%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KRS216+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:29:08 AM UTC 2026 % Result : Theorem 209.18s 209.50s % Output : Proof 209.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS216+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 05:28:59 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 209.18/209.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 209.18/209.50 --- Run --no-e-matching --full-saturate-quant at 6... % 209.18/209.50 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 209.18/209.50 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 209.18/209.50 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 209.18/209.50 --- Run --trigger-sel=max --full-saturate-quant at 15... % 209.18/209.50 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 209.18/209.50 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 209.18/209.50 --- Run --prenex-quant=none --full-saturate-quant at 30... % 209.18/209.50 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 209.18/209.50 --- Run --relevant-triggers --full-saturate-quant at 30... % 209.18/209.50 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 209.18/209.50 % SZS status Theorem % 209.18/209.50 % SZS output start Proof % 209.18/209.50 ( % 209.18/209.50 (declare-sort $$unsorted 0) % 209.18/209.50 (declare-const tptp.xora (-> $$unsorted $$unsorted Bool)) % 209.18/209.50 (declare-const tptp.nevera (-> $$unsorted $$unsorted Bool)) % 209.18/209.51 (declare-const tptp.nota (-> $$unsorted $$unsorted Bool)) % 209.18/209.51 (declare-const tptp.mighta (-> $$unsorted $$unsorted Bool)) % 209.18/209.51 (declare-const tptp.noc $$unsorted) % 209.18/209.51 (declare-const tptp.uns $$unsorted) % 209.18/209.51 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 209.18/209.51 (declare-const tptp.tca $$unsorted) % 209.18/209.51 (declare-const tptp.sca $$unsorted) % 209.18/209.51 (declare-const tptp.wth $$unsorted) % 209.18/209.51 (declare-const tptp.unp $$unsorted) % 209.18/209.51 (declare-const tptp.wca $$unsorted) % 209.18/209.51 (declare-const tptp.wec $$unsorted) % 209.18/209.51 (declare-const tptp.sap $$unsorted) % 209.18/209.51 (declare-const tptp.wtc $$unsorted) % 209.18/209.51 (declare-const tptp.model (-> $$unsorted $$unsorted Bool)) % 209.18/209.51 (declare-const tptp.sat $$unsorted) % 209.18/209.51 (declare-const tptp.cax $$unsorted) % 209.18/209.51 (declare-const tptp.eqv $$unsorted) % 209.18/209.51 (declare-const tptp.esa $$unsorted) % 209.18/209.51 (declare-const tptp.csa $$unsorted) % 209.18/209.51 (declare-const tptp.status (-> $$unsorted $$unsorted $$unsorted Bool)) % 209.18/209.51 (declare-const tptp.thm $$unsorted) % 209.18/209.51 (declare-const tptp.isa (-> $$unsorted $$unsorted Bool)) % 209.18/209.51 (declare-const tptp.eth $$unsorted) % 209.18/209.51 (declare-const tptp.tac $$unsorted) % 209.18/209.51 (declare-const tptp.tau $$unsorted) % 209.18/209.51 (define @t1 () (@var "C" $$unsorted)) % 209.18/209.51 (define @t2 () (@var "Ax" $$unsorted)) % 209.18/209.51 (define @t3 () (@var "I2" $$unsorted)) % 209.18/209.51 (define @t4 () (tptp.model @t3 @t1)) % 209.18/209.51 (define @t5 () (@list @t3)) % 209.18/209.51 (define @t6 () (exists @t5 @t4)) % 209.18/209.51 (define @t7 () (@var "I1" $$unsorted)) % 209.18/209.51 (define @t8 () (tptp.model @t7 @t2)) % 209.18/209.51 (define @t9 () (@list @t7)) % 209.18/209.51 (define @t10 () (exists @t9 @t8)) % 209.18/209.51 (define @t11 () (not @t10)) % 209.18/209.51 (define @t12 () (@list @t2 @t1)) % 209.18/209.51 (define @t13 () (tptp.model @t7 @t1)) % 209.18/209.51 (define @t14 () (and @t8 @t13)) % 209.18/209.51 (define @t15 () (exists @t9 @t14)) % 209.18/209.51 (define @t16 () (tptp.status @t2 @t1 tptp.thm)) % 209.18/209.51 (define @t17 () (forall @t9 (=> @t8 @t13))) % 209.18/209.51 (define @t18 () (= @t17 @t16)) % 209.18/209.51 (define @t19 () (forall @t12 @t18)) % 209.18/209.51 (define @t20 () (tptp.model @t3 @t2)) % 209.18/209.51 (define @t21 () (forall @t5 @t4)) % 209.18/209.51 (define @t22 () (@var "I3" $$unsorted)) % 209.18/209.51 (define @t23 () (tptp.model @t22 @t2)) % 209.18/209.51 (define @t24 () (not @t23)) % 209.18/209.51 (define @t25 () (tptp.model @t22 @t1)) % 209.18/209.51 (define @t26 () (@list @t22)) % 209.18/209.51 (define @t27 () (exists @t26 (and @t25 @t24))) % 209.18/209.51 (define @t28 () (forall @t5 (=> @t20 @t4))) % 209.18/209.51 (define @t29 () (not @t20)) % 209.18/209.51 (define @t30 () (exists @t5 @t29)) % 209.18/209.51 (define @t31 () (@var "I4" $$unsorted)) % 209.18/209.51 (define @t32 () (exists (@list @t31) (not (tptp.model @t31 @t1)))) % 209.18/209.51 (define @t33 () (tptp.not @t1)) % 209.18/209.51 (define @t34 () (tptp.model @t3 @t33)) % 209.18/209.51 (define @t35 () (forall @t12 (= (and (forall @t9 @t8) (forall @t5 @t34)) (tptp.status @t2 @t1 tptp.uns)))) % 209.18/209.51 (define @t36 () (@var "S2" $$unsorted)) % 209.18/209.51 (define @t37 () (@var "S1" $$unsorted)) % 209.18/209.51 (define @t38 () (tptp.status @t2 @t1 @t36)) % 209.18/209.51 (define @t39 () (tptp.status @t2 @t1 @t37)) % 209.18/209.51 (define @t40 () (@list @t37 @t36)) % 209.18/209.51 (define @t41 () (tptp.nota @t37 @t36)) % 209.18/209.51 (define @t42 () (not @t38)) % 209.18/209.51 (define @t43 () (and @t39 @t42)) % 209.18/209.51 (define @t44 () (exists @t12 @t43)) % 209.18/209.51 (define @t45 () (= @t44 @t41)) % 209.18/209.51 (define @t46 () (forall @t40 @t45)) % 209.18/209.51 (define @t47 () (@var "F" $$unsorted)) % 209.18/209.51 (define @t48 () (tptp.not @t47)) % 209.18/209.51 (define @t49 () (@var "I" $$unsorted)) % 209.18/209.51 (define @t50 () (tptp.model @t49 @t48)) % 209.18/209.51 (define @t51 () (tptp.model @t49 @t47)) % 209.18/209.51 (define @t52 () (@list @t49 @t47)) % 209.18/209.51 (define @t53 () (forall @t52 (xor @t51 @t50))) % 209.18/209.51 (define @t54 () (@list @t49)) % 209.18/209.51 (define @t55 () (forall @t54 @t51)) % 209.18/209.51 (define @t56 () (@list @t47)) % 209.18/209.51 (define @t57 () (exists @t56 @t55)) % 209.18/209.51 (define @t58 () (not @t51)) % 209.18/209.51 (define @t59 () (forall @t54 @t58)) % 209.18/209.51 (define @t60 () (exists @t56 @t59)) % 209.18/209.51 (define @t61 () (not (tptp.nota tptp.uns tptp.thm))) % 209.18/209.51 (define @t62 () (@var "b_I" it_8_$$unsorted)) % 209.18/209.51 (define @t63 () (@const 0 (-> it_8_$$unsorted $$unsorted Bool))) % 209.18/209.51 (define @t64 () (@list @t62)) % 209.18/209.51 (define @t65 () (forall @t56 (not (forall @t64 (_ @t63 @t62 @t47))))) % 209.18/209.51 (define @t66 () (not @t65)) % 209.18/209.51 (define @t67 () (not (forall @t56 (not @t55)))) % 209.18/209.51 (define @t68 () (@quantifiers_skolemize @t65 0)) % 209.18/209.51 (define @t69 () (forall @t64 (_ @t63 @t62 @t68))) % 209.18/209.51 (define @t70 () (not (not @t69))) % 209.18/209.51 (define @t71 () (@list true)) % 209.18/209.51 (define @t72 () (@var "b_I" it_8_$$unsorted)) % 209.18/209.51 (define @t73 () (@list @t72)) % 209.18/209.51 (define @t74 () (forall @t56 (not (forall @t73 (not (_ @t63 @t72 @t47)))))) % 209.18/209.51 (define @t75 () (@quantifiers_skolemize @t74 0)) % 209.18/209.51 (define @t76 () (tptp.not @t75)) % 209.18/209.51 (define @t77 () (@var "b_I2" it_8_$$unsorted)) % 209.18/209.51 (define @t78 () (@list @t77)) % 209.18/209.51 (define @t79 () (forall @t78 (_ @t63 @t77 @t76))) % 209.18/209.51 (define @t80 () (@quantifiers_skolemize @t79 0)) % 209.18/209.51 (define @t81 () (@list @t80)) % 209.18/209.51 (define @t82 () (not @t74)) % 209.18/209.51 (define @t83 () (not (forall @t56 (not @t59)))) % 209.18/209.51 (define @t84 () (forall @t73 (not (_ @t63 @t72 @t75)))) % 209.18/209.51 (define @t85 () (not (not @t84))) % 209.18/209.51 (define @t86 () (@var "b_I1" it_8_$$unsorted)) % 209.18/209.51 (define @t87 () (forall (@list @t86) (or (not (_ @t63 @t86 @t75)) (not (_ @t63 @t86 @t68))))) % 209.18/209.51 (define @t88 () (@quantifiers_skolemize @t87 0)) % 209.18/209.51 (define @t89 () (_ @t63 @t88 @t75)) % 209.18/209.51 (define @t90 () (not @t89)) % 209.18/209.51 (define @t91 () (or @t90 (not (_ @t63 @t88 @t68)))) % 209.18/209.51 (define @t92 () (not @t91)) % 209.18/209.51 (define @t93 () (not @t87)) % 209.18/209.51 (define @t94 () (@list false)) % 209.18/209.51 (define @t95 () (_ @t63 @t80 @t68)) % 209.18/209.51 (define @t96 () (not @t95)) % 209.18/209.51 (define @t97 () (_ @t63 @t80 @t75)) % 209.18/209.51 (define @t98 () (not @t97)) % 209.18/209.51 (define @t99 () (or @t98 @t96)) % 209.18/209.51 (define @t100 () (@var "b_I" it_8_$$unsorted)) % 209.18/209.51 (define @t101 () (@var "b_I1" it_8_$$unsorted)) % 209.18/209.51 (define @t102 () (@list @t101)) % 209.18/209.51 (define @t103 () (forall @t102 (_ @t63 @t101 @t68))) % 209.18/209.51 (define @t104 () (@const 1 it_7_$$unsorted)) % 209.18/209.51 (define @t105 () (@const 2 (-> $$unsorted $$unsorted it_7_$$unsorted Bool))) % 209.18/209.51 (define @t106 () (_ @t105 @t2 @t1 @t104)) % 209.18/209.51 (define @t107 () (@list @t68 @t75)) % 209.18/209.51 (define @t108 () (@var "b_S2" it_7_$$unsorted)) % 209.18/209.51 (define @t109 () (@var "b_S1" it_7_$$unsorted)) % 209.18/209.51 (define @t110 () (@const 3 (-> it_7_$$unsorted it_7_$$unsorted Bool))) % 209.18/209.51 (define @t111 () (not @t39)) % 209.18/209.51 (define @t112 () (not (forall @t12 (or @t111 @t38)))) % 209.18/209.51 (define @t113 () (forall @t12 (not @t43))) % 209.18/209.51 (define @t114 () (not @t113)) % 209.18/209.51 (define @t115 () (@const 4 it_7_$$unsorted)) % 209.18/209.51 (define @t116 () (_ @t110 @t104 @t115)) % 209.18/209.51 (define @t117 () (_ @t105 @t2 @t1 @t115)) % 209.18/209.51 (define @t118 () (forall @t12 (or (not @t106) @t117))) % 209.18/209.51 (define @t119 () (not @t118)) % 209.18/209.51 (define @t120 () (= @t116 @t119)) % 209.18/209.51 (define @t121 () (not @t120)) % 209.18/209.51 (define @t122 () (@list true false)) % 209.18/209.51 (define @t123 () (@var "b_I1" it_8_$$unsorted)) % 209.18/209.51 (define @t124 () (@list @t123)) % 209.18/209.51 (define @t125 () (forall @t9 (or (not @t8) @t13))) % 209.18/209.51 (define @t126 () (@var "b_BOUND_VARIABLE_7854" it_8_$$unsorted)) % 209.18/209.51 (define @t127 () (@var "b_BOUND_VARIABLE_7850" it_8_$$unsorted)) % 209.18/209.51 (define @t128 () (@quantifiers_skolemize (forall (@list @t47 @t127 @t126) (or (not (_ @t63 @t127 @t47)) (_ @t63 @t126 @t47))) 1)) % 209.18/209.51 (define @t129 () (@list @t128)) % 209.18/209.51 (define @t130 () (_ @t63 @t128 @t75)) % 209.18/209.51 (define @t131 () (_ @t63 @t128 @t68)) % 209.18/209.51 (define @t132 () (not @t131)) % 209.18/209.51 (define @t133 () (or @t132 @t130)) % 209.18/209.51 (define @t134 () (not @t133)) % 209.18/209.51 (define @t135 () (forall @t124 (or (not (_ @t63 @t123 @t68)) (_ @t63 @t123 @t75)))) % 209.18/209.51 (define @t136 () (_ @t105 @t68 @t75 @t115)) % 209.18/209.51 (define @t137 () (= @t136 @t135)) % 209.18/209.51 (define @t138 () (not @t136)) % 209.18/209.51 (define @t139 () (_ @t105 @t68 @t75 @t104)) % 209.18/209.51 (define @t140 () (not @t139)) % 209.18/209.51 (define @t141 () (or @t140 @t136)) % 209.18/209.51 (define @t142 () (and @t103 @t79)) % 209.18/209.51 (define @t143 () (= @t142 @t139)) % 209.18/209.51 (define @t144 () (not @t142)) % 209.18/209.51 (define @t145 () (not @t79)) % 209.18/209.51 (define @t146 () (_ @t63 @t80 @t76)) % 209.18/209.51 (define @t147 () (not @t146)) % 209.18/209.51 (define @t148 () (= @t146 @t98)) % 209.18/209.51 (define @t149 () (not @t148)) % 209.18/209.51 (assume @p1 (forall @t12 (= (=> @t11 (not @t6)) (tptp.status @t2 @t1 tptp.unp)))) % 209.18/209.51 (assume @p2 (forall @t12 (= (=> @t10 @t6) (tptp.status @t2 @t1 tptp.sap)))) % 209.18/209.51 (assume @p3 (forall @t12 (= (= @t10 @t6) (tptp.status @t2 @t1 tptp.esa)))) % 209.18/209.51 (assume @p4 (forall @t12 (= @t15 (tptp.status @t2 @t1 tptp.sat)))) % 209.18/209.51 (assume @p5 @t19) % 209.18/209.51 (assume @p6 (forall @t12 (= (and @t10 (forall @t5 (= @t20 @t4))) (tptp.status @t2 @t1 tptp.eqv)))) % 209.18/209.51 (assume @p7 (forall @t12 (= (and @t10 @t21) (tptp.status @t2 @t1 tptp.tac)))) % 209.18/209.51 (assume @p8 (forall @t12 (= (and @t10 @t28 @t27) (tptp.status @t2 @t1 tptp.wec)))) % 209.18/209.51 (assume @p9 (forall @t12 (= (and @t10 @t30 (forall @t26 (= @t23 @t25))) (tptp.status @t2 @t1 tptp.eth)))) % 209.18/209.51 (assume @p10 (forall @t12 (= (forall @t9 @t14) (tptp.status @t2 @t1 tptp.tau)))) % 209.18/209.51 (assume @p11 (forall @t12 (= (and @t10 @t30 (forall @t26 @t25)) (tptp.status @t2 @t1 tptp.wtc)))) % 209.18/209.51 (assume @p12 (forall @t12 (= (and @t10 @t28 @t27 @t32) (tptp.status @t2 @t1 tptp.wth)))) % 209.18/209.51 (assume @p13 (forall @t12 (= @t11 (tptp.status @t2 @t1 tptp.cax)))) % 209.18/209.51 (assume @p14 (forall @t12 (= (and @t11 @t6) (tptp.status @t2 @t1 tptp.sca)))) % 209.18/209.51 (assume @p15 (forall @t12 (= (and @t11 @t21) (tptp.status @t2 @t1 tptp.tca)))) % 209.18/209.51 (assume @p16 (forall @t12 (= (and @t11 @t6 (exists @t26 (not @t25))) (tptp.status @t2 @t1 tptp.wca)))) % 209.18/209.51 (assume @p17 (forall @t12 (= (exists @t9 (and @t8 (tptp.model @t7 @t33))) (tptp.status @t2 @t1 tptp.csa)))) % 209.18/209.51 (assume @p18 @t35) % 209.18/209.51 (assume @p19 (forall @t12 (= (and @t15 (exists @t5 (and @t20 @t34))) (tptp.status @t2 @t1 tptp.noc)))) % 209.18/209.51 (assume @p20 (forall @t40 (= (exists @t12 (and @t39 @t38)) (tptp.mighta @t37 @t36)))) % 209.18/209.51 (assume @p21 (forall @t40 (= (forall @t12 (=> @t39 @t38)) (tptp.isa @t37 @t36)))) % 209.18/209.51 (assume @p22 @t46) % 209.18/209.51 (assume @p23 (forall @t40 (= (forall @t12 (=> @t39 @t42)) (tptp.nevera @t37 @t36)))) % 209.18/209.51 (assume @p24 (forall @t40 (= (forall @t12 (xor @t39 @t38)) (tptp.xora @t37 @t36)))) % 209.18/209.51 (assume @p25 @t53) % 209.18/209.51 (assume @p26 (forall @t52 (= @t51 (not @t50)))) % 209.18/209.51 (assume @p27 @t57) % 209.18/209.51 (assume @p28 (exists @t56 (and (exists @t9 (tptp.model @t7 @t47)) (exists @t5 (not (tptp.model @t3 @t47)))))) % 209.18/209.51 (assume @p29 @t60) % 209.18/209.51 (assume @p30 (exists @t12 (and @t15 (exists @t5 (or @t29 (not @t4)))))) % 209.18/209.51 (assume @p31 (exists @t12 (and @t10 @t28 (exists @t26 (and @t24 @t25)) @t32))) % 209.18/209.51 (assume @p32 (exists (@list @t7 @t2 @t1) (and @t8 (not @t13) @t6))) % 209.18/209.51 (assume @p33 @t61) % 209.18/209.51 (assume @p34 true) % 209.18/209.51 ; WARNING: add trust step for TRUST % 209.18/209.51 ; trust TRUST PREPROCESS_SORT_INFER % 209.18/209.51 (step @p35 :rule trust :premises () :args ((= @t67 @t66))) % 209.18/209.51 (step @p36 :rule exists-elim :args ((= @t57 @t67))) % 209.18/209.51 (step @p37 :rule trans :premises (@p36 @p35)) % 209.18/209.51 (step @p38 :rule eq_resolve :premises (@p27 @p37)) % 209.18/209.51 (step @p39 :rule refl :args (@t69)) % 209.18/209.51 (step @p40 :rule bool-double-not-elim :args (@t65)) % 209.18/209.51 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t66) @t69))) % 209.18/209.51 (step @p42 :rule bool-double-not-elim :args (@t69)) % 209.18/209.51 (step @p43 :rule refl :args (@t66)) % 209.18/209.51 (step @p44 :rule cong :premises (@p43 @p42) :args ((=> @t66 @t70))) % 209.18/209.51 (assume-push @p195 @t66) % 209.18/209.51 (step @p46 :rule skolemize :premises (@p38)) % 209.18/209.51 (step-pop @p196 :rule scope :premises (@p46)) % 209.18/209.51 (step @p47 :rule process_scope :premises (@p196) :args (@t70)) % 209.18/209.51 (step @p49 :rule eq_resolve :premises (@p47 @p44)) % 209.18/209.51 (step @p50 :rule implies_elim :premises (@p49)) % 209.18/209.51 (step @p51 :rule eq_resolve :premises (@p50 @p41)) % 209.18/209.51 (step @p52 :rule chain_m_resolution :premises (@p51 @p38) :args (@t69 @t71 (@list @t65))) % 209.18/209.51 (step @p53 :rule instantiate :premises (@p52) :args (@t81)) % 209.18/209.51 ; trust TRUST PREPROCESS_SORT_INFER % 209.18/209.51 (step @p54 :rule trust :premises () :args ((= @t83 @t82))) % 209.18/209.51 (step @p55 :rule exists-elim :args ((= @t60 @t83))) % 209.18/209.51 (step @p56 :rule trans :premises (@p55 @p54)) % 209.18/209.51 (step @p57 :rule eq_resolve :premises (@p29 @p56)) % 209.18/209.51 (step @p58 :rule refl :args (@t84)) % 209.18/209.51 (step @p59 :rule bool-double-not-elim :args (@t74)) % 209.18/209.51 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or (not @t82) @t84))) % 209.18/209.51 (step @p61 :rule bool-double-not-elim :args (@t84)) % 209.18/209.51 (step @p62 :rule refl :args (@t82)) % 209.18/209.51 (step @p63 :rule cong :premises (@p62 @p61) :args ((=> @t82 @t85))) % 209.18/209.51 (assume-push @p197 @t82) % 209.18/209.51 (step @p65 :rule skolemize :premises (@p57)) % 209.18/209.51 (step-pop @p198 :rule scope :premises (@p65)) % 209.18/209.51 (step @p66 :rule process_scope :premises (@p198) :args (@t85)) % 209.18/209.51 (step @p68 :rule eq_resolve :premises (@p66 @p63)) % 209.18/209.51 (step @p69 :rule implies_elim :premises (@p68)) % 209.18/209.51 (step @p70 :rule eq_resolve :premises (@p69 @p60)) % 209.18/209.51 (step @p71 :rule chain_m_resolution :premises (@p70 @p57) :args (@t84 @t71 (@list @t74))) % 209.18/209.51 (step @p72 :rule instantiate :premises (@p71) :args ((@list @t88))) % 209.18/209.51 (step @p73 :rule bool-double-not-elim :args (@t89)) % 209.18/209.51 (step @p74 :rule refl :args (@t91)) % 209.18/209.51 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t91 (not @t90)))) % 209.18/209.51 (step @p76 :rule cnf_or_neg :args (@t91 0)) % 209.18/209.51 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 209.18/209.51 (step @p78 :rule reordering :premises (@p77) :args ((or @t89 @t91))) % 209.18/209.51 (step @p79 :rule chain_m_resolution :premises (@p78 @p72) :args (@t91 @t71 (@list @t89))) % 209.18/209.51 (step @p80 :rule refl :args (@t92)) % 209.18/209.51 (step @p81 :rule bool-double-not-elim :args (@t87)) % 209.18/209.51 (step @p82 :rule nary_cong :premises (@p81 @p80) :args ((or (not @t93) @t92))) % 209.18/209.51 (assume-push @p199 @t93) % 209.18/209.51 (step @p84 :rule skolemize :premises (@p199)) % 209.18/209.51 (step-pop @p200 :rule scope :premises (@p84)) % 209.18/209.51 (step @p85 :rule process_scope :premises (@p200) :args (@t92)) % 209.18/209.51 (step @p87 :rule implies_elim :premises (@p85)) % 209.18/209.51 (step @p88 :rule eq_resolve :premises (@p87 @p82)) % 209.18/209.51 (step @p89 :rule chain_m_resolution :premises (@p88 @p79) :args (@t87 @t94 (@list @t91))) % 209.18/209.51 (assume-push @p201 @t87) % 209.18/209.51 (step @p91 :rule instantiate :premises (@p201) :args (@t81)) % 209.18/209.51 (step-pop @p202 :rule scope :premises (@p91)) % 209.18/209.51 (step @p92 :rule process_scope :premises (@p202) :args (@t99)) % 209.18/209.51 (step @p94 :rule implies_elim :premises (@p92)) % 209.18/209.51 (step @p95 :rule chain_m_resolution :premises (@p94 @p89) :args (@t99 @t94 (@list @t87))) % 209.18/209.51 ; trust TRUST PREPROCESS_SORT_INFER % 209.18/209.51 (step @p96 :rule trust :premises () :args ((= (forall @t52 (= @t50 @t58)) (forall (@list @t100 @t47) (= (_ @t63 @t100 @t48) (not (_ @t63 @t100 @t47))))))) % 209.18/209.51 (step @p97 :rule eq-symm :args (@t58 @t50)) % 209.18/209.51 (step @p98 :rule cong :premises (@p97) :args ((forall @t52 (= @t58 @t50)))) % 209.18/209.51 (step @p99 :rule bool-xor-elim :args (@t51 @t50)) % 209.18/209.51 (step @p100 :rule cong :premises (@p99) :args (@t53)) % 209.18/209.51 (step @p101 :rule trans :premises (@p100 @p98)) % 209.18/209.51 (step @p102 :rule trans :premises (@p101 @p96)) % 209.18/209.51 (step @p103 :rule eq_resolve :premises (@p25 @p102)) % 209.18/209.51 (step @p104 :rule instantiate :premises (@p103) :args ((@list @t80 @t75))) % 209.18/209.51 (step @p105 :rule alpha_equiv :args (@t69 (@list @t62) (@list @t101))) % 209.18/209.51 (step @p106 :rule equiv_elim1 :premises (@p105)) % 209.18/209.51 (step @p107 :rule chain_m_resolution :premises (@p106 @p52) :args (@t103 @t94 (@list @t69))) % 209.18/209.51 ; trust TRUST PREPROCESS_SORT_INFER % 209.18/209.51 (step @p108 :rule trust :premises () :args ((= @t35 (forall @t12 (= (and (forall @t102 (_ @t63 @t101 @t2)) (forall @t78 (_ @t63 @t77 @t33))) @t106))))) % 209.18/209.51 (step @p109 :rule eq_resolve :premises (@p18 @p108)) % 209.18/209.51 (step @p110 :rule instantiate :premises (@p109) :args (@t107)) % 209.18/209.51 ; trust TRUST PREPROCESS_SORT_INFER % 209.18/209.51 (step @p111 :rule trust :premises () :args ((= (forall @t40 (= @t41 @t112)) (forall (@list @t109 @t108) (= (_ @t110 @t109 @t108) (not (forall @t12 (or (not (_ @t105 @t2 @t1 @t109)) (_ @t105 @t2 @t1 @t108))))))))) % 209.18/209.51 (step @p112 :rule eq-symm :args (@t112 @t41)) % 209.18/209.51 (step @p113 :rule refl :args (@t41)) % 209.18/209.51 (step @p114 :rule bool-double-not-elim :args (@t38)) % 209.18/209.51 (step @p115 :rule refl :args (@t111)) % 209.18/209.51 (step @p116 :rule nary_cong :premises (@p115 @p114) :args ((or @t111 (not @t42)))) % 209.18/209.51 (step @p117 :rule bool-and-de-morgan :args (@t39 @t42 true)) % 209.18/209.51 (step @p118 :rule trans :premises (@p117 @p116)) % 209.18/209.51 (step @p119 :rule cong :premises (@p118) :args (@t113)) % 209.18/209.51 (step @p120 :rule cong :premises (@p119) :args (@t114)) % 209.18/209.51 (step @p121 :rule exists-elim :args ((= @t44 @t114))) % 209.18/209.51 (step @p122 :rule trans :premises (@p121 @p120)) % 209.18/209.51 (step @p123 :rule cong :premises (@p122 @p113) :args (@t45)) % 209.18/209.51 (step @p124 :rule trans :premises (@p123 @p112)) % 209.18/209.51 (step @p125 :rule cong :premises (@p124) :args (@t46)) % 209.18/209.51 (step @p126 :rule trans :premises (@p125 @p111)) % 209.18/209.51 (step @p127 :rule eq_resolve :premises (@p22 @p126)) % 209.18/209.51 (step @p128 :rule instantiate :premises (@p127) :args ((@list @t104 @t115))) % 209.18/209.51 ; trust TRUST PREPROCESS_SORT_INFER % 209.18/209.51 (step @p129 :rule trust :premises () :args ((= @t61 (not @t116)))) % 209.18/209.51 (step @p130 :rule eq_resolve :premises (@p33 @p129)) % 209.18/209.51 (step @p131 :rule bool-double-not-elim :args (@t118)) % 209.18/209.51 (step @p132 :rule refl :args (@t116)) % 209.18/209.51 (step @p133 :rule refl :args (@t121)) % 209.18/209.51 (step @p134 :rule nary_cong :premises (@p133 @p132 @p131) :args ((or @t121 @t116 (not @t119)))) % 209.18/209.51 (step @p135 :rule cnf_equiv_pos2 :args (@t120)) % 209.18/209.51 (step @p136 :rule eq_resolve :premises (@p135 @p134)) % 209.18/209.51 (step @p137 :rule reordering :premises (@p136) :args ((or @t116 @t118 @t121))) % 209.18/209.51 (step @p138 :rule chain_m_resolution :premises (@p137 @p130 @p128) :args (@t118 @t122 (@list @t116 @t120))) % 209.18/209.51 (step @p139 :rule instantiate :premises (@p138) :args (@t107)) % 209.18/209.51 ; trust TRUST PREPROCESS_SORT_INFER % 209.18/209.51 (step @p140 :rule trust :premises () :args ((= (forall @t12 (= @t16 @t125)) (forall @t12 (= @t117 (forall @t124 (or (not (_ @t63 @t123 @t2)) (_ @t63 @t123 @t1)))))))) % 209.18/209.51 (step @p141 :rule eq-symm :args (@t125 @t16)) % 209.18/209.51 (step @p142 :rule refl :args (@t16)) % 209.18/209.51 (step @p143 :rule bool-impl-elim :args (@t8 @t13)) % 209.18/209.51 (step @p144 :rule cong :premises (@p143) :args (@t17)) % 209.18/209.51 (step @p145 :rule cong :premises (@p144 @p142) :args (@t18)) % 209.18/209.51 (step @p146 :rule trans :premises (@p145 @p141)) % 209.18/209.51 (step @p147 :rule cong :premises (@p146) :args (@t19)) % 209.18/209.51 (step @p148 :rule trans :premises (@p147 @p140)) % 209.18/209.51 (step @p149 :rule eq_resolve :premises (@p5 @p148)) % 209.18/209.51 (step @p150 :rule instantiate :premises (@p149) :args (@t107)) % 209.18/209.51 (step @p151 :rule instantiate :premises (@p52) :args (@t129)) % 209.18/209.51 (step @p152 :rule instantiate :premises (@p71) :args (@t129)) % 209.18/209.51 (step @p153 :rule cnf_or_pos :args (@t133)) % 209.18/209.51 (step @p154 :rule reordering :premises (@p153) :args ((or @t130 @t132 @t134))) % 209.18/209.51 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p151) :args (@t134 @t122 (@list @t130 @t131))) % 209.18/209.51 (assume-push @p203 @t135) % 209.18/209.51 (step @p157 :rule instantiate :premises (@p203) :args (@t129)) % 209.18/209.51 (step-pop @p204 :rule scope :premises (@p157)) % 209.18/209.51 (step @p158 :rule process_scope :premises (@p204) :args (@t133)) % 209.18/209.51 (step @p160 :rule implies_elim :premises (@p158)) % 209.18/209.51 (step @p161 :rule chain_m_resolution :premises (@p160 @p155) :args ((not @t135) @t71 (@list @t133))) % 209.18/209.51 (step @p162 :rule cnf_equiv_pos1 :args (@t137)) % 209.18/209.51 (step @p163 :rule reordering :premises (@p162) :args ((or @t135 @t138 (not @t137)))) % 209.18/209.51 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p150) :args (@t138 @t122 (@list @t135 @t137))) % 209.18/209.51 (step @p165 :rule cnf_or_pos :args (@t141)) % 209.18/209.51 (step @p166 :rule reordering :premises (@p165) :args ((or @t136 @t140 (not @t141)))) % 209.18/209.51 (step @p167 :rule chain_m_resolution :premises (@p166 @p164 @p139) :args (@t140 @t122 (@list @t136 @t141))) % 209.18/209.51 (step @p168 :rule cnf_equiv_pos1 :args (@t143)) % 209.18/209.51 (step @p169 :rule reordering :premises (@p168) :args ((or @t139 @t144 (not @t143)))) % 209.18/209.51 (step @p170 :rule chain_m_resolution :premises (@p169 @p167 @p110) :args (@t144 @t122 (@list @t139 @t143))) % 209.18/209.51 (step @p171 :rule cnf_and_neg :args (@t142)) % 209.18/209.51 (step @p172 :rule reordering :premises (@p171) :args ((or @t142 @t145 (not @t103)))) % 209.18/209.51 (step @p173 :rule chain_m_resolution :premises (@p172 @p170 @p107) :args (@t145 @t122 (@list @t142 @t103))) % 209.18/209.51 (step @p174 :rule refl :args (@t147)) % 209.18/209.51 (step @p175 :rule bool-double-not-elim :args (@t79)) % 209.18/209.51 (step @p176 :rule nary_cong :premises (@p175 @p174) :args ((or (not @t145) @t147))) % 209.18/209.51 (assume-push @p205 @t145) % 209.18/209.51 (step @p178 :rule skolemize :premises (@p205)) % 209.18/209.51 (step-pop @p206 :rule scope :premises (@p178)) % 209.18/209.51 (step @p179 :rule process_scope :premises (@p206) :args (@t147)) % 209.18/209.51 (step @p181 :rule implies_elim :premises (@p179)) % 209.18/209.51 (step @p182 :rule eq_resolve :premises (@p181 @p176)) % 209.18/209.51 (step @p183 :rule chain_m_resolution :premises (@p182 @p173) :args (@t147 @t71 (@list @t79))) % 209.18/209.51 (step @p184 :rule bool-double-not-elim :args (@t97)) % 209.18/209.51 (step @p185 :rule refl :args (@t146)) % 209.18/209.51 (step @p186 :rule refl :args (@t149)) % 209.18/209.51 (step @p187 :rule nary_cong :premises (@p186 @p185 @p184) :args ((or @t149 @t146 (not @t98)))) % 209.18/209.51 (step @p188 :rule cnf_equiv_pos2 :args (@t148)) % 209.18/209.51 (step @p189 :rule eq_resolve :premises (@p188 @p187)) % 209.18/209.51 (step @p190 :rule reordering :premises (@p189) :args ((or @t146 @t97 @t149))) % 209.18/209.51 (step @p191 :rule chain_m_resolution :premises (@p190 @p183 @p104) :args (@t97 @t122 (@list @t146 @t148))) % 209.18/209.51 (step @p192 :rule cnf_or_pos :args (@t99)) % 209.18/209.51 (step @p193 :rule reordering :premises (@p192) :args ((or @t96 @t98 (not @t99)))) % 209.18/209.51 (step @p194 false :rule chain_m_resolution :premises (@p193 @p191 @p95 @p53) :args (false (@list false false false) (@list @t97 @t99 @t95))) % 209.18/209.51 ) % 209.18/209.51 % SZS output end Proof % 209.18/209.51 % cvc5 exiting %------------------------------------------------------------------------------