%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU267+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 08:51:11 AM UTC 2026 % Result : Theorem 15.40s 15.61s % Output : Proof 15.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SEU267+1 : TPTP v9.2.1. Released v3.3.0. % 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n005.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:49:18 EDT 2026 % 0.16/0.35 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 15.40/15.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.40/15.61 --- Run --no-e-matching --full-saturate-quant at 6... % 15.40/15.61 % SZS status Theorem % 15.40/15.61 % SZS output start Proof % 15.40/15.61 ( % 15.40/15.61 (declare-sort $$unsorted 0) % 15.40/15.61 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 15.40/15.61 (declare-const tptp.pair_first (-> $$unsorted $$unsorted)) % 15.40/15.61 (declare-const tptp.empty_set $$unsorted) % 15.40/15.61 (declare-const tptp.empty (-> $$unsorted Bool)) % 15.40/15.61 (declare-const tptp.pair_second (-> $$unsorted $$unsorted)) % 15.40/15.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 15.40/15.61 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 15.40/15.61 (define @t1 () (@var "A" $$unsorted)) % 15.40/15.61 (define @t2 () (@var "B" $$unsorted)) % 15.40/15.61 (define @t3 () (@list @t2)) % 15.40/15.61 (define @t4 () (@list @t1)) % 15.40/15.61 (define @t5 () (tptp.in @t1 @t2)) % 15.40/15.61 (define @t6 () (tptp.empty @t2)) % 15.40/15.61 (define @t7 () (tptp.element @t1 @t2)) % 15.40/15.61 (define @t8 () (@list @t1 @t2)) % 15.40/15.61 (define @t9 () (tptp.empty @t1)) % 15.40/15.61 (define @t10 () (tptp.ordered_pair @t1 @t2)) % 15.40/15.61 (define @t11 () (tptp.pair_second @t10)) % 15.40/15.61 (define @t12 () (tptp.pair_first @t10)) % 15.40/15.61 (define @t13 () (and (= @t12 @t1) (= @t11 @t2))) % 15.40/15.61 (define @t14 () (forall @t8 @t13)) % 15.40/15.61 (define @t15 () (not @t14)) % 15.40/15.61 (define @t16 () (@var "C" $$unsorted)) % 15.40/15.61 (define @t17 () (= @t2 @t16)) % 15.40/15.61 (define @t18 () (@var "D" $$unsorted)) % 15.40/15.61 (define @t19 () (tptp.ordered_pair @t16 @t18)) % 15.40/15.61 (define @t20 () (= @t1 @t19)) % 15.40/15.61 (define @t21 () (@list @t16 @t18)) % 15.40/15.61 (define @t22 () (forall @t21 (=> @t20 @t17))) % 15.40/15.61 (define @t23 () (tptp.pair_first @t1)) % 15.40/15.61 (define @t24 () (= @t2 @t23)) % 15.40/15.61 (define @t25 () (= @t24 @t22)) % 15.40/15.61 (define @t26 () (forall @t3 @t25)) % 15.40/15.61 (define @t27 () (= @t1 (tptp.ordered_pair @t2 @t16))) % 15.40/15.61 (define @t28 () (@list @t2 @t16)) % 15.40/15.61 (define @t29 () (exists @t28 @t27)) % 15.40/15.61 (define @t30 () (=> @t29 @t26)) % 15.40/15.61 (define @t31 () (forall @t4 @t30)) % 15.40/15.61 (define @t32 () (= @t2 @t18)) % 15.40/15.61 (define @t33 () (forall @t21 (=> @t20 @t32))) % 15.40/15.61 (define @t34 () (tptp.pair_second @t1)) % 15.40/15.61 (define @t35 () (= @t2 @t34)) % 15.40/15.61 (define @t36 () (= @t35 @t33)) % 15.40/15.61 (define @t37 () (forall @t3 @t36)) % 15.40/15.61 (define @t38 () (=> @t29 @t37)) % 15.40/15.61 (define @t39 () (forall @t4 @t38)) % 15.40/15.61 (define @t40 () (@var "BOUND_VARIABLE_7571" $$unsorted)) % 15.40/15.61 (define @t41 () (= @t16 @t40)) % 15.40/15.61 (define @t42 () (@var "BOUND_VARIABLE_7566" $$unsorted)) % 15.40/15.61 (define @t43 () (@var "BOUND_VARIABLE_7564" $$unsorted)) % 15.40/15.61 (define @t44 () (tptp.ordered_pair @t43 @t42)) % 15.40/15.61 (define @t45 () (tptp.pair_first @t44)) % 15.40/15.61 (define @t46 () (= (= @t40 @t45) (forall @t21 (or (not (= @t19 @t44)) @t41)))) % 15.40/15.61 (define @t47 () (not (= @t44 @t19))) % 15.40/15.61 (define @t48 () (or @t47 @t41)) % 15.40/15.61 (define @t49 () (forall @t21 @t48)) % 15.40/15.61 (define @t50 () (= (= @t45 @t40) @t49)) % 15.40/15.61 (define @t51 () (not (= @t44 @t44))) % 15.40/15.61 (define @t52 () (or @t51 @t50)) % 15.40/15.61 (define @t53 () (@list @t43 @t42 @t40)) % 15.40/15.61 (define @t54 () (not @t20)) % 15.40/15.61 (define @t55 () (= (= @t23 @t40) (forall @t21 (or @t54 @t41)))) % 15.40/15.61 (define @t56 () (not (= @t1 @t44))) % 15.40/15.61 (define @t57 () (or @t56 @t56 @t55)) % 15.40/15.61 (define @t58 () (or @t56 @t55)) % 15.40/15.61 (define @t59 () (forall @t4 @t58)) % 15.40/15.61 (define @t60 () (forall @t53 @t59)) % 15.40/15.61 (define @t61 () (forall (@list @t43 @t42 @t40 @t1) @t58)) % 15.40/15.61 (define @t62 () (@list @t1 @t43 @t42 @t40)) % 15.40/15.61 (define @t63 () (or @t54 (= @t40 @t16))) % 15.40/15.61 (define @t64 () (forall @t21 @t63)) % 15.40/15.61 (define @t65 () (= (= @t40 @t23) @t64)) % 15.40/15.61 (define @t66 () (or @t56 @t65)) % 15.40/15.61 (define @t67 () (forall @t62 @t66)) % 15.40/15.61 (define @t68 () (forall @t53 @t66)) % 15.40/15.61 (define @t69 () (forall (@list @t40) @t65)) % 15.40/15.61 (define @t70 () (@list @t2)) % 15.40/15.61 (define @t71 () (forall (@list @t43 @t42) @t56)) % 15.40/15.61 (define @t72 () (@list @t2 @t16)) % 15.40/15.61 (define @t73 () (or @t71 @t69)) % 15.40/15.61 (define @t74 () (forall @t3 (= @t24 (forall @t21 (or @t54 @t17))))) % 15.40/15.61 (define @t75 () (forall @t28 (not @t27))) % 15.40/15.61 (define @t76 () (not @t75)) % 15.40/15.61 (define @t77 () (not @t76)) % 15.40/15.61 (define @t78 () (@var "BOUND_VARIABLE_7533" $$unsorted)) % 15.40/15.61 (define @t79 () (@var "BOUND_VARIABLE_7531" $$unsorted)) % 15.40/15.61 (define @t80 () (forall (@list @t79 @t78) (= @t79 (tptp.pair_first (tptp.ordered_pair @t79 @t78))))) % 15.40/15.61 (define @t81 () (@quantifiers_skolemize @t80 1)) % 15.40/15.61 (define @t82 () (@quantifiers_skolemize @t80 0)) % 15.40/15.61 (define @t83 () (tptp.ordered_pair @t82 @t81)) % 15.40/15.61 (define @t84 () (tptp.pair_first @t83)) % 15.40/15.61 (define @t85 () (forall @t21 (or (not (= @t19 @t83)) (= @t16 @t84)))) % 15.40/15.61 (define @t86 () (= (= @t84 @t84) @t85)) % 15.40/15.61 (define @t87 () (forall @t53 @t46)) % 15.40/15.61 (define @t88 () (@list false)) % 15.40/15.61 (define @t89 () (= @t82 @t84)) % 15.40/15.61 (define @t90 () (not (= @t83 @t83))) % 15.40/15.61 (define @t91 () (or @t90 @t89)) % 15.40/15.61 (define @t92 () (not @t89)) % 15.40/15.61 (define @t93 () (not @t80)) % 15.40/15.61 (define @t94 () (= @t2 @t11)) % 15.40/15.61 (define @t95 () (forall @t8 @t94)) % 15.40/15.61 (define @t96 () (@list @t1 @t2)) % 15.40/15.61 (define @t97 () (@var "BOUND_VARIABLE_7542" $$unsorted)) % 15.40/15.61 (define @t98 () (@var "BOUND_VARIABLE_7540" $$unsorted)) % 15.40/15.61 (define @t99 () (= @t1 @t12)) % 15.40/15.61 (define @t100 () (forall @t8 @t99)) % 15.40/15.61 (define @t101 () (and @t100 @t95)) % 15.40/15.61 (define @t102 () (forall (@list @t98 @t97) (= @t97 (tptp.pair_second (tptp.ordered_pair @t98 @t97))))) % 15.40/15.61 (define @t103 () (not @t102)) % 15.40/15.61 (define @t104 () (@quantifiers_skolemize @t102 1)) % 15.40/15.61 (define @t105 () (@quantifiers_skolemize @t102 0)) % 15.40/15.61 (define @t106 () (tptp.ordered_pair @t105 @t104)) % 15.40/15.61 (define @t107 () (tptp.pair_second @t106)) % 15.40/15.61 (define @t108 () (= @t104 @t107)) % 15.40/15.61 (define @t109 () (not @t108)) % 15.40/15.61 (define @t110 () (@var "BOUND_VARIABLE_7624" $$unsorted)) % 15.40/15.61 (define @t111 () (= @t18 @t110)) % 15.40/15.61 (define @t112 () (@var "BOUND_VARIABLE_7619" $$unsorted)) % 15.40/15.61 (define @t113 () (@var "BOUND_VARIABLE_7617" $$unsorted)) % 15.40/15.61 (define @t114 () (tptp.ordered_pair @t113 @t112)) % 15.40/15.61 (define @t115 () (tptp.pair_second @t114)) % 15.40/15.61 (define @t116 () (= (= @t110 @t115) (forall @t21 (or (not (= @t19 @t114)) @t111)))) % 15.40/15.61 (define @t117 () (not (= @t114 @t19))) % 15.40/15.61 (define @t118 () (or @t117 @t111)) % 15.40/15.61 (define @t119 () (forall @t21 @t118)) % 15.40/15.61 (define @t120 () (= (= @t115 @t110) @t119)) % 15.40/15.61 (define @t121 () (not (= @t114 @t114))) % 15.40/15.61 (define @t122 () (or @t121 @t120)) % 15.40/15.61 (define @t123 () (@list @t113 @t112 @t110)) % 15.40/15.61 (define @t124 () (= (= @t34 @t110) (forall @t21 (or @t54 @t111)))) % 15.40/15.61 (define @t125 () (not (= @t1 @t114))) % 15.40/15.61 (define @t126 () (or @t125 @t125 @t124)) % 15.40/15.61 (define @t127 () (or @t125 @t124)) % 15.40/15.61 (define @t128 () (forall @t4 @t127)) % 15.40/15.61 (define @t129 () (forall @t123 @t128)) % 15.40/15.61 (define @t130 () (forall (@list @t113 @t112 @t110 @t1) @t127)) % 15.40/15.61 (define @t131 () (@list @t1 @t113 @t112 @t110)) % 15.40/15.61 (define @t132 () (or @t54 (= @t110 @t18))) % 15.40/15.61 (define @t133 () (forall @t21 @t132)) % 15.40/15.61 (define @t134 () (= (= @t110 @t34) @t133)) % 15.40/15.61 (define @t135 () (or @t125 @t134)) % 15.40/15.61 (define @t136 () (forall @t131 @t135)) % 15.40/15.61 (define @t137 () (forall @t123 @t135)) % 15.40/15.61 (define @t138 () (forall (@list @t110) @t134)) % 15.40/15.61 (define @t139 () (forall (@list @t113 @t112) @t125)) % 15.40/15.61 (define @t140 () (or @t139 @t138)) % 15.40/15.61 (define @t141 () (forall @t3 (= @t35 (forall @t21 (or @t54 @t32))))) % 15.40/15.61 (define @t142 () (forall @t21 (or (not (= @t19 @t106)) (= @t18 @t107)))) % 15.40/15.61 (define @t143 () (= (= @t107 @t107) @t142)) % 15.40/15.61 (define @t144 () (forall @t123 @t116)) % 15.40/15.61 (define @t145 () (not (= @t106 @t106))) % 15.40/15.61 (define @t146 () (or @t145 @t108)) % 15.40/15.61 (assume @p1 (forall @t4 (exists @t3 (tptp.element @t2 @t1)))) % 15.40/15.61 (assume @p2 true) % 15.40/15.61 (assume @p3 (forall @t8 (=> @t7 (or @t6 @t5)))) % 15.40/15.61 (assume @p4 (forall @t8 (=> @t5 (not (tptp.in @t2 @t1))))) % 15.40/15.61 (assume @p5 (tptp.empty tptp.empty_set)) % 15.40/15.61 (assume @p6 (forall @t8 (=> @t5 @t7))) % 15.40/15.61 (assume @p7 (exists @t4 @t9)) % 15.40/15.61 (assume @p8 (exists @t4 (not @t9))) % 15.40/15.61 (assume @p9 (forall @t4 (=> @t9 (= @t1 tptp.empty_set)))) % 15.40/15.61 (assume @p10 (forall @t8 (not (and @t5 @t6)))) % 15.40/15.61 (assume @p11 (forall @t8 (not (and @t9 (not (= @t1 @t2)) @t6)))) % 15.40/15.61 (assume @p12 (forall @t8 (not (tptp.empty @t10)))) % 15.40/15.61 (assume @p13 @t15) % 15.40/15.61 (assume @p14 @t31) % 15.40/15.61 (assume @p15 @t39) % 15.40/15.61 (step @p16 :rule aci_norm :args ((= (or false @t46) @t46))) % 15.40/15.61 (step @p17 :rule refl :args (@t41)) % 15.40/15.61 (step @p18 :rule eq-symm :args (@t44 @t19)) % 15.40/15.61 (step @p19 :rule cong :premises (@p18) :args (@t47)) % 15.40/15.61 (step @p20 :rule nary_cong :premises (@p19 @p17) :args (@t48)) % 15.40/15.61 (step @p21 :rule cong :premises (@p20) :args (@t49)) % 15.40/15.61 (step @p22 :rule eq-symm :args (@t45 @t40)) % 15.40/15.61 (step @p23 :rule cong :premises (@p22 @p21) :args (@t50)) % 15.40/15.61 (step @p24 :rule evaluate :args ((not true))) % 15.40/15.61 (step @p25 :rule eq-refl :args (@t44)) % 15.40/15.61 (step @p26 :rule cong :premises (@p25) :args (@t51)) % 15.40/15.61 (step @p27 :rule trans :premises (@p26 @p24)) % 15.40/15.61 (step @p28 :rule nary_cong :premises (@p27 @p23) :args (@t52)) % 15.40/15.61 (step @p29 :rule trans :premises (@p28 @p16)) % 15.40/15.61 (step @p30 :rule cong :premises (@p29) :args ((forall @t53 @t52))) % 15.40/15.61 (step @p31 :rule quant-var-elim-eq :args ((= (forall @t4 @t57) @t52))) % 15.40/15.61 (step @p32 :rule aci_norm :args ((= @t58 @t57))) % 15.40/15.61 (step @p33 :rule cong :premises (@p32) :args (@t59)) % 15.40/15.61 (step @p34 :rule trans :premises (@p33 @p31)) % 15.40/15.61 (step @p35 :rule cong :premises (@p34) :args (@t60)) % 15.40/15.61 (step @p36 :rule quant-merge-prenex :args ((= @t60 @t61))) % 15.40/15.61 (step @p37 :rule symm :premises (@p36)) % 15.40/15.61 (step @p38 :rule quant_var_reordering :args ((= (forall @t62 @t58) @t61))) % 15.40/15.61 (step @p39 :rule trans :premises (@p38 @p37 @p35)) % 15.40/15.61 (step @p40 :rule trans :premises (@p39 @p30)) % 15.40/15.61 (step @p41 :rule eq-symm :args (@t40 @t16)) % 15.40/15.61 (step @p42 :rule refl :args (@t54)) % 15.40/15.61 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t63)) % 15.40/15.61 (step @p44 :rule cong :premises (@p43) :args (@t64)) % 15.40/15.61 (step @p45 :rule eq-symm :args (@t40 @t23)) % 15.40/15.61 (step @p46 :rule cong :premises (@p45 @p44) :args (@t65)) % 15.40/15.61 (step @p47 :rule refl :args (@t56)) % 15.40/15.61 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t66)) % 15.40/15.61 (step @p49 :rule cong :premises (@p48) :args (@t67)) % 15.40/15.61 (step @p50 :rule trans :premises (@p49 @p40)) % 15.40/15.61 (step @p51 :rule quant-merge-prenex :args ((= (forall @t4 @t68) @t67))) % 15.40/15.61 (step @p52 :rule alpha_equiv :args (@t69 (@list @t40) @t70)) % 15.40/15.61 (step @p53 :rule alpha_equiv :args (@t71 (@list @t43 @t42) @t72)) % 15.40/15.61 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t73)) % 15.40/15.61 (step @p55 :rule quant-miniscope-or :args ((= @t68 @t73))) % 15.40/15.61 (step @p56 :rule trans :premises (@p55 @p54)) % 15.40/15.61 (step @p57 :rule symm :premises (@p56)) % 15.40/15.61 (step @p58 :rule cong :premises (@p57) :args ((forall @t4 (or @t75 @t74)))) % 15.40/15.61 (step @p59 :rule trans :premises (@p58 @p51)) % 15.40/15.61 (step @p60 :rule trans :premises (@p59 @p50)) % 15.40/15.61 (step @p61 :rule refl :args (@t74)) % 15.40/15.61 (step @p62 :rule bool-double-not-elim :args (@t75)) % 15.40/15.61 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or @t77 @t74))) % 15.40/15.61 (step @p64 :rule bool-impl-elim :args (@t76 @t74)) % 15.40/15.61 (step @p65 :rule trans :premises (@p64 @p63)) % 15.40/15.61 (step @p66 :rule cong :premises (@p65) :args ((forall @t4 (=> @t76 @t74)))) % 15.40/15.61 (step @p67 :rule trans :premises (@p66 @p60)) % 15.40/15.61 (step @p68 :rule bool-impl-elim :args (@t20 @t17)) % 15.40/15.61 (step @p69 :rule cong :premises (@p68) :args (@t22)) % 15.40/15.61 (step @p70 :rule refl :args (@t24)) % 15.40/15.61 (step @p71 :rule cong :premises (@p70 @p69) :args (@t25)) % 15.40/15.61 (step @p72 :rule cong :premises (@p71) :args (@t26)) % 15.40/15.61 (step @p73 :rule exists-elim :args ((= @t29 @t76))) % 15.40/15.61 (step @p74 :rule cong :premises (@p73 @p72) :args (@t30)) % 15.40/15.61 (step @p75 :rule cong :premises (@p74) :args (@t31)) % 15.40/15.61 (step @p76 :rule trans :premises (@p75 @p67)) % 15.40/15.61 (step @p77 :rule eq_resolve :premises (@p14 @p76)) % 15.40/15.61 (step @p78 :rule bool-eq-true :args (@t85)) % 15.40/15.61 (step @p79 :rule eq-symm :args (true @t85)) % 15.40/15.61 (step @p80 :rule trans :premises (@p79 @p78)) % 15.40/15.61 (step @p81 :rule refl :args (@t85)) % 15.40/15.61 (step @p82 :rule eq-refl :args (@t84)) % 15.40/15.61 (step @p83 :rule cong :premises (@p82 @p81) :args (@t86)) % 15.40/15.61 (step @p84 :rule trans :premises (@p83 @p80)) % 15.40/15.61 (step @p85 :rule refl :args (@t87)) % 15.40/15.61 (step @p86 :rule cong :premises (@p85 @p84) :args ((=> @t87 @t86))) % 15.40/15.61 (assume-push @p234 @t87) % 15.40/15.61 (step @p88 :rule instantiate :premises (@p77) :args ((@list @t82 @t81 @t84))) % 15.40/15.61 (step-pop @p235 :rule scope :premises (@p88)) % 15.40/15.61 (step @p89 :rule process_scope :premises (@p235) :args (@t86)) % 15.40/15.61 (step @p91 :rule eq_resolve :premises (@p89 @p86)) % 15.40/15.61 (step @p92 :rule implies_elim :premises (@p91)) % 15.40/15.61 (step @p93 :rule chain_m_resolution :premises (@p92 @p77) :args (@t85 @t88 (@list @t87))) % 15.40/15.61 (step @p94 :rule aci_norm :args ((= (or false @t89) @t89))) % 15.40/15.61 (step @p95 :rule refl :args (@t89)) % 15.40/15.61 (step @p96 :rule eq-refl :args (@t83)) % 15.40/15.61 (step @p97 :rule cong :premises (@p96) :args (@t90)) % 15.40/15.61 (step @p98 :rule trans :premises (@p97 @p24)) % 15.40/15.61 (step @p99 :rule nary_cong :premises (@p98 @p95) :args (@t91)) % 15.40/15.61 (step @p100 :rule trans :premises (@p99 @p94)) % 15.40/15.61 (step @p101 :rule cong :premises (@p81 @p100) :args ((=> @t85 @t91))) % 15.40/15.61 (assume-push @p236 @t85) % 15.40/15.61 (step @p103 :rule instantiate :premises (@p93) :args ((@list @t82 @t81))) % 15.40/15.61 (step-pop @p237 :rule scope :premises (@p103)) % 15.40/15.61 (step @p104 :rule process_scope :premises (@p237) :args (@t91)) % 15.40/15.61 (step @p106 :rule eq_resolve :premises (@p104 @p101)) % 15.40/15.61 (step @p107 :rule implies_elim :premises (@p106)) % 15.40/15.61 (step @p108 :rule reordering :premises (@p107) :args ((or @t89 (not @t85)))) % 15.40/15.61 (step @p109 :rule chain_m_resolution :premises (@p108 @p93) :args (@t89 @t88 (@list @t85))) % 15.40/15.61 (step @p110 :rule refl :args (@t92)) % 15.40/15.61 (step @p111 :rule bool-double-not-elim :args (@t80)) % 15.40/15.61 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((or (not @t93) @t92))) % 15.40/15.61 (assume-push @p238 @t93) % 15.40/15.61 (step @p114 :rule skolemize :premises (@p238)) % 15.40/15.61 (step-pop @p239 :rule scope :premises (@p114)) % 15.40/15.61 (step @p115 :rule process_scope :premises (@p239) :args (@t92)) % 15.40/15.61 (step @p117 :rule implies_elim :premises (@p115)) % 15.40/15.61 (step @p118 :rule eq_resolve :premises (@p117 @p112)) % 15.40/15.61 (step @p119 :rule chain_m_resolution :premises (@p118 @p109) :args (@t80 @t88 (@list @t89))) % 15.40/15.61 (step @p120 :rule alpha_equiv :args (@t95 @t96 (@list @t98 @t97))) % 15.40/15.61 (step @p121 :rule alpha_equiv :args (@t100 @t96 (@list @t79 @t78))) % 15.40/15.61 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t101)) % 15.40/15.61 (step @p123 :rule quant-miniscope-and :args ((= (forall @t8 (and @t99 @t94)) @t101))) % 15.40/15.61 (step @p124 :rule trans :premises (@p123 @p122)) % 15.40/15.61 (step @p125 :rule eq-symm :args (@t11 @t2)) % 15.40/15.61 (step @p126 :rule eq-symm :args (@t12 @t1)) % 15.40/15.61 (step @p127 :rule nary_cong :premises (@p126 @p125) :args (@t13)) % 15.40/15.61 (step @p128 :rule cong :premises (@p127) :args (@t14)) % 15.40/15.61 (step @p129 :rule trans :premises (@p128 @p124)) % 15.40/15.61 (step @p130 :rule cong :premises (@p129) :args (@t15)) % 15.40/15.61 (step @p131 :rule eq_resolve :premises (@p13 @p130)) % 15.40/15.61 (step @p132 :rule not_and :premises (@p131)) % 15.40/15.61 (step @p133 :rule chain_m_resolution :premises (@p132 @p119) :args (@t103 @t88 (@list @t80))) % 15.40/15.61 (step @p134 :rule refl :args (@t109)) % 15.40/15.61 (step @p135 :rule bool-double-not-elim :args (@t102)) % 15.40/15.61 (step @p136 :rule nary_cong :premises (@p135 @p134) :args ((or (not @t103) @t109))) % 15.40/15.61 (assume-push @p240 @t103) % 15.40/15.61 (step @p138 :rule skolemize :premises (@p240)) % 15.40/15.61 (step-pop @p241 :rule scope :premises (@p138)) % 15.40/15.61 (step @p139 :rule process_scope :premises (@p241) :args (@t109)) % 15.40/15.61 (step @p141 :rule implies_elim :premises (@p139)) % 15.40/15.61 (step @p142 :rule eq_resolve :premises (@p141 @p136)) % 15.40/15.61 (step @p143 :rule chain_m_resolution :premises (@p142 @p133) :args (@t109 (@list true) (@list @t102))) % 15.40/15.61 (step @p144 :rule aci_norm :args ((= (or false @t116) @t116))) % 15.40/15.61 (step @p145 :rule refl :args (@t111)) % 15.40/15.61 (step @p146 :rule eq-symm :args (@t114 @t19)) % 15.40/15.61 (step @p147 :rule cong :premises (@p146) :args (@t117)) % 15.40/15.61 (step @p148 :rule nary_cong :premises (@p147 @p145) :args (@t118)) % 15.40/15.61 (step @p149 :rule cong :premises (@p148) :args (@t119)) % 15.40/15.61 (step @p150 :rule eq-symm :args (@t115 @t110)) % 15.40/15.61 (step @p151 :rule cong :premises (@p150 @p149) :args (@t120)) % 15.40/15.61 (step @p152 :rule eq-refl :args (@t114)) % 15.40/15.61 (step @p153 :rule cong :premises (@p152) :args (@t121)) % 15.40/15.61 (step @p154 :rule trans :premises (@p153 @p24)) % 15.40/15.61 (step @p155 :rule nary_cong :premises (@p154 @p151) :args (@t122)) % 15.40/15.61 (step @p156 :rule trans :premises (@p155 @p144)) % 15.40/15.61 (step @p157 :rule cong :premises (@p156) :args ((forall @t123 @t122))) % 15.40/15.61 (step @p158 :rule quant-var-elim-eq :args ((= (forall @t4 @t126) @t122))) % 15.40/15.61 (step @p159 :rule aci_norm :args ((= @t127 @t126))) % 15.40/15.61 (step @p160 :rule cong :premises (@p159) :args (@t128)) % 15.40/15.61 (step @p161 :rule trans :premises (@p160 @p158)) % 15.40/15.61 (step @p162 :rule cong :premises (@p161) :args (@t129)) % 15.40/15.61 (step @p163 :rule quant-merge-prenex :args ((= @t129 @t130))) % 15.40/15.61 (step @p164 :rule symm :premises (@p163)) % 15.40/15.61 (step @p165 :rule quant_var_reordering :args ((= (forall @t131 @t127) @t130))) % 15.40/15.61 (step @p166 :rule trans :premises (@p165 @p164 @p162)) % 15.40/15.61 (step @p167 :rule trans :premises (@p166 @p157)) % 15.40/15.61 (step @p168 :rule eq-symm :args (@t110 @t18)) % 15.40/15.61 (step @p169 :rule nary_cong :premises (@p42 @p168) :args (@t132)) % 15.40/15.61 (step @p170 :rule cong :premises (@p169) :args (@t133)) % 15.40/15.61 (step @p171 :rule eq-symm :args (@t110 @t34)) % 15.40/15.61 (step @p172 :rule cong :premises (@p171 @p170) :args (@t134)) % 15.40/15.61 (step @p173 :rule refl :args (@t125)) % 15.40/15.61 (step @p174 :rule nary_cong :premises (@p173 @p172) :args (@t135)) % 15.40/15.61 (step @p175 :rule cong :premises (@p174) :args (@t136)) % 15.40/15.61 (step @p176 :rule trans :premises (@p175 @p167)) % 15.40/15.61 (step @p177 :rule quant-merge-prenex :args ((= (forall @t4 @t137) @t136))) % 15.40/15.61 (step @p178 :rule alpha_equiv :args (@t138 (@list @t110) @t70)) % 15.40/15.61 (step @p179 :rule alpha_equiv :args (@t139 (@list @t113 @t112) @t72)) % 15.40/15.61 (step @p180 :rule nary_cong :premises (@p179 @p178) :args (@t140)) % 15.40/15.61 (step @p181 :rule quant-miniscope-or :args ((= @t137 @t140))) % 15.40/15.61 (step @p182 :rule trans :premises (@p181 @p180)) % 15.40/15.61 (step @p183 :rule symm :premises (@p182)) % 15.40/15.61 (step @p184 :rule cong :premises (@p183) :args ((forall @t4 (or @t75 @t141)))) % 15.40/15.61 (step @p185 :rule trans :premises (@p184 @p177)) % 15.40/15.61 (step @p186 :rule trans :premises (@p185 @p176)) % 15.40/15.61 (step @p187 :rule refl :args (@t141)) % 15.40/15.61 (step @p188 :rule nary_cong :premises (@p62 @p187) :args ((or @t77 @t141))) % 15.40/15.61 (step @p189 :rule bool-impl-elim :args (@t76 @t141)) % 15.40/15.61 (step @p190 :rule trans :premises (@p189 @p188)) % 15.40/15.61 (step @p191 :rule cong :premises (@p190) :args ((forall @t4 (=> @t76 @t141)))) % 15.40/15.61 (step @p192 :rule trans :premises (@p191 @p186)) % 15.40/15.61 (step @p193 :rule bool-impl-elim :args (@t20 @t32)) % 15.40/15.61 (step @p194 :rule cong :premises (@p193) :args (@t33)) % 15.40/15.61 (step @p195 :rule refl :args (@t35)) % 15.40/15.61 (step @p196 :rule cong :premises (@p195 @p194) :args (@t36)) % 15.40/15.61 (step @p197 :rule cong :premises (@p196) :args (@t37)) % 15.40/15.61 (step @p198 :rule cong :premises (@p73 @p197) :args (@t38)) % 15.40/15.61 (step @p199 :rule cong :premises (@p198) :args (@t39)) % 15.40/15.61 (step @p200 :rule trans :premises (@p199 @p192)) % 15.40/15.61 (step @p201 :rule eq_resolve :premises (@p15 @p200)) % 15.40/15.61 (step @p202 :rule bool-eq-true :args (@t142)) % 15.40/15.61 (step @p203 :rule eq-symm :args (true @t142)) % 15.40/15.61 (step @p204 :rule trans :premises (@p203 @p202)) % 15.40/15.61 (step @p205 :rule refl :args (@t142)) % 15.40/15.61 (step @p206 :rule eq-refl :args (@t107)) % 15.40/15.61 (step @p207 :rule cong :premises (@p206 @p205) :args (@t143)) % 15.40/15.61 (step @p208 :rule trans :premises (@p207 @p204)) % 15.40/15.61 (step @p209 :rule refl :args (@t144)) % 15.40/15.61 (step @p210 :rule cong :premises (@p209 @p208) :args ((=> @t144 @t143))) % 15.40/15.61 (assume-push @p242 @t144) % 15.40/15.61 (step @p212 :rule instantiate :premises (@p201) :args ((@list @t105 @t104 @t107))) % 15.40/15.61 (step-pop @p243 :rule scope :premises (@p212)) % 15.40/15.61 (step @p213 :rule process_scope :premises (@p243) :args (@t143)) % 15.40/15.61 (step @p215 :rule eq_resolve :premises (@p213 @p210)) % 15.40/15.61 (step @p216 :rule implies_elim :premises (@p215)) % 15.40/15.61 (step @p217 :rule chain_m_resolution :premises (@p216 @p201) :args (@t142 @t88 (@list @t144))) % 15.40/15.61 (step @p218 :rule aci_norm :args ((= (or false @t108) @t108))) % 15.40/15.61 (step @p219 :rule refl :args (@t108)) % 15.40/15.61 (step @p220 :rule eq-refl :args (@t106)) % 15.40/15.61 (step @p221 :rule cong :premises (@p220) :args (@t145)) % 15.40/15.61 (step @p222 :rule trans :premises (@p221 @p24)) % 15.40/15.61 (step @p223 :rule nary_cong :premises (@p222 @p219) :args (@t146)) % 15.40/15.61 (step @p224 :rule trans :premises (@p223 @p218)) % 15.40/15.61 (step @p225 :rule cong :premises (@p205 @p224) :args ((=> @t142 @t146))) % 15.40/15.61 (assume-push @p244 @t142) % 15.40/15.61 (step @p227 :rule instantiate :premises (@p217) :args ((@list @t105 @t104))) % 15.40/15.61 (step-pop @p245 :rule scope :premises (@p227)) % 15.40/15.61 (step @p228 :rule process_scope :premises (@p245) :args (@t146)) % 15.40/15.61 (step @p230 :rule eq_resolve :premises (@p228 @p225)) % 15.40/15.61 (step @p231 :rule implies_elim :premises (@p230)) % 15.40/15.61 (step @p232 :rule reordering :premises (@p231) :args ((or @t108 (not @t142)))) % 15.40/15.61 (step @p233 false :rule chain_m_resolution :premises (@p232 @p217 @p143) :args (false (@list false true) (@list @t142 @t108))) % 15.40/15.61 ) % 15.40/15.61 % SZS output end Proof % 15.40/15.61 % cvc5 exiting %------------------------------------------------------------------------------