%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU726^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n010.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 08:52:54 AM UTC 2026 % Result : Theorem 151.48s 151.85s % Output : Proof 151.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU726^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:49:25 EDT 2026 % 0.17/0.35 % CPUTime : % 0.34/0.49 %----Proving TH0 % 151.48/151.85 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 151.48/151.85 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 151.48/151.85 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 151.48/151.85 --- Run --ho-elim --full-saturate-quant at 18s... % 151.48/151.85 % SZS status Theorem % 151.48/151.85 % SZS output start Proof % 151.48/151.85 ( % 151.48/151.85 (declare-sort $$unsorted 0) % 151.48/151.85 (declare-const tptp.setminusER Bool) % 151.48/151.85 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 151.48/151.85 (declare-const tptp.setminus (-> $$unsorted $$unsorted $$unsorted)) % 151.48/151.85 (declare-const tptp.subsetE Bool) % 151.48/151.85 (declare-const tptp.subsetTI Bool) % 151.48/151.85 (declare-const tptp.setminusI Bool) % 151.48/151.85 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 151.48/151.85 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 151.48/151.85 (define @t1 () (@var "B" $$unsorted)) % 151.48/151.85 (define @t2 () (@var "Xx" $$unsorted)) % 151.48/151.85 (define @t3 () (_ tptp.in @t2)) % 151.48/151.85 (define @t4 () (_ @t3 @t1)) % 151.48/151.85 (define @t5 () (@var "A" $$unsorted)) % 151.48/151.85 (define @t6 () (_ @t3 @t5)) % 151.48/151.85 (define @t7 () (=> @t6 @t4)) % 151.48/151.85 (define @t8 () (_ (_ tptp.subset @t5) @t1)) % 151.48/151.85 (define @t9 () (@list @t5 @t1 @t2)) % 151.48/151.85 (define @t10 () (forall @t9 (=> @t8 @t7))) % 151.48/151.85 (define @t11 () (= tptp.subsetE @t10)) % 151.48/151.85 (define @t12 () (_ tptp.setminus @t5)) % 151.48/151.85 (define @t13 () (_ @t12 @t1)) % 151.48/151.85 (define @t14 () (_ @t3 @t13)) % 151.48/151.85 (define @t15 () (not @t4)) % 151.48/151.85 (define @t16 () (=> @t15 @t14)) % 151.48/151.85 (define @t17 () (forall @t9 (=> @t6 @t16))) % 151.48/151.85 (define @t18 () (= tptp.setminusI @t17)) % 151.48/151.85 (define @t19 () (forall @t9 (=> @t14 @t15))) % 151.48/151.85 (define @t20 () (= tptp.setminusER @t19)) % 151.48/151.85 (define @t21 () (@var "Y" $$unsorted)) % 151.48/151.85 (define @t22 () (@var "X" $$unsorted)) % 151.48/151.85 (define @t23 () (_ (_ tptp.subset @t22) @t21)) % 151.48/151.85 (define @t24 () (_ @t3 @t21)) % 151.48/151.85 (define @t25 () (_ @t3 @t22)) % 151.48/151.85 (define @t26 () (=> @t25 @t24)) % 151.48/151.85 (define @t27 () (@list @t2)) % 151.48/151.85 (define @t28 () (forall @t27 (=> @t6 @t26))) % 151.48/151.85 (define @t29 () (=> @t28 @t23)) % 151.48/151.85 (define @t30 () (_ tptp.powerset @t5)) % 151.48/151.85 (define @t31 () (_ tptp.in @t21)) % 151.48/151.85 (define @t32 () (_ @t31 @t30)) % 151.48/151.85 (define @t33 () (=> @t32 @t29)) % 151.48/151.85 (define @t34 () (@list @t21)) % 151.48/151.85 (define @t35 () (forall @t34 @t33)) % 151.48/151.85 (define @t36 () (_ tptp.in @t22)) % 151.48/151.85 (define @t37 () (_ @t36 @t30)) % 151.48/151.85 (define @t38 () (=> @t37 @t35)) % 151.48/151.85 (define @t39 () (@list @t5 @t22)) % 151.48/151.85 (define @t40 () (forall @t39 @t38)) % 151.48/151.85 (define @t41 () (= tptp.subsetTI @t40)) % 151.48/151.85 (define @t42 () (_ @t12 @t22)) % 151.48/151.85 (define @t43 () (_ @t12 @t21)) % 151.48/151.85 (define @t44 () (_ (_ tptp.subset @t43) @t42)) % 151.48/151.85 (define @t45 () (=> @t44 @t23)) % 151.48/151.85 (define @t46 () (forall @t34 (=> @t32 @t45))) % 151.48/151.85 (define @t47 () (=> @t37 @t46)) % 151.48/151.85 (define @t48 () (forall @t39 @t47)) % 151.48/151.85 (define @t49 () (=> tptp.subsetTI @t48)) % 151.48/151.85 (define @t50 () (=> tptp.setminusER @t49)) % 151.48/151.85 (define @t51 () (=> tptp.setminusI @t50)) % 151.48/151.85 (define @t52 () (=> tptp.subsetE @t51)) % 151.48/151.85 (define @t53 () (not @t52)) % 151.48/151.85 (define @t54 () (@var "BOUND_VARIABLE_7582" $$unsorted)) % 151.48/151.85 (define @t55 () (@const 0 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 151.48/151.85 (define @t56 () (@const 1 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 151.48/151.85 (define @t57 () (_ @t56 @t55 @t22)) % 151.48/151.85 (define @t58 () (@const 2 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 151.48/151.85 (define @t59 () (@const 3 (@ho-elim-sort (-> $$unsorted $$unsorted $$unsorted)))) % 151.48/151.85 (define @t60 () (@const 4 (-> (@ho-elim-sort (-> $$unsorted $$unsorted $$unsorted)) $$unsorted (@ho-elim-sort (-> $$unsorted $$unsorted))))) % 151.48/151.85 (define @t61 () (_ @t60 @t59 @t5)) % 151.48/151.85 (define @t62 () (@const 5 (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted))) % 151.48/151.85 (define @t63 () (@const 6 (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.48/151.85 (define @t64 () (_ @t62 @t63 @t5)) % 151.48/151.85 (define @t65 () (@const 7 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 151.48/151.85 (define @t66 () (not (_ @t58 (_ @t56 @t65 @t22) @t64))) % 151.48/151.85 (define @t67 () (@list @t5 @t22 @t54)) % 151.48/151.85 (define @t68 () (forall @t67 (or @t66 (not (_ @t58 (_ @t56 @t65 @t54) @t64)) (not (_ @t58 (_ @t56 @t55 (_ @t62 @t61 @t54)) (_ @t62 @t61 @t22))) (_ @t58 @t57 @t54)))) % 151.48/151.85 (define @t69 () (@var "BOUND_VARIABLE_7547" $$unsorted)) % 151.48/151.85 (define @t70 () (_ @t56 @t65 @t2)) % 151.48/151.85 (define @t71 () (not (_ @t58 @t70 @t5))) % 151.48/151.85 (define @t72 () (@list @t5 @t22 @t69)) % 151.48/151.85 (define @t73 () (_ @t58 @t70 @t1)) % 151.48/151.85 (define @t74 () (_ @t58 @t70 (_ @t62 @t61 @t1))) % 151.48/151.85 (define @t75 () (forall @t9 (or (not @t74) (not @t73)))) % 151.48/151.85 (define @t76 () (tptp.subset @t22 @t54)) % 151.48/151.85 (define @t77 () (tptp.setminus @t5 @t22)) % 151.48/151.85 (define @t78 () (not (tptp.subset (tptp.setminus @t5 @t54) @t77))) % 151.48/151.85 (define @t79 () (tptp.powerset @t5)) % 151.48/151.85 (define @t80 () (not (tptp.in @t54 @t79))) % 151.48/151.85 (define @t81 () (tptp.in @t22 @t79)) % 151.48/151.85 (define @t82 () (not @t81)) % 151.48/151.85 (define @t83 () (or @t82 @t80 @t78 @t76)) % 151.48/151.85 (define @t84 () (forall @t67 @t83)) % 151.48/151.85 (define @t85 () (tptp.subset @t22 @t69)) % 151.48/151.85 (define @t86 () (tptp.in @t2 @t22)) % 151.48/151.85 (define @t87 () (not @t86)) % 151.48/151.85 (define @t88 () (tptp.in @t2 @t5)) % 151.48/151.85 (define @t89 () (not @t88)) % 151.48/151.85 (define @t90 () (not (forall @t27 (or @t89 @t87 (tptp.in @t2 @t69))))) % 151.48/151.85 (define @t91 () (not (tptp.in @t69 @t79))) % 151.48/151.85 (define @t92 () (or @t82 @t91 @t90 @t85)) % 151.48/151.85 (define @t93 () (tptp.in @t2 @t1)) % 151.48/151.85 (define @t94 () (tptp.setminus @t5 @t1)) % 151.48/151.85 (define @t95 () (tptp.in @t2 @t94)) % 151.48/151.85 (define @t96 () (tptp.subset @t5 @t1)) % 151.48/151.85 (define @t97 () (or @t91 @t90 @t85)) % 151.48/151.85 (define @t98 () (or @t82 @t97)) % 151.48/151.85 (define @t99 () (forall @t72 @t98)) % 151.48/151.85 (define @t100 () (@list @t69)) % 151.48/151.85 (define @t101 () (forall @t100 @t98)) % 151.48/151.85 (define @t102 () (forall @t100 @t97)) % 151.48/151.85 (define @t103 () (@list @t21)) % 151.48/151.85 (define @t104 () (or @t82 @t102)) % 151.48/151.85 (define @t105 () (tptp.subset @t22 @t21)) % 151.48/151.85 (define @t106 () (tptp.in @t2 @t21)) % 151.48/151.85 (define @t107 () (forall @t27 (or @t89 @t87 @t106))) % 151.48/151.85 (define @t108 () (not @t107)) % 151.48/151.85 (define @t109 () (tptp.in @t21 @t79)) % 151.48/151.85 (define @t110 () (not @t109)) % 151.48/151.85 (define @t111 () (forall @t34 (or @t110 @t108 @t105))) % 151.48/151.85 (define @t112 () (not @t37)) % 151.48/151.85 (define @t113 () (or @t112 @t111)) % 151.48/151.85 (define @t114 () (not @t32)) % 151.48/151.85 (define @t115 () (or @t114 @t108 @t23)) % 151.48/151.85 (define @t116 () (=> @t107 @t23)) % 151.48/151.85 (define @t117 () (not @t25)) % 151.48/151.85 (define @t118 () (not @t6)) % 151.48/151.85 (define @t119 () (or @t118 @t117 @t24)) % 151.48/151.85 (define @t120 () (=> tptp.subsetTI @t84)) % 151.48/151.85 (define @t121 () (not @t14)) % 151.48/151.85 (define @t122 () (or @t121 @t15)) % 151.48/151.85 (define @t123 () (=> tptp.setminusER @t120)) % 151.48/151.85 (define @t124 () (or @t118 @t4 @t14)) % 151.48/151.85 (define @t125 () (=> tptp.setminusI @t123)) % 151.48/151.85 (define @t126 () (not @t8)) % 151.48/151.85 (define @t127 () (or @t126 @t118 @t4)) % 151.48/151.85 (define @t128 () (=> tptp.subsetE @t125)) % 151.48/151.85 (define @t129 () (or @t80 @t78 @t76)) % 151.48/151.85 (define @t130 () (or @t82 @t129)) % 151.48/151.85 (define @t131 () (forall @t67 @t130)) % 151.48/151.85 (define @t132 () (@list @t54)) % 151.48/151.85 (define @t133 () (forall @t132 @t130)) % 151.48/151.85 (define @t134 () (forall @t132 @t129)) % 151.48/151.85 (define @t135 () (or @t82 @t134)) % 151.48/151.85 (define @t136 () (tptp.setminus @t5 @t21)) % 151.48/151.85 (define @t137 () (tptp.subset @t136 @t77)) % 151.48/151.85 (define @t138 () (forall @t34 (or @t110 (not @t137) @t105))) % 151.48/151.85 (define @t139 () (or @t112 @t138)) % 151.48/151.85 (define @t140 () (not @t44)) % 151.48/151.85 (define @t141 () (or @t114 @t140 @t23)) % 151.48/151.85 (define @t142 () (@quantifiers_skolemize @t68 2)) % 151.48/151.85 (define @t143 () (@quantifiers_skolemize @t68 1)) % 151.48/151.85 (define @t144 () (@quantifiers_skolemize @t68 0)) % 151.48/151.85 (define @t145 () (forall @t27 (or (not (_ @t58 @t70 @t144)) (not (_ @t58 @t70 @t143)) (_ @t58 @t70 @t142)))) % 151.48/151.85 (define @t146 () (@quantifiers_skolemize @t145 0)) % 151.48/151.85 (define @t147 () (_ @t60 @t59 @t144)) % 151.48/151.85 (define @t148 () (_ @t62 @t147 @t143)) % 151.48/151.85 (define @t149 () (_ @t62 @t147 @t142)) % 151.48/151.85 (define @t150 () (_ @t58 (_ @t56 @t55 @t143) @t142)) % 151.48/151.85 (define @t151 () (_ @t58 (_ @t56 @t55 @t149) @t148)) % 151.48/151.85 (define @t152 () (not @t151)) % 151.48/151.85 (define @t153 () (_ @t62 @t63 @t144)) % 151.48/151.85 (define @t154 () (_ @t58 (_ @t56 @t65 @t142) @t153)) % 151.48/151.85 (define @t155 () (not @t154)) % 151.48/151.85 (define @t156 () (_ @t58 (_ @t56 @t65 @t143) @t153)) % 151.48/151.85 (define @t157 () (not @t156)) % 151.48/151.85 (define @t158 () (or @t157 @t155 @t152 @t150)) % 151.48/151.85 (define @t159 () (@list true)) % 151.48/151.85 (define @t160 () (@list @t158)) % 151.48/151.85 (define @t161 () (not @t145)) % 151.48/151.85 (define @t162 () (or @t157 @t155 @t161 @t150)) % 151.48/151.85 (define @t163 () (_ @t56 @t65 @t146)) % 151.48/151.85 (define @t164 () (_ @t58 @t163 @t142)) % 151.48/151.85 (define @t165 () (_ @t58 @t163 @t143)) % 151.48/151.85 (define @t166 () (not @t165)) % 151.48/151.85 (define @t167 () (_ @t58 @t163 @t144)) % 151.48/151.85 (define @t168 () (not @t167)) % 151.48/151.85 (define @t169 () (or @t168 @t166 @t164)) % 151.48/151.85 (define @t170 () (@list @t169)) % 151.48/151.85 (define @t171 () (_ @t58 @t163 @t149)) % 151.48/151.85 (define @t172 () (or @t168 @t164 @t171)) % 151.48/151.85 (define @t173 () (_ @t58 @t163 @t148)) % 151.48/151.85 (define @t174 () (not @t171)) % 151.48/151.85 (define @t175 () (or @t152 @t174 @t173)) % 151.48/151.85 (define @t176 () (not @t173)) % 151.48/151.85 (define @t177 () (or @t176 @t166)) % 151.48/151.85 (define @t178 () (not @t177)) % 151.48/151.85 (assume @p1 @t11) % 151.48/151.85 (assume @p2 @t18) % 151.48/151.85 (assume @p3 @t20) % 151.48/151.85 (assume @p4 @t41) % 151.48/151.85 (assume @p5 @t53) % 151.48/151.85 (assume @p6 true) % 151.48/151.85 ; WARNING: add trust step for TRUST % 151.48/151.85 ; trust TRUST PREPROCESS_HO_ELIM % 151.48/151.85 (step @p7 :rule trust :premises () :args ((= (not (=> (forall @t9 (or (not @t96) @t89 @t93)) (=> (forall @t9 (or @t89 @t93 @t95)) (=> (forall @t9 (or (not @t95) (not @t93))) (=> (forall @t72 @t92) @t84))))) (not (=> (forall @t9 (or (not (_ @t58 (_ @t56 @t55 @t5) @t1)) @t71 @t73)) (=> (forall @t9 (or @t71 @t73 @t74)) (=> @t75 (=> (forall @t72 (or @t66 (not (_ @t58 (_ @t56 @t65 @t69) @t64)) (not (forall @t27 (or @t71 (not (_ @t58 @t70 @t22)) (_ @t58 @t70 @t69)))) (_ @t58 @t57 @t69))) @t68)))))))) % 151.48/151.85 (step @p8 :rule refl :args (@t84)) % 151.48/151.85 (step @p9 :rule aci_norm :args ((= @t98 @t92))) % 151.48/151.85 (step @p10 :rule cong :premises (@p9) :args (@t99)) % 151.48/151.85 (step @p11 :rule quant-merge-prenex :args ((= (forall @t39 @t101) @t99))) % 151.48/151.85 (step @p12 :rule alpha_equiv :args (@t102 (@list @t69) @t103)) % 151.48/151.85 (step @p13 :rule refl :args (@t82)) % 151.48/151.85 (step @p14 :rule nary_cong :premises (@p13 @p12) :args (@t104)) % 151.48/151.85 (step @p15 :rule quant-miniscope-or :args ((= @t101 @t104))) % 151.48/151.85 (step @p16 :rule trans :premises (@p15 @p14)) % 151.48/151.85 (step @p17 :rule symm :premises (@p16)) % 151.48/151.85 (step @p18 :rule cong :premises (@p17) :args ((forall @t39 (or @t82 @t111)))) % 151.48/151.85 (step @p19 :rule trans :premises (@p18 @p11)) % 151.48/151.85 (step @p20 :rule trans :premises (@p19 @p10)) % 151.48/151.85 (step @p21 :rule refl :args (@t111)) % 151.48/151.85 (step @p22 :rule refl :args ((tptp.in @t22 @t30))) % 151.48/151.85 (step @p23 :rule refl :args (@t79)) % 151.48/151.85 (step @p24 :rule refl :args (@t22)) % 151.48/151.85 (step @p25 :rule cong :premises (@p24 @p23) :args (@t81)) % 151.48/151.85 (step @p26 :rule trans :premises (@p25 @p22)) % 151.48/151.85 (step @p27 :rule refl :args (@t36)) % 151.48/151.85 (step @p28 :rule ho_cong :premises (@p27 @p23)) % 151.48/151.85 (step @p29 :rule cong :premises (@p28 @p26) :args ((= (_ @t36 @t79) @t81))) % 151.48/151.85 (step @p30 :rule symm :premises (@p29)) % 151.48/151.85 (step @p31 :rule refl :args (@t37)) % 151.48/151.85 (step @p32 :rule eq_resolve :premises (@p31 @p30)) % 151.48/151.85 (step @p33 :rule refl :args (@t30)) % 151.48/151.85 (step @p34 :rule cong :premises (@p33 @p23) :args ((= @t30 @t79))) % 151.48/151.85 (step @p35 :rule symm :premises (@p34)) % 151.48/151.85 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 151.48/151.85 (step @p37 :rule ho_cong :premises (@p27 @p36)) % 151.48/151.85 (step @p38 :rule trans :premises (@p37 @p32)) % 151.48/151.85 (step @p39 :rule cong :premises (@p38) :args (@t112)) % 151.48/151.85 (step @p40 :rule nary_cong :premises (@p39 @p21) :args (@t113)) % 151.48/151.85 (step @p41 :rule cong :premises (@p40) :args ((forall @t39 @t113))) % 151.48/151.85 (step @p42 :rule trans :premises (@p41 @p20)) % 151.48/151.85 (step @p43 :rule bool-impl-elim :args (@t37 @t111)) % 151.48/151.85 (step @p44 :rule cong :premises (@p43) :args ((forall @t39 (=> @t37 @t111)))) % 151.48/151.85 (step @p45 :rule trans :premises (@p44 @p42)) % 151.48/151.85 (step @p46 :rule refl :args (@t105)) % 151.48/151.85 (step @p47 :rule refl :args (@t23)) % 151.48/151.85 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t23 @t105))) % 151.48/151.85 (step @p49 :rule symm :premises (@p48)) % 151.48/151.85 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 151.48/151.85 (step @p51 :rule refl :args (@t108)) % 151.48/151.85 (step @p52 :rule refl :args ((tptp.in @t21 @t30))) % 151.48/151.85 (step @p53 :rule refl :args (@t21)) % 151.48/151.85 (step @p54 :rule cong :premises (@p53 @p23) :args (@t109)) % 151.48/151.85 (step @p55 :rule trans :premises (@p54 @p52)) % 151.48/151.85 (step @p56 :rule refl :args (@t31)) % 151.48/151.85 (step @p57 :rule ho_cong :premises (@p56 @p23)) % 151.48/151.85 (step @p58 :rule cong :premises (@p57 @p55) :args ((= (_ @t31 @t79) @t109))) % 151.48/151.85 (step @p59 :rule symm :premises (@p58)) % 151.48/151.85 (step @p60 :rule refl :args (@t32)) % 151.48/151.85 (step @p61 :rule eq_resolve :premises (@p60 @p59)) % 151.48/151.85 (step @p62 :rule ho_cong :premises (@p56 @p36)) % 151.48/151.85 (step @p63 :rule trans :premises (@p62 @p61)) % 151.48/151.85 (step @p64 :rule cong :premises (@p63) :args (@t114)) % 151.48/151.85 (step @p65 :rule nary_cong :premises (@p64 @p51 @p50) :args (@t115)) % 151.48/151.85 (step @p66 :rule cong :premises (@p65) :args ((forall @t34 @t115))) % 151.48/151.85 (step @p67 :rule aci_norm :args ((= (or @t114 (or @t108 @t23)) @t115))) % 151.48/151.85 (step @p68 :rule bool-impl-elim :args (@t107 @t23)) % 151.48/151.85 (step @p69 :rule refl :args (@t114)) % 151.48/151.85 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or @t114 @t116))) % 151.48/151.85 (step @p71 :rule trans :premises (@p70 @p67)) % 151.48/151.85 (step @p72 :rule bool-impl-elim :args (@t32 @t116)) % 151.48/151.85 (step @p73 :rule trans :premises (@p72 @p71)) % 151.48/151.85 (step @p74 :rule cong :premises (@p73) :args ((forall @t34 (=> @t32 @t116)))) % 151.48/151.85 (step @p75 :rule trans :premises (@p74 @p66)) % 151.48/151.85 (step @p76 :rule refl :args (@t23)) % 151.48/151.85 (step @p77 :rule refl :args (@t106)) % 151.48/151.85 (step @p78 :rule refl :args (@t24)) % 151.48/151.85 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t24 @t106))) % 151.48/151.85 (step @p80 :rule symm :premises (@p79)) % 151.48/151.85 (step @p81 :rule eq_resolve :premises (@p78 @p80)) % 151.48/151.85 (step @p82 :rule refl :args (@t86)) % 151.48/151.85 (step @p83 :rule refl :args (@t25)) % 151.48/151.85 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t25 @t86))) % 151.48/151.85 (step @p85 :rule symm :premises (@p84)) % 151.48/151.85 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 151.48/151.85 (step @p87 :rule cong :premises (@p86) :args (@t117)) % 151.48/151.85 (step @p88 :rule refl :args (@t88)) % 151.48/151.85 (step @p89 :rule refl :args (@t6)) % 151.48/151.85 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t6 @t88))) % 151.48/151.85 (step @p91 :rule symm :premises (@p90)) % 151.48/151.85 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 151.48/151.85 (step @p93 :rule cong :premises (@p92) :args (@t118)) % 151.48/151.85 (step @p94 :rule nary_cong :premises (@p93 @p87 @p81) :args (@t119)) % 151.48/151.85 (step @p95 :rule cong :premises (@p94) :args ((forall @t27 @t119))) % 151.48/151.85 (step @p96 :rule aci_norm :args ((= (or @t118 (or @t117 @t24)) @t119))) % 151.48/151.85 (step @p97 :rule bool-impl-elim :args (@t25 @t24)) % 151.48/151.85 (step @p98 :rule refl :args (@t118)) % 151.48/151.85 (step @p99 :rule nary_cong :premises (@p98 @p97) :args ((or @t118 @t26))) % 151.48/151.85 (step @p100 :rule trans :premises (@p99 @p96)) % 151.48/151.85 (step @p101 :rule bool-impl-elim :args (@t6 @t26)) % 151.48/151.85 (step @p102 :rule trans :premises (@p101 @p100)) % 151.48/151.85 (step @p103 :rule cong :premises (@p102) :args (@t28)) % 151.48/151.85 (step @p104 :rule trans :premises (@p103 @p95)) % 151.48/151.85 (step @p105 :rule cong :premises (@p104 @p76) :args (@t29)) % 151.48/151.85 (step @p106 :rule refl :args (@t32)) % 151.48/151.85 (step @p107 :rule cong :premises (@p106 @p105) :args (@t33)) % 151.48/151.85 (step @p108 :rule cong :premises (@p107) :args (@t35)) % 151.48/151.85 (step @p109 :rule trans :premises (@p108 @p75)) % 151.48/151.85 (step @p110 :rule refl :args (@t37)) % 151.48/151.85 (step @p111 :rule cong :premises (@p110 @p109) :args (@t38)) % 151.48/151.85 (step @p112 :rule cong :premises (@p111) :args (@t40)) % 151.48/151.85 (step @p113 :rule trans :premises (@p112 @p45)) % 151.48/151.85 (step @p114 :rule refl :args (tptp.subsetTI)) % 151.48/151.85 (step @p115 :rule cong :premises (@p114 @p113) :args (@t41)) % 151.48/151.85 (step @p116 :rule eq_resolve :premises (@p4 @p115)) % 151.48/151.85 (step @p117 :rule cong :premises (@p116 @p8) :args (@t120)) % 151.48/151.85 (step @p118 :rule refl :args (@t93)) % 151.48/151.85 (step @p119 :rule refl :args (@t4)) % 151.48/151.85 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t4 @t93))) % 151.48/151.85 (step @p121 :rule symm :premises (@p120)) % 151.48/151.85 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 151.48/151.85 (step @p123 :rule cong :premises (@p122) :args (@t15)) % 151.48/151.85 (step @p124 :rule refl :args ((tptp.in @t2 @t13))) % 151.48/151.85 (step @p125 :rule refl :args (@t94)) % 151.48/151.85 (step @p126 :rule refl :args (@t2)) % 151.48/151.85 (step @p127 :rule cong :premises (@p126 @p125) :args (@t95)) % 151.48/151.85 (step @p128 :rule trans :premises (@p127 @p124)) % 151.48/151.85 (step @p129 :rule refl :args (@t3)) % 151.48/151.85 (step @p130 :rule ho_cong :premises (@p129 @p125)) % 151.48/151.85 (step @p131 :rule cong :premises (@p130 @p128) :args ((= (_ @t3 @t94) @t95))) % 151.48/151.85 (step @p132 :rule symm :premises (@p131)) % 151.48/151.85 (step @p133 :rule refl :args (@t14)) % 151.48/151.85 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 151.48/151.85 (step @p135 :rule refl :args (@t13)) % 151.48/151.85 (step @p136 :rule cong :premises (@p135 @p125) :args ((= @t13 @t94))) % 151.48/151.85 (step @p137 :rule symm :premises (@p136)) % 151.48/151.85 (step @p138 :rule eq_resolve :premises (@p135 @p137)) % 151.48/151.85 (step @p139 :rule ho_cong :premises (@p129 @p138)) % 151.48/151.85 (step @p140 :rule trans :premises (@p139 @p134)) % 151.48/151.85 (step @p141 :rule cong :premises (@p140) :args (@t121)) % 151.48/151.85 (step @p142 :rule nary_cong :premises (@p141 @p123) :args (@t122)) % 151.48/151.85 (step @p143 :rule cong :premises (@p142) :args ((forall @t9 @t122))) % 151.48/151.85 (step @p144 :rule bool-impl-elim :args (@t14 @t15)) % 151.48/151.85 (step @p145 :rule cong :premises (@p144) :args (@t19)) % 151.48/151.85 (step @p146 :rule trans :premises (@p145 @p143)) % 151.48/151.85 (step @p147 :rule refl :args (tptp.setminusER)) % 151.48/151.85 (step @p148 :rule cong :premises (@p147 @p146) :args (@t20)) % 151.48/151.85 (step @p149 :rule eq_resolve :premises (@p3 @p148)) % 151.48/151.85 (step @p150 :rule cong :premises (@p149 @p117) :args (@t123)) % 151.48/151.85 (step @p151 :rule nary_cong :premises (@p93 @p122 @p140) :args (@t124)) % 151.48/151.85 (step @p152 :rule cong :premises (@p151) :args ((forall @t9 @t124))) % 151.48/151.85 (step @p153 :rule aci_norm :args ((= (or @t118 (or @t4 @t14)) @t124))) % 151.48/151.85 (step @p154 :rule bool-double-not-elim :args (@t4)) % 151.48/151.85 (step @p155 :rule nary_cong :premises (@p154 @p133) :args ((or (not @t15) @t14))) % 151.48/151.85 (step @p156 :rule bool-impl-elim :args (@t15 @t14)) % 151.48/151.85 (step @p157 :rule trans :premises (@p156 @p155)) % 151.48/151.85 (step @p158 :rule nary_cong :premises (@p98 @p157) :args ((or @t118 @t16))) % 151.48/151.85 (step @p159 :rule trans :premises (@p158 @p153)) % 151.48/151.85 (step @p160 :rule bool-impl-elim :args (@t6 @t16)) % 151.48/151.85 (step @p161 :rule trans :premises (@p160 @p159)) % 151.48/151.85 (step @p162 :rule cong :premises (@p161) :args (@t17)) % 151.48/151.85 (step @p163 :rule trans :premises (@p162 @p152)) % 151.48/151.85 (step @p164 :rule refl :args (tptp.setminusI)) % 151.48/151.85 (step @p165 :rule cong :premises (@p164 @p163) :args (@t18)) % 151.48/151.85 (step @p166 :rule eq_resolve :premises (@p2 @p165)) % 151.48/151.85 (step @p167 :rule cong :premises (@p166 @p150) :args (@t125)) % 151.48/151.85 (step @p168 :rule refl :args (@t96)) % 151.48/151.85 (step @p169 :rule refl :args (@t8)) % 151.48/151.85 (step @p170 :rule cong :premises (@p169 @p168) :args ((= @t8 @t96))) % 151.48/151.85 (step @p171 :rule symm :premises (@p170)) % 151.48/151.85 (step @p172 :rule eq_resolve :premises (@p169 @p171)) % 151.48/151.85 (step @p173 :rule cong :premises (@p172) :args (@t126)) % 151.48/151.85 (step @p174 :rule nary_cong :premises (@p173 @p93 @p122) :args (@t127)) % 151.48/151.85 (step @p175 :rule cong :premises (@p174) :args ((forall @t9 @t127))) % 151.48/151.85 (step @p176 :rule aci_norm :args ((= (or @t126 (or @t118 @t4)) @t127))) % 151.48/151.85 (step @p177 :rule bool-impl-elim :args (@t6 @t4)) % 151.48/151.85 (step @p178 :rule refl :args (@t126)) % 151.48/151.85 (step @p179 :rule nary_cong :premises (@p178 @p177) :args ((or @t126 @t7))) % 151.48/151.85 (step @p180 :rule trans :premises (@p179 @p176)) % 151.48/151.85 (step @p181 :rule bool-impl-elim :args (@t8 @t7)) % 151.48/151.85 (step @p182 :rule trans :premises (@p181 @p180)) % 151.48/151.85 (step @p183 :rule cong :premises (@p182) :args (@t10)) % 151.48/151.85 (step @p184 :rule trans :premises (@p183 @p175)) % 151.48/151.85 (step @p185 :rule refl :args (tptp.subsetE)) % 151.48/151.85 (step @p186 :rule cong :premises (@p185 @p184) :args (@t11)) % 151.48/151.85 (step @p187 :rule eq_resolve :premises (@p1 @p186)) % 151.48/151.85 (step @p188 :rule cong :premises (@p187 @p167) :args (@t128)) % 151.48/151.85 (step @p189 :rule cong :premises (@p188) :args ((not @t128))) % 151.48/151.85 (step @p190 :rule aci_norm :args ((= @t130 @t83))) % 151.48/151.85 (step @p191 :rule cong :premises (@p190) :args (@t131)) % 151.48/151.85 (step @p192 :rule quant-merge-prenex :args ((= (forall @t39 @t133) @t131))) % 151.48/151.85 (step @p193 :rule alpha_equiv :args (@t134 (@list @t54) @t103)) % 151.48/151.85 (step @p194 :rule nary_cong :premises (@p13 @p193) :args (@t135)) % 151.48/151.85 (step @p195 :rule quant-miniscope-or :args ((= @t133 @t135))) % 151.48/151.85 (step @p196 :rule trans :premises (@p195 @p194)) % 151.48/151.85 (step @p197 :rule symm :premises (@p196)) % 151.48/151.85 (step @p198 :rule cong :premises (@p197) :args ((forall @t39 (or @t82 @t138)))) % 151.48/151.85 (step @p199 :rule trans :premises (@p198 @p192)) % 151.48/151.85 (step @p200 :rule trans :premises (@p199 @p191)) % 151.48/151.85 (step @p201 :rule refl :args (@t138)) % 151.48/151.85 (step @p202 :rule nary_cong :premises (@p39 @p201) :args (@t139)) % 151.48/151.85 (step @p203 :rule cong :premises (@p202) :args ((forall @t39 @t139))) % 151.48/151.85 (step @p204 :rule trans :premises (@p203 @p200)) % 151.48/151.85 (step @p205 :rule bool-impl-elim :args (@t37 @t138)) % 151.48/151.85 (step @p206 :rule cong :premises (@p205) :args ((forall @t39 (=> @t37 @t138)))) % 151.48/151.85 (step @p207 :rule trans :premises (@p206 @p204)) % 151.48/151.85 (step @p208 :rule refl :args ((tptp.subset @t43 @t42))) % 151.48/151.85 (step @p209 :rule refl :args (@t77)) % 151.48/151.85 (step @p210 :rule refl :args (@t136)) % 151.48/151.85 (step @p211 :rule cong :premises (@p210 @p209) :args (@t137)) % 151.48/151.85 (step @p212 :rule trans :premises (@p211 @p208)) % 151.48/151.85 (step @p213 :rule refl :args (tptp.subset)) % 151.48/151.85 (step @p214 :rule ho_cong :premises (@p213 @p210)) % 151.48/151.85 (step @p215 :rule ho_cong :premises (@p214 @p209)) % 151.48/151.85 (step @p216 :rule cong :premises (@p215 @p212) :args ((= (_ (_ tptp.subset @t136) @t77) @t137))) % 151.48/151.85 (step @p217 :rule symm :premises (@p216)) % 151.48/151.85 (step @p218 :rule refl :args (@t44)) % 151.48/151.85 (step @p219 :rule eq_resolve :premises (@p218 @p217)) % 151.48/151.85 (step @p220 :rule refl :args (@t42)) % 151.48/151.85 (step @p221 :rule cong :premises (@p220 @p209) :args ((= @t42 @t77))) % 151.48/151.85 (step @p222 :rule symm :premises (@p221)) % 151.48/151.85 (step @p223 :rule eq_resolve :premises (@p220 @p222)) % 151.48/151.85 (step @p224 :rule refl :args (@t43)) % 151.48/151.85 (step @p225 :rule cong :premises (@p224 @p210) :args ((= @t43 @t136))) % 151.48/151.85 (step @p226 :rule symm :premises (@p225)) % 151.48/151.85 (step @p227 :rule eq_resolve :premises (@p224 @p226)) % 151.48/151.85 (step @p228 :rule ho_cong :premises (@p213 @p227)) % 151.48/151.85 (step @p229 :rule ho_cong :premises (@p228 @p223)) % 151.48/151.85 (step @p230 :rule trans :premises (@p229 @p219)) % 151.48/151.85 (step @p231 :rule cong :premises (@p230) :args (@t140)) % 151.48/151.85 (step @p232 :rule nary_cong :premises (@p64 @p231 @p50) :args (@t141)) % 151.48/151.85 (step @p233 :rule cong :premises (@p232) :args ((forall @t34 @t141))) % 151.48/151.85 (step @p234 :rule aci_norm :args ((= (or @t114 (or @t140 @t23)) @t141))) % 151.48/151.85 (step @p235 :rule bool-impl-elim :args (@t44 @t23)) % 151.48/151.85 (step @p236 :rule nary_cong :premises (@p69 @p235) :args ((or @t114 @t45))) % 151.48/151.85 (step @p237 :rule trans :premises (@p236 @p234)) % 151.48/151.85 (step @p238 :rule bool-impl-elim :args (@t32 @t45)) % 151.48/151.85 (step @p239 :rule trans :premises (@p238 @p237)) % 151.48/151.85 (step @p240 :rule cong :premises (@p239) :args (@t46)) % 151.48/151.85 (step @p241 :rule trans :premises (@p240 @p233)) % 151.48/151.85 (step @p242 :rule cong :premises (@p110 @p241) :args (@t47)) % 151.48/151.85 (step @p243 :rule cong :premises (@p242) :args (@t48)) % 151.48/151.85 (step @p244 :rule trans :premises (@p243 @p207)) % 151.48/151.85 (step @p245 :rule cong :premises (@p114 @p244) :args (@t49)) % 151.48/151.85 (step @p246 :rule cong :premises (@p147 @p245) :args (@t50)) % 151.48/151.85 (step @p247 :rule cong :premises (@p164 @p246) :args (@t51)) % 151.48/151.85 (step @p248 :rule cong :premises (@p185 @p247) :args (@t52)) % 151.48/151.85 (step @p249 :rule cong :premises (@p248) :args (@t53)) % 151.48/151.85 (step @p250 :rule trans :premises (@p249 @p189 @p7)) % 151.48/151.85 (step @p251 :rule eq_resolve :premises (@p5 @p250)) % 151.48/151.85 (step @p252 :rule not_implies_elim2 :premises (@p251)) % 151.48/151.85 (step @p253 :rule not_implies_elim2 :premises (@p252)) % 151.48/151.85 (step @p254 :rule not_implies_elim1 :premises (@p253)) % 151.48/151.85 (step @p255 :rule not_implies_elim1 :premises (@p251)) % 151.48/151.85 (step @p256 :rule instantiate :premises (@p255) :args ((@list @t149 @t148 @t146))) % 151.48/151.85 (step @p257 :rule not_implies_elim1 :premises (@p252)) % 151.48/151.85 (step @p258 :rule instantiate :premises (@p257) :args ((@list @t144 @t142 @t146))) % 151.48/151.85 (step @p259 :rule not_implies_elim2 :premises (@p253)) % 151.48/151.85 (step @p260 :rule not_implies_elim1 :premises (@p259)) % 151.48/151.85 (step @p261 :rule instantiate :premises (@p260) :args ((@list @t144 @t143 @t142))) % 151.48/151.85 (step @p262 :rule not_implies_elim2 :premises (@p259)) % 151.48/151.85 (step @p263 :rule skolemize :premises (@p262)) % 151.48/151.85 (step @p264 :rule cnf_or_neg :args (@t158 3)) % 151.48/151.85 (step @p265 :rule chain_m_resolution :premises (@p264 @p263) :args ((not @t150) @t159 @t160)) % 151.48/151.85 (step @p266 :rule bool-double-not-elim :args (@t154)) % 151.48/151.85 (step @p267 :rule refl :args (@t158)) % 151.48/151.85 (step @p268 :rule nary_cong :premises (@p267 @p266) :args ((or @t158 (not @t155)))) % 151.48/151.85 (step @p269 :rule cnf_or_neg :args (@t158 1)) % 151.48/151.85 (step @p270 :rule eq_resolve :premises (@p269 @p268)) % 151.48/151.85 (step @p271 :rule reordering :premises (@p270) :args ((or @t154 @t158))) % 151.48/151.85 (step @p272 :rule chain_m_resolution :premises (@p271 @p263) :args (@t154 @t159 @t160)) % 151.48/151.85 (step @p273 :rule bool-double-not-elim :args (@t156)) % 151.48/151.85 (step @p274 :rule nary_cong :premises (@p267 @p273) :args ((or @t158 (not @t157)))) % 151.48/151.85 (step @p275 :rule cnf_or_neg :args (@t158 0)) % 151.48/151.85 (step @p276 :rule eq_resolve :premises (@p275 @p274)) % 151.48/151.85 (step @p277 :rule reordering :premises (@p276) :args ((or @t156 @t158))) % 151.48/151.85 (step @p278 :rule chain_m_resolution :premises (@p277 @p263) :args (@t156 @t159 @t160)) % 151.48/151.85 (step @p279 :rule cnf_or_pos :args (@t162)) % 151.48/151.85 (step @p280 :rule reordering :premises (@p279) :args ((or @t157 @t155 @t150 @t161 (not @t162)))) % 151.48/151.85 (step @p281 :rule chain_m_resolution :premises (@p280 @p278 @p272 @p265 @p261) :args (@t161 (@list false false true false) (@list @t156 @t154 @t150 @t162))) % 151.48/151.85 (step @p282 :rule skolemize :premises (@p281)) % 151.48/151.85 (step @p283 :rule cnf_or_neg :args (@t169 2)) % 151.48/151.85 (step @p284 :rule chain_m_resolution :premises (@p283 @p282) :args ((not @t164) @t159 @t170)) % 151.48/151.85 (step @p285 :rule bool-double-not-elim :args (@t167)) % 151.48/151.85 (step @p286 :rule refl :args (@t169)) % 151.48/151.85 (step @p287 :rule nary_cong :premises (@p286 @p285) :args ((or @t169 (not @t168)))) % 151.48/151.85 (step @p288 :rule cnf_or_neg :args (@t169 0)) % 151.48/151.85 (step @p289 :rule eq_resolve :premises (@p288 @p287)) % 151.48/151.85 (step @p290 :rule reordering :premises (@p289) :args ((or @t167 @t169))) % 151.48/151.85 (step @p291 :rule chain_m_resolution :premises (@p290 @p282) :args (@t167 @t159 @t170)) % 151.48/151.85 (step @p292 :rule cnf_or_pos :args (@t172)) % 151.48/151.85 (step @p293 :rule reordering :premises (@p292) :args ((or @t168 @t164 @t171 (not @t172)))) % 151.48/151.85 (step @p294 :rule chain_m_resolution :premises (@p293 @p291 @p284 @p258) :args (@t171 (@list false true false) (@list @t167 @t164 @t172))) % 151.48/151.85 (step @p295 :rule bool-double-not-elim :args (@t151)) % 151.48/151.85 (step @p296 :rule nary_cong :premises (@p267 @p295) :args ((or @t158 (not @t152)))) % 151.48/151.85 (step @p297 :rule cnf_or_neg :args (@t158 2)) % 151.48/151.85 (step @p298 :rule eq_resolve :premises (@p297 @p296)) % 151.48/151.85 (step @p299 :rule reordering :premises (@p298) :args ((or @t151 @t158))) % 151.48/151.85 (step @p300 :rule chain_m_resolution :premises (@p299 @p263) :args (@t151 @t159 @t160)) % 151.48/151.85 (step @p301 :rule cnf_or_pos :args (@t175)) % 151.48/151.85 (step @p302 :rule reordering :premises (@p301) :args ((or @t152 @t174 @t173 (not @t175)))) % 151.48/151.85 (step @p303 :rule chain_m_resolution :premises (@p302 @p300 @p294 @p256) :args (@t173 (@list false false false) (@list @t151 @t171 @t175))) % 151.48/151.85 (step @p304 :rule bool-double-not-elim :args (@t165)) % 151.48/151.85 (step @p305 :rule nary_cong :premises (@p286 @p304) :args ((or @t169 (not @t166)))) % 151.48/151.85 (step @p306 :rule cnf_or_neg :args (@t169 1)) % 151.48/151.85 (step @p307 :rule eq_resolve :premises (@p306 @p305)) % 151.48/151.85 (step @p308 :rule reordering :premises (@p307) :args ((or @t165 @t169))) % 151.48/151.85 (step @p309 :rule chain_m_resolution :premises (@p308 @p282) :args (@t165 @t159 @t170)) % 151.48/151.85 (step @p310 :rule cnf_or_pos :args (@t177)) % 151.48/151.85 (step @p311 :rule reordering :premises (@p310) :args ((or @t166 @t176 @t178))) % 151.48/151.85 (step @p312 :rule chain_m_resolution :premises (@p311 @p309 @p303) :args (@t178 (@list false false) (@list @t165 @t173))) % 151.48/151.85 (assume-push @p319 @t75) % 151.48/151.85 (step @p314 :rule instantiate :premises (@p254) :args ((@list @t144 @t143 @t146))) % 151.48/151.85 (step-pop @p320 :rule scope :premises (@p314)) % 151.48/151.85 (step @p315 :rule process_scope :premises (@p320) :args (@t177)) % 151.48/151.85 (step @p317 :rule implies_elim :premises (@p315)) % 151.48/151.85 (step @p318 false :rule chain_m_resolution :premises (@p317 @p312 @p254) :args (false (@list true false) (@list @t177 @t75))) % 151.48/151.85 ) % 151.48/151.85 % SZS output end Proof % 151.48/151.85 % cvc5 exiting %------------------------------------------------------------------------------