%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET753^4 : 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 : n020.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:34 AM UTC 2026 % Result : Theorem 0.42s 0.60s % Output : Proof 0.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET753^4 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n020.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:11:10 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.51 %----Proving TH0 % 0.42/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.42/0.60 % SZS status Theorem % 0.42/0.60 % SZS output start Proof % 0.42/0.60 ( % 0.42/0.60 (declare-sort $$unsorted 0) % 0.42/0.60 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.42/0.60 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.42/0.60 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.42/0.60 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.42/0.60 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.42/0.60 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.42/0.60 (define tptp.excl_union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.42/0.60 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.42/0.60 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.42/0.60 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.42/0.60 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.42/0.60 (define tptp.subset () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.42/0.60 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.42/0.60 (define tptp.misses () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))))) % 0.42/0.60 (define tptp.fun_image () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_4 _let_3) (exists (@list _let_1) (and (_ _let_4 _let_1) (= _let_3 (_ _let_2 _let_1)))))))))) % 0.42/0.60 (define tptp.fun_composition () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "G" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_3 _let_1) (_ _let_3 (_ _let_2 _let_1))))))) % 0.42/0.60 (define tptp.fun_inv_image () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "B" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_4 _let_1) (exists (@list _let_3) (and (_ _let_4 _let_3) (= _let_3 (_ _let_2 _let_1)))))))))) % 0.42/0.60 (define tptp.fun_injective () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "F" (-> $$unsorted $$unsorted)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (= (_ _let_3 _let_2) (_ _let_3 _let_1)) (= _let_2 _let_1)))))))) % 0.42/0.60 (define tptp.fun_surjective () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (lambda (@list _let_2) (forall (@list _let_3) (exists (@list _let_1) (= _let_3 (_ _let_2 _let_1))))))))) % 0.42/0.60 (define tptp.fun_bijective () (let ((_let_1 (@var "F" (-> $$unsorted $$unsorted)))) (lambda (@list _let_1) (and (_ tptp.fun_injective _let_1) (_ tptp.fun_surjective _let_1))))) % 0.42/0.60 (define tptp.fun_decreasing () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "SMALLER" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_4) (forall (@list _let_1 _let_3) (=> (_ (_ _let_4 _let_1) _let_3) (_ (_ _let_4 (_ _let_2 _let_3)) (_ _let_2 _let_1)))))))))) % 0.42/0.60 (define tptp.fun_increasing () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "SMALLER" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_4) (forall (@list _let_3 _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ (_ _let_4 (_ _let_2 _let_3)) (_ _let_2 _let_1)))))))))) % 0.42/0.60 (define @t1 () (@var "Y" (-> $$unsorted Bool))) % 0.42/0.60 (define @t2 () (@var "F" (-> $$unsorted $$unsorted))) % 0.42/0.60 (define @t3 () (_ tptp.fun_image @t2)) % 0.42/0.60 (define @t4 () (@var "X" (-> $$unsorted Bool))) % 0.42/0.60 (define @t5 () (_ (_ tptp.intersection @t4) @t1)) % 0.42/0.60 (define @t6 () (@list @t4 @t1 @t2)) % 0.42/0.60 (define @t7 () (forall @t6 (_ (_ tptp.subset (_ @t3 @t5)) (_ (_ tptp.intersection (_ @t3 @t4)) (_ @t3 @t1))))) % 0.42/0.60 (define @t8 () (not @t7)) % 0.42/0.60 (define @t9 () (@var "X" $$unsorted)) % 0.42/0.60 (define @t10 () (@var "M" (-> $$unsorted Bool))) % 0.42/0.60 (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9))) % 0.42/0.60 (define @t12 () (@list @t9)) % 0.42/0.60 (define @t13 () (lambda @t12 false)) % 0.42/0.60 (define @t14 () (@var "Y" $$unsorted)) % 0.42/0.60 (define @t15 () (@var "U" $$unsorted)) % 0.42/0.60 (define @t16 () (= @t15 @t9)) % 0.42/0.60 (define @t17 () (lambda (@list @t9 @t14 @t15) (or @t16 (= @t15 @t14)))) % 0.42/0.60 (define @t18 () (lambda (@list @t9 @t15) @t16)) % 0.42/0.60 (define @t19 () (_ @t1 @t15)) % 0.42/0.60 (define @t20 () (_ @t4 @t15)) % 0.42/0.60 (define @t21 () (@list @t4 @t1 @t15)) % 0.42/0.60 (define @t22 () (lambda @t21 (or @t20 @t19))) % 0.42/0.60 (define @t23 () (not @t20)) % 0.42/0.60 (define @t24 () (and @t20 (not @t19))) % 0.42/0.60 (define @t25 () (lambda @t21 (or @t24 (and @t23 @t19)))) % 0.42/0.60 (define @t26 () (and @t20 @t19)) % 0.42/0.60 (define @t27 () (lambda @t21 @t26)) % 0.42/0.60 (define @t28 () (lambda @t21 @t24)) % 0.42/0.60 (define @t29 () (lambda (@list @t4 @t15) @t23)) % 0.42/0.60 (define @t30 () (@list @t4 @t1)) % 0.42/0.60 (define @t31 () (lambda @t30 (= @t5 tptp.emptyset))) % 0.42/0.60 (define @t32 () (@list @t15)) % 0.42/0.60 (define @t33 () (forall @t32 (=> @t20 @t19))) % 0.42/0.60 (define @t34 () (lambda @t30 @t33)) % 0.42/0.60 (define @t35 () (exists @t32 @t26)) % 0.42/0.60 (define @t36 () (lambda @t30 @t35)) % 0.42/0.60 (define @t37 () (lambda @t30 (not @t35))) % 0.42/0.60 (define @t38 () (_ @t2 @t9)) % 0.42/0.60 (define @t39 () (= @t14 @t38)) % 0.42/0.60 (define @t40 () (@var "A" (-> $$unsorted Bool))) % 0.42/0.60 (define @t41 () (_ @t40 @t9)) % 0.42/0.60 (define @t42 () (and @t41 @t39)) % 0.42/0.60 (define @t43 () (exists @t12 @t42)) % 0.42/0.60 (define @t44 () (@list @t2 @t40 @t14)) % 0.42/0.60 (define @t45 () (lambda @t44 @t43)) % 0.42/0.60 (define @t46 () (@var "G" (-> $$unsorted $$unsorted))) % 0.42/0.60 (define @t47 () (lambda (@list @t2 @t46 @t9) (_ @t46 @t38))) % 0.42/0.60 (define @t48 () (@var "B" (-> $$unsorted Bool))) % 0.42/0.60 (define @t49 () (@list @t14)) % 0.42/0.60 (define @t50 () (lambda (@list @t2 @t48 @t9) (exists @t49 (and (_ @t48 @t14) @t39)))) % 0.42/0.60 (define @t51 () (_ @t2 @t14)) % 0.42/0.60 (define @t52 () (@list @t9 @t14)) % 0.42/0.60 (define @t53 () (@list @t2)) % 0.42/0.60 (define @t54 () (lambda @t53 (forall @t52 (=> (= @t38 @t51) (= @t9 @t14))))) % 0.42/0.60 (define @t55 () (lambda @t53 (forall @t49 (exists @t12 @t39)))) % 0.42/0.60 (define @t56 () (lambda @t53 (and (_ tptp.fun_injective @t2) (_ tptp.fun_surjective @t2)))) % 0.42/0.60 (define @t57 () (@var "SMALLER" (-> $$unsorted $$unsorted Bool))) % 0.42/0.60 (define @t58 () (_ (_ @t57 @t9) @t14)) % 0.42/0.60 (define @t59 () (@list @t2 @t57)) % 0.42/0.60 (define @t60 () (lambda @t59 (forall @t52 (=> @t58 (_ (_ @t57 @t51) @t38))))) % 0.42/0.60 (define @t61 () (lambda @t59 (forall @t52 (=> @t58 (_ (_ @t57 @t38) @t51))))) % 0.42/0.60 (define @t62 () (@var "BOUND_VARIABLE_7906" $$unsorted)) % 0.42/0.60 (define @t63 () (not (_ @t1 @t62))) % 0.42/0.60 (define @t64 () (not (_ @t4 @t62))) % 0.42/0.60 (define @t65 () (_ @t2 @t62)) % 0.42/0.60 (define @t66 () (_ @t2 @t9)) % 0.42/0.60 (define @t67 () (not (= @t66 @t65))) % 0.42/0.60 (define @t68 () (_ @t1 @t9)) % 0.42/0.60 (define @t69 () (not @t68)) % 0.42/0.60 (define @t70 () (_ @t4 @t9)) % 0.42/0.60 (define @t71 () (not @t70)) % 0.42/0.60 (define @t72 () (or (and (not (forall @t12 (or @t71 @t67))) (not (forall @t12 (or @t69 @t67)))) @t64 @t63)) % 0.42/0.60 (define @t73 () (forall (@list @t4 @t1 @t2 @t62) @t72)) % 0.42/0.60 (define @t74 () (@list @t62)) % 0.42/0.60 (define @t75 () (not (= @t65 @t66))) % 0.42/0.60 (define @t76 () (or @t69 @t75)) % 0.42/0.60 (define @t77 () (forall @t12 @t76)) % 0.42/0.60 (define @t78 () (not @t77)) % 0.42/0.60 (define @t79 () (or @t71 @t75)) % 0.42/0.60 (define @t80 () (forall @t12 @t79)) % 0.42/0.60 (define @t81 () (not @t80)) % 0.42/0.60 (define @t82 () (and @t81 @t78)) % 0.42/0.60 (define @t83 () (not (= @t15 @t66))) % 0.42/0.60 (define @t84 () (not (forall @t12 (or @t69 @t83)))) % 0.42/0.60 (define @t85 () (not (forall @t12 (or @t71 @t83)))) % 0.42/0.60 (define @t86 () (lambda @t32 (and @t85 @t84))) % 0.42/0.60 (define @t87 () (_ @t86 @t65)) % 0.42/0.60 (define @t88 () (or @t87 @t64 @t63)) % 0.42/0.60 (define @t89 () (forall @t74 @t88)) % 0.42/0.60 (define @t90 () (@var "BOUND_VARIABLE_7883" (-> $$unsorted Bool))) % 0.42/0.60 (define @t91 () (_ @t90 @t65)) % 0.42/0.60 (define @t92 () (or @t91 @t64 @t63)) % 0.42/0.60 (define @t93 () (@list @t90)) % 0.42/0.60 (define @t94 () (not (= @t14 @t66))) % 0.42/0.60 (define @t95 () (lambda @t49 (not (forall @t12 (or @t69 @t94))))) % 0.42/0.60 (define @t96 () (_ @t95 @t15)) % 0.42/0.60 (define @t97 () (and @t85 @t96)) % 0.42/0.60 (define @t98 () (lambda @t32 @t97)) % 0.42/0.60 (define @t99 () (@list @t1 @t15)) % 0.42/0.60 (define @t100 () (_ @t40 @t9)) % 0.42/0.60 (define @t101 () (not (forall @t12 (or (not @t100) @t94)))) % 0.42/0.60 (define @t102 () (lambda (@list @t40 @t14) @t101)) % 0.42/0.60 (define @t103 () (_ (lambda @t44 @t101) @t2)) % 0.42/0.60 (define @t104 () (lambda @t49 (not (forall @t12 (or @t71 @t94))))) % 0.42/0.60 (define @t105 () (_ @t104 @t15)) % 0.42/0.60 (define @t106 () (and @t105 @t19)) % 0.42/0.60 (define @t107 () (lambda @t99 @t106)) % 0.42/0.60 (define @t108 () (not (= @t65 @t65))) % 0.42/0.60 (define @t109 () (or @t91 @t64 @t63 @t108)) % 0.42/0.60 (define @t110 () (not (= @t15 @t65))) % 0.42/0.60 (define @t111 () (_ @t90 @t15)) % 0.42/0.60 (define @t112 () (or @t110 @t111 @t64 @t63 @t110)) % 0.42/0.60 (define @t113 () (or @t111 @t64 @t63 @t110)) % 0.42/0.60 (define @t114 () (forall @t32 @t113)) % 0.42/0.60 (define @t115 () (forall @t74 @t114)) % 0.42/0.60 (define @t116 () (forall (@list @t62 @t15) @t113)) % 0.42/0.60 (define @t117 () (@list @t15 @t62)) % 0.42/0.60 (define @t118 () (or @t64 @t63 @t110)) % 0.42/0.60 (define @t119 () (or @t118 @t111)) % 0.42/0.60 (define @t120 () (forall @t117 @t119)) % 0.42/0.60 (define @t121 () (forall @t74 @t119)) % 0.42/0.60 (define @t122 () (forall @t74 @t118)) % 0.42/0.60 (define @t123 () (or @t122 @t111)) % 0.42/0.60 (define @t124 () (forall @t12 (or @t71 @t69 @t83))) % 0.42/0.60 (define @t125 () (lambda @t49 (not (forall @t12 (or @t71 @t69 @t94))))) % 0.42/0.60 (define @t126 () (_ @t125 @t15)) % 0.42/0.60 (define @t127 () (not @t126)) % 0.42/0.60 (define @t128 () (or @t127 @t111)) % 0.42/0.60 (define @t129 () (forall @t32 @t128)) % 0.42/0.60 (define @t130 () (lambda @t93 @t129)) % 0.42/0.60 (define @t131 () (_ @t4 @t15)) % 0.42/0.60 (define @t132 () (not @t131)) % 0.42/0.60 (define @t133 () (_ @t1 @t15)) % 0.42/0.60 (define @t134 () (lambda @t30 (forall @t32 (or @t132 @t133)))) % 0.42/0.60 (define @t135 () (_ @t1 @t9)) % 0.42/0.60 (define @t136 () (not @t135)) % 0.42/0.60 (define @t137 () (_ @t4 @t9)) % 0.42/0.60 (define @t138 () (not @t137)) % 0.42/0.60 (define @t139 () (or @t138 @t136 @t94)) % 0.42/0.60 (define @t140 () (and @t137 @t135)) % 0.42/0.60 (define @t141 () (or (not @t140) @t94)) % 0.42/0.60 (define @t142 () (lambda @t32 @t26)) % 0.42/0.60 (define @t143 () (_ @t142 @t9)) % 0.42/0.60 (define @t144 () (not @t143)) % 0.42/0.60 (define @t145 () (or @t144 @t94)) % 0.42/0.60 (define @t146 () (forall @t12 @t145)) % 0.42/0.60 (define @t147 () (not @t146)) % 0.42/0.60 (define @t148 () (lambda @t49 @t147)) % 0.42/0.60 (define @t149 () (lambda @t99 @t26)) % 0.42/0.60 (define @t150 () (_ @t27 @t4)) % 0.42/0.60 (define @t151 () (forall @t6 (_ (_ @t134 (_ @t103 (_ @t150 @t1))) (_ (_ @t27 (_ @t103 @t4)) (_ @t103 @t1))))) % 0.42/0.60 (define @t152 () (not @t39)) % 0.42/0.60 (define @t153 () (not @t41)) % 0.42/0.60 (define @t154 () (or @t153 @t152)) % 0.42/0.60 (define @t155 () (forall @t12 (not @t42))) % 0.42/0.60 (define @t156 () (not @t155)) % 0.42/0.60 (define @t157 () (or @t23 @t19)) % 0.42/0.60 (define @t158 () (@quantifiers_skolemize @t73 3)) % 0.42/0.60 (define @t159 () (@quantifiers_skolemize @t73 1)) % 0.42/0.60 (define @t160 () (_ @t159 @t158)) % 0.42/0.60 (define @t161 () (not @t160)) % 0.42/0.60 (define @t162 () (@quantifiers_skolemize @t73 0)) % 0.42/0.60 (define @t163 () (_ @t162 @t158)) % 0.42/0.60 (define @t164 () (not @t163)) % 0.42/0.60 (define @t165 () (@quantifiers_skolemize @t73 2)) % 0.42/0.60 (define @t166 () (_ @t165 @t158)) % 0.42/0.60 (define @t167 () (not (= (_ @t165 @t9) @t166))) % 0.42/0.60 (define @t168 () (forall @t12 (or (not (_ @t159 @t9)) @t167))) % 0.42/0.60 (define @t169 () (not @t168)) % 0.42/0.60 (define @t170 () (forall @t12 (or (not (_ @t162 @t9)) @t167))) % 0.42/0.60 (define @t171 () (not @t170)) % 0.42/0.60 (define @t172 () (and @t171 @t169)) % 0.42/0.60 (define @t173 () (or @t172 @t164 @t161)) % 0.42/0.60 (define @t174 () (@list true)) % 0.42/0.60 (define @t175 () (@list @t173)) % 0.42/0.60 (define @t176 () (not (= @t166 @t166))) % 0.42/0.60 (define @t177 () (or @t164 @t176)) % 0.42/0.60 (define @t178 () (@list 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0.42/0.60 (step @p60 :rule beta-reduce :args ((= (_ @t27 @t104) @t107))) % 0.42/0.60 (step @p61 :rule trans :premises (@p60 @p59)) % 0.42/0.60 (step @p62 :rule beta-reduce :args ((= (_ @t102 @t4) @t104))) % 0.42/0.60 (step @p63 :rule refl :args (@t4)) % 0.42/0.60 (step @p64 :rule ho_cong :premises (@p53 @p63)) % 0.42/0.60 (step @p65 :rule trans :premises (@p64 @p62)) % 0.42/0.60 (step @p66 :rule refl :args (@t27)) % 0.42/0.60 (step @p67 :rule ho_cong :premises (@p66 @p65)) % 0.42/0.60 (step @p68 :rule trans :premises (@p67 @p61)) % 0.42/0.60 (step @p69 :rule ho_cong :premises (@p68 @p55)) % 0.42/0.60 (step @p70 :rule trans :premises (@p69 @p50)) % 0.42/0.60 (step @p71 :rule aci_norm :args ((= (or @t91 @t64 @t63 false) @t92))) % 0.42/0.60 (step @p72 :rule evaluate :args ((not true))) % 0.42/0.60 (step @p73 :rule eq-refl :args (@t65)) % 0.42/0.60 (step @p74 :rule cong :premises (@p73) :args (@t108)) % 0.42/0.60 (step @p75 :rule trans :premises (@p74 @p72)) % 0.42/0.60 (step @p76 :rule 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@p198 :rule cong :premises (@p197 @p196) :args ((= @t19 @t133))) % 0.42/0.60 (step @p199 :rule symm :premises (@p198)) % 0.42/0.60 (step @p200 :rule eq_resolve :premises (@p197 @p199)) % 0.42/0.60 (step @p201 :rule refl :args (@t131)) % 0.42/0.60 (step @p202 :rule refl :args (@t20)) % 0.42/0.60 (step @p203 :rule cong :premises (@p202 @p201) :args ((= @t20 @t131))) % 0.42/0.60 (step @p204 :rule symm :premises (@p203)) % 0.42/0.60 (step @p205 :rule eq_resolve :premises (@p202 @p204)) % 0.42/0.60 (step @p206 :rule cong :premises (@p205) :args (@t23)) % 0.42/0.60 (step @p207 :rule nary_cong :premises (@p206 @p200) :args (@t157)) % 0.42/0.60 (step @p208 :rule cong :premises (@p207) :args ((forall @t32 @t157))) % 0.42/0.60 (step @p209 :rule bool-impl-elim :args (@t20 @t19)) % 0.42/0.60 (step @p210 :rule cong :premises (@p209) :args (@t33)) % 0.42/0.60 (step @p211 :rule trans :premises (@p210 @p208)) % 0.42/0.60 (step @p212 :rule cong :premises (@p211) :args (@t34)) % 0.42/0.60 (step @p213 :rule trans :premises (@p14 @p212)) % 0.42/0.60 (step @p214 :rule ho_cong :premises (@p213 @p195)) % 0.42/0.60 (step @p215 :rule ho_cong :premises (@p214 @p192)) % 0.42/0.60 (step @p216 :rule cong :premises (@p215) :args (@t7)) % 0.42/0.61 (step @p217 :rule cong :premises (@p216) :args (@t8)) % 0.42/0.61 (step @p218 :rule trans :premises (@p217 @p162)) % 0.42/0.61 (step @p219 :rule eq_resolve :premises (@p1 @p218)) % 0.42/0.61 (step @p220 :rule skolemize :premises (@p219)) % 0.42/0.61 (step @p221 :rule bool-double-not-elim :args (@t160)) % 0.42/0.61 (step @p222 :rule refl :args (@t173)) % 0.42/0.61 (step @p223 :rule nary_cong :premises (@p222 @p221) :args ((or @t173 (not @t161)))) % 0.42/0.61 (step @p224 :rule cnf_or_neg :args (@t173 2)) % 0.42/0.61 (step @p225 :rule eq_resolve :premises (@p224 @p223)) % 0.42/0.61 (step @p226 :rule reordering :premises (@p225) :args ((or @t160 @t173))) % 0.42/0.61 (step @p227 :rule chain_m_resolution :premises (@p226 @p220) :args (@t160 @t174 @t175)) % 0.42/0.61 (step @p228 :rule cnf_or_neg :args (@t173 0)) % 0.42/0.61 (step @p229 :rule chain_m_resolution :premises (@p228 @p220) :args ((not @t172) @t174 @t175)) % 0.42/0.61 (step @p230 :rule bool-double-not-elim :args (@t163)) % 0.42/0.61 (step @p231 :rule nary_cong :premises (@p222 @p230) :args ((or @t173 (not @t164)))) % 0.42/0.61 (step @p232 :rule cnf_or_neg :args (@t173 1)) % 0.42/0.61 (step @p233 :rule eq_resolve :premises (@p232 @p231)) % 0.42/0.61 (step @p234 :rule reordering :premises (@p233) :args ((or @t163 @t173))) % 0.42/0.61 (step @p235 :rule chain_m_resolution :premises (@p234 @p220) :args (@t163 @t174 @t175)) % 0.42/0.61 (step @p236 :rule aci_norm :args ((= (or @t164 false) @t164))) % 0.42/0.61 (step @p237 :rule eq-refl :args (@t166)) % 0.42/0.61 (step @p238 :rule cong :premises (@p237) :args (@t176)) % 0.42/0.61 (step @p239 :rule trans :premises (@p238 @p72)) % 0.42/0.61 (step @p240 :rule refl :args (@t164)) % 0.42/0.61 (step @p241 :rule nary_cong :premises (@p240 @p239) :args (@t177)) % 0.42/0.61 (step @p242 :rule trans :premises (@p241 @p236)) % 0.42/0.61 (step @p243 :rule refl :args (@t170)) % 0.42/0.61 (step @p244 :rule cong :premises (@p243 @p242) :args ((=> @t170 @t177))) % 0.42/0.61 (assume-push @p273 @t170) % 0.42/0.61 (step @p246 :rule instantiate :premises (@p273) :args (@t178)) % 0.42/0.61 (step-pop @p274 :rule scope :premises (@p246)) % 0.42/0.61 (step @p247 :rule process_scope :premises (@p274) :args (@t177)) % 0.42/0.61 (step @p249 :rule eq_resolve :premises (@p247 @p244)) % 0.42/0.61 (step @p250 :rule implies_elim :premises (@p249)) % 0.42/0.61 (step @p251 :rule chain_m_resolution :premises (@p250 @p235) :args (@t171 (@list false) (@list @t163))) % 0.42/0.61 (step @p252 :rule bool-double-not-elim :args (@t168)) % 0.42/0.61 (step @p253 :rule bool-double-not-elim :args (@t170)) % 0.42/0.61 (step @p254 :rule refl :args (@t172)) % 0.42/0.61 (step @p255 :rule nary_cong :premises (@p254 @p253 @p252) :args ((or @t172 (not @t171) (not @t169)))) % 0.42/0.61 (step @p256 :rule cnf_and_neg :args (@t172)) % 0.42/0.61 (step @p257 :rule eq_resolve :premises (@p256 @p255)) % 0.42/0.61 (step @p258 :rule reordering :premises (@p257) :args ((or @t170 @t168 @t172))) % 0.42/0.61 (step @p259 :rule chain_m_resolution :premises (@p258 @p251 @p229) :args (@t168 (@list true true) (@list @t170 @t172))) % 0.42/0.61 (step @p260 :rule aci_norm :args ((= (or @t161 false) @t161))) % 0.42/0.61 (step @p261 :rule refl :args (@t161)) % 0.42/0.61 (step @p262 :rule nary_cong :premises (@p261 @p239) :args (@t179)) % 0.42/0.61 (step @p263 :rule trans :premises (@p262 @p260)) % 0.42/0.61 (step @p264 :rule refl :args (@t168)) % 0.42/0.61 (step @p265 :rule cong :premises (@p264 @p263) :args ((=> @t168 @t179))) % 0.42/0.61 (assume-push @p275 @t168) % 0.42/0.61 (step @p267 :rule instantiate :premises (@p275) :args (@t178)) % 0.42/0.61 (step-pop @p276 :rule scope :premises (@p267)) % 0.42/0.61 (step @p268 :rule process_scope :premises (@p276) :args (@t179)) % 0.42/0.61 (step @p270 :rule eq_resolve :premises (@p268 @p265)) % 0.42/0.61 (step @p271 :rule implies_elim :premises (@p270)) % 0.42/0.61 (step @p272 false :rule chain_m_resolution :premises (@p271 @p259 @p227) :args (false (@list false false) (@list @t168 @t160))) % 0.42/0.61 ) % 0.42/0.61 % SZS output end Proof % 0.42/0.61 % cvc5 exiting %------------------------------------------------------------------------------