%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KRS202+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 : n004.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 08:29:07 AM UTC 2026 % Result : Theorem 204.20s 204.50s % Output : Proof 202.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : KRS202+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.10/0.12 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n004.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 05:28:52 EDT 2026 % 0.15/0.33 % CPUTime : % 0.29/0.48 %----Proving TF0_NAR, FOF, or CNF % 204.20/204.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 204.20/204.50 --- Run --no-e-matching --full-saturate-quant at 6... % 204.20/204.50 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 204.20/204.50 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 204.20/204.50 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 204.20/204.50 --- Run --trigger-sel=max --full-saturate-quant at 15... % 204.20/204.50 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 204.20/204.50 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 204.20/204.50 --- Run --prenex-quant=none --full-saturate-quant at 30... % 204.20/204.50 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 204.20/204.50 --- Run --relevant-triggers --full-saturate-quant at 30... % 204.20/204.50 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 204.20/204.50 % SZS status Theorem % 204.20/204.50 % SZS output start Proof % 204.20/204.50 ( % 204.20/204.50 (declare-sort $$unsorted 0) % 204.20/204.50 (declare-const tptp.xora (-> $$unsorted $$unsorted Bool)) % 204.20/204.50 (declare-const tptp.nevera (-> $$unsorted $$unsorted Bool)) % 204.20/204.50 (declare-const tptp.nota (-> $$unsorted $$unsorted Bool)) % 204.20/204.50 (declare-const tptp.mighta (-> $$unsorted $$unsorted Bool)) % 204.20/204.50 (declare-const tptp.noc $$unsorted) % 204.20/204.50 (declare-const tptp.uns $$unsorted) % 204.20/204.50 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 204.20/204.50 (declare-const tptp.tca $$unsorted) % 204.20/204.50 (declare-const tptp.sca $$unsorted) % 204.20/204.50 (declare-const tptp.wth $$unsorted) % 204.20/204.50 (declare-const tptp.unp $$unsorted) % 204.20/204.50 (declare-const tptp.wca $$unsorted) % 204.20/204.50 (declare-const tptp.wec $$unsorted) % 204.20/204.50 (declare-const tptp.sap $$unsorted) % 204.20/204.50 (declare-const tptp.wtc $$unsorted) % 204.20/204.50 (declare-const tptp.model (-> $$unsorted $$unsorted Bool)) % 204.20/204.50 (declare-const tptp.sat $$unsorted) % 204.20/204.50 (declare-const tptp.cax $$unsorted) % 204.20/204.50 (declare-const tptp.eqv $$unsorted) % 204.20/204.50 (declare-const tptp.esa $$unsorted) % 204.20/204.50 (declare-const tptp.csa $$unsorted) % 204.20/204.50 (declare-const tptp.status (-> $$unsorted $$unsorted $$unsorted Bool)) % 204.20/204.50 (declare-const tptp.thm $$unsorted) % 204.20/204.50 (declare-const tptp.isa (-> $$unsorted $$unsorted Bool)) % 204.20/204.50 (declare-const tptp.eth $$unsorted) % 204.20/204.50 (declare-const tptp.tac $$unsorted) % 204.20/204.50 (declare-const tptp.tau $$unsorted) % 204.20/204.50 (define @t1 () (@var "C" $$unsorted)) % 204.20/204.50 (define @t2 () (@var "Ax" $$unsorted)) % 204.20/204.50 (define @t3 () (@var "I2" $$unsorted)) % 204.20/204.50 (define @t4 () (tptp.model @t3 @t1)) % 204.20/204.50 (define @t5 () (@list @t3)) % 204.20/204.50 (define @t6 () (exists @t5 @t4)) % 204.20/204.50 (define @t7 () (@var "I1" $$unsorted)) % 204.20/204.50 (define @t8 () (tptp.model @t7 @t2)) % 204.20/204.50 (define @t9 () (@list @t7)) % 204.20/204.50 (define @t10 () (exists @t9 @t8)) % 204.20/204.50 (define @t11 () (not @t10)) % 204.20/204.50 (define @t12 () (@list @t2 @t1)) % 204.20/204.50 (define @t13 () (tptp.status @t2 @t1 tptp.esa)) % 204.20/204.50 (define @t14 () (= @t10 @t6)) % 204.20/204.50 (define @t15 () (= @t14 @t13)) % 204.20/204.50 (define @t16 () (forall @t12 @t15)) % 204.20/204.50 (define @t17 () (tptp.model @t7 @t1)) % 204.20/204.50 (define @t18 () (and @t8 @t17)) % 204.20/204.50 (define @t19 () (exists @t9 @t18)) % 204.20/204.50 (define @t20 () (tptp.status @t2 @t1 tptp.thm)) % 204.20/204.50 (define @t21 () (forall @t9 (=> @t8 @t17))) % 204.20/204.50 (define @t22 () (= @t21 @t20)) % 204.20/204.50 (define @t23 () (forall @t12 @t22)) % 204.20/204.50 (define @t24 () (tptp.model @t3 @t2)) % 204.20/204.50 (define @t25 () (forall @t5 @t4)) % 204.20/204.50 (define @t26 () (@var "I3" $$unsorted)) % 204.20/204.50 (define @t27 () (tptp.model @t26 @t2)) % 204.20/204.50 (define @t28 () (not @t27)) % 204.20/204.50 (define @t29 () (tptp.model @t26 @t1)) % 204.20/204.50 (define @t30 () (@list @t26)) % 204.20/204.50 (define @t31 () (exists @t30 (and @t29 @t28))) % 204.20/204.50 (define @t32 () (forall @t5 (=> @t24 @t4))) % 204.20/204.50 (define @t33 () (not @t24)) % 204.20/204.50 (define @t34 () (exists @t5 @t33)) % 204.20/204.50 (define @t35 () (@var "I4" $$unsorted)) % 204.20/204.50 (define @t36 () (exists (@list @t35) (not (tptp.model @t35 @t1)))) % 204.20/204.50 (define @t37 () (tptp.not @t1)) % 204.20/204.50 (define @t38 () (tptp.model @t3 @t37)) % 204.20/204.50 (define @t39 () (@var "S2" $$unsorted)) % 204.20/204.50 (define @t40 () (@var "S1" $$unsorted)) % 204.20/204.50 (define @t41 () (tptp.status @t2 @t1 @t39)) % 204.20/204.50 (define @t42 () (tptp.status @t2 @t1 @t40)) % 204.20/204.50 (define @t43 () (@list @t40 @t39)) % 204.20/204.50 (define @t44 () (tptp.nota @t40 @t39)) % 204.20/204.50 (define @t45 () (not @t41)) % 204.20/204.50 (define @t46 () (and @t42 @t45)) % 204.20/204.50 (define @t47 () (exists @t12 @t46)) % 204.20/204.50 (define @t48 () (= @t47 @t44)) % 204.20/204.50 (define @t49 () (forall @t43 @t48)) % 204.20/204.50 (define @t50 () (@var "F" $$unsorted)) % 204.20/204.50 (define @t51 () (@var "I" $$unsorted)) % 204.20/204.50 (define @t52 () (tptp.model @t51 (tptp.not @t50))) % 204.20/204.50 (define @t53 () (tptp.model @t51 @t50)) % 204.20/204.50 (define @t54 () (@list @t51 @t50)) % 204.20/204.50 (define @t55 () (@list @t51)) % 204.20/204.50 (define @t56 () (forall @t55 @t53)) % 204.20/204.50 (define @t57 () (@list @t50)) % 204.20/204.50 (define @t58 () (exists @t57 @t56)) % 204.20/204.50 (define @t59 () (tptp.model @t3 @t50)) % 204.20/204.50 (define @t60 () (not @t59)) % 204.20/204.50 (define @t61 () (exists @t5 @t60)) % 204.20/204.50 (define @t62 () (tptp.model @t7 @t50)) % 204.20/204.50 (define @t63 () (exists @t9 @t62)) % 204.20/204.50 (define @t64 () (and @t63 @t61)) % 204.20/204.50 (define @t65 () (exists @t57 @t64)) % 204.20/204.50 (define @t66 () (not @t4)) % 204.20/204.50 (define @t67 () (not (tptp.nota tptp.esa tptp.thm))) % 204.20/204.50 (define @t68 () (@var "b_I1" it_8_$$unsorted)) % 204.20/204.50 (define @t69 () (@const 0 (-> it_8_$$unsorted $$unsorted Bool))) % 204.20/204.50 (define @t70 () (@list @t68)) % 204.20/204.50 (define @t71 () (@const 1 it_7_$$unsorted)) % 204.20/204.50 (define @t72 () (@const 2 (-> $$unsorted $$unsorted it_7_$$unsorted Bool))) % 204.20/204.50 (define @t73 () (_ @t72 @t2 @t1 @t71)) % 204.20/204.50 (define @t74 () (not @t8)) % 204.20/204.50 (define @t75 () (forall @t9 (or @t74 @t17))) % 204.20/204.50 (define @t76 () (@var "b_BOUND_VARIABLE_7854" it_8_$$unsorted)) % 204.20/204.50 (define @t77 () (@var "b_BOUND_VARIABLE_7850" it_8_$$unsorted)) % 204.20/204.50 (define @t78 () (forall (@list @t50 @t77 @t76) (or (not (_ @t69 @t77 @t50)) (_ @t69 @t76 @t50)))) % 204.20/204.50 (define @t79 () (@quantifiers_skolemize @t78 0)) % 204.20/204.50 (define @t80 () (@var "b_I" it_8_$$unsorted)) % 204.20/204.50 (define @t81 () (@list @t80)) % 204.20/204.50 (define @t82 () (forall @t57 (not (forall @t81 (_ @t69 @t80 @t50))))) % 204.20/204.50 (define @t83 () (@quantifiers_skolemize @t82 0)) % 204.20/204.50 (define @t84 () (@list @t83 @t79)) % 204.20/204.50 (define @t85 () (@var "b_S2" it_7_$$unsorted)) % 204.20/204.50 (define @t86 () (@var "b_S1" it_7_$$unsorted)) % 204.20/204.50 (define @t87 () (@const 3 (-> it_7_$$unsorted it_7_$$unsorted Bool))) % 204.20/204.50 (define @t88 () (not @t42)) % 204.20/204.50 (define @t89 () (not (forall @t12 (or @t88 @t41)))) % 204.20/204.50 (define @t90 () (forall @t12 (not @t46))) % 204.20/204.50 (define @t91 () (not @t90)) % 204.20/204.50 (define @t92 () (@const 4 it_7_$$unsorted)) % 204.20/204.50 (define @t93 () (_ @t87 @t92 @t71)) % 204.20/204.50 (define @t94 () (_ @t72 @t2 @t1 @t92)) % 204.20/204.50 (define @t95 () (forall @t12 (or (not @t94) @t73))) % 204.20/204.50 (define @t96 () (not @t95)) % 204.20/204.50 (define @t97 () (= @t93 @t96)) % 204.20/204.50 (define @t98 () (not @t97)) % 204.20/204.50 (define @t99 () (@list true false)) % 204.20/204.50 (define @t100 () (@var "b_I2" it_8_$$unsorted)) % 204.20/204.50 (define @t101 () (@list @t100)) % 204.20/204.50 (define @t102 () (@var "b_I1" it_8_$$unsorted)) % 204.20/204.50 (define @t103 () (@list @t102)) % 204.20/204.50 (define @t104 () (forall @t12 (= @t94 (= (not (forall @t103 (not (_ @t69 @t102 @t2)))) (not (forall @t101 (not (_ @t69 @t100 @t1)))))))) % 204.20/204.50 (define @t105 () (not (forall @t5 @t66))) % 204.20/204.50 (define @t106 () (not (forall @t9 @t74))) % 204.20/204.50 (define @t107 () (= @t106 @t105)) % 204.20/204.50 (define @t108 () (forall @t103 (not (_ @t69 @t102 @t83)))) % 204.20/204.50 (define @t109 () (not @t108)) % 204.20/204.50 (define @t110 () (forall @t101 (not (_ @t69 @t100 @t79)))) % 204.20/204.50 (define @t111 () (not @t110)) % 204.20/204.50 (define @t112 () (_ @t72 @t83 @t79 @t92)) % 204.20/204.50 (define @t113 () (= @t112 (= @t109 @t111))) % 204.20/204.50 (define @t114 () (= @t111 @t109)) % 204.20/204.50 (define @t115 () (= @t112 @t114)) % 204.20/204.50 (define @t116 () (@list false)) % 204.20/204.50 (define @t117 () (not @t82)) % 204.20/204.50 (define @t118 () (not (forall @t57 (not @t56)))) % 204.20/204.50 (define @t119 () (forall @t81 (_ @t69 @t80 @t83))) % 204.20/204.50 (define @t120 () (not (not @t119))) % 204.20/204.50 (define @t121 () (@list true)) % 204.20/204.50 (define @t122 () (@quantifiers_skolemize @t78 1)) % 204.20/204.50 (define @t123 () (@list @t122)) % 204.20/204.50 (define @t124 () (@var "b_I2" it_8_$$unsorted)) % 204.20/204.50 (define @t125 () (forall (@list @t124) (not (_ @t69 @t124 @t83)))) % 204.20/204.50 (define @t126 () (_ @t69 @t122 @t83)) % 204.20/204.50 (define @t127 () (not @t126)) % 204.20/204.50 (define @t128 () (not @t125)) % 204.20/204.50 (define @t129 () (@var "BOUND_VARIABLE_7854" $$unsorted)) % 204.20/204.50 (define @t130 () (tptp.model @t129 @t50)) % 204.20/204.50 (define @t131 () (@var "BOUND_VARIABLE_7850" $$unsorted)) % 204.20/204.50 (define @t132 () (not (tptp.model @t131 @t50))) % 204.20/204.50 (define @t133 () (or @t132 @t130)) % 204.20/204.50 (define @t134 () (forall (@list @t50 @t131 @t129) @t133)) % 204.20/204.50 (define @t135 () (forall (@list @t131 @t129) @t133)) % 204.20/204.50 (define @t136 () (forall (@list @t129) @t130)) % 204.20/204.50 (define @t137 () (forall (@list @t131) @t132)) % 204.20/204.50 (define @t138 () (or @t137 @t136)) % 204.20/204.50 (define @t139 () (forall @t5 @t59)) % 204.20/204.50 (define @t140 () (forall @t9 (not @t62))) % 204.20/204.50 (define @t141 () (not @t139)) % 204.20/204.50 (define @t142 () (not @t140)) % 204.20/204.50 (define @t143 () (and @t142 @t141)) % 204.20/204.50 (define @t144 () (forall @t57 (not @t143))) % 204.20/204.50 (define @t145 () (not @t144)) % 204.20/204.50 (define @t146 () (forall @t5 (not @t60))) % 204.20/204.50 (define @t147 () (not @t146)) % 204.20/204.50 (define @t148 () (_ @t69 @t122 @t79)) % 204.20/204.50 (define @t149 () (@quantifiers_skolemize @t78 2)) % 204.20/204.50 (define @t150 () (_ @t69 @t149 @t79)) % 204.20/204.50 (define @t151 () (not @t148)) % 204.20/204.50 (define @t152 () (or @t151 @t150)) % 204.20/204.50 (define @t153 () (@list @t152)) % 204.20/204.50 (define @t154 () (@var "b_I1" it_8_$$unsorted)) % 204.20/204.50 (define @t155 () (forall (@list @t154) (not (_ @t69 @t154 @t79)))) % 204.20/204.50 (define @t156 () (not @t155)) % 204.20/204.50 (define @t157 () (@list false false)) % 204.20/204.50 (define @t158 () (_ @t72 @t83 @t79 @t71)) % 204.20/204.50 (define @t159 () (not @t112)) % 204.20/204.50 (define @t160 () (or @t159 @t158)) % 204.20/204.50 (define @t161 () (forall @t70 (or (not (_ @t69 @t68 @t83)) (_ @t69 @t68 @t79)))) % 204.20/204.50 (define @t162 () (= @t158 @t161)) % 204.20/204.50 (define @t163 () (@list @t149)) % 204.20/204.50 (define @t164 () (_ @t69 @t149 @t83)) % 204.20/204.50 (define @t165 () (not @t164)) % 204.20/204.50 (define @t166 () (or @t165 @t150)) % 204.20/204.50 (define @t167 () (not @t166)) % 204.20/204.50 (assume @p1 (forall @t12 (= (=> @t11 (not @t6)) (tptp.status @t2 @t1 tptp.unp)))) % 204.20/204.50 (assume @p2 (forall @t12 (= (=> @t10 @t6) (tptp.status @t2 @t1 tptp.sap)))) % 204.20/204.50 (assume @p3 @t16) % 204.20/204.50 (assume @p4 (forall @t12 (= @t19 (tptp.status @t2 @t1 tptp.sat)))) % 204.20/204.50 (assume @p5 @t23) % 204.20/204.50 (assume @p6 (forall @t12 (= (and @t10 (forall @t5 (= @t24 @t4))) (tptp.status @t2 @t1 tptp.eqv)))) % 204.20/204.50 (assume @p7 (forall @t12 (= (and @t10 @t25) (tptp.status @t2 @t1 tptp.tac)))) % 204.20/204.50 (assume @p8 (forall @t12 (= (and @t10 @t32 @t31) (tptp.status @t2 @t1 tptp.wec)))) % 204.20/204.50 (assume @p9 (forall @t12 (= (and @t10 @t34 (forall @t30 (= @t27 @t29))) (tptp.status @t2 @t1 tptp.eth)))) % 204.20/204.50 (assume @p10 (forall @t12 (= (forall @t9 @t18) (tptp.status @t2 @t1 tptp.tau)))) % 204.20/204.50 (assume @p11 (forall @t12 (= (and @t10 @t34 (forall @t30 @t29)) (tptp.status @t2 @t1 tptp.wtc)))) % 204.20/204.50 (assume @p12 (forall @t12 (= (and @t10 @t32 @t31 @t36) (tptp.status @t2 @t1 tptp.wth)))) % 204.20/204.50 (assume @p13 (forall @t12 (= @t11 (tptp.status @t2 @t1 tptp.cax)))) % 204.20/204.50 (assume @p14 (forall @t12 (= (and @t11 @t6) (tptp.status @t2 @t1 tptp.sca)))) % 204.20/204.50 (assume @p15 (forall @t12 (= (and @t11 @t25) (tptp.status @t2 @t1 tptp.tca)))) % 204.20/204.50 (assume @p16 (forall @t12 (= (and @t11 @t6 (exists @t30 (not @t29))) (tptp.status @t2 @t1 tptp.wca)))) % 204.20/204.50 (assume @p17 (forall @t12 (= (exists @t9 (and @t8 (tptp.model @t7 @t37))) (tptp.status @t2 @t1 tptp.csa)))) % 204.20/204.50 (assume @p18 (forall @t12 (= (and (forall @t9 @t8) (forall @t5 @t38)) (tptp.status @t2 @t1 tptp.uns)))) % 204.20/204.50 (assume @p19 (forall @t12 (= (and @t19 (exists @t5 (and @t24 @t38))) (tptp.status @t2 @t1 tptp.noc)))) % 204.20/204.50 (assume @p20 (forall @t43 (= (exists @t12 (and @t42 @t41)) (tptp.mighta @t40 @t39)))) % 204.20/204.50 (assume @p21 (forall @t43 (= (forall @t12 (=> @t42 @t41)) (tptp.isa @t40 @t39)))) % 204.20/204.50 (assume @p22 @t49) % 204.20/204.50 (assume @p23 (forall @t43 (= (forall @t12 (=> @t42 @t45)) (tptp.nevera @t40 @t39)))) % 204.20/204.50 (assume @p24 (forall @t43 (= (forall @t12 (xor @t42 @t41)) (tptp.xora @t40 @t39)))) % 204.20/204.50 (assume @p25 (forall @t54 (xor @t53 @t52))) % 204.20/204.50 (assume @p26 (forall @t54 (= @t53 (not @t52)))) % 204.20/204.50 (assume @p27 @t58) % 204.20/204.50 (assume @p28 @t65) % 204.20/204.50 (assume @p29 (exists @t57 (forall @t55 (not @t53)))) % 204.20/204.50 (assume @p30 (exists @t12 (and @t19 (exists @t5 (or @t33 @t66))))) % 204.20/204.50 (assume @p31 (exists @t12 (and @t10 @t32 (exists @t30 (and @t28 @t29)) @t36))) % 204.20/204.50 (assume @p32 (exists (@list @t7 @t2 @t1) (and @t8 (not @t17) @t6))) % 204.20/204.50 (assume @p33 @t67) % 204.20/204.50 (assume @p34 true) % 204.20/204.50 ; WARNING: add trust step for TRUST % 202.37/204.50 ; trust TRUST PREPROCESS_SORT_INFER % 202.37/204.50 (step @p35 :rule trust :premises () :args ((= (forall @t12 (= @t20 @t75)) (forall @t12 (= @t73 (forall @t70 (or (not (_ @t69 @t68 @t2)) (_ @t69 @t68 @t1)))))))) % 202.37/204.50 (step @p36 :rule eq-symm :args (@t75 @t20)) % 202.37/204.50 (step @p37 :rule refl :args (@t20)) % 202.37/204.50 (step @p38 :rule bool-impl-elim :args (@t8 @t17)) % 202.37/204.50 (step @p39 :rule cong :premises (@p38) :args (@t21)) % 202.37/204.50 (step @p40 :rule cong :premises (@p39 @p37) :args (@t22)) % 202.37/204.50 (step @p41 :rule trans :premises (@p40 @p36)) % 202.37/204.50 (step @p42 :rule cong :premises (@p41) :args (@t23)) % 202.37/204.50 (step @p43 :rule trans :premises (@p42 @p35)) % 202.37/204.50 (step @p44 :rule eq_resolve :premises (@p5 @p43)) % 202.37/204.50 (step @p45 :rule instantiate :premises (@p44) :args (@t84)) % 202.37/204.50 ; trust TRUST PREPROCESS_SORT_INFER % 202.37/204.50 (step @p46 :rule trust :premises () :args ((= (forall @t43 (= @t44 @t89)) (forall (@list @t86 @t85) (= (_ @t87 @t86 @t85) (not (forall @t12 (or (not (_ @t72 @t2 @t1 @t86)) (_ @t72 @t2 @t1 @t85))))))))) % 202.37/204.50 (step @p47 :rule eq-symm :args (@t89 @t44)) % 202.37/204.50 (step @p48 :rule refl :args (@t44)) % 202.37/204.50 (step @p49 :rule bool-double-not-elim :args (@t41)) % 202.37/204.50 (step @p50 :rule refl :args (@t88)) % 202.37/204.50 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or @t88 (not @t45)))) % 202.37/204.50 (step @p52 :rule bool-and-de-morgan :args (@t42 @t45 true)) % 202.37/204.50 (step @p53 :rule trans :premises (@p52 @p51)) % 202.37/204.50 (step @p54 :rule cong :premises (@p53) :args (@t90)) % 202.37/204.50 (step @p55 :rule cong :premises (@p54) :args (@t91)) % 202.37/204.50 (step @p56 :rule exists-elim :args ((= @t47 @t91))) % 202.37/204.50 (step @p57 :rule trans :premises (@p56 @p55)) % 202.37/204.50 (step @p58 :rule cong :premises (@p57 @p48) :args (@t48)) % 202.37/204.50 (step @p59 :rule trans :premises (@p58 @p47)) % 202.37/204.50 (step @p60 :rule cong :premises (@p59) :args (@t49)) % 202.37/204.50 (step @p61 :rule trans :premises (@p60 @p46)) % 202.37/204.50 (step @p62 :rule eq_resolve :premises (@p22 @p61)) % 202.37/204.50 (step @p63 :rule instantiate :premises (@p62) :args ((@list @t92 @t71))) % 202.37/204.50 ; trust TRUST PREPROCESS_SORT_INFER % 202.37/204.50 (step @p64 :rule trust :premises () :args ((= @t67 (not @t93)))) % 202.37/204.50 (step @p65 :rule eq_resolve :premises (@p33 @p64)) % 202.37/204.50 (step @p66 :rule bool-double-not-elim :args (@t95)) % 202.37/204.50 (step @p67 :rule refl :args (@t93)) % 202.37/204.50 (step @p68 :rule refl :args (@t98)) % 202.37/204.50 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66) :args ((or @t98 @t93 (not @t96)))) % 202.37/204.50 (step @p70 :rule cnf_equiv_pos2 :args (@t97)) % 202.37/204.50 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 202.37/204.50 (step @p72 :rule reordering :premises (@p71) :args ((or @t93 @t95 @t98))) % 202.37/204.50 (step @p73 :rule chain_m_resolution :premises (@p72 @p65 @p63) :args (@t95 @t99 (@list @t93 @t97))) % 202.37/204.50 (step @p74 :rule instantiate :premises (@p73) :args (@t84)) % 202.37/204.50 ; trust TRUST PREPROCESS_SORT_INFER % 202.37/204.50 (step @p75 :rule trust :premises () :args ((= (forall @t12 (= @t13 @t107)) @t104))) % 202.37/204.50 (step @p76 :rule eq-symm :args (@t107 @t13)) % 202.37/204.50 (step @p77 :rule refl :args (@t13)) % 202.37/204.50 (step @p78 :rule exists-elim :args ((= @t6 @t105))) % 202.37/204.50 (step @p79 :rule exists-elim :args ((= @t10 @t106))) % 202.37/204.50 (step @p80 :rule cong :premises (@p79 @p78) :args (@t14)) % 202.37/204.50 (step @p81 :rule cong :premises (@p80 @p77) :args (@t15)) % 202.37/204.50 (step @p82 :rule trans :premises (@p81 @p76)) % 202.37/204.50 (step @p83 :rule cong :premises (@p82) :args (@t16)) % 202.37/204.50 (step @p84 :rule trans :premises (@p83 @p75)) % 202.37/204.50 (step @p85 :rule eq_resolve :premises (@p3 @p84)) % 202.37/204.50 (step @p86 :rule eq-symm :args (@t109 @t111)) % 202.37/204.50 (step @p87 :rule refl :args (@t112)) % 202.37/204.50 (step @p88 :rule cong :premises (@p87 @p86) :args (@t113)) % 202.37/204.50 (step @p89 :rule refl :args (@t104)) % 202.37/204.50 (step @p90 :rule cong :premises (@p89 @p88) :args ((=> @t104 @t113))) % 202.37/204.50 (assume-push @p205 @t104) % 202.37/204.50 (step @p92 :rule instantiate :premises (@p85) :args (@t84)) % 202.37/204.50 (step-pop @p206 :rule scope :premises (@p92)) % 202.37/204.50 (step @p93 :rule process_scope :premises (@p206) :args (@t113)) % 202.37/204.50 (step @p95 :rule eq_resolve :premises (@p93 @p90)) % 202.37/204.50 (step @p96 :rule implies_elim :premises (@p95)) % 202.37/204.50 (step @p97 :rule chain_m_resolution :premises (@p96 @p85) :args (@t115 @t116 (@list @t104))) % 202.37/204.50 ; trust TRUST PREPROCESS_SORT_INFER % 202.37/204.50 (step @p98 :rule trust :premises () :args ((= @t118 @t117))) % 202.37/204.50 (step @p99 :rule exists-elim :args ((= @t58 @t118))) % 202.37/204.50 (step @p100 :rule trans :premises (@p99 @p98)) % 202.37/204.50 (step @p101 :rule eq_resolve :premises (@p27 @p100)) % 202.37/204.50 (step @p102 :rule refl :args (@t119)) % 202.37/204.50 (step @p103 :rule bool-double-not-elim :args (@t82)) % 202.37/204.50 (step @p104 :rule nary_cong :premises (@p103 @p102) :args ((or (not @t117) @t119))) % 202.37/204.50 (step @p105 :rule bool-double-not-elim :args (@t119)) % 202.37/204.50 (step @p106 :rule refl :args (@t117)) % 202.37/204.50 (step @p107 :rule cong :premises (@p106 @p105) :args ((=> @t117 @t120))) % 202.37/204.50 (assume-push @p207 @t117) % 202.37/204.50 (step @p109 :rule skolemize :premises (@p101)) % 202.37/204.50 (step-pop @p208 :rule scope :premises (@p109)) % 202.37/204.50 (step @p110 :rule process_scope :premises (@p208) :args (@t120)) % 202.37/204.50 (step @p112 :rule eq_resolve :premises (@p110 @p107)) % 202.37/204.50 (step @p113 :rule implies_elim :premises (@p112)) % 202.37/204.50 (step @p114 :rule eq_resolve :premises (@p113 @p104)) % 202.37/204.50 (step @p115 :rule chain_m_resolution :premises (@p114 @p101) :args (@t119 @t121 (@list @t82))) % 202.37/204.50 (step @p116 :rule instantiate :premises (@p115) :args (@t123)) % 202.37/204.50 (assume-push @p209 @t125) % 202.37/204.50 (step @p118 :rule instantiate :premises (@p209) :args (@t123)) % 202.37/204.50 (step-pop @p210 :rule scope :premises (@p118)) % 202.37/204.50 (step @p119 :rule process_scope :premises (@p210) :args (@t127)) % 202.37/204.50 (step @p121 :rule implies_elim :premises (@p119)) % 202.37/204.50 (step @p122 :rule reordering :premises (@p121) :args ((or @t127 @t128))) % 202.37/204.50 (step @p123 :rule chain_m_resolution :premises (@p122 @p116) :args (@t128 @t116 (@list @t126))) % 202.37/204.50 (step @p124 :rule alpha_equiv :args (@t125 (@list @t124) (@list @t102))) % 202.37/204.50 (step @p125 :rule equiv_elim2 :premises (@p124)) % 202.37/204.50 (step @p126 :rule chain_m_resolution :premises (@p125 @p123) :args (@t109 @t121 (@list @t125))) % 202.37/204.50 ; trust TRUST PREPROCESS_SORT_INFER % 202.37/204.50 (step @p127 :rule trust :premises () :args ((= (not @t134) (not @t78)))) % 202.37/204.50 (step @p128 :rule quant-merge-prenex :args ((= (forall @t57 @t135) @t134))) % 202.37/204.50 (step @p129 :rule alpha_equiv :args (@t136 (@list @t129) (@list @t3))) % 202.37/204.50 (step @p130 :rule alpha_equiv :args (@t137 (@list @t131) (@list @t7))) % 202.37/204.50 (step @p131 :rule nary_cong :premises (@p130 @p129) :args (@t138)) % 202.37/204.50 (step @p132 :rule quant-miniscope-or :args ((= @t135 @t138))) % 202.37/204.50 (step @p133 :rule trans :premises (@p132 @p131)) % 202.37/204.50 (step @p134 :rule symm :premises (@p133)) % 202.37/204.50 (step @p135 :rule cong :premises (@p134) :args ((forall @t57 (or @t140 @t139)))) % 202.37/204.50 (step @p136 :rule trans :premises (@p135 @p128)) % 202.37/204.50 (step @p137 :rule bool-double-not-elim :args (@t139)) % 202.37/204.50 (step @p138 :rule bool-double-not-elim :args (@t140)) % 202.37/204.50 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or (not @t142) (not @t141)))) % 202.37/204.50 (step @p140 :rule bool-and-de-morgan :args (@t142 @t141 true)) % 202.37/204.50 (step @p141 :rule trans :premises (@p140 @p139)) % 202.37/204.50 (step @p142 :rule cong :premises (@p141) :args (@t144)) % 202.37/204.50 (step @p143 :rule trans :premises (@p142 @p136)) % 202.37/204.50 (step @p144 :rule cong :premises (@p143) :args (@t145)) % 202.37/204.50 (step @p145 :rule exists-elim :args ((= (exists @t57 @t143) @t145))) % 202.37/204.50 (step @p146 :rule trans :premises (@p145 @p144)) % 202.37/204.50 (step @p147 :rule bool-double-not-elim :args (@t59)) % 202.37/204.50 (step @p148 :rule cong :premises (@p147) :args (@t146)) % 202.37/204.50 (step @p149 :rule cong :premises (@p148) :args (@t147)) % 202.37/204.50 (step @p150 :rule exists-elim :args ((= @t61 @t147))) % 202.37/204.50 (step @p151 :rule trans :premises (@p150 @p149)) % 202.37/204.50 (step @p152 :rule exists-elim :args ((= @t63 @t142))) % 202.37/204.50 (step @p153 :rule nary_cong :premises (@p152 @p151) :args (@t64)) % 202.37/204.50 (step @p154 :rule cong :premises (@p153) :args (@t65)) % 202.37/204.50 (step @p155 :rule trans :premises (@p154 @p146)) % 202.37/204.50 (step @p156 :rule trans :premises (@p155 @p127)) % 202.37/204.50 (step @p157 :rule eq_resolve :premises (@p28 @p156)) % 202.37/204.50 (step @p158 :rule skolemize :premises (@p157)) % 202.37/204.50 (step @p159 :rule bool-double-not-elim :args (@t148)) % 202.37/204.50 (step @p160 :rule refl :args (@t152)) % 202.37/204.50 (step @p161 :rule nary_cong :premises (@p160 @p159) :args ((or @t152 (not @t151)))) % 202.37/204.50 (step @p162 :rule cnf_or_neg :args (@t152 0)) % 202.37/204.50 (step @p163 :rule eq_resolve :premises (@p162 @p161)) % 202.37/204.50 (step @p164 :rule reordering :premises (@p163) :args ((or @t148 @t152))) % 202.37/204.50 (step @p165 :rule chain_m_resolution :premises (@p164 @p158) :args (@t148 @t121 @t153)) % 202.37/204.50 (assume-push @p211 @t155) % 202.37/204.50 (step @p167 :rule instantiate :premises (@p211) :args (@t123)) % 202.37/204.50 (step-pop @p212 :rule scope :premises (@p167)) % 202.37/204.50 (step @p168 :rule process_scope :premises (@p212) :args (@t151)) % 202.37/204.50 (step @p170 :rule implies_elim :premises (@p168)) % 202.37/204.50 (step @p171 :rule reordering :premises (@p170) :args ((or @t151 @t156))) % 202.37/204.50 (step @p172 :rule chain_m_resolution :premises (@p171 @p165) :args (@t156 @t116 (@list @t148))) % 202.37/204.50 (step @p173 :rule alpha_equiv :args (@t155 (@list @t154) (@list @t100))) % 202.37/204.50 (step @p174 :rule equiv_elim2 :premises (@p173)) % 202.37/204.50 (step @p175 :rule chain_m_resolution :premises (@p174 @p172) :args (@t111 @t121 (@list @t155))) % 202.37/204.50 (step @p176 :rule bool-double-not-elim :args (@t108)) % 202.37/204.50 (step @p177 :rule bool-double-not-elim :args (@t110)) % 202.37/204.50 (step @p178 :rule refl :args (@t114)) % 202.37/204.50 (step @p179 :rule nary_cong :premises (@p178 @p177 @p176) :args ((or @t114 (not @t111) (not @t109)))) % 202.37/204.50 (step @p180 :rule cnf_equiv_neg2 :args (@t114)) % 202.37/204.50 (step @p181 :rule eq_resolve :premises (@p180 @p179)) % 202.37/204.50 (step @p182 :rule reordering :premises (@p181) :args ((or @t110 @t108 @t114))) % 202.37/204.50 (step @p183 :rule chain_m_resolution :premises (@p182 @p175 @p126) :args (@t114 (@list true true) (@list @t110 @t108))) % 202.37/204.50 (step @p184 :rule cnf_equiv_pos2 :args (@t115)) % 202.37/204.50 (step @p185 :rule reordering :premises (@p184) :args ((or @t112 (not @t114) (not @t115)))) % 202.37/204.50 (step @p186 :rule chain_m_resolution :premises (@p185 @p183 @p97) :args (@t112 @t157 (@list @t114 @t115))) % 202.37/204.50 (step @p187 :rule cnf_or_pos :args (@t160)) % 202.37/204.50 (step @p188 :rule reordering :premises (@p187) :args ((or @t158 @t159 (not @t160)))) % 202.37/204.50 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p74) :args (@t158 @t157 (@list @t112 @t160))) % 202.37/204.50 (step @p190 :rule cnf_equiv_pos1 :args (@t162)) % 202.37/204.50 (step @p191 :rule reordering :premises (@p190) :args ((or @t161 (not @t158) (not @t162)))) % 202.37/204.50 (step @p192 :rule chain_m_resolution :premises (@p191 @p189 @p45) :args (@t161 @t157 (@list @t158 @t162))) % 202.37/204.50 (step @p193 :rule instantiate :premises (@p115) :args (@t163)) % 202.37/204.50 (step @p194 :rule cnf_or_neg :args (@t152 1)) % 202.37/204.50 (step @p195 :rule chain_m_resolution :premises (@p194 @p158) :args ((not @t150) @t121 @t153)) % 202.37/204.50 (step @p196 :rule cnf_or_pos :args (@t166)) % 202.37/204.50 (step @p197 :rule reordering :premises (@p196) :args ((or @t150 @t165 @t167))) % 202.37/204.50 (step @p198 :rule chain_m_resolution :premises (@p197 @p195 @p193) :args (@t167 @t99 (@list @t150 @t164))) % 202.37/204.50 (assume-push @p213 @t161) % 202.37/204.50 (step @p200 :rule instantiate :premises (@p213) :args (@t163)) % 202.37/204.50 (step-pop @p214 :rule scope :premises (@p200)) % 202.37/204.50 (step @p201 :rule process_scope :premises (@p214) :args (@t166)) % 202.37/204.50 (step @p203 :rule implies_elim :premises (@p201)) % 202.37/204.50 (step @p204 false :rule chain_m_resolution :premises (@p203 @p198 @p192) :args (false @t99 (@list @t166 @t161))) % 202.37/204.50 ) % 202.37/204.50 % SZS output end Proof % 202.37/204.50 % cvc5 exiting %------------------------------------------------------------------------------