%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWW469+5 : TPTP v9.2.1. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:04:59 AM UTC 2026 % Result : Theorem 0.37s 0.62s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWW469+5 : TPTP v9.2.1. Released v5.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n014.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 22:02:43 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.62 % SZS status Theorem % 0.37/0.62 % SZS output start Proof % 0.37/0.62 ( % 0.37/0.62 (declare-sort $$unsorted 0) % 0.37/0.62 (declare-const tptp.hBOOL (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.fequal (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.type_definition (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.hoare_1580379338ep_set (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.hAPP (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.com $$unsorted) % 0.37/0.62 (declare-const tptp.equal_equal (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.node (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.bool $$unsorted) % 0.37/0.62 (declare-const tptp.state $$unsorted) % 0.37/0.62 (declare-const tptp.ti (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.collect (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.hoare_509422987triple (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.induct_equal (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.hoare_2037801986triple (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.induct_false $$unsorted) % 0.37/0.62 (declare-const tptp.cl_HOL_Oequal (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.sum_sum (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.enum (-> $$unsorted Bool)) % 0.37/0.62 (declare-const tptp.induct_true $$unsorted) % 0.37/0.62 (declare-const tptp.fun (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.hoare_244953527triple (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.member (-> $$unsorted $$unsorted)) % 0.37/0.62 (declare-const tptp.hoare_1883395792gleton $$unsorted) % 0.37/0.62 (declare-const tptp.undefined (-> $$unsorted $$unsorted)) % 0.37/0.62 (define @t1 () (@var "X_a" $$unsorted)) % 0.37/0.62 (define @t2 () (tptp.equal_equal @t1)) % 0.37/0.62 (define @t3 () (tptp.fun @t1 tptp.bool)) % 0.37/0.62 (define @t4 () (tptp.fun @t1 @t3)) % 0.37/0.62 (define @t5 () (tptp.cl_HOL_Oequal @t1)) % 0.37/0.62 (define @t6 () (@list @t1)) % 0.37/0.62 (define @t7 () (tptp.induct_equal @t1)) % 0.37/0.62 (define @t8 () (tptp.undefined @t1)) % 0.37/0.62 (define @t9 () (tptp.hoare_244953527triple @t1)) % 0.37/0.62 (define @t10 () (tptp.hoare_509422987triple @t1)) % 0.37/0.62 (define @t11 () (tptp.fun (tptp.node (tptp.sum_sum tptp.com (tptp.fun @t1 (tptp.fun tptp.state tptp.bool))) (tptp.sum_sum tptp.state @t1)) tptp.bool)) % 0.37/0.62 (define @t12 () (tptp.fun @t11 @t10)) % 0.37/0.62 (define @t13 () (tptp.hoare_2037801986triple @t1)) % 0.37/0.62 (define @t14 () (tptp.fun @t10 @t11)) % 0.37/0.62 (define @t15 () (tptp.hoare_1580379338ep_set @t1)) % 0.37/0.62 (define @t16 () (tptp.fun @t11 tptp.bool)) % 0.37/0.62 (define @t17 () (tptp.collect @t1)) % 0.37/0.62 (define @t18 () (@var "X_b" $$unsorted)) % 0.37/0.62 (define @t19 () (tptp.type_definition @t1 @t18)) % 0.37/0.62 (define @t20 () (tptp.fun @t18 tptp.bool)) % 0.37/0.62 (define @t21 () (tptp.fun @t20 tptp.bool)) % 0.37/0.62 (define @t22 () (tptp.fun @t18 @t1)) % 0.37/0.62 (define @t23 () (tptp.fun @t22 @t21)) % 0.37/0.62 (define @t24 () (tptp.fun @t1 @t18)) % 0.37/0.62 (define @t25 () (tptp.fequal @t1)) % 0.37/0.62 (define @t26 () (@var "B_2" $$unsorted)) % 0.37/0.62 (define @t27 () (@var "B_1" $$unsorted)) % 0.37/0.62 (define @t28 () (tptp.hAPP @t18 @t1 @t27 @t26)) % 0.37/0.62 (define @t29 () (@list @t18 @t1 @t27 @t26)) % 0.37/0.62 (define @t30 () (tptp.member @t18)) % 0.37/0.62 (define @t31 () (@var "T" $$unsorted)) % 0.37/0.62 (define @t32 () (@var "S" $$unsorted)) % 0.37/0.62 (define @t33 () (tptp.ti tptp.state @t32)) % 0.37/0.62 (define @t34 () (= @t33 (tptp.ti tptp.state @t31))) % 0.37/0.62 (define @t35 () (not @t34)) % 0.37/0.62 (define @t36 () (@list @t32 @t31)) % 0.37/0.62 (define @t37 () (exists @t36 @t35)) % 0.37/0.62 (define @t38 () (tptp.hBOOL tptp.hoare_1883395792gleton)) % 0.37/0.62 (define @t39 () (= @t38 @t37)) % 0.37/0.62 (define @t40 () (@var "Y_1" $$unsorted)) % 0.37/0.62 (define @t41 () (@var "X_1" $$unsorted)) % 0.37/0.62 (define @t42 () (= @t41 @t40)) % 0.37/0.62 (define @t43 () (@list @t1 @t41 @t40)) % 0.37/0.62 (define @t44 () (tptp.hAPP @t10 @t11 @t13 @t41)) % 0.37/0.62 (define @t45 () (@var "X" $$unsorted)) % 0.37/0.62 (define @t46 () (tptp.ti @t1 @t41)) % 0.37/0.62 (define @t47 () (= @t46 (tptp.ti @t1 @t40))) % 0.37/0.62 (define @t48 () (@list @t1 @t41)) % 0.37/0.62 (define @t49 () (tptp.hAPP @t16 @t16 (tptp.collect @t11) @t15)) % 0.37/0.62 (define @t50 () (tptp.member @t11)) % 0.37/0.62 (define @t51 () (tptp.fun @t16 tptp.bool)) % 0.37/0.62 (define @t52 () (@var "P" $$unsorted)) % 0.37/0.62 (define @t53 () (@var "X_2" $$unsorted)) % 0.37/0.62 (define @t54 () (tptp.hAPP @t10 @t11 @t13 @t53)) % 0.37/0.62 (define @t55 () (@list @t53)) % 0.37/0.62 (define @t56 () (tptp.hBOOL (tptp.hAPP @t16 tptp.bool (tptp.hAPP @t11 @t51 @t50 @t40) @t49))) % 0.37/0.62 (define @t57 () (@list @t1 @t40)) % 0.37/0.62 (define @t58 () (tptp.hAPP @t11 @t10 @t9 @t40)) % 0.37/0.62 (define @t59 () (@var "Y_2" $$unsorted)) % 0.37/0.62 (define @t60 () (tptp.hAPP @t11 @t10 @t9 @t59)) % 0.37/0.62 (define @t61 () (tptp.hBOOL (tptp.hAPP @t16 tptp.bool (tptp.hAPP @t11 @t51 @t50 @t59) @t49))) % 0.37/0.62 (define @t62 () (@list @t59)) % 0.37/0.62 (define @t63 () (tptp.ti @t18 @t40)) % 0.37/0.62 (define @t64 () (@var "Abs" $$unsorted)) % 0.37/0.62 (define @t65 () (tptp.hAPP @t18 @t1 @t64 @t40)) % 0.37/0.62 (define @t66 () (@var "A_1" $$unsorted)) % 0.37/0.62 (define @t67 () (tptp.hBOOL (tptp.hAPP @t20 tptp.bool (tptp.hAPP @t18 @t21 @t30 @t40) @t66))) % 0.37/0.62 (define @t68 () (@var "Rep" $$unsorted)) % 0.37/0.62 (define @t69 () (tptp.hBOOL (tptp.hAPP @t20 tptp.bool (tptp.hAPP @t22 @t21 (tptp.hAPP @t24 @t23 @t19 @t68) @t64) @t66))) % 0.37/0.62 (define @t70 () (@list @t18 @t1 @t40 @t68 @t64 @t66)) % 0.37/0.62 (define @t71 () (tptp.hAPP @t1 @t18 @t68 @t41)) % 0.37/0.62 (define @t72 () (@list @t18 @t1 @t41 @t68 @t64 @t66)) % 0.37/0.62 (define @t73 () (tptp.hAPP @t1 @t18 @t68 @t53)) % 0.37/0.62 (define @t74 () (tptp.hBOOL (tptp.hAPP @t20 tptp.bool (tptp.hAPP @t18 @t21 @t30 @t59) @t66))) % 0.37/0.62 (define @t75 () (tptp.hAPP @t18 @t1 @t64 @t59)) % 0.37/0.62 (define @t76 () (@var "G" $$unsorted)) % 0.37/0.62 (define @t77 () (@var "F" $$unsorted)) % 0.37/0.62 (define @t78 () (@var "T_1_1" $$unsorted)) % 0.37/0.62 (define @t79 () (@var "T_2" $$unsorted)) % 0.37/0.62 (define @t80 () (tptp.sum_sum @t79 @t78)) % 0.37/0.62 (define @t81 () (tptp.enum @t79)) % 0.37/0.62 (define @t82 () (and (tptp.enum @t78) @t81)) % 0.37/0.62 (define @t83 () (@list @t79 @t78)) % 0.37/0.62 (define @t84 () (tptp.fun @t79 @t78)) % 0.37/0.62 (define @t85 () (@var "A" $$unsorted)) % 0.37/0.62 (define @t86 () (@var "T_1" $$unsorted)) % 0.37/0.62 (define @t87 () (tptp.ti @t86 @t85)) % 0.37/0.62 (define @t88 () (@var "Y" $$unsorted)) % 0.37/0.62 (define @t89 () (= (tptp.ti @t1 @t45) (tptp.ti @t1 @t88))) % 0.37/0.62 (define @t90 () (tptp.hBOOL (tptp.hAPP @t1 tptp.bool (tptp.hAPP @t1 @t3 @t25 @t45) @t88))) % 0.37/0.62 (define @t91 () (@list @t1 @t45 @t88)) % 0.37/0.62 (define @t92 () (@list @t32)) % 0.37/0.62 (define @t93 () (forall (@list @t31) (not (forall @t92 @t34)))) % 0.37/0.62 (define @t94 () (not @t93)) % 0.37/0.62 (define @t95 () (tptp.ti tptp.state (@quantifiers_skolemize @t93 0))) % 0.37/0.62 (define @t96 () (forall @t92 (= @t33 @t95))) % 0.37/0.62 (define @t97 () (not (not @t96))) % 0.37/0.62 (define @t98 () (forall @t36 @t34)) % 0.37/0.62 (define @t99 () (forall @t36 (not @t35))) % 0.37/0.62 (define @t100 () (not @t99)) % 0.37/0.62 (define @t101 () (not @t98)) % 0.37/0.62 (assume @p1 (forall @t6 (=> @t5 (= (tptp.ti @t4 @t2) @t2)))) % 0.37/0.62 (assume @p2 (forall @t6 (= (tptp.ti @t4 @t7) @t7))) % 0.37/0.62 (assume @p3 (= (tptp.ti tptp.bool tptp.induct_false) tptp.induct_false)) % 0.37/0.62 (assume @p4 (= (tptp.ti tptp.bool tptp.induct_true) tptp.induct_true)) % 0.37/0.62 (assume @p5 (forall @t6 (= (tptp.ti @t1 @t8) @t8))) % 0.37/0.62 (assume @p6 (forall @t6 (= (tptp.ti @t12 @t9) @t9))) % 0.37/0.62 (assume @p7 (forall @t6 (= (tptp.ti @t14 @t13) @t13))) % 0.37/0.62 (assume @p8 (= (tptp.ti tptp.bool tptp.hoare_1883395792gleton) tptp.hoare_1883395792gleton)) % 0.37/0.62 (assume @p9 (forall @t6 (= (tptp.ti @t16 @t15) @t15))) % 0.37/0.62 (assume @p10 (forall @t6 (= (tptp.ti (tptp.fun @t3 @t3) @t17) @t17))) % 0.37/0.62 (assume @p11 (forall (@list @t1 @t18) (= (tptp.ti (tptp.fun @t24 @t23) @t19) @t19))) % 0.37/0.62 (assume @p12 (forall @t6 (= (tptp.ti @t4 @t25) @t25))) % 0.37/0.62 (assume @p13 (forall @t29 (= (tptp.hAPP @t18 @t1 (tptp.ti @t22 @t27) @t26) @t28))) % 0.37/0.62 (assume @p14 (forall @t29 (= (tptp.hAPP @t18 @t1 @t27 (tptp.ti @t18 @t26)) @t28))) % 0.37/0.62 (assume @p15 (forall (@list @t1 @t18 @t27 @t26) (= (tptp.ti @t1 @t28) @t28))) % 0.37/0.62 (assume @p16 (forall (@list @t27) (= (tptp.hBOOL (tptp.ti tptp.bool @t27)) (tptp.hBOOL @t27)))) % 0.37/0.62 (assume @p17 (forall (@list @t18) (= (tptp.ti (tptp.fun @t18 @t21) @t30) @t30))) % 0.37/0.62 (assume @p18 @t39) % 0.37/0.62 (assume @p19 (forall @t43 (= (tptp.hBOOL (tptp.hAPP @t10 tptp.bool (tptp.hAPP @t10 (tptp.fun @t10 tptp.bool) (tptp.equal_equal @t10) @t41) @t40)) @t42))) % 0.37/0.62 (assume @p20 (forall @t43 (= (= @t44 (tptp.hAPP @t10 @t11 @t13 @t40)) @t42))) % 0.37/0.62 (assume @p21 (forall @t6 (=> @t5 (= @t2 @t25)))) % 0.37/0.62 (assume @p22 (forall @t6 (=> @t5 (forall (@list @t45) (tptp.hBOOL (tptp.hAPP @t1 tptp.bool (tptp.hAPP @t1 @t3 @t2 @t45) @t45)))))) % 0.37/0.62 (assume @p23 (forall @t6 (=> @t5 (forall (@list @t41 @t40) (= (tptp.hBOOL (tptp.hAPP @t1 tptp.bool (tptp.hAPP @t1 @t3 @t2 @t41) @t40)) @t47))))) % 0.37/0.62 (assume @p24 (forall @t6 (=> @t5 (= @t25 @t2)))) % 0.37/0.62 (assume @p25 (forall @t48 (= (tptp.hAPP @t11 @t10 @t9 @t44) @t41))) % 0.37/0.62 (assume @p26 (forall @t48 (tptp.hBOOL (tptp.hAPP @t16 tptp.bool (tptp.hAPP @t11 @t51 @t50 @t44) @t49)))) % 0.37/0.62 (assume @p27 (forall (@list @t1 @t52 @t40) (=> @t56 (=> (forall @t55 (tptp.hBOOL (tptp.hAPP @t11 tptp.bool @t52 @t54))) (tptp.hBOOL (tptp.hAPP @t11 tptp.bool @t52 @t40)))))) % 0.37/0.62 (assume @p28 (forall @t57 (=> @t56 (not (forall @t55 (not (= @t40 @t54))))))) % 0.37/0.62 (assume @p29 (forall @t57 (=> @t56 (= (tptp.hAPP @t10 @t11 @t13 @t58) @t40)))) % 0.37/0.62 (assume @p30 (forall @t6 (tptp.hBOOL (tptp.hAPP @t16 tptp.bool (tptp.hAPP @t12 @t51 (tptp.hAPP @t14 (tptp.fun @t12 @t51) (tptp.type_definition @t10 @t11) @t13) @t9) @t49)))) % 0.37/0.62 (assume @p31 (forall (@list @t1 @t40 @t41) (=> (tptp.hBOOL (tptp.hAPP @t16 tptp.bool (tptp.hAPP @t11 @t51 @t50 @t41) @t49)) (=> @t56 (= (= (tptp.hAPP @t11 @t10 @t9 @t41) @t58) @t42))))) % 0.37/0.62 (assume @p32 (forall (@list @t1 @t41 @t52) (=> (forall @t62 (=> @t61 (tptp.hBOOL (tptp.hAPP @t10 tptp.bool @t52 @t60)))) (tptp.hBOOL (tptp.hAPP @t10 tptp.bool @t52 @t41))))) % 0.37/0.62 (assume @p33 (forall @t48 (not (forall @t62 (=> (= @t41 @t60) (not @t61)))))) % 0.37/0.62 (assume @p34 (forall (@list @t18 @t1 @t40 @t41 @t68 @t64 @t66) (=> @t69 (=> (tptp.hBOOL (tptp.hAPP @t20 tptp.bool (tptp.hAPP @t18 @t21 @t30 @t41) @t66)) (=> @t67 (= (= (tptp.hAPP @t18 @t1 @t64 @t41) @t65) (= (tptp.ti @t18 @t41) @t63))))))) % 0.37/0.62 (assume @p35 (forall @t70 (=> @t69 (=> @t67 (= (tptp.hAPP @t1 @t18 @t68 @t65) @t63))))) % 0.37/0.62 (assume @p36 (forall (@list @t18 @t1 @t41 @t40 @t68 @t64 @t66) (=> @t69 (= (= @t71 (tptp.hAPP @t1 @t18 @t68 @t40)) @t47)))) % 0.37/0.62 (assume @p37 (forall @t72 (=> @t69 (= (tptp.hAPP @t18 @t1 @t64 @t71) @t46)))) % 0.37/0.62 (assume @p38 (forall @t72 (=> @t69 (tptp.hBOOL (tptp.hAPP @t20 tptp.bool (tptp.hAPP @t18 @t21 @t30 @t71) @t66))))) % 0.37/0.62 (assume @p39 (not (tptp.hBOOL tptp.induct_false))) % 0.37/0.62 (assume @p40 (forall @t70 (=> @t69 (=> @t67 (not (forall @t55 (not (= @t63 @t73)))))))) % 0.37/0.62 (assume @p41 (forall @t72 (=> @t69 (not (forall @t62 (=> (= @t46 @t75) (not @t74))))))) % 0.37/0.62 (assume @p42 (forall (@list @t18 @t1 @t41 @t52 @t68 @t64 @t66) (=> @t69 (=> (forall @t62 (=> @t74 (tptp.hBOOL (tptp.hAPP @t1 tptp.bool @t52 @t75)))) (tptp.hBOOL (tptp.hAPP @t1 tptp.bool @t52 @t41)))))) % 0.37/0.63 (assume @p43 (forall (@list @t18 @t1 @t52 @t40 @t68 @t64 @t66) (=> @t69 (=> @t67 (=> (forall @t55 (tptp.hBOOL (tptp.hAPP @t18 tptp.bool @t52 @t73))) (tptp.hBOOL (tptp.hAPP @t18 tptp.bool @t52 @t40))))))) % 0.37/0.63 (assume @p44 (tptp.hBOOL tptp.induct_true)) % 0.37/0.63 (assume @p45 (forall @t43 (= (tptp.hBOOL (tptp.hAPP @t1 tptp.bool (tptp.hAPP @t1 @t3 @t7 @t41) @t40)) @t47))) % 0.37/0.63 (assume @p46 (forall (@list @t1 @t18 @t77 @t76) (=> (forall @t55 (= (tptp.hAPP @t1 @t18 @t77 @t53) (tptp.hAPP @t1 @t18 @t76 @t53))) (= (tptp.ti @t24 @t77) (tptp.ti @t24 @t76))))) % 0.37/0.63 (assume @p47 (forall (@list @t1 @t41 @t66) (= (tptp.hBOOL (tptp.hAPP @t3 tptp.bool (tptp.hAPP @t1 (tptp.fun @t3 tptp.bool) (tptp.member @t1) @t41) @t66)) (tptp.hBOOL (tptp.hAPP @t1 tptp.bool @t66 @t41))))) % 0.37/0.63 (assume @p48 (forall (@list @t1 @t52) (= (tptp.hAPP @t3 @t3 @t17 @t52) (tptp.ti @t3 @t52)))) % 0.37/0.63 (assume @p49 (forall @t83 (=> @t82 (tptp.enum @t80)))) % 0.37/0.63 (assume @p50 (tptp.enum tptp.bool)) % 0.37/0.63 (assume @p51 (forall @t83 (=> @t82 (tptp.enum @t84)))) % 0.37/0.63 (assume @p52 (forall @t83 (=> (and (tptp.cl_HOL_Oequal @t78) @t81) (tptp.cl_HOL_Oequal @t84)))) % 0.37/0.63 (assume @p53 (tptp.cl_HOL_Oequal tptp.com)) % 0.37/0.63 (assume @p54 (tptp.cl_HOL_Oequal tptp.bool)) % 0.37/0.63 (assume @p55 (tptp.cl_HOL_Oequal tptp.state)) % 0.37/0.63 (assume @p56 (forall @t83 (tptp.cl_HOL_Oequal @t80))) % 0.37/0.63 (assume @p57 (forall (@list @t78) (tptp.cl_HOL_Oequal (tptp.hoare_509422987triple @t78)))) % 0.37/0.63 (assume @p58 (forall (@list @t86 @t85) (= (tptp.ti @t86 @t87) @t87))) % 0.37/0.63 (assume @p59 (forall @t91 (or (not @t90) @t89))) % 0.37/0.63 (assume @p60 (forall @t91 (or (not @t89) @t90))) % 0.37/0.63 (assume @p61 @t38) % 0.37/0.63 (assume @p62 @t94) % 0.37/0.63 (assume @p63 true) % 0.37/0.63 (step @p64 :rule evaluate :args ((= false true))) % 0.37/0.63 (step @p65 :rule skolem_intro :args ((@purify @t95))) % 0.37/0.63 (step @p66 :rule symm :premises (@p65)) % 0.37/0.63 (step @p67 :rule refl :args (@t96)) % 0.37/0.63 (step @p68 :rule bool-double-not-elim :args (@t93)) % 0.37/0.63 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or (not @t94) @t96))) % 0.37/0.63 (step @p70 :rule bool-double-not-elim :args (@t96)) % 0.37/0.63 (step @p71 :rule refl :args (@t94)) % 0.37/0.63 (step @p72 :rule cong :premises (@p71 @p70) :args ((=> @t94 @t97))) % 0.37/0.63 (assume-push @p103 @t94) % 0.37/0.63 (step @p74 :rule skolemize :premises (@p62)) % 0.37/0.63 (step-pop @p104 :rule scope :premises (@p74)) % 0.37/0.63 (step @p75 :rule process_scope :premises (@p104) :args (@t97)) % 0.37/0.63 (step @p77 :rule eq_resolve :premises (@p75 @p72)) % 0.37/0.63 (step @p78 :rule implies_elim :premises (@p77)) % 0.37/0.63 (step @p79 :rule eq_resolve :premises (@p78 @p69)) % 0.37/0.63 (step @p80 :rule chain_m_resolution :premises (@p79 @p62) :args (@t96 (@list true) (@list @t93))) % 0.37/0.63 (step @p81 :rule instantiate :premises (@p80) :args ((@list (@quantifiers_skolemize @t98 1)))) % 0.37/0.63 (step @p82 :rule trans :premises (@p81 @p66)) % 0.37/0.63 (step @p83 :rule symm :premises (@p82)) % 0.37/0.63 (step @p84 :rule instantiate :premises (@p80) :args ((@list (@quantifiers_skolemize @t98 0)))) % 0.37/0.63 (step @p85 :rule trans :premises (@p84 @p66 @p83)) % 0.37/0.63 (step @p86 :rule true_intro :premises (@p85)) % 0.37/0.63 (step @p87 :rule bool-double-not-elim :args (@t34)) % 0.37/0.63 (step @p88 :rule cong :premises (@p87) :args (@t99)) % 0.37/0.63 (step @p89 :rule cong :premises (@p88) :args (@t100)) % 0.37/0.63 (step @p90 :rule exists-elim :args ((= @t37 @t100))) % 0.37/0.63 (step @p91 :rule trans :premises (@p90 @p89)) % 0.37/0.63 (step @p92 :rule refl :args (@t38)) % 0.37/0.63 (step @p93 :rule cong :premises (@p92 @p91) :args (@t39)) % 0.37/0.63 (step @p94 :rule eq_resolve :premises (@p18 @p93)) % 0.37/0.63 (step @p95 :rule equiv_elim1 :premises (@p94)) % 0.37/0.63 (step @p96 :rule reordering :premises (@p95) :args ((or @t101 (not @t38)))) % 0.37/0.63 (step @p97 :rule chain_m_resolution :premises (@p96 @p61) :args (@t101 (@list false) (@list @t38))) % 0.37/0.63 (step @p98 :rule skolemize :premises (@p97)) % 0.37/0.63 (step @p99 :rule false_intro :premises (@p98)) % 0.37/0.63 (step @p100 :rule symm :premises (@p99)) % 0.37/0.63 (step @p101 :rule trans :premises (@p100 @p86)) % 0.37/0.63 (step @p102 false :rule eq_resolve :premises (@p101 @p64)) % 0.37/0.63 ) % 0.37/0.63 % SZS output end Proof % 0.37/0.63 % cvc5 exiting %------------------------------------------------------------------------------