t111 () (@var "BOUND_VARIABLE_8282" $$unsorted)) % 0.61/0.87 (define @t112 () (tptp.b @t111)) % 0.61/0.87 (define @t113 () (not (tptp.a @t111))) % 0.61/0.87 (define @t114 () (not (tptp.rel @t29 @t111))) % 0.61/0.87 (define @t115 () (@var "BOUND_VARIABLE_8235" $$unsorted)) % 0.61/0.87 (define @t116 () (tptp.b @t115)) % 0.61/0.87 (define @t117 () (not (tptp.a @t115))) % 0.61/0.87 (define @t118 () (@var "BOUND_VARIABLE_8255" $$unsorted)) % 0.61/0.87 (define @t119 () (not (tptp.rel @t118 @t115))) % 0.61/0.87 (define @t120 () (tptp.b @t118)) % 0.61/0.87 (define @t121 () (@list @t118 @t115)) % 0.61/0.87 (define @t122 () (forall @t121 (or (not (tptp.rel @t29 @t118)) @t120 @t119 @t117 @t116))) % 0.61/0.87 (define @t123 () (not @t122)) % 0.61/0.87 (define @t124 () (or @t71 @t123 @t114 @t113 @t112)) % 0.61/0.87 (define @t125 () (forall (@list @t39 @t29 @t111) @t124)) % 0.61/0.87 (define @t126 () (@list @t29 @t111)) % 0.61/0.87 (define @t127 () (forall @t126 @t124)) % 0.61/0.87 (define @t128 () (or @t78 @t123 @t114 @t113 @t112)) % 0.61/0.87 (define @t129 () (lambda @t81 (forall @t126 @t128))) % 0.61/0.87 (define @t130 () (_ @t129 @t39)) % 0.61/0.87 (define @t131 () (forall @t48 @t130)) % 0.61/0.87 (define @t132 () (forall @t48 (_ @t15 @t39))) % 0.61/0.87 (define @t133 () (lambda @t67 @t132)) % 0.61/0.87 (define @t134 () (or @t114 @t113 @t112)) % 0.61/0.87 (define @t135 () (or @t78 @t123 @t134)) % 0.61/0.87 (define @t136 () (forall @t126 @t135)) % 0.61/0.87 (define @t137 () (@list @t111)) % 0.61/0.87 (define @t138 () (forall @t137 @t135)) % 0.61/0.87 (define @t139 () (forall @t137 @t134)) % 0.61/0.87 (define @t140 () (@var "BOUND_VARIABLE_8217" $$unsorted)) % 0.61/0.87 (define @t141 () (@list @t140)) % 0.61/0.87 (define @t142 () (or @t78 @t123 @t139)) % 0.61/0.87 (define @t143 () (tptp.b @t140)) % 0.61/0.87 (define @t144 () (not (tptp.a @t140))) % 0.61/0.87 (define @t145 () (@list @t140)) % 0.61/0.87 (define @t146 () (forall @t145 (or (not (tptp.rel @t29 @t140)) @t144 @t143))) % 0.61/0.87 (define @t147 () (tptp.b @t29)) % 0.61/0.87 (define @t148 () (tptp.a @t29)) % 0.61/0.87 (define @t149 () (not @t148)) % 0.61/0.87 (define @t150 () (forall @t34 (or @t78 @t149 @t147))) % 0.61/0.87 (define @t151 () (@list @t29)) % 0.61/0.87 (define @t152 () (lambda @t81 @t150)) % 0.61/0.87 (define @t153 () (_ @t152 @t29)) % 0.61/0.87 (define @t154 () (or @t78 @t123 @t153)) % 0.61/0.87 (define @t155 () (forall @t34 @t154)) % 0.61/0.87 (define @t156 () (lambda @t81 @t155)) % 0.61/0.87 (define @t157 () (_ @t5 @t29)) % 0.61/0.87 (define @t158 () (@list @t5 @t23)) % 0.61/0.87 (define @t159 () (_ tptp.b @t29)) % 0.61/0.87 (define @t160 () (or @t78 @t149 @t159)) % 0.61/0.87 (define @t161 () (lambda @t81 (_ tptp.b @t23))) % 0.61/0.87 (define @t162 () (_ @t161 @t29)) % 0.61/0.87 (define @t163 () (or @t78 @t149 @t162)) % 0.61/0.87 (define @t164 () (forall @t34 @t163)) % 0.61/0.87 (define @t165 () (lambda @t81 @t164)) % 0.61/0.87 (define @t166 () (_ @t58 tptp.b)) % 0.61/0.87 (define @t167 () (_ tptp.a @t29)) % 0.61/0.87 (define @t168 () (not @t167)) % 0.61/0.87 (define @t169 () (or @t78 @t168 @t157)) % 0.61/0.87 (define @t170 () (lambda @t81 (_ tptp.a @t23))) % 0.61/0.87 (define @t171 () (_ @t170 @t29)) % 0.61/0.87 (define @t172 () (not @t171)) % 0.61/0.87 (define @t173 () (or @t78 @t172 @t157)) % 0.61/0.87 (define @t174 () (forall @t34 @t173)) % 0.61/0.87 (define @t175 () (lambda @t158 @t174)) % 0.61/0.87 (define @t176 () (not @t70)) % 0.61/0.87 (define @t177 () (forall @t34 (or @t78 @t176 @t157))) % 0.61/0.87 (define @t178 () (lambda @t59 @t177)) % 0.61/0.87 (define @t179 () (_ @t58 tptp.a)) % 0.61/0.87 (define @t180 () (not (tptp.rel @t29 @t115))) % 0.61/0.87 (define @t181 () (or @t78 @t147 @t180 @t117 @t116)) % 0.61/0.87 (define @t182 () (@list @t29 @t115)) % 0.61/0.87 (define @t183 () (forall @t182 @t181)) % 0.61/0.87 (define @t184 () (lambda @t81 @t183)) % 0.61/0.87 (define @t185 () (not (_ @t184 @t29))) % 0.61/0.87 (define @t186 () (or @t78 @t185 @t157)) % 0.61/0.87 (define @t187 () (forall @t34 @t186)) % 0.61/0.87 (define @t188 () (lambda @t158 @t187)) % 0.61/0.87 (define @t189 () (or @t180 @t117 @t116)) % 0.61/0.87 (define @t190 () (or @t78 @t147 @t189)) % 0.61/0.87 (define @t191 () (forall @t182 @t190)) % 0.61/0.87 (define @t192 () (@list @t115)) % 0.61/0.87 (define @t193 () (forall @t192 @t190)) % 0.61/0.87 (define @t194 () (forall @t192 @t189)) % 0.61/0.87 (define @t195 () (or @t78 @t147 @t194)) % 0.61/0.87 (define @t196 () (or @t78 @t147 @t153)) % 0.61/0.87 (define @t197 () (forall @t34 @t196)) % 0.61/0.87 (define @t198 () (lambda @t81 @t197)) % 0.61/0.87 (define @t199 () (_ @t64 @t29)) % 0.61/0.87 (define @t200 () (@list @t64 @t23)) % 0.61/0.87 (define @t201 () (or @t78 @t159 @t199)) % 0.61/0.87 (define @t202 () (or @t78 @t162 @t199)) % 0.61/0.87 (define @t203 () (forall @t34 @t202)) % 0.61/0.87 (define @t204 () (lambda @t200 @t203)) % 0.61/0.87 (define @t205 () (forall @t34 (or @t78 @t70 @t199))) % 0.61/0.87 (define @t206 () (lambda @t65 @t205)) % 0.61/0.87 (define @t207 () (_ (_ @t178 @t179) @t166)) % 0.61/0.87 (define @t208 () (_ @t5 @t29)) % 0.61/0.87 (define @t209 () (_ @t1 @t29)) % 0.61/0.87 (define @t210 () (not @t209)) % 0.61/0.87 (define @t211 () (or @t89 @t210 @t208)) % 0.61/0.87 (define @t212 () (or @t210 @t208)) % 0.61/0.87 (define @t213 () (not @t77)) % 0.61/0.87 (define @t214 () (lambda @t81 (or @t213 (_ @t5 @t23)))) % 0.61/0.87 (define @t215 () (_ @t214 @t29)) % 0.61/0.87 (define @t216 () (or @t89 @t215)) % 0.61/0.87 (define @t217 () (forall @t34 @t216)) % 0.61/0.87 (define @t218 () (lambda @t11 @t217)) % 0.61/0.87 (define @t219 () (lambda @t88 (or @t213 @t87))) % 0.61/0.87 (define @t220 () (_ @t64 @t29)) % 0.61/0.87 (define @t221 () (or @t89 @t209 @t220)) % 0.61/0.87 (define @t222 () (or @t209 @t220)) % 0.61/0.87 (define @t223 () (_ @t1 @t14)) % 0.61/0.87 (define @t224 () (lambda @t104 (or @t223 (_ @t64 @t14)))) % 0.61/0.87 (define @t225 () (_ @t224 @t29)) % 0.61/0.87 (define @t226 () (or @t89 @t225)) % 0.61/0.87 (define @t227 () (forall @t34 @t226)) % 0.61/0.87 (define @t228 () (lambda @t11 @t227)) % 0.61/0.87 (define @t229 () (lambda @t106 (or @t223 @t19))) % 0.61/0.87 (define @t230 () (@quantifiers_skolemize @t125 1)) % 0.61/0.87 (define @t231 () (forall @t121 (or (not (tptp.rel @t230 @t118)) @t120 @t119 @t117 @t116))) % 0.61/0.87 (define @t232 () (@quantifiers_skolemize @t125 2)) % 0.61/0.87 (define @t233 () (tptp.b @t232)) % 0.61/0.87 (define @t234 () (tptp.a @t232)) % 0.61/0.87 (define @t235 () (not @t234)) % 0.61/0.87 (define @t236 () (tptp.rel @t230 @t232)) % 0.61/0.87 (define @t237 () (not @t236)) % 0.61/0.87 (define @t238 () (not @t231)) % 0.61/0.87 (define @t239 () (or (not (tptp.rel (@quantifiers_skolemize @t125 0) @t230)) @t238 @t237 @t235 @t233)) % 0.61/0.87 (define @t240 () (@list true)) % 0.61/0.87 (define @t241 () (@list @t239)) % 0.61/0.87 (define @t242 () (tptp.rel @t232 @t232)) % 0.61/0.87 (define @t243 () (not @t242)) % 0.61/0.87 (define @t244 () (or @t237 @t233 @t243 @t235 @t233)) % 0.61/0.87 (define @t245 () (_ tptp.rel @t232)) % 0.61/0.87 (define @t246 () (_ @t245 @t232)) % 0.61/0.87 (define @t247 () (_ @t245 @t232)) % 0.61/0.87 (define @t248 () (tptp.rel @t232 @t29)) % 0.61/0.87 (define @t249 () (not @t248)) % 0.61/0.87 (define @t250 () (_ @t245 @t29)) % 0.61/0.87 (define @t251 () (or @t249 @t250)) % 0.61/0.87 (define @t252 () (_ @t245 @t29)) % 0.61/0.87 (define @t253 () (or @t249 @t252)) % 0.61/0.87 (define @t254 () (forall @t34 @t253)) % 0.61/0.87 (define @t255 () (not @t254)) % 0.61/0.87 (define @t256 () (or @t255 @t247)) % 0.61/0.87 (assume @p1 (= tptp.icl_true tptp.mtrue)) % 0.61/0.87 (assume @p2 (= tptp.icl_false tptp.mfalse)) % 0.61/0.87 (assume @p3 @t4) % 0.61/0.87 (assume @p4 (forall (@list @t5) (_ tptp.mvalid (_ (_ tptp.mimpl @t6) (_ @t2 @t6))))) % 0.61/0.87 (assume @p5 @t9) % 0.61/0.87 (assume @p6 true) % 0.61/0.87 (step @p7 (= tptp.mfalse @t12) :rule refl :args (@t12)) % 0.61/0.87 (step @p8 (= tptp.mtrue @t13) :rule refl :args (@t13)) % 0.61/0.87 (step @p9 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.61/0.87 (step @p10 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.61/0.87 (step @p11 (= tptp.mand @t22) :rule refl :args (@t22)) % 0.61/0.87 (step @p12 (= tptp.mimpl @t27) :rule refl :args (@t27)) % 0.61/0.87 (step @p13 (= tptp.miff @t28) :rule refl :args (@t28)) % 0.61/0.87 (step @p14 (= tptp.mbox @t37) :rule refl :args (@t37)) % 0.61/0.87 (step @p15 (= tptp.mdia @t38) :rule refl :args (@t38)) % 0.61/0.87 (step @p16 (= tptp.mall @t45) :rule refl :args (@t45)) % 0.61/0.87 (step @p17 (= tptp.mexists @t46) :rule refl :args (@t46)) % 0.61/0.87 (step @p18 (= tptp.mvalid @t51) :rule refl :args (@t51)) % 0.61/0.87 (step @p19 (= tptp.msatisfiable @t52) :rule refl :args (@t52)) % 0.61/0.87 (step @p20 (= tptp.mcountersatisfiable @t54) :rule refl :args (@t54)) % 0.61/0.87 (step @p21 (= tptp.minvalid @t55) :rule refl :args (@t55)) % 0.61/0.87 (step @p22 (= tptp.icl_atom @t57) :rule refl :args (@t57)) % 0.61/0.87 (step @p23 (= tptp.icl_princ @t58) :rule refl :args (@t58)) % 0.61/0.87 (step @p24 (= tptp.icl_and @t60) :rule refl :args (@t60)) % 0.61/0.87 (step @p25 (= tptp.icl_or @t62) :rule refl :args (@t62)) % 0.61/0.87 (step @p26 (= tptp.icl_impl @t63) :rule refl :args (@t63)) % 0.61/0.87 (step @p27 (= tptp.icl_says @t66) :rule refl :args (@t66)) % 0.61/0.87 (step @p28 (= tptp.iclval @t68) :rule refl :args (@t68)) % 0.61/0.87 (step @p29 (= tptp.icl_impl_princ @t63) :rule refl :args (@t63)) % 0.61/0.87 (step @p30 :rule quant-merge-prenex :args ((= (forall @t3 (forall @t48 @t73)) @t74))) % 0.61/0.87 (step @p31 :rule refl :args (@t69)) % 0.61/0.87 (step @p32 :rule refl :args (@t75)) % 0.61/0.87 (step @p33 :rule cong :premises (@p32 @p31) :args ((= @t75 @t69))) % 0.61/0.87 (step @p34 :rule symm :premises (@p33)) % 0.61/0.87 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.61/0.87 (step @p36 :rule refl :args (@t72)) % 0.61/0.87 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t76)) % 0.61/0.87 (step @p38 :rule cong :premises (@p37) :args ((forall @t48 @t76))) % 0.61/0.87 (step @p39 :rule beta-reduce :args ((= @t83 @t76))) % 0.61/0.87 (step @p40 :rule cong :premises (@p39) :args (@t84)) % 0.61/0.87 (step @p41 :rule trans :premises (@p40 @p38)) % 0.61/0.87 (step @p42 :rule beta-reduce :args ((= (_ @t86 @t82) @t84))) % 0.61/0.87 (step @p43 :rule trans :premises (@p42 @p41)) % 0.61/0.87 (step @p44 :rule beta-reduce :args ((= (_ (lambda @t88 (or @t80 @t87)) @t1) @t82))) % 0.61/0.87 (step @p45 :rule refl :args (@t1)) % 0.61/0.87 (step @p46 :rule refl :args (@t87)) % 0.61/0.87 (step @p47 :rule beta-reduce :args ((= @t91 @t79))) % 0.61/0.87 (step @p48 :rule cong :premises (@p47) :args (@t92)) % 0.61/0.87 (step @p49 :rule nary_cong :premises (@p48 @p46) :args (@t93)) % 0.61/0.87 (step @p50 :rule cong :premises (@p49) :args (@t94)) % 0.61/0.87 (step @p51 :rule beta-reduce :args ((= (_ @t96 @t90) @t94))) % 0.61/0.87 (step @p52 :rule trans :premises (@p51 @p50)) % 0.61/0.87 (step @p53 :rule beta-reduce :args ((= (_ @t98 @t1) @t90))) % 0.61/0.87 (step @p54 :rule beta-reduce :args ((= @t100 @t98))) % 0.61/0.87 (step @p55 :rule ho_cong :premises (@p54 @p45)) % 0.61/0.87 (step @p56 :rule trans :premises (@p55 @p53)) % 0.61/0.87 (step @p57 :rule refl :args (@t96)) % 0.61/0.87 (step @p58 :rule ho_cong :premises (@p57 @p56)) % 0.61/0.87 (step @p59 :rule trans :premises (@p58 @p52)) % 0.61/0.87 (step @p60 :rule ho_cong :premises (@p59 @p45)) % 0.61/0.87 (step @p61 :rule trans :premises (@p60 @p44)) % 0.61/0.87 (step @p62 :rule refl :args (@t86)) % 0.61/0.87 (step @p63 :rule ho_cong :premises (@p62 @p61)) % 0.61/0.87 (step @p64 :rule trans :premises (@p63 @p43)) % 0.61/0.87 (step @p65 :rule cong :premises (@p64) :args ((forall @t3 (_ @t86 (_ (_ @t96 (_ @t100 @t1)) @t1))))) % 0.61/0.87 (step @p66 :rule trans :premises (@p65 @p30)) % 0.61/0.87 (step @p67 :rule refl :args (tptp.rel)) % 0.61/0.87 (step @p68 :rule refl :args (@t97)) % 0.61/0.87 (step @p69 :rule refl :args (@t31)) % 0.61/0.87 (step @p70 :rule cong :premises (@p69 @p68) :args ((= @t31 @t97))) % 0.61/0.87 (step @p71 :rule symm :premises (@p70)) % 0.61/0.87 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 0.61/0.87 (step @p73 :rule refl :args (@t99)) % 0.61/0.87 (step @p74 :rule refl :args (@t33)) % 0.61/0.87 (step @p75 :rule cong :premises (@p74 @p73) :args ((= @t33 @t99))) % 0.61/0.87 (step @p76 :rule symm :premises (@p75)) % 0.61/0.87 (step @p77 :rule eq_resolve :premises (@p74 @p76)) % 0.61/0.87 (step @p78 :rule cong :premises (@p77) :args (@t101)) % 0.61/0.87 (step @p79 :rule nary_cong :premises (@p78 @p72) :args (@t102)) % 0.61/0.87 (step @p80 :rule cong :premises (@p79) :args ((forall @t34 @t102))) % 0.61/0.87 (step @p81 :rule bool-impl-elim :args (@t33 @t31)) % 0.61/0.87 (step @p82 :rule cong :premises (@p81) :args (@t35)) % 0.61/0.87 (step @p83 :rule trans :premises (@p82 @p80)) % 0.61/0.87 (step @p84 :rule cong :premises (@p83) :args (@t37)) % 0.61/0.87 (step @p85 :rule trans :premises (@p14 @p84)) % 0.61/0.87 (step @p86 :rule ho_cong :premises (@p85 @p67)) % 0.61/0.87 (step @p87 :rule ho_cong :premises (@p86 @p45)) % 0.61/0.87 (step @p88 :rule beta-reduce :args ((= (_ @t105 @t23) @t95))) % 0.61/0.87 (step @p89 :rule refl :args (@t23)) % 0.61/0.87 (step @p90 :rule beta-reduce :args ((= (_ (lambda @t106 (or @t103 @t19)) @t24) @t105))) % 0.61/0.87 (step @p91 :rule refl :args (@t24)) % 0.61/0.87 (step @p92 :rule refl :args (@t19)) % 0.61/0.87 (step @p93 :rule beta-reduce :args ((= @t108 @t103))) % 0.61/0.87 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t109)) % 0.61/0.87 (step @p95 :rule cong :premises (@p94) :args (@t110)) % 0.61/0.87 (step @p96 :rule beta-reduce :args ((= (_ @t21 @t107) @t110))) % 0.61/0.87 (step @p97 :rule trans :premises (@p96 @p95)) % 0.61/0.87 (step @p98 :rule beta-reduce :args ((= (_ @t17 @t25) @t107))) % 0.61/0.87 (step @p99 :rule refl :args (@t21)) % 0.61/0.87 (step @p100 :rule ho_cong :premises (@p99 @p98)) % 0.61/0.87 (step @p101 :rule trans :premises (@p100 @p97)) % 0.61/0.87 (step @p102 :rule ho_cong :premises (@p101 @p91)) % 0.61/0.87 (step @p103 :rule trans :premises (@p102 @p90)) % 0.61/0.87 (step @p104 :rule ho_cong :premises (@p103 @p89)) % 0.61/0.87 (step @p105 :rule trans :premises (@p104 @p88)) % 0.61/0.87 (step @p106 :rule refl :args (@t25)) % 0.61/0.87 (step @p107 :rule ho_cong :premises (@p9 @p106)) % 0.61/0.87 (step @p108 :rule ho_cong :premises (@p10 @p107)) % 0.61/0.87 (step @p109 :rule ho_cong :premises (@p108 @p91)) % 0.61/0.87 (step @p110 :rule ho_cong :premises (@p109 @p89)) % 0.61/0.87 (step @p111 :rule trans :premises (@p110 @p105)) % 0.61/0.87 (step @p112 :rule cong :premises (@p111) :args (@t27)) % 0.61/0.87 (step @p113 :rule trans :premises (@p12 @p112)) % 0.61/0.87 (step @p114 :rule ho_cong :premises (@p113 @p87)) % 0.61/0.87 (step @p115 :rule ho_cong :premises (@p114 @p45)) % 0.61/0.87 (step @p116 :rule refl :args (@t85)) % 0.61/0.87 (step @p117 :rule refl :args (@t47)) % 0.61/0.87 (step @p118 :rule cong :premises (@p117 @p116) :args ((= @t47 @t85))) % 0.61/0.87 (step @p119 :rule symm :premises (@p118)) % 0.61/0.87 (step @p120 :rule eq_resolve :premises (@p117 @p119)) % 0.61/0.87 (step @p121 :rule cong :premises (@p120) :args (@t49)) % 0.61/0.87 (step @p122 :rule cong :premises (@p121) :args (@t51)) % 0.61/0.87 (step @p123 :rule trans :premises (@p18 @p122)) % 0.61/0.87 (step @p124 :rule ho_cong :premises (@p123 @p115)) % 0.61/0.87 (step @p125 :rule cong :premises (@p124) :args (@t4)) % 0.61/0.87 (step @p126 :rule trans :premises (@p125 @p66)) % 0.61/0.87 (step @p127 :rule eq_resolve :premises (@p3 @p126)) % 0.61/0.87 (step @p128 :rule quant-merge-prenex :args ((= (forall @t48 @t127) @t125))) % 0.61/0.87 (step @p129 :rule beta-reduce :args ((= @t130 @t127))) % 0.61/0.87 (step @p130 :rule cong :premises (@p129) :args (@t131)) % 0.61/0.87 (step @p131 :rule trans :premises (@p130 @p128)) % 0.61/0.87 (step @p132 :rule beta-reduce :args ((= (_ @t133 @t129) @t131))) % 0.61/0.87 (step @p133 :rule trans :premises (@p132 @p131)) % 0.61/0.87 (step @p134 :rule aci_norm :args ((= @t135 @t128))) % 0.61/0.87 (step @p135 :rule cong :premises (@p134) :args (@t136)) % 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:args (@t251)) % 0.61/0.88 (step @p398 :rule cong :premises (@p397) :args ((forall @t34 @t251))) % 0.61/0.88 (step @p399 :rule trans :premises (@p398 @p390)) % 0.61/0.88 (step @p400 :rule refl :args (@t252)) % 0.61/0.88 (step @p401 :rule refl :args (@t249)) % 0.61/0.88 (step @p402 :rule nary_cong :premises (@p401 @p400) :args (@t253)) % 0.61/0.88 (step @p403 :rule cong :premises (@p402) :args (@t254)) % 0.61/0.88 (step @p404 :rule trans :premises (@p403 @p399)) % 0.61/0.88 (step @p405 :rule cong :premises (@p404) :args (@t255)) % 0.61/0.88 (step @p406 :rule trans :premises (@p405 @p386)) % 0.61/0.88 (step @p407 :rule nary_cong :premises (@p406 @p385) :args (@t256)) % 0.61/0.88 (step @p408 :rule trans :premises (@p407 @p384)) % 0.61/0.88 (step @p409 :rule cong :premises (@p382 @p408) :args ((=> @t74 @t256))) % 0.61/0.88 (assume-push @p418 @t74) % 0.61/0.88 (step @p411 :rule instantiate :premises (@p127) :args ((@list @t245 @t232))) % 0.61/0.88 (step-pop @p419 :rule scope :premises (@p411)) % 0.61/0.88 (step @p412 :rule process_scope :premises (@p419) :args (@t256)) % 0.61/0.88 (step @p414 :rule eq_resolve :premises (@p412 @p409)) % 0.61/0.88 (step @p415 :rule eq_resolve :premises (@p414 @p383)) % 0.61/0.88 (step @p416 :rule implies_elim :premises (@p415)) % 0.61/0.88 (step @p417 false :rule chain_m_resolution :premises (@p416 @p376 @p127) :args (false (@list true false) (@list @t242 @t74))) % 0.61/0.88 ) % 0.61/0.88 % SZS output end Proof % 0.61/0.88 % cvc5 exiting %------------------------------------------------------------------------------