%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET624^3 : 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 08:48:17 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET624^3 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n020.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 16:05:25 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.57 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.57 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.38/0.57 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.38/0.57 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.38/0.57 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.57 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.38/0.57 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.57 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.38/0.57 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.57 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.38/0.57 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.38/0.57 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.57 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.38/0.57 (define @t1 () (@var "Z" (-> $$unsorted Bool))) % 0.38/0.57 (define @t2 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.57 (define @t3 () (_ tptp.meets @t2)) % 0.38/0.57 (define @t4 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.57 (define @t5 () (or (_ @t3 @t4) (_ @t3 @t1))) % 0.38/0.57 (define @t6 () (= (_ @t3 (_ (_ tptp.union @t4) @t1)) @t5)) % 0.38/0.57 (define @t7 () (@list @t2 @t4 @t1)) % 0.38/0.57 (define @t8 () (forall @t7 @t6)) % 0.38/0.57 (define @t9 () (not @t8)) % 0.38/0.57 (define @t10 () (@var "X" $$unsorted)) % 0.38/0.57 (define @t11 () (@var "M" (-> $$unsorted Bool))) % 0.38/0.57 (define @t12 () (lambda (@list @t10 @t11) (_ @t11 @t10))) % 0.38/0.57 (define @t13 () (lambda (@list @t10) false)) % 0.38/0.57 (define @t14 () (@var "Y" $$unsorted)) % 0.38/0.57 (define @t15 () (@var "U" $$unsorted)) % 0.38/0.57 (define @t16 () (= @t15 @t10)) % 0.38/0.57 (define @t17 () (lambda (@list @t10 @t14 @t15) (or @t16 (= @t15 @t14)))) % 0.38/0.57 (define @t18 () (lambda (@list @t10 @t15) @t16)) % 0.38/0.57 (define @t19 () (_ @t4 @t15)) % 0.38/0.57 (define @t20 () (_ @t2 @t15)) % 0.38/0.57 (define @t21 () (@list @t2 @t4 @t15)) % 0.38/0.57 (define @t22 () (lambda @t21 (or @t20 @t19))) % 0.38/0.57 (define @t23 () (not @t20)) % 0.38/0.57 (define @t24 () (not @t19)) % 0.38/0.57 (define @t25 () (and @t20 @t24)) % 0.38/0.57 (define @t26 () (lambda @t21 (or @t25 (and @t23 @t19)))) % 0.38/0.57 (define @t27 () (and @t20 @t19)) % 0.38/0.57 (define @t28 () (lambda @t21 @t27)) % 0.38/0.57 (define @t29 () (lambda @t21 @t25)) % 0.38/0.57 (define @t30 () (lambda (@list @t2 @t15) @t23)) % 0.38/0.57 (define @t31 () (@list @t2 @t4)) % 0.38/0.57 (define @t32 () (lambda @t31 (= (_ (_ tptp.intersection @t2) @t4) tptp.emptyset))) % 0.38/0.57 (define @t33 () (@list @t15)) % 0.38/0.57 (define @t34 () (lambda @t31 (forall @t33 (=> @t20 @t19)))) % 0.38/0.57 (define @t35 () (exists @t33 @t27)) % 0.38/0.57 (define @t36 () (lambda @t31 @t35)) % 0.38/0.57 (define @t37 () (lambda @t31 (not @t35))) % 0.38/0.57 (define @t38 () (_ @t1 @t15)) % 0.38/0.57 (define @t39 () (not @t38)) % 0.38/0.57 (define @t40 () (_ @t4 @t15)) % 0.38/0.57 (define @t41 () (not @t40)) % 0.38/0.57 (define @t42 () (_ @t2 @t15)) % 0.38/0.57 (define @t43 () (not @t42)) % 0.38/0.57 (define @t44 () (not (forall @t33 (or @t43 @t39)))) % 0.38/0.57 (define @t45 () (not (forall @t33 (or @t43 @t41)))) % 0.38/0.57 (define @t46 () (forall @t7 (= (or @t45 @t44) (not (forall @t33 (or @t43 (and @t41 @t39))))))) % 0.38/0.57 (define @t47 () (@quantifiers_skolemize @t46 2)) % 0.38/0.57 (define @t48 () (not (_ @t47 @t15))) % 0.38/0.57 (define @t49 () (@quantifiers_skolemize @t46 0)) % 0.38/0.57 (define @t50 () (not (_ @t49 @t15))) % 0.38/0.57 (define @t51 () (forall @t33 (or @t50 @t48))) % 0.38/0.57 (define @t52 () (not @t51)) % 0.38/0.57 (define @t53 () (@quantifiers_skolemize @t46 1)) % 0.38/0.57 (define @t54 () (not (_ @t53 @t15))) % 0.38/0.57 (define @t55 () (forall @t33 (or @t50 @t54))) % 0.38/0.57 (define @t56 () (not @t55)) % 0.38/0.57 (define @t57 () (or @t56 @t52)) % 0.38/0.57 (define @t58 () (not @t52)) % 0.38/0.57 (define @t59 () (_ @t1 @t15)) % 0.38/0.57 (define @t60 () (not @t59)) % 0.38/0.57 (define @t61 () (and @t24 @t60)) % 0.38/0.57 (define @t62 () (or @t43 @t61)) % 0.38/0.57 (define @t63 () (or @t19 @t59)) % 0.38/0.57 (define @t64 () (or @t43 (not @t63))) % 0.38/0.57 (define @t65 () (lambda @t33 @t63)) % 0.38/0.57 (define @t66 () (_ @t65 @t15)) % 0.38/0.57 (define @t67 () (not @t66)) % 0.38/0.57 (define @t68 () (or @t43 @t67)) % 0.38/0.57 (define @t69 () (forall @t33 @t68)) % 0.38/0.57 (define @t70 () (not @t69)) % 0.38/0.57 (define @t71 () (lambda (@list @t4) @t45)) % 0.38/0.57 (define @t72 () (@var "BOUND_VARIABLE_7648" (-> $$unsorted Bool))) % 0.38/0.57 (define @t73 () (_ @t72 @t15)) % 0.38/0.57 (define @t74 () (lambda (@list @t72 @t15) (or @t19 @t73))) % 0.38/0.57 (define @t75 () (_ (lambda @t31 @t45) @t2)) % 0.38/0.57 (define @t76 () (or (_ @t75 @t4) (_ @t75 @t1))) % 0.38/0.57 (define @t77 () (_ @t75 (_ (_ @t22 @t4) @t1))) % 0.38/0.57 (define @t78 () (forall @t7 (= @t77 @t76))) % 0.38/0.57 (define @t79 () (or @t23 @t24)) % 0.38/0.57 (define @t80 () (forall @t33 (not @t27))) % 0.38/0.57 (define @t81 () (not @t80)) % 0.38/0.57 (define @t82 () (forall @t33 (or @t50 (and @t54 @t48)))) % 0.38/0.57 (define @t83 () (not @t57)) % 0.38/0.57 (define @t84 () (not @t82)) % 0.38/0.57 (define @t85 () (= @t57 @t84)) % 0.38/0.57 (define @t86 () (not @t84)) % 0.38/0.57 (define @t87 () (@quantifiers_skolemize @t51 0)) % 0.38/0.57 (define @t88 () (_ @t47 @t87)) % 0.38/0.57 (define @t89 () (not @t88)) % 0.38/0.57 (define @t90 () (_ @t49 @t87)) % 0.38/0.57 (define @t91 () (not @t90)) % 0.38/0.57 (define @t92 () (or @t91 @t89)) % 0.38/0.57 (define @t93 () (not @t92)) % 0.38/0.57 (define @t94 () (and (not (_ @t53 @t87)) @t89)) % 0.38/0.57 (define @t95 () (or @t91 @t94)) % 0.38/0.57 (define @t96 () (@list false true false false true false true false)) % 0.38/0.57 (define @t97 () (not @t56)) % 0.38/0.57 (define @t98 () (@quantifiers_skolemize @t55 0)) % 0.38/0.57 (define @t99 () (_ @t53 @t98)) % 0.38/0.57 (define @t100 () (not @t99)) % 0.38/0.57 (define @t101 () (_ @t49 @t98)) % 0.38/0.57 (define @t102 () (not @t101)) % 0.38/0.57 (define @t103 () (or @t102 @t100)) % 0.38/0.57 (define @t104 () (not @t103)) % 0.38/0.57 (define @t105 () (and @t100 (not (_ @t47 @t98)))) % 0.38/0.57 (define @t106 () (or @t102 @t105)) % 0.38/0.57 (define @t107 () (@list false false)) % 0.38/0.57 (define @t108 () (@list true true)) % 0.38/0.57 (define @t109 () (@quantifiers_skolemize @t82 0)) % 0.38/0.57 (define @t110 () (_ @t47 @t109)) % 0.38/0.57 (define @t111 () (not @t110)) % 0.38/0.57 (define @t112 () (_ @t53 @t109)) % 0.38/0.57 (define @t113 () (not @t112)) % 0.38/0.57 (define @t114 () (and @t113 @t111)) % 0.38/0.57 (define @t115 () (_ @t49 @t109)) % 0.38/0.57 (define @t116 () (not @t115)) % 0.38/0.57 (define @t117 () (or @t116 @t114)) % 0.38/0.57 (define @t118 () (not @t117)) % 0.38/0.57 (define @t119 () (@list true)) % 0.38/0.57 (define @t120 () (@list @t117)) % 0.38/0.57 (define @t121 () (@list @t109)) % 0.38/0.57 (define @t122 () (or @t116 @t113)) % 0.38/0.57 (define @t123 () (or @t116 @t111)) % 0.38/0.57 (define @t124 () (not @t123)) % 0.38/0.57 (assume @p1 @t9) % 0.38/0.57 (assume @p2 true) % 0.38/0.57 (step @p3 (= tptp.in @t12) :rule refl :args (@t12)) % 0.38/0.57 (step @p4 (= tptp.is_a @t12) :rule refl :args (@t12)) % 0.38/0.57 (step @p5 (= tptp.emptyset @t13) :rule refl :args (@t13)) % 0.38/0.57 (step @p6 (= tptp.unord_pair @t17) :rule refl :args (@t17)) % 0.38/0.57 (step @p7 (= tptp.singleton @t18) :rule refl :args (@t18)) % 0.38/0.57 (step @p8 (= tptp.union @t22) :rule refl :args (@t22)) % 0.38/0.57 (step @p9 (= tptp.excl_union @t26) :rule refl :args (@t26)) % 0.38/0.57 (step @p10 (= tptp.intersection @t28) :rule refl :args (@t28)) % 0.38/0.57 (step @p11 (= tptp.setminus @t29) :rule refl :args (@t29)) % 0.38/0.57 (step @p12 (= tptp.complement @t30) :rule refl :args (@t30)) % 0.38/0.57 (step @p13 (= tptp.disjoint @t32) :rule refl :args (@t32)) % 0.38/0.57 (step @p14 (= tptp.subset @t34) :rule refl :args (@t34)) % 0.38/0.57 (step @p15 (= tptp.meets @t36) :rule refl :args (@t36)) % 0.38/0.57 (step @p16 (= tptp.misses @t37) :rule refl :args (@t37)) % 0.38/0.57 (step @p17 :rule bool-double-not-elim :args (@t51)) % 0.38/0.57 (step @p18 :rule refl :args (@t57)) % 0.38/0.57 (step @p19 :rule nary_cong :premises (@p18 @p17) :args ((or @t57 @t58))) % 0.38/0.57 (step @p20 :rule cnf_or_neg :args (@t57 1)) % 0.38/0.57 (step @p21 :rule eq_resolve :premises (@p20 @p19)) % 0.38/0.57 (step @p22 :rule reordering :premises (@p21) :args ((or @t51 @t57))) % 0.38/0.57 (step @p23 :rule refl :args (@t38)) % 0.38/0.57 (step @p24 :rule refl :args (@t59)) % 0.38/0.57 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t59 @t38))) % 0.38/0.57 (step @p26 :rule symm :premises (@p25)) % 0.38/0.57 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.38/0.57 (step @p28 :rule cong :premises (@p27) :args (@t60)) % 0.38/0.57 (step @p29 :rule refl :args (@t40)) % 0.38/0.57 (step @p30 :rule refl :args (@t19)) % 0.38/0.57 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t19 @t40))) % 0.38/0.57 (step @p32 :rule symm :premises (@p31)) % 0.38/0.57 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.38/0.57 (step @p34 :rule cong :premises (@p33) :args (@t24)) % 0.38/0.57 (step @p35 :rule nary_cong :premises (@p34 @p28) :args (@t61)) % 0.38/0.57 (step @p36 :rule refl :args (@t43)) % 0.38/0.57 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t62)) % 0.38/0.57 (step @p38 :rule cong :premises (@p37) :args ((forall @t33 @t62))) % 0.38/0.57 (step @p39 :rule bool-or-de-morgan :args (@t19 @t59 false)) % 0.38/0.57 (step @p40 :rule nary_cong :premises (@p36 @p39) :args (@t64)) % 0.38/0.57 (step @p41 :rule cong :premises (@p40) :args ((forall @t33 @t64))) % 0.38/0.57 (step @p42 :rule trans :premises (@p41 @p38)) % 0.38/0.57 (step @p43 :rule beta-reduce :args ((= @t66 @t63))) % 0.38/0.57 (step @p44 :rule cong :premises (@p43) :args (@t67)) % 0.38/0.57 (step @p45 :rule refl :args (@t43)) % 0.38/0.57 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t68)) % 0.38/0.57 (step @p47 :rule cong :premises (@p46) :args (@t69)) % 0.38/0.57 (step @p48 :rule trans :premises (@p47 @p42)) % 0.38/0.57 (step @p49 :rule cong :premises (@p48) :args (@t70)) % 0.38/0.57 (step @p50 :rule beta-reduce :args ((= (_ @t71 @t65) @t70))) % 0.38/0.57 (step @p51 :rule trans :premises (@p50 @p49)) % 0.38/0.57 (step @p52 :rule beta-reduce :args ((= (_ @t74 @t1) @t65))) % 0.38/0.57 (step @p53 :rule refl :args (@t1)) % 0.38/0.57 (step @p54 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t72 @t15) (or @t20 @t73)) @t4) @t74))) % 0.38/0.57 (step @p55 :rule refl :args (@t4)) % 0.38/0.57 (step @p56 :rule alpha_equiv :args (@t22 (@list @t4) (@list @t72))) % 0.38/0.57 (step @p57 :rule ho_cong :premises (@p56 @p55)) % 0.38/0.57 (step @p58 :rule trans :premises (@p57 @p54)) % 0.38/0.57 (step @p59 :rule ho_cong :premises (@p58 @p53)) % 0.38/0.57 (step @p60 :rule trans :premises (@p59 @p52)) % 0.38/0.57 (step @p61 :rule beta-reduce :args ((= @t75 @t71))) % 0.38/0.57 (step @p62 :rule ho_cong :premises (@p61 @p60)) % 0.38/0.57 (step @p63 :rule trans :premises (@p62 @p51)) % 0.38/0.57 (step @p64 :rule beta-reduce :args ((= (_ @t71 @t1) @t44))) % 0.38/0.57 (step @p65 :rule ho_cong :premises (@p61 @p53)) % 0.38/0.57 (step @p66 :rule trans :premises (@p65 @p64)) % 0.38/0.57 (step @p67 :rule beta-reduce :args ((= (_ @t71 @t4) @t45))) % 0.38/0.57 (step @p68 :rule refl :args (@t4)) % 0.38/0.57 (step @p69 :rule ho_cong :premises (@p61 @p68)) % 0.38/0.57 (step @p70 :rule trans :premises (@p69 @p67)) % 0.38/0.57 (step @p71 :rule nary_cong :premises (@p70 @p66) :args (@t76)) % 0.38/0.57 (step @p72 :rule cong :premises (@p71 @p63) :args ((= @t76 @t77))) % 0.38/0.57 (step @p73 :rule eq-symm :args (@t77 @t76)) % 0.38/0.57 (step @p74 :rule trans :premises (@p73 @p72)) % 0.38/0.57 (step @p75 :rule cong :premises (@p74) :args (@t78)) % 0.38/0.57 (step @p76 :rule cong :premises (@p75) :args ((not @t78))) % 0.38/0.57 (step @p77 :rule refl :args (@t2)) % 0.38/0.57 (step @p78 :rule refl :args (@t42)) % 0.38/0.57 (step @p79 :rule refl :args (@t20)) % 0.38/0.57 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t20 @t42))) % 0.38/0.57 (step @p81 :rule symm :premises (@p80)) % 0.38/0.57 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.38/0.57 (step @p83 :rule cong :premises (@p82) :args (@t23)) % 0.38/0.57 (step @p84 :rule nary_cong :premises (@p83 @p34) :args (@t79)) % 0.38/0.57 (step @p85 :rule cong :premises (@p84) :args ((forall @t33 @t79))) % 0.38/0.57 (step @p86 :rule bool-and-de-morgan :args (@t20 @t19 true)) % 0.38/0.57 (step @p87 :rule cong :premises (@p86) :args (@t80)) % 0.38/0.57 (step @p88 :rule trans :premises (@p87 @p85)) % 0.38/0.57 (step @p89 :rule cong :premises (@p88) :args (@t81)) % 0.38/0.57 (step @p90 :rule exists-elim :args ((= @t35 @t81))) % 0.38/0.57 (step @p91 :rule trans :premises (@p90 @p89)) % 0.38/0.57 (step @p92 :rule cong :premises (@p91) :args (@t36)) % 0.38/0.57 (step @p93 :rule trans :premises (@p15 @p92)) % 0.38/0.57 (step @p94 :rule ho_cong :premises (@p93 @p77)) % 0.38/0.57 (step @p95 :rule ho_cong :premises (@p94 @p53)) % 0.38/0.57 (step @p96 :rule ho_cong :premises (@p94 @p68)) % 0.38/0.57 (step @p97 :rule nary_cong :premises (@p96 @p95) :args (@t5)) % 0.38/0.57 (step @p98 :rule ho_cong :premises (@p8 @p68)) % 0.38/0.57 (step @p99 :rule ho_cong :premises (@p98 @p53)) % 0.38/0.57 (step @p100 :rule ho_cong :premises (@p94 @p99)) % 0.38/0.57 (step @p101 :rule cong :premises (@p100 @p97) :args (@t6)) % 0.38/0.57 (step @p102 :rule cong :premises (@p101) :args (@t8)) % 0.38/0.57 (step @p103 :rule cong :premises (@p102) :args (@t9)) % 0.38/0.57 (step @p104 :rule trans :premises (@p103 @p76)) % 0.38/0.57 (step @p105 :rule eq_resolve :premises (@p1 @p104)) % 0.38/0.57 (step @p106 :rule skolemize :premises (@p105)) % 0.38/0.57 (step @p107 :rule bool-double-not-elim :args (@t82)) % 0.38/0.57 (step @p108 :rule refl :args (@t83)) % 0.38/0.57 (step @p109 :rule refl :args (@t85)) % 0.38/0.57 (step @p110 :rule nary_cong :premises (@p109 @p108 @p107) :args ((or @t85 @t83 @t86))) % 0.38/0.57 (step @p111 :rule cnf_equiv_neg2 :args (@t85)) % 0.38/0.57 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.38/0.57 (step @p113 :rule reordering :premises (@p112) :args ((or @t82 @t85 @t83))) % 0.38/0.57 (step @p114 :rule refl :args (@t93)) % 0.38/0.57 (step @p115 :rule nary_cong :premises (@p17 @p114) :args ((or @t58 @t93))) % 0.38/0.57 (assume-push @p227 @t52) % 0.38/0.57 (step @p117 :rule skolemize :premises (@p227)) % 0.38/0.57 (step-pop @p228 :rule scope :premises (@p117)) % 0.38/0.57 (step @p118 :rule process_scope :premises (@p228) :args (@t93)) % 0.38/0.57 (step @p120 :rule implies_elim :premises (@p118)) % 0.38/0.57 (step @p121 :rule eq_resolve :premises (@p120 @p115)) % 0.38/0.57 (step @p122 :rule bool-double-not-elim :args (@t90)) % 0.38/0.57 (step @p123 :rule refl :args (@t92)) % 0.38/0.57 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or @t92 (not @t91)))) % 0.38/0.57 (step @p125 :rule cnf_or_neg :args (@t92 0)) % 0.38/0.57 (step @p126 :rule eq_resolve :premises (@p125 @p124)) % 0.38/0.57 (step @p127 :rule reordering :premises (@p126) :args ((or @t90 @t92))) % 0.38/0.57 (step @p128 :rule bool-double-not-elim :args (@t88)) % 0.38/0.57 (step @p129 :rule nary_cong :premises (@p123 @p128) :args ((or @t92 (not @t89)))) % 0.38/0.57 (step @p130 :rule cnf_or_neg :args (@t92 1)) % 0.38/0.57 (step @p131 :rule eq_resolve :premises (@p130 @p129)) % 0.38/0.57 (step @p132 :rule reordering :premises (@p131) :args ((or @t88 @t92))) % 0.38/0.57 (step @p133 :rule cnf_and_pos :args (@t94 1)) % 0.38/0.57 (step @p134 :rule reordering :premises (@p133) :args ((or @t89 (not @t94)))) % 0.38/0.57 (assume-push @p229 @t82) % 0.38/0.57 (step @p136 :rule instantiate :premises (@p229) :args ((@list @t87))) % 0.38/0.57 (step-pop @p230 :rule scope :premises (@p136)) % 0.38/0.57 (step @p137 :rule process_scope :premises (@p230) :args (@t95)) % 0.38/0.57 (step @p139 :rule implies_elim :premises (@p137)) % 0.38/0.57 (step @p140 :rule cnf_or_pos :args (@t95)) % 0.38/0.57 (step @p141 :rule reordering :premises (@p140) :args ((or @t91 @t94 (not @t95)))) % 0.38/0.57 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p134 @p132 @p127 @p121 @p113 @p106 @p22) :args (@t51 @t96 (@list @t95 @t94 @t88 @t90 @t92 @t82 @t85 @t57))) % 0.38/0.57 (step @p143 :rule bool-double-not-elim :args (@t55)) % 0.38/0.57 (step @p144 :rule nary_cong :premises (@p18 @p143) :args ((or @t57 @t97))) % 0.38/0.57 (step @p145 :rule cnf_or_neg :args (@t57 0)) % 0.38/0.57 (step @p146 :rule eq_resolve :premises (@p145 @p144)) % 0.38/0.57 (step @p147 :rule reordering :premises (@p146) :args ((or @t55 @t57))) % 0.38/0.57 (step @p148 :rule refl :args (@t104)) % 0.38/0.57 (step @p149 :rule nary_cong :premises (@p143 @p148) :args ((or @t97 @t104))) % 0.38/0.57 (assume-push @p231 @t56) % 0.38/0.57 (step @p151 :rule skolemize :premises (@p231)) % 0.38/0.57 (step-pop @p232 :rule scope :premises (@p151)) % 0.38/0.57 (step @p152 :rule process_scope :premises (@p232) :args (@t104)) % 0.38/0.57 (step @p154 :rule implies_elim :premises (@p152)) % 0.38/0.57 (step @p155 :rule eq_resolve :premises (@p154 @p149)) % 0.38/0.57 (step @p156 :rule bool-double-not-elim :args (@t101)) % 0.38/0.57 (step @p157 :rule refl :args (@t103)) % 0.38/0.57 (step @p158 :rule nary_cong :premises (@p157 @p156) :args ((or @t103 (not @t102)))) % 0.38/0.57 (step @p159 :rule cnf_or_neg :args (@t103 0)) % 0.38/0.57 (step @p160 :rule eq_resolve :premises (@p159 @p158)) % 0.38/0.57 (step @p161 :rule reordering :premises (@p160) :args ((or @t101 @t103))) % 0.38/0.57 (step @p162 :rule bool-double-not-elim :args (@t99)) % 0.38/0.57 (step @p163 :rule nary_cong :premises (@p157 @p162) :args ((or @t103 (not @t100)))) % 0.38/0.57 (step @p164 :rule cnf_or_neg :args (@t103 1)) % 0.38/0.57 (step @p165 :rule eq_resolve :premises (@p164 @p163)) % 0.38/0.57 (step @p166 :rule reordering :premises (@p165) :args ((or @t99 @t103))) % 0.38/0.57 (step @p167 :rule cnf_and_pos :args (@t105 0)) % 0.38/0.57 (step @p168 :rule reordering :premises (@p167) :args ((or @t100 (not @t105)))) % 0.38/0.57 (assume-push @p233 @t82) % 0.38/0.57 (step @p170 :rule instantiate :premises (@p233) :args ((@list @t98))) % 0.38/0.57 (step-pop @p234 :rule scope :premises (@p170)) % 0.38/0.57 (step @p171 :rule process_scope :premises (@p234) :args (@t106)) % 0.38/0.57 (step @p173 :rule implies_elim :premises (@p171)) % 0.38/0.57 (step @p174 :rule cnf_or_pos :args (@t106)) % 0.38/0.57 (step @p175 :rule reordering :premises (@p174) :args ((or @t102 @t105 (not @t106)))) % 0.38/0.57 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p168 @p166 @p161 @p155 @p113 @p106 @p147) :args (@t55 @t96 (@list @t106 @t105 @t99 @t101 @t103 @t82 @t85 @t57))) % 0.38/0.57 (step @p177 :rule cnf_or_pos :args (@t57)) % 0.38/0.57 (step @p178 :rule reordering :premises (@p177) :args ((or @t56 @t52 @t83))) % 0.38/0.57 (step @p179 :rule chain_m_resolution :premises (@p178 @p176 @p142) :args (@t83 @t107 (@list @t55 @t51))) % 0.38/0.57 (step @p180 :rule cnf_equiv_neg1 :args (@t85)) % 0.38/0.57 (step @p181 :rule reordering :premises (@p180) :args ((or @t57 @t84 @t85))) % 0.38/0.57 (step @p182 :rule chain_m_resolution :premises (@p181 @p179 @p106) :args (@t84 @t108 (@list @t57 @t85))) % 0.38/0.57 (step @p183 :rule refl :args (@t118)) % 0.38/0.57 (step @p184 :rule nary_cong :premises (@p107 @p183) :args ((or @t86 @t118))) % 0.38/0.57 (assume-push @p235 @t84) % 0.38/0.57 (step @p186 :rule skolemize :premises (@p235)) % 0.38/0.57 (step-pop @p236 :rule scope :premises (@p186)) % 0.38/0.57 (step @p187 :rule process_scope :premises (@p236) :args (@t118)) % 0.38/0.57 (step @p189 :rule implies_elim :premises (@p187)) % 0.38/0.57 (step @p190 :rule eq_resolve :premises (@p189 @p184)) % 0.38/0.57 (step @p191 :rule chain_m_resolution :premises (@p190 @p182) :args (@t118 @t119 (@list @t82))) % 0.38/0.57 (step @p192 :rule cnf_or_neg :args (@t117 1)) % 0.38/0.57 (step @p193 :rule chain_m_resolution :premises (@p192 @p191) :args ((not @t114) @t119 @t120)) % 0.38/0.57 (assume-push @p237 @t55) % 0.38/0.57 (step @p195 :rule instantiate :premises (@p237) :args (@t121)) % 0.38/0.57 (step-pop @p238 :rule scope :premises (@p195)) % 0.38/0.57 (step @p196 :rule process_scope :premises (@p238) :args (@t122)) % 0.38/0.57 (step @p198 :rule implies_elim :premises (@p196)) % 0.38/0.57 (step @p199 :rule chain_m_resolution :premises (@p198 @p176) :args (@t122 (@list false) (@list @t55))) % 0.38/0.57 (step @p200 :rule bool-double-not-elim :args (@t115)) % 0.38/0.57 (step @p201 :rule refl :args (@t117)) % 0.38/0.57 (step @p202 :rule nary_cong :premises (@p201 @p200) :args ((or @t117 (not @t116)))) % 0.38/0.57 (step @p203 :rule cnf_or_neg :args (@t117 0)) % 0.38/0.57 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.38/0.57 (step @p205 :rule reordering :premises (@p204) :args ((or @t115 @t117))) % 0.38/0.57 (step @p206 :rule chain_m_resolution :premises (@p205 @p191) :args (@t115 @t119 @t120)) % 0.38/0.57 (step @p207 :rule cnf_or_pos :args (@t122)) % 0.38/0.57 (step @p208 :rule reordering :premises (@p207) :args ((or @t116 @t113 (not @t122)))) % 0.38/0.57 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p199) :args (@t113 @t107 (@list @t115 @t122))) % 0.38/0.57 (step @p210 :rule bool-double-not-elim :args (@t110)) % 0.38/0.57 (step @p211 :rule bool-double-not-elim :args (@t112)) % 0.38/0.57 (step @p212 :rule refl :args (@t114)) % 0.38/0.57 (step @p213 :rule nary_cong :premises (@p212 @p211 @p210) :args ((or @t114 (not @t113) (not @t111)))) % 0.38/0.57 (step @p214 :rule cnf_and_neg :args (@t114)) % 0.38/0.57 (step @p215 :rule eq_resolve :premises (@p214 @p213)) % 0.38/0.57 (step @p216 :rule reordering :premises (@p215) :args ((or @t112 @t110 @t114))) % 0.38/0.57 (step @p217 :rule chain_m_resolution :premises (@p216 @p209 @p193) :args (@t110 @t108 (@list @t112 @t114))) % 0.38/0.57 (step @p218 :rule cnf_or_pos :args (@t123)) % 0.38/0.57 (step @p219 :rule reordering :premises (@p218) :args ((or @t116 @t111 @t124))) % 0.38/0.57 (step @p220 :rule chain_m_resolution :premises (@p219 @p206 @p217) :args (@t124 @t107 (@list @t115 @t110))) % 0.38/0.58 (assume-push @p239 @t51) % 0.38/0.58 (step @p222 :rule instantiate :premises (@p239) :args (@t121)) % 0.38/0.58 (step-pop @p240 :rule scope :premises (@p222)) % 0.38/0.58 (step @p223 :rule process_scope :premises (@p240) :args (@t123)) % 0.38/0.58 (step @p225 :rule implies_elim :premises (@p223)) % 0.38/0.58 (step @p226 false :rule chain_m_resolution :premises (@p225 @p220 @p142) :args (false (@list true false) (@list @t123 @t51))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------