%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU173+2 : 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 : n016.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 08:50:50 AM UTC 2026 % Result : Theorem 220.19s 220.41s % Output : Proof 220.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU173+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.14/0.32 % Computer : n016.cluster.edu % 0.14/0.32 % Model : x86_64 x86_64 % 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.32 % Memory : 8042.1875MB % 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.32 % CPULimit : 300 % 0.14/0.32 % WCLimit : 300 % 0.14/0.32 % DateTime : Tue Jun 2 16:34:09 EDT 2026 % 0.14/0.32 % CPUTime : % 0.28/0.48 %----Proving TF0_NAR, FOF, or CNF % 220.19/220.41 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 220.19/220.41 --- Run --no-e-matching --full-saturate-quant at 6... % 220.19/220.41 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 220.19/220.41 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 220.19/220.41 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 220.19/220.41 --- Run --trigger-sel=max --full-saturate-quant at 15... % 220.19/220.41 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 220.19/220.41 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 220.19/220.41 --- Run --prenex-quant=none --full-saturate-quant at 30... % 220.19/220.41 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 220.19/220.41 --- Run --relevant-triggers --full-saturate-quant at 30... % 220.19/220.41 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 220.19/220.41 --- Run --pre-skolem-quant=on --full-saturate-quant at 15... % 220.19/220.41 % SZS status Theorem % 220.19/220.41 % SZS output start Proof % 220.19/220.41 ( % 220.19/220.41 (declare-sort $$unsorted 0) % 220.19/220.41 (declare-const tptp.subset_complement (-> $$unsorted $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 220.19/220.41 (declare-const tptp.are_equipotent (-> $$unsorted $$unsorted Bool)) % 220.19/220.41 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 220.19/220.41 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 220.19/220.41 (declare-const tptp.union (-> $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 220.19/220.41 (declare-const tptp.empty_set $$unsorted) % 220.19/220.41 (declare-const tptp.empty (-> $$unsorted Bool)) % 220.19/220.41 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 220.19/220.41 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 220.19/220.41 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 220.19/220.41 (define @t1 () (@var "A" $$unsorted)) % 220.19/220.41 (define @t2 () (@var "B" $$unsorted)) % 220.19/220.41 (define @t3 () (tptp.in @t2 @t1)) % 220.19/220.41 (define @t4 () (not @t3)) % 220.19/220.41 (define @t5 () (tptp.in @t1 @t2)) % 220.19/220.41 (define @t6 () (@list @t1 @t2)) % 220.19/220.41 (define @t7 () (tptp.proper_subset @t2 @t1)) % 220.19/220.41 (define @t8 () (tptp.proper_subset @t1 @t2)) % 220.19/220.41 (define @t9 () (tptp.unordered_pair @t1 @t2)) % 220.19/220.41 (define @t10 () (tptp.set_union2 @t2 @t1)) % 220.19/220.41 (define @t11 () (tptp.set_union2 @t1 @t2)) % 220.19/220.41 (define @t12 () (tptp.set_intersection2 @t1 @t2)) % 220.19/220.41 (define @t13 () (tptp.subset @t1 @t2)) % 220.19/220.41 (define @t14 () (= @t1 @t2)) % 220.19/220.41 (define @t15 () (@var "C" $$unsorted)) % 220.19/220.41 (define @t16 () (tptp.in @t15 @t2)) % 220.19/220.41 (define @t17 () (@list @t15)) % 220.19/220.41 (define @t18 () (tptp.singleton @t1)) % 220.19/220.41 (define @t19 () (@list @t2)) % 220.19/220.41 (define @t20 () (= @t1 tptp.empty_set)) % 220.19/220.41 (define @t21 () (@list @t1)) % 220.19/220.41 (define @t22 () (tptp.powerset @t1)) % 220.19/220.41 (define @t23 () (forall @t6 (= (= @t2 @t22) (forall @t17 (= @t16 (tptp.subset @t15 @t1)))))) % 220.19/220.41 (define @t24 () (tptp.empty @t2)) % 220.19/220.41 (define @t25 () (tptp.element @t2 @t1)) % 220.19/220.41 (define @t26 () (= @t25 @t24)) % 220.19/220.41 (define @t27 () (tptp.empty @t1)) % 220.19/220.41 (define @t28 () (=> @t27 @t26)) % 220.19/220.41 (define @t29 () (not @t27)) % 220.19/220.41 (define @t30 () (=> @t29 (= @t25 @t3))) % 220.19/220.41 (define @t31 () (and @t30 @t28)) % 220.19/220.41 (define @t32 () (forall @t6 @t31)) % 220.19/220.41 (define @t33 () (@var "D" $$unsorted)) % 220.19/220.41 (define @t34 () (tptp.in @t33 @t15)) % 220.19/220.41 (define @t35 () (@list @t33)) % 220.19/220.41 (define @t36 () (@list @t1 @t2 @t15)) % 220.19/220.41 (define @t37 () (tptp.in @t33 @t2)) % 220.19/220.41 (define @t38 () (tptp.in @t33 @t1)) % 220.19/220.41 (define @t39 () (@var "F" $$unsorted)) % 220.19/220.41 (define @t40 () (@var "E" $$unsorted)) % 220.19/220.41 (define @t41 () (tptp.in @t15 @t1)) % 220.19/220.41 (define @t42 () (forall @t17 (=> @t41 @t16))) % 220.19/220.41 (define @t43 () (= @t13 @t42)) % 220.19/220.41 (define @t44 () (forall @t6 @t43)) % 220.19/220.41 (define @t45 () (tptp.set_difference @t1 @t2)) % 220.19/220.41 (define @t46 () (tptp.subset_complement @t1 @t2)) % 220.19/220.41 (define @t47 () (tptp.element @t2 @t22)) % 220.19/220.41 (define @t48 () (tptp.ordered_pair @t1 @t2)) % 220.19/220.41 (define @t49 () (tptp.disjoint @t1 @t2)) % 220.19/220.41 (define @t50 () (not @t14)) % 220.19/220.41 (define @t51 () (tptp.disjoint @t18 @t2)) % 220.19/220.41 (define @t52 () (tptp.singleton @t2)) % 220.19/220.41 (define @t53 () (tptp.in @t1 @t15)) % 220.19/220.41 (define @t54 () (@list @t1 @t2 @t15 @t33)) % 220.19/220.41 (define @t55 () (tptp.element @t1 (tptp.powerset @t2))) % 220.19/220.41 (define @t56 () (=> @t42 @t55)) % 220.19/220.41 (define @t57 () (forall @t6 @t56)) % 220.19/220.41 (define @t58 () (not @t57)) % 220.19/220.41 (define @t59 () (= @t1 @t15)) % 220.19/220.41 (define @t60 () (tptp.cartesian_product2 @t1 @t15)) % 220.19/220.41 (define @t61 () (not @t16)) % 220.19/220.41 (define @t62 () (tptp.subset @t15 @t2)) % 220.19/220.41 (define @t63 () (forall @t17 (not (and @t62 (not (tptp.are_equipotent @t15 @t2)) @t61)))) % 220.19/220.41 (define @t64 () (forall (@list @t15 @t33) (=> (and @t16 (tptp.subset @t33 @t15)) @t37))) % 220.19/220.41 (define @t65 () (tptp.set_intersection2 @t2 @t15)) % 220.19/220.41 (define @t66 () (tptp.subset @t1 @t15)) % 220.19/220.41 (define @t67 () (tptp.in @t2 @t15)) % 220.19/220.41 (define @t68 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 220.19/220.41 (define @t69 () (and @t41 @t16)) % 220.19/220.41 (define @t70 () (not @t49)) % 220.19/220.41 (define @t71 () (tptp.subset_complement @t1 @t15)) % 220.19/220.41 (define @t72 () (tptp.disjoint @t2 @t15)) % 220.19/220.41 (define @t73 () (tptp.element @t15 @t22)) % 220.19/220.41 (define @t74 () (tptp.in @t15 @t12)) % 220.19/220.41 (define @t75 () (= @t18 (tptp.unordered_pair @t2 @t15))) % 220.19/220.41 (define @t76 () (forall @t17 (or (not @t41) @t16))) % 220.19/220.41 (define @t77 () (forall @t6 (or (not @t76) @t55))) % 220.19/220.41 (define @t78 () (@quantifiers_skolemize @t77 1)) % 220.19/220.41 (define @t79 () (tptp.powerset @t78)) % 220.19/220.41 (define @t80 () (forall @t17 (= (tptp.in @t15 @t79) (tptp.subset @t15 @t78)))) % 220.19/220.41 (define @t81 () (= (= @t79 @t79) @t80)) % 220.19/220.41 (define @t82 () (@list false)) % 220.19/220.41 (define @t83 () (@quantifiers_skolemize @t77 0)) % 220.19/220.41 (define @t84 () (or @t29 @t26)) % 220.19/220.41 (define @t85 () (forall @t6 @t84)) % 220.19/220.41 (define @t86 () (@list @t1 @t2)) % 220.19/220.41 (define @t87 () (= @t3 @t25)) % 220.19/220.41 (define @t88 () (or @t27 @t87)) % 220.19/220.41 (define @t89 () (forall @t6 @t88)) % 220.19/220.41 (define @t90 () (@var "BOUND_VARIABLE_7920" $$unsorted)) % 220.19/220.41 (define @t91 () (@var "BOUND_VARIABLE_7918" $$unsorted)) % 220.19/220.41 (define @t92 () (and @t89 @t85)) % 220.19/220.41 (define @t93 () (and (=> @t29 @t87) @t28)) % 220.19/220.41 (define @t94 () (tptp.in @t83 @t79)) % 220.19/220.41 (define @t95 () (tptp.element @t83 @t79)) % 220.19/220.41 (define @t96 () (tptp.empty @t79)) % 220.19/220.41 (define @t97 () (or @t96 (= @t94 @t95))) % 220.19/220.41 (define @t98 () (forall (@list @t91 @t90) (or (tptp.empty @t91) (= (tptp.in @t90 @t91) (tptp.element @t90 @t91))))) % 220.19/220.41 (define @t99 () (= @t95 @t94)) % 220.19/220.41 (define @t100 () (or @t96 @t99)) % 220.19/220.41 (define @t101 () (@list true false)) % 220.19/220.41 (define @t102 () (forall @t17 (or (not (tptp.in @t15 @t83)) (tptp.in @t15 @t78)))) % 220.19/220.41 (define @t103 () (not @t102)) % 220.19/220.41 (define @t104 () (not @t94)) % 220.19/220.41 (define @t105 () (tptp.subset @t83 @t78)) % 220.19/220.41 (define @t106 () (= @t94 @t105)) % 220.19/220.41 (define @t107 () (not @t105)) % 220.19/220.41 (define @t108 () (= @t102 @t105)) % 220.19/220.41 (define @t109 () (not @t108)) % 220.19/220.41 (define @t110 () (forall @t6 (= @t13 @t76))) % 220.19/220.41 (define @t111 () (= @t105 @t102)) % 220.19/220.41 (assume @p1 (forall @t6 (=> @t5 @t4))) % 220.19/220.41 (assume @p2 (forall @t6 (=> @t8 (not @t7)))) % 220.19/220.41 (assume @p3 (forall @t6 (= @t9 (tptp.unordered_pair @t2 @t1)))) % 220.19/220.41 (assume @p4 (forall @t6 (= @t11 @t10))) % 220.19/220.41 (assume @p5 (forall @t6 (= @t12 (tptp.set_intersection2 @t2 @t1)))) % 220.19/220.41 (assume @p6 (forall @t6 (= @t14 (and @t13 (tptp.subset @t2 @t1))))) % 220.19/220.41 (assume @p7 (forall @t6 (= (= @t2 @t18) (forall @t17 (= @t16 (= @t15 @t1)))))) % 220.19/220.41 (assume @p8 (forall @t21 (= @t20 (forall @t19 @t4)))) % 220.19/220.41 (assume @p9 @t23) % 220.19/220.41 (assume @p10 @t32) % 220.19/220.41 (assume @p11 (forall @t36 (= (= @t15 @t9) (forall @t35 (= @t34 (or (= @t33 @t1) (= @t33 @t2))))))) % 220.19/220.41 (assume @p12 (forall @t36 (= (= @t15 @t11) (forall @t35 (= @t34 (or @t38 @t37)))))) % 220.19/220.41 (assume @p13 (forall @t36 (= (= @t15 (tptp.cartesian_product2 @t1 @t2)) (forall @t35 (= @t34 (exists (@list @t40 @t39) (and (tptp.in @t40 @t1) (tptp.in @t39 @t2) (= @t33 (tptp.ordered_pair @t40 @t39))))))))) % 220.19/220.41 (assume @p14 @t44) % 220.19/220.41 (assume @p15 (forall @t36 (= (= @t15 @t12) (forall @t35 (= @t34 (and @t38 @t37)))))) % 220.19/220.41 (assume @p16 (forall @t6 (= (= @t2 (tptp.union @t1)) (forall @t17 (= @t16 (exists @t35 (and (tptp.in @t15 @t33) @t38))))))) % 220.19/220.41 (assume @p17 (forall @t36 (= (= @t15 @t45) (forall @t35 (= @t34 (and @t38 (not @t37))))))) % 220.19/220.41 (assume @p18 (forall @t6 (=> @t47 (= @t46 @t45)))) % 220.19/220.41 (assume @p19 (forall @t6 (= @t48 (tptp.unordered_pair @t9 @t18)))) % 220.19/220.41 (assume @p20 (forall @t6 (= @t49 (= @t12 tptp.empty_set)))) % 220.19/220.41 (assume @p21 (forall @t6 (= @t8 (and @t13 @t50)))) % 220.19/220.41 (assume @p22 true) % 220.19/220.41 (assume @p23 (forall @t6 (=> @t47 (tptp.element @t46 @t22)))) % 220.19/220.41 (assume @p24 (forall @t21 (exists @t19 @t25))) % 220.19/220.41 (assume @p25 (forall @t21 (not (tptp.empty @t22)))) % 220.19/220.41 (assume @p26 (tptp.empty tptp.empty_set)) % 220.19/220.41 (assume @p27 (forall @t6 (not (tptp.empty @t48)))) % 220.19/220.41 (assume @p28 (forall @t6 (=> @t29 (not (tptp.empty @t11))))) % 220.19/220.41 (assume @p29 (forall @t6 (=> @t29 (not (tptp.empty @t10))))) % 220.19/220.41 (assume @p30 (forall @t6 (= (tptp.set_union2 @t1 @t1) @t1))) % 220.19/220.41 (assume @p31 (forall @t6 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 220.19/220.41 (assume @p32 (forall @t6 (=> @t47 (= (tptp.subset_complement @t1 @t46) @t2)))) % 220.19/220.41 (assume @p33 (forall @t6 (not (tptp.proper_subset @t1 @t1)))) % 220.19/220.41 (assume @p34 (forall @t21 (not (= @t18 tptp.empty_set)))) % 220.19/220.41 (assume @p35 (forall @t6 (=> @t5 (= (tptp.set_union2 @t18 @t2) @t2)))) % 220.19/220.41 (assume @p36 (forall @t6 (not (and @t51 @t5)))) % 220.19/220.41 (assume @p37 (forall @t6 (=> (not @t5) @t51))) % 220.19/220.41 (assume @p38 (forall @t6 (= (tptp.subset @t18 @t2) @t5))) % 220.19/220.41 (assume @p39 (forall @t6 (= (= @t45 tptp.empty_set) @t13))) % 220.19/220.41 (assume @p40 (forall @t6 (=> @t47 (forall @t17 (=> @t16 @t41))))) % 220.19/220.41 (assume @p41 (forall @t36 (=> @t13 (or @t41 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t15))))))) % 220.19/220.41 (assume @p42 (forall @t6 (= (tptp.subset @t1 @t52) (or @t20 (= @t1 @t52))))) % 220.19/220.41 (assume @p43 (forall @t6 (=> @t5 (tptp.subset @t1 (tptp.union @t2))))) % 220.19/220.41 (assume @p44 (forall @t54 (= (tptp.in @t48 (tptp.cartesian_product2 @t15 @t33)) (and @t53 (tptp.in @t2 @t33))))) % 220.19/220.41 (assume @p45 @t58) % 220.19/220.41 (assume @p46 (forall @t21 (=> @t29 (exists @t19 (and @t47 (not @t24)))))) % 220.19/220.41 (assume @p47 (exists @t21 @t27)) % 220.19/220.41 (assume @p48 (forall @t21 (exists @t19 (and @t47 @t24)))) % 220.19/220.41 (assume @p49 (exists @t21 @t29)) % 220.19/220.41 (assume @p50 (forall @t6 (tptp.subset @t1 @t1))) % 220.19/220.41 (assume @p51 (forall @t6 (=> @t49 (tptp.disjoint @t2 @t1)))) % 220.19/220.41 (assume @p52 (forall @t54 (not (and (= @t9 (tptp.unordered_pair @t15 @t33)) (not @t59) (not (= @t1 @t33)))))) % 220.19/220.41 (assume @p53 (forall @t36 (=> @t13 (and (tptp.subset @t60 (tptp.cartesian_product2 @t2 @t15)) (tptp.subset (tptp.cartesian_product2 @t15 @t1) (tptp.cartesian_product2 @t15 @t2)))))) % 220.19/220.41 (assume @p54 (forall @t54 (=> (and @t13 (tptp.subset @t15 @t33)) (tptp.subset @t60 (tptp.cartesian_product2 @t2 @t33))))) % 220.19/220.41 (assume @p55 (forall @t6 (=> @t13 (= @t11 @t2)))) % 220.19/220.41 (assume @p56 (forall @t21 (exists @t19 (and @t5 @t64 (forall @t17 (=> @t16 (tptp.in (tptp.powerset @t15) @t2))) @t63)))) % 220.19/220.41 (assume @p57 (forall @t6 (tptp.subset @t12 @t1))) % 220.19/220.41 (assume @p58 (forall @t36 (=> (and @t13 @t66) (tptp.subset @t1 @t65)))) % 220.19/220.41 (assume @p59 (forall @t21 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 220.19/220.41 (assume @p60 (forall @t36 (=> (and @t13 (tptp.subset @t2 @t15)) @t66))) % 220.19/220.41 (assume @p61 (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set))) % 220.19/220.41 (assume @p62 (forall @t36 (=> @t13 (tptp.subset (tptp.set_intersection2 @t1 @t15) @t65)))) % 220.19/220.41 (assume @p63 (forall @t6 (=> @t13 (= @t12 @t1)))) % 220.19/220.41 (assume @p64 (forall @t21 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 220.19/220.41 (assume @p65 (forall @t6 (=> (forall @t17 (= @t41 @t16)) @t14))) % 220.19/220.41 (assume @p66 (forall @t21 (tptp.subset tptp.empty_set @t1))) % 220.19/220.41 (assume @p67 (forall @t36 (=> @t13 (tptp.subset (tptp.set_difference @t1 @t15) (tptp.set_difference @t2 @t15))))) % 220.19/220.41 (assume @p68 (forall @t54 (=> (= @t48 (tptp.ordered_pair @t15 @t33)) (and @t59 (= @t2 @t33))))) % 220.19/220.41 (assume @p69 (forall @t6 (tptp.subset @t45 @t1))) % 220.19/220.41 (assume @p70 (forall @t36 (= (tptp.subset @t9 @t15) (and @t53 @t67)))) % 220.19/220.41 (assume @p71 (forall @t6 (= @t68 @t11))) % 220.19/220.41 (assume @p72 (forall @t21 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 220.19/220.41 (assume @p73 (forall @t6 (and (not (and @t70 (forall @t17 (not @t69)))) (not (and (exists @t17 @t69) @t49))))) % 220.19/220.41 (assume @p74 (forall @t21 (=> (tptp.subset @t1 tptp.empty_set) @t20))) % 220.19/220.41 (assume @p75 (forall @t6 (= (tptp.set_difference @t11 @t2) @t45))) % 220.19/220.41 (assume @p76 (forall @t6 (=> @t47 (forall @t17 (=> @t73 (= @t72 (tptp.subset @t2 @t71))))))) % 220.19/220.41 (assume @p77 (forall @t6 (=> @t13 (= @t2 @t68)))) % 220.19/220.41 (assume @p78 (forall @t6 (= (tptp.set_difference @t1 @t45) @t12))) % 220.19/220.41 (assume @p79 (forall @t21 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 220.19/220.41 (assume @p80 (forall @t6 (and (not (and @t70 (forall @t17 (not @t74)))) (not (and (exists @t17 @t74) @t49))))) % 220.19/220.41 (assume @p81 (forall @t21 (=> (not @t20) (forall @t19 (=> @t47 (forall @t17 (=> (tptp.element @t15 @t1) (=> @t61 (tptp.in @t15 @t46))))))))) % 220.19/220.41 (assume @p82 (forall @t36 (=> @t73 (not (and (tptp.in @t2 @t71) @t67))))) % 220.19/220.41 (assume @p83 (forall @t6 (not (and @t13 @t7)))) % 220.19/220.41 (assume @p84 (forall @t36 (=> (and @t13 @t72) (tptp.disjoint @t1 @t15)))) % 220.19/220.41 (assume @p85 (forall @t6 (= (= (tptp.set_difference @t1 @t52) @t1) @t4))) % 220.19/220.41 (assume @p86 (forall @t21 (= (tptp.unordered_pair @t1 @t1) @t18))) % 220.19/220.41 (assume @p87 (forall @t21 (=> @t27 @t20))) % 220.19/220.41 (assume @p88 (forall @t6 (=> (tptp.subset @t18 @t52) @t14))) % 220.19/220.41 (assume @p89 (forall @t6 (not (and @t5 @t24)))) % 220.19/220.41 (assume @p90 (forall @t6 (tptp.subset @t1 @t11))) % 220.19/220.41 (assume @p91 (forall @t6 (= @t49 (= @t45 @t1)))) % 220.19/220.41 (assume @p92 (forall @t6 (not (and @t27 @t50 @t24)))) % 220.19/220.41 (assume @p93 (forall @t36 (=> (and @t13 @t62) (tptp.subset (tptp.set_union2 @t1 @t15) @t2)))) % 220.19/220.41 (assume @p94 (forall @t36 (=> @t75 @t14))) % 220.19/220.41 (assume @p95 (forall @t21 (= (tptp.union @t22) @t1))) % 220.19/220.41 (assume @p96 (forall @t21 (exists @t19 (and @t5 @t64 (forall @t17 (not (and @t16 (forall @t35 (not (and @t37 (forall (@list @t40) (=> (tptp.subset @t40 @t15) (tptp.in @t40 @t33))))))))) @t63)))) % 220.19/220.41 (assume @p97 (forall @t36 (=> @t75 (= @t2 @t15)))) % 220.19/220.41 (step @p98 :rule bool-impl-elim :args (@t41 @t16)) % 220.19/220.41 (step @p99 :rule cong :premises (@p98) :args (@t42)) % 220.19/220.41 (step @p100 :rule refl :args (@t13)) % 220.19/220.41 (step @p101 :rule cong :premises (@p100 @p99) :args (@t43)) % 220.19/220.41 (step @p102 :rule cong :premises (@p101) :args (@t44)) % 220.19/220.41 (step @p103 :rule eq_resolve :premises (@p14 @p102)) % 220.19/220.41 (step @p104 :rule bool-eq-true :args (@t80)) % 220.19/220.41 (step @p105 :rule eq-symm :args (true @t80)) % 220.19/220.41 (step @p106 :rule trans :premises (@p105 @p104)) % 220.19/220.41 (step @p107 :rule refl :args (@t80)) % 220.19/220.41 (step @p108 :rule eq-refl :args (@t79)) % 220.19/220.41 (step @p109 :rule cong :premises (@p108 @p107) :args (@t81)) % 220.19/220.41 (step @p110 :rule trans :premises (@p109 @p106)) % 220.19/220.41 (step @p111 :rule refl :args (@t23)) % 220.19/220.41 (step @p112 :rule cong :premises (@p111 @p110) :args ((=> @t23 @t81))) % 220.19/220.41 (assume-push @p192 @t23) % 220.19/220.41 (step @p114 :rule instantiate :premises (@p9) :args ((@list @t78 @t79))) % 220.19/220.41 (step-pop @p193 :rule scope :premises (@p114)) % 220.19/220.41 (step @p115 :rule process_scope :premises (@p193) :args (@t81)) % 220.19/220.41 (step @p117 :rule eq_resolve :premises (@p115 @p112)) % 220.19/220.41 (step @p118 :rule implies_elim :premises (@p117)) % 220.19/220.41 (step @p119 :rule chain_m_resolution :premises (@p118 @p9) :args (@t80 @t82 (@list @t23))) % 220.19/220.41 (step @p120 :rule instantiate :premises (@p119) :args ((@list @t83))) % 220.19/220.41 (step @p121 :rule alpha_equiv :args (@t85 @t86 (@list (@var "BOUND_VARIABLE_7929" $$unsorted) (@var "BOUND_VARIABLE_7931" $$unsorted)))) % 220.19/220.41 (step @p122 :rule alpha_equiv :args (@t89 @t86 (@list @t91 @t90))) % 220.19/220.41 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t92)) % 220.19/220.41 (step @p124 :rule quant-miniscope-and :args ((= (forall @t6 (and @t88 @t84)) @t92))) % 220.19/220.41 (step @p125 :rule trans :premises (@p124 @p123)) % 220.19/220.41 (step @p126 :rule bool-impl-elim :args (@t27 @t26)) % 220.19/220.41 (step @p127 :rule refl :args (@t87)) % 220.19/220.41 (step @p128 :rule bool-double-not-elim :args (@t27)) % 220.19/220.41 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or (not @t29) @t87))) % 220.19/220.41 (step @p130 :rule bool-impl-elim :args (@t29 @t87)) % 220.19/220.41 (step @p131 :rule trans :premises (@p130 @p129)) % 220.19/220.41 (step @p132 :rule nary_cong :premises (@p131 @p126) :args (@t93)) % 220.19/220.41 (step @p133 :rule cong :premises (@p132) :args ((forall @t6 @t93))) % 220.19/220.41 (step @p134 :rule trans :premises (@p133 @p125)) % 220.19/220.41 (step @p135 :rule refl :args (@t28)) % 220.19/220.41 (step @p136 :rule eq-symm :args (@t25 @t3)) % 220.19/220.41 (step @p137 :rule refl :args (@t29)) % 220.19/220.41 (step @p138 :rule cong :premises (@p137 @p136) :args (@t30)) % 220.19/220.41 (step @p139 :rule nary_cong :premises (@p138 @p135) :args (@t31)) % 220.19/220.41 (step @p140 :rule cong :premises (@p139) :args (@t32)) % 220.19/220.41 (step @p141 :rule trans :premises (@p140 @p134)) % 220.19/220.41 (step @p142 :rule eq_resolve :premises (@p10 @p141)) % 220.19/220.41 (step @p143 :rule and_elim :premises (@p142) :args (0)) % 220.19/220.41 (step @p144 :rule eq-symm :args (@t94 @t95)) % 220.19/220.41 (step @p145 :rule refl :args (@t96)) % 220.19/220.41 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t97)) % 220.19/220.41 (step @p147 :rule refl :args (@t98)) % 220.19/220.41 (step @p148 :rule cong :premises (@p147 @p146) :args ((=> @t98 @t97))) % 220.19/220.41 (assume-push @p194 @t98) % 220.19/220.41 (step @p150 :rule instantiate :premises (@p143) :args ((@list @t79 @t83))) % 220.19/220.41 (step-pop @p195 :rule scope :premises (@p150)) % 220.19/220.41 (step @p151 :rule process_scope :premises (@p195) :args (@t97)) % 220.19/220.41 (step @p153 :rule eq_resolve :premises (@p151 @p148)) % 220.19/220.41 (step @p154 :rule implies_elim :premises (@p153)) % 220.19/220.41 (step @p155 :rule chain_m_resolution :premises (@p154 @p143) :args (@t100 @t82 (@list @t98))) % 220.19/220.41 (step @p156 :rule instantiate :premises (@p25) :args ((@list @t78))) % 220.19/220.41 (step @p157 :rule cnf_or_pos :args (@t100)) % 220.19/220.41 (step @p158 :rule reordering :premises (@p157) :args ((or @t96 @t99 (not @t100)))) % 220.19/220.41 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p155) :args (@t99 @t101 (@list @t96 @t100))) % 220.19/220.41 ; WARNING: add trust step for TRUST % 220.19/220.41 ; trust TRUST PREPROCESS_QUANTIFIERS_PP % 220.19/220.41 (step @p160 :rule trust :premises () :args ((= (not @t77) (not (or @t103 @t95))))) % 220.19/220.41 (step @p161 :rule bool-impl-elim :args (@t76 @t55)) % 220.19/220.41 (step @p162 :rule cong :premises (@p161) :args ((forall @t6 (=> @t76 @t55)))) % 220.19/220.41 (step @p163 :rule refl :args (@t55)) % 220.19/220.41 (step @p164 :rule cong :premises (@p99 @p163) :args (@t56)) % 220.19/220.41 (step @p165 :rule cong :premises (@p164) :args (@t57)) % 220.19/220.41 (step @p166 :rule trans :premises (@p165 @p162)) % 220.19/220.41 (step @p167 :rule cong :premises (@p166) :args (@t58)) % 220.19/220.41 (step @p168 :rule trans :premises (@p167 @p160)) % 220.19/220.41 (step @p169 :rule eq_resolve :premises (@p45 @p168)) % 220.19/220.41 (step @p170 :rule not_or_elim :premises (@p169) :args (1)) % 220.19/220.41 (step @p171 :rule cnf_equiv_pos2 :args (@t99)) % 220.19/220.41 (step @p172 :rule reordering :premises (@p171) :args ((or @t95 @t104 (not @t99)))) % 220.19/220.41 (step @p173 :rule chain_m_resolution :premises (@p172 @p170 @p159) :args (@t104 @t101 (@list @t95 @t99))) % 220.19/220.41 (step @p174 :rule cnf_equiv_pos2 :args (@t106)) % 220.19/220.41 (step @p175 :rule reordering :premises (@p174) :args ((or @t94 @t107 (not @t106)))) % 220.19/220.41 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p120) :args (@t107 @t101 (@list @t94 @t106))) % 220.19/220.41 (step @p177 :rule not_or_elim :premises (@p169) :args (0)) % 220.19/220.41 (step @p178 :rule not_not_elim :premises (@p177)) % 220.19/220.41 (step @p179 :rule cnf_equiv_pos1 :args (@t108)) % 220.19/220.41 (step @p180 :rule reordering :premises (@p179) :args ((or @t103 @t105 @t109))) % 220.19/220.41 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p176) :args (@t109 (@list false true) (@list @t102 @t105))) % 220.19/220.41 (step @p182 :rule eq-symm :args (@t105 @t102)) % 220.19/220.41 (step @p183 :rule refl :args (@t110)) % 220.19/220.41 (step @p184 :rule cong :premises (@p183 @p182) :args ((=> @t110 @t111))) % 220.19/220.41 (assume-push @p196 @t110) % 220.19/220.41 (step @p186 :rule instantiate :premises (@p103) :args ((@list @t83 @t78))) % 220.19/220.41 (step-pop @p197 :rule scope :premises (@p186)) % 220.19/220.41 (step @p187 :rule process_scope :premises (@p197) :args (@t111)) % 220.19/220.41 (step @p189 :rule eq_resolve :premises (@p187 @p184)) % 220.19/220.41 (step @p190 :rule implies_elim :premises (@p189)) % 220.19/220.41 (step @p191 false :rule chain_m_resolution :premises (@p190 @p181 @p103) :args (false @t101 (@list @t108 @t110))) % 220.19/220.41 ) % 220.19/220.41 % SZS output end Proof % 220.19/220.41 % cvc5 exiting %------------------------------------------------------------------------------