%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KRS201+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 : n019.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 08:29:06 AM UTC 2026 % Result : Theorem 203.53s 203.82s % Output : Proof 203.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS201+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 : n019.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 05:29:04 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 203.53/203.82 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 203.53/203.82 --- Run --no-e-matching --full-saturate-quant at 6... % 203.53/203.82 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 203.53/203.82 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 203.53/203.82 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 203.53/203.82 --- Run --trigger-sel=max --full-saturate-quant at 15... % 203.53/203.82 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 203.53/203.82 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 203.53/203.82 --- Run --prenex-quant=none --full-saturate-quant at 30... % 203.53/203.82 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 203.53/203.82 --- Run --relevant-triggers --full-saturate-quant at 30... % 203.53/203.82 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 203.53/203.82 % SZS status Theorem % 203.53/203.82 % SZS output start Proof % 203.53/203.82 ( % 203.53/203.82 (declare-sort $$unsorted 0) % 203.53/203.82 (declare-const tptp.xora (-> $$unsorted $$unsorted Bool)) % 203.53/203.82 (declare-const tptp.nevera (-> $$unsorted $$unsorted Bool)) % 203.53/203.82 (declare-const tptp.nota (-> $$unsorted $$unsorted Bool)) % 203.53/203.82 (declare-const tptp.mighta (-> $$unsorted $$unsorted Bool)) % 203.53/203.82 (declare-const tptp.noc $$unsorted) % 203.53/203.82 (declare-const tptp.uns $$unsorted) % 203.53/203.82 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 203.53/203.82 (declare-const tptp.tca $$unsorted) % 203.53/203.82 (declare-const tptp.sca $$unsorted) % 203.53/203.82 (declare-const tptp.wth $$unsorted) % 203.53/203.82 (declare-const tptp.unp $$unsorted) % 203.53/203.82 (declare-const tptp.wca $$unsorted) % 203.53/203.82 (declare-const tptp.wec $$unsorted) % 203.53/203.82 (declare-const tptp.sap $$unsorted) % 203.53/203.82 (declare-const tptp.wtc $$unsorted) % 203.53/203.82 (declare-const tptp.model (-> $$unsorted $$unsorted Bool)) % 203.53/203.82 (declare-const tptp.sat $$unsorted) % 203.53/203.82 (declare-const tptp.cax $$unsorted) % 203.53/203.82 (declare-const tptp.eqv $$unsorted) % 203.53/203.82 (declare-const tptp.esa $$unsorted) % 203.53/203.82 (declare-const tptp.csa $$unsorted) % 203.53/203.82 (declare-const tptp.status (-> $$unsorted $$unsorted $$unsorted Bool)) % 203.53/203.82 (declare-const tptp.thm $$unsorted) % 203.53/203.82 (declare-const tptp.isa (-> $$unsorted $$unsorted Bool)) % 203.53/203.82 (declare-const tptp.eth $$unsorted) % 203.53/203.82 (declare-const tptp.tac $$unsorted) % 203.53/203.82 (declare-const tptp.tau $$unsorted) % 203.53/203.82 (define @t1 () (@var "C" $$unsorted)) % 203.53/203.82 (define @t2 () (@var "Ax" $$unsorted)) % 203.53/203.82 (define @t3 () (@var "I2" $$unsorted)) % 203.53/203.82 (define @t4 () (tptp.model @t3 @t1)) % 203.53/203.82 (define @t5 () (@list @t3)) % 203.53/203.82 (define @t6 () (exists @t5 @t4)) % 203.53/203.82 (define @t7 () (@var "I1" $$unsorted)) % 203.53/203.82 (define @t8 () (tptp.model @t7 @t2)) % 203.53/203.82 (define @t9 () (@list @t7)) % 203.53/203.82 (define @t10 () (exists @t9 @t8)) % 203.53/203.82 (define @t11 () (not @t10)) % 203.53/203.82 (define @t12 () (@list @t2 @t1)) % 203.53/203.82 (define @t13 () (tptp.status @t2 @t1 tptp.sap)) % 203.53/203.82 (define @t14 () (=> @t10 @t6)) % 203.53/203.82 (define @t15 () (= @t14 @t13)) % 203.53/203.82 (define @t16 () (forall @t12 @t15)) % 203.53/203.82 (define @t17 () (tptp.model @t7 @t1)) % 203.53/203.82 (define @t18 () (and @t8 @t17)) % 203.53/203.82 (define @t19 () (exists @t9 @t18)) % 203.53/203.82 (define @t20 () (tptp.status @t2 @t1 tptp.thm)) % 203.53/203.82 (define @t21 () (forall @t9 (=> @t8 @t17))) % 203.53/203.82 (define @t22 () (= @t21 @t20)) % 203.53/203.82 (define @t23 () (forall @t12 @t22)) % 203.53/203.82 (define @t24 () (tptp.model @t3 @t2)) % 203.53/203.82 (define @t25 () (forall @t5 @t4)) % 203.53/203.82 (define @t26 () (@var "I3" $$unsorted)) % 203.53/203.82 (define @t27 () (tptp.model @t26 @t2)) % 203.53/203.82 (define @t28 () (not @t27)) % 203.53/203.82 (define @t29 () (tptp.model @t26 @t1)) % 203.53/203.82 (define @t30 () (@list @t26)) % 203.53/203.82 (define @t31 () (exists @t30 (and @t29 @t28))) % 203.53/203.82 (define @t32 () (forall @t5 (=> @t24 @t4))) % 203.53/203.82 (define @t33 () (not @t24)) % 203.53/203.82 (define @t34 () (exists @t5 @t33)) % 203.53/203.82 (define @t35 () (@var "I4" $$unsorted)) % 203.53/203.82 (define @t36 () (exists (@list @t35) (not (tptp.model @t35 @t1)))) % 203.53/203.82 (define @t37 () (tptp.not @t1)) % 203.53/203.82 (define @t38 () (tptp.model @t3 @t37)) % 203.53/203.82 (define @t39 () (@var "S2" $$unsorted)) % 203.53/203.82 (define @t40 () (@var "S1" $$unsorted)) % 203.53/203.82 (define @t41 () (tptp.status @t2 @t1 @t39)) % 203.53/203.82 (define @t42 () (tptp.status @t2 @t1 @t40)) % 203.53/203.82 (define @t43 () (@list @t40 @t39)) % 203.53/203.82 (define @t44 () (tptp.nota @t40 @t39)) % 203.53/203.82 (define @t45 () (not @t41)) % 203.53/203.82 (define @t46 () (and @t42 @t45)) % 203.53/203.82 (define @t47 () (exists @t12 @t46)) % 203.53/203.82 (define @t48 () (= @t47 @t44)) % 203.53/203.82 (define @t49 () (forall @t43 @t48)) % 203.53/203.82 (define @t50 () (@var "F" $$unsorted)) % 203.53/203.82 (define @t51 () (@var "I" $$unsorted)) % 203.53/203.82 (define @t52 () (tptp.model @t51 (tptp.not @t50))) % 203.53/203.82 (define @t53 () (tptp.model @t51 @t50)) % 203.53/203.82 (define @t54 () (@list @t51 @t50)) % 203.53/203.82 (define @t55 () (@list @t51)) % 203.53/203.82 (define @t56 () (forall @t55 @t53)) % 203.53/203.82 (define @t57 () (@list @t50)) % 203.53/203.82 (define @t58 () (exists @t57 @t56)) % 203.53/203.82 (define @t59 () (tptp.model @t3 @t50)) % 203.53/203.82 (define @t60 () (not @t59)) % 203.53/203.82 (define @t61 () (exists @t5 @t60)) % 203.53/203.82 (define @t62 () (tptp.model @t7 @t50)) % 203.53/203.82 (define @t63 () (exists @t9 @t62)) % 203.53/203.82 (define @t64 () (and @t63 @t61)) % 203.53/203.82 (define @t65 () (exists @t57 @t64)) % 203.53/203.82 (define @t66 () (not @t4)) % 203.53/203.82 (define @t67 () (not (tptp.nota tptp.sap tptp.thm))) % 203.53/203.82 (define @t68 () (@var "b_I1" it_8_$$unsorted)) % 203.53/203.82 (define @t69 () (@const 0 (-> it_8_$$unsorted $$unsorted Bool))) % 203.53/203.82 (define @t70 () (@list @t68)) % 203.53/203.82 (define @t71 () (@const 1 it_7_$$unsorted)) % 203.53/203.82 (define @t72 () (@const 2 (-> $$unsorted $$unsorted it_7_$$unsorted Bool))) % 203.53/203.82 (define @t73 () (_ @t72 @t2 @t1 @t71)) % 203.53/203.82 (define @t74 () (not @t8)) % 203.53/203.82 (define @t75 () (forall @t9 (or @t74 @t17))) % 203.53/203.82 (define @t76 () (@var "b_BOUND_VARIABLE_7854" it_8_$$unsorted)) % 203.53/203.82 (define @t77 () (@var "b_BOUND_VARIABLE_7850" it_8_$$unsorted)) % 203.53/203.82 (define @t78 () (forall (@list @t50 @t77 @t76) (or (not (_ @t69 @t77 @t50)) (_ @t69 @t76 @t50)))) % 203.53/203.82 (define @t79 () (@quantifiers_skolemize @t78 0)) % 203.53/203.82 (define @t80 () (@var "b_I" it_8_$$unsorted)) % 203.53/203.82 (define @t81 () (@list @t80)) % 203.53/203.82 (define @t82 () (forall @t57 (not (forall @t81 (_ @t69 @t80 @t50))))) % 203.53/203.82 (define @t83 () (@quantifiers_skolemize @t82 0)) % 203.53/203.82 (define @t84 () (@list @t83 @t79)) % 203.53/203.82 (define @t85 () (@var "b_S2" it_7_$$unsorted)) % 203.53/203.82 (define @t86 () (@var "b_S1" it_7_$$unsorted)) % 203.53/203.82 (define @t87 () (@const 3 (-> it_7_$$unsorted it_7_$$unsorted Bool))) % 203.53/203.82 (define @t88 () (not @t42)) % 203.53/203.82 (define @t89 () (not (forall @t12 (or @t88 @t41)))) % 203.53/203.82 (define @t90 () (forall @t12 (not @t46))) % 203.53/203.82 (define @t91 () (not @t90)) % 203.53/203.82 (define @t92 () (@const 4 it_7_$$unsorted)) % 203.53/203.82 (define @t93 () (_ @t87 @t92 @t71)) % 203.53/203.82 (define @t94 () (_ @t72 @t2 @t1 @t92)) % 203.53/203.82 (define @t95 () (forall @t12 (or (not @t94) @t73))) % 203.53/203.82 (define @t96 () (not @t95)) % 203.53/203.82 (define @t97 () (= @t93 @t96)) % 203.53/203.82 (define @t98 () (not @t97)) % 203.53/203.82 (define @t99 () (@list true false)) % 203.53/203.82 (define @t100 () (@var "b_I2" it_8_$$unsorted)) % 203.53/203.82 (define @t101 () (@list @t100)) % 203.53/203.82 (define @t102 () (@var "b_I1" it_8_$$unsorted)) % 203.53/203.82 (define @t103 () (@list @t102)) % 203.53/203.82 (define @t104 () (not (forall @t5 @t66))) % 203.53/203.82 (define @t105 () (forall @t9 @t74)) % 203.53/203.82 (define @t106 () (not @t105)) % 203.53/203.82 (define @t107 () (=> @t106 @t104)) % 203.53/203.82 (define @t108 () (= @t13 @t107)) % 203.53/203.82 (define @t109 () (@var "BOUND_VARIABLE_7854" $$unsorted)) % 203.53/203.82 (define @t110 () (tptp.model @t109 @t50)) % 203.53/203.82 (define @t111 () (@var "BOUND_VARIABLE_7850" $$unsorted)) % 203.53/203.82 (define @t112 () (not (tptp.model @t111 @t50))) % 203.53/203.82 (define @t113 () (or @t112 @t110)) % 203.53/203.82 (define @t114 () (forall (@list @t50 @t111 @t109) @t113)) % 203.53/203.82 (define @t115 () (forall (@list @t111 @t109) @t113)) % 203.53/203.82 (define @t116 () (forall (@list @t109) @t110)) % 203.53/203.82 (define @t117 () (forall (@list @t111) @t112)) % 203.53/203.82 (define @t118 () (or @t117 @t116)) % 203.53/203.82 (define @t119 () (forall @t5 @t59)) % 203.53/203.82 (define @t120 () (forall @t9 (not @t62))) % 203.53/203.82 (define @t121 () (not @t119)) % 203.53/203.82 (define @t122 () (not @t120)) % 203.53/203.82 (define @t123 () (and @t122 @t121)) % 203.53/203.82 (define @t124 () (forall @t57 (not @t123))) % 203.53/203.82 (define @t125 () (not @t124)) % 203.53/203.82 (define @t126 () (forall @t5 (not @t60))) % 203.53/203.82 (define @t127 () (not @t126)) % 203.53/203.82 (define @t128 () (@quantifiers_skolemize @t78 1)) % 203.53/203.82 (define @t129 () (_ @t69 @t128 @t79)) % 203.53/203.82 (define @t130 () (@quantifiers_skolemize @t78 2)) % 203.53/203.82 (define @t131 () (_ @t69 @t130 @t79)) % 203.53/203.82 (define @t132 () (not @t129)) % 203.53/203.82 (define @t133 () (or @t132 @t131)) % 203.53/203.82 (define @t134 () (@list true)) % 203.53/203.82 (define @t135 () (@list @t133)) % 203.53/203.82 (define @t136 () (@var "b_I1" it_8_$$unsorted)) % 203.53/203.82 (define @t137 () (forall (@list @t136) (not (_ @t69 @t136 @t79)))) % 203.53/203.82 (define @t138 () (not @t137)) % 203.53/203.82 (define @t139 () (forall @t101 (not (_ @t69 @t100 @t79)))) % 203.53/203.82 (define @t140 () (not @t139)) % 203.53/203.82 (define @t141 () (or (forall @t103 (not (_ @t69 @t102 @t83))) @t140)) % 203.53/203.82 (define @t142 () (_ @t72 @t83 @t79 @t92)) % 203.53/203.82 (define @t143 () (= @t142 @t141)) % 203.53/203.82 (define @t144 () (@list false false)) % 203.53/203.82 (define @t145 () (_ @t72 @t83 @t79 @t71)) % 203.53/203.82 (define @t146 () (not @t142)) % 203.53/203.82 (define @t147 () (or @t146 @t145)) % 203.53/203.82 (define @t148 () (forall @t70 (or (not (_ @t69 @t68 @t83)) (_ @t69 @t68 @t79)))) % 203.53/203.82 (define @t149 () (= @t145 @t148)) % 203.53/203.82 (define @t150 () (not @t82)) % 203.53/203.82 (define @t151 () (not (forall @t57 (not @t56)))) % 203.53/203.82 (define @t152 () (forall @t81 (_ @t69 @t80 @t83))) % 203.53/203.82 (define @t153 () (not (not @t152))) % 203.53/203.82 (define @t154 () (@list @t130)) % 203.53/203.82 (define @t155 () (_ @t69 @t130 @t83)) % 203.53/203.82 (define @t156 () (not @t155)) % 203.53/203.82 (define @t157 () (or @t156 @t131)) % 203.53/203.82 (define @t158 () (not @t157)) % 203.53/203.82 (assume @p1 (forall @t12 (= (=> @t11 (not @t6)) (tptp.status @t2 @t1 tptp.unp)))) % 203.53/203.82 (assume @p2 @t16) % 203.53/203.82 (assume @p3 (forall @t12 (= (= @t10 @t6) (tptp.status @t2 @t1 tptp.esa)))) % 203.53/203.82 (assume @p4 (forall @t12 (= @t19 (tptp.status @t2 @t1 tptp.sat)))) % 203.53/203.82 (assume @p5 @t23) % 203.53/203.82 (assume @p6 (forall @t12 (= (and @t10 (forall @t5 (= @t24 @t4))) (tptp.status @t2 @t1 tptp.eqv)))) % 203.53/203.82 (assume @p7 (forall @t12 (= (and @t10 @t25) (tptp.status @t2 @t1 tptp.tac)))) % 203.53/203.82 (assume @p8 (forall @t12 (= (and @t10 @t32 @t31) (tptp.status @t2 @t1 tptp.wec)))) % 203.53/203.82 (assume @p9 (forall @t12 (= (and @t10 @t34 (forall @t30 (= @t27 @t29))) (tptp.status @t2 @t1 tptp.eth)))) % 203.53/203.82 (assume @p10 (forall @t12 (= (forall @t9 @t18) (tptp.status @t2 @t1 tptp.tau)))) % 203.53/203.82 (assume @p11 (forall @t12 (= (and @t10 @t34 (forall @t30 @t29)) (tptp.status @t2 @t1 tptp.wtc)))) % 203.53/203.82 (assume @p12 (forall @t12 (= (and @t10 @t32 @t31 @t36) (tptp.status @t2 @t1 tptp.wth)))) % 203.53/203.82 (assume @p13 (forall @t12 (= @t11 (tptp.status @t2 @t1 tptp.cax)))) % 203.53/203.82 (assume @p14 (forall @t12 (= (and @t11 @t6) (tptp.status @t2 @t1 tptp.sca)))) % 203.53/203.82 (assume @p15 (forall @t12 (= (and @t11 @t25) (tptp.status @t2 @t1 tptp.tca)))) % 203.53/203.82 (assume @p16 (forall @t12 (= (and @t11 @t6 (exists @t30 (not @t29))) (tptp.status @t2 @t1 tptp.wca)))) % 203.53/203.82 (assume @p17 (forall @t12 (= (exists @t9 (and @t8 (tptp.model @t7 @t37))) (tptp.status @t2 @t1 tptp.csa)))) % 203.53/203.82 (assume @p18 (forall @t12 (= (and (forall @t9 @t8) (forall @t5 @t38)) (tptp.status @t2 @t1 tptp.uns)))) % 203.53/203.82 (assume @p19 (forall @t12 (= (and @t19 (exists @t5 (and @t24 @t38))) (tptp.status @t2 @t1 tptp.noc)))) % 203.53/203.82 (assume @p20 (forall @t43 (= (exists @t12 (and @t42 @t41)) (tptp.mighta @t40 @t39)))) % 203.53/203.82 (assume @p21 (forall @t43 (= (forall @t12 (=> @t42 @t41)) (tptp.isa @t40 @t39)))) % 203.53/203.82 (assume @p22 @t49) % 203.53/203.82 (assume @p23 (forall @t43 (= (forall @t12 (=> @t42 @t45)) (tptp.nevera @t40 @t39)))) % 203.53/203.82 (assume @p24 (forall @t43 (= (forall @t12 (xor @t42 @t41)) (tptp.xora @t40 @t39)))) % 203.53/203.82 (assume @p25 (forall @t54 (xor @t53 @t52))) % 203.53/203.82 (assume @p26 (forall @t54 (= @t53 (not @t52)))) % 203.53/203.82 (assume @p27 @t58) % 203.53/203.82 (assume @p28 @t65) % 203.53/203.82 (assume @p29 (exists @t57 (forall @t55 (not @t53)))) % 203.53/203.82 (assume @p30 (exists @t12 (and @t19 (exists @t5 (or @t33 @t66))))) % 203.53/203.82 (assume @p31 (exists @t12 (and @t10 @t32 (exists @t30 (and @t28 @t29)) @t36))) % 203.53/203.82 (assume @p32 (exists (@list @t7 @t2 @t1) (and @t8 (not @t17) @t6))) % 203.53/203.82 (assume @p33 @t67) % 203.53/203.82 (assume @p34 true) % 203.53/203.82 ; WARNING: add trust step for TRUST % 203.53/203.82 ; trust TRUST PREPROCESS_SORT_INFER % 203.53/203.82 (step @p35 :rule trust :premises () :args ((= (forall @t12 (= @t20 @t75)) (forall @t12 (= @t73 (forall @t70 (or (not (_ @t69 @t68 @t2)) (_ @t69 @t68 @t1)))))))) % 203.53/203.82 (step @p36 :rule eq-symm :args (@t75 @t20)) % 203.53/203.82 (step @p37 :rule refl :args (@t20)) % 203.53/203.82 (step @p38 :rule bool-impl-elim :args (@t8 @t17)) % 203.53/203.82 (step @p39 :rule cong :premises (@p38) :args (@t21)) % 203.53/203.82 (step @p40 :rule cong :premises (@p39 @p37) :args (@t22)) % 203.53/203.82 (step @p41 :rule trans :premises (@p40 @p36)) % 203.53/203.82 (step @p42 :rule cong :premises (@p41) :args (@t23)) % 203.53/203.82 (step @p43 :rule trans :premises (@p42 @p35)) % 203.53/203.82 (step @p44 :rule eq_resolve :premises (@p5 @p43)) % 203.53/203.82 (step @p45 :rule instantiate :premises (@p44) :args (@t84)) % 203.53/203.82 ; trust TRUST PREPROCESS_SORT_INFER % 203.53/203.82 (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))))))))) % 203.53/203.82 (step @p47 :rule eq-symm :args (@t89 @t44)) % 203.53/203.82 (step @p48 :rule refl :args (@t44)) % 203.53/203.82 (step @p49 :rule bool-double-not-elim :args (@t41)) % 203.53/203.82 (step @p50 :rule refl :args (@t88)) % 203.53/203.82 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or @t88 (not @t45)))) % 203.53/203.82 (step @p52 :rule bool-and-de-morgan :args (@t42 @t45 true)) % 203.53/203.82 (step @p53 :rule trans :premises (@p52 @p51)) % 203.53/203.82 (step @p54 :rule cong :premises (@p53) :args (@t90)) % 203.53/203.82 (step @p55 :rule cong :premises (@p54) :args (@t91)) % 203.53/203.82 (step @p56 :rule exists-elim :args ((= @t47 @t91))) % 203.53/203.82 (step @p57 :rule trans :premises (@p56 @p55)) % 203.53/203.82 (step @p58 :rule cong :premises (@p57 @p48) :args (@t48)) % 203.53/203.82 (step @p59 :rule trans :premises (@p58 @p47)) % 203.53/203.82 (step @p60 :rule cong :premises (@p59) :args (@t49)) % 203.53/203.82 (step @p61 :rule trans :premises (@p60 @p46)) % 203.53/203.82 (step @p62 :rule eq_resolve :premises (@p22 @p61)) % 203.53/203.82 (step @p63 :rule instantiate :premises (@p62) :args ((@list @t92 @t71))) % 203.53/203.82 ; trust TRUST PREPROCESS_SORT_INFER % 203.53/203.82 (step @p64 :rule trust :premises () :args ((= @t67 (not @t93)))) % 203.53/203.82 (step @p65 :rule eq_resolve :premises (@p33 @p64)) % 203.53/203.82 (step @p66 :rule bool-double-not-elim :args (@t95)) % 203.53/203.82 (step @p67 :rule refl :args (@t93)) % 203.53/203.82 (step @p68 :rule refl :args (@t98)) % 203.53/203.82 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66) :args ((or @t98 @t93 (not @t96)))) % 203.53/203.82 (step @p70 :rule cnf_equiv_pos2 :args (@t97)) % 203.53/203.82 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 203.53/203.82 (step @p72 :rule reordering :premises (@p71) :args ((or @t93 @t95 @t98))) % 203.53/203.82 (step @p73 :rule chain_m_resolution :premises (@p72 @p65 @p63) :args (@t95 @t99 (@list @t93 @t97))) % 203.53/203.82 (step @p74 :rule instantiate :premises (@p73) :args (@t84)) % 203.53/203.82 ; trust TRUST PREPROCESS_SORT_INFER % 203.53/203.82 (step @p75 :rule trust :premises () :args ((= (forall @t12 (= @t13 (or @t105 @t104))) (forall @t12 (= @t94 (or (forall @t103 (not (_ @t69 @t102 @t2))) (not (forall @t101 (not (_ @t69 @t100 @t1)))))))))) % 203.53/203.82 (step @p76 :rule refl :args (@t104)) % 203.53/203.82 (step @p77 :rule bool-double-not-elim :args (@t105)) % 203.53/203.82 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or (not @t106) @t104))) % 203.53/203.82 (step @p79 :rule bool-impl-elim :args (@t106 @t104)) % 203.53/203.82 (step @p80 :rule trans :premises (@p79 @p78)) % 203.53/203.82 (step @p81 :rule refl :args (@t13)) % 203.53/203.82 (step @p82 :rule cong :premises (@p81 @p80) :args (@t108)) % 203.53/203.82 (step @p83 :rule cong :premises (@p82) :args ((forall @t12 @t108))) % 203.53/203.82 (step @p84 :rule eq-symm :args (@t107 @t13)) % 203.53/203.82 (step @p85 :rule refl :args (@t13)) % 203.53/203.82 (step @p86 :rule exists-elim :args ((= @t6 @t104))) % 203.53/203.82 (step @p87 :rule exists-elim :args ((= @t10 @t106))) % 203.53/203.82 (step @p88 :rule cong :premises (@p87 @p86) :args (@t14)) % 203.53/203.82 (step @p89 :rule cong :premises (@p88 @p85) :args (@t15)) % 203.53/203.82 (step @p90 :rule trans :premises (@p89 @p84)) % 203.53/203.82 (step @p91 :rule cong :premises (@p90) :args (@t16)) % 203.53/203.82 (step @p92 :rule trans :premises (@p91 @p83)) % 203.53/203.82 (step @p93 :rule trans :premises (@p92 @p75)) % 203.53/203.82 (step @p94 :rule eq_resolve :premises (@p2 @p93)) % 203.53/203.82 (step @p95 :rule instantiate :premises (@p94) :args (@t84)) % 203.53/203.82 ; trust TRUST PREPROCESS_SORT_INFER % 203.53/203.82 (step @p96 :rule trust :premises () :args ((= (not @t114) (not @t78)))) % 203.53/203.82 (step @p97 :rule quant-merge-prenex :args ((= (forall @t57 @t115) @t114))) % 203.53/203.82 (step @p98 :rule alpha_equiv :args (@t116 (@list @t109) (@list @t3))) % 203.53/203.82 (step @p99 :rule alpha_equiv :args (@t117 (@list @t111) (@list @t7))) % 203.53/203.82 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t118)) % 203.53/203.82 (step @p101 :rule quant-miniscope-or :args ((= @t115 @t118))) % 203.53/203.82 (step @p102 :rule trans :premises (@p101 @p100)) % 203.53/203.82 (step @p103 :rule symm :premises (@p102)) % 203.53/203.82 (step @p104 :rule cong :premises (@p103) :args ((forall @t57 (or @t120 @t119)))) % 203.53/203.82 (step @p105 :rule trans :premises (@p104 @p97)) % 203.53/203.82 (step @p106 :rule bool-double-not-elim :args (@t119)) % 203.53/203.82 (step @p107 :rule bool-double-not-elim :args (@t120)) % 203.53/203.82 (step @p108 :rule nary_cong :premises (@p107 @p106) :args ((or (not @t122) (not @t121)))) % 203.53/203.82 (step @p109 :rule bool-and-de-morgan :args (@t122 @t121 true)) % 203.53/203.82 (step @p110 :rule trans :premises (@p109 @p108)) % 203.53/203.82 (step @p111 :rule cong :premises (@p110) :args (@t124)) % 203.53/203.82 (step @p112 :rule trans :premises (@p111 @p105)) % 203.53/203.82 (step @p113 :rule cong :premises (@p112) :args (@t125)) % 203.53/203.82 (step @p114 :rule exists-elim :args ((= (exists @t57 @t123) @t125))) % 203.53/203.82 (step @p115 :rule trans :premises (@p114 @p113)) % 203.53/203.82 (step @p116 :rule bool-double-not-elim :args (@t59)) % 203.53/203.82 (step @p117 :rule cong :premises (@p116) :args (@t126)) % 203.53/203.82 (step @p118 :rule cong :premises (@p117) :args (@t127)) % 203.53/203.82 (step @p119 :rule exists-elim :args ((= @t61 @t127))) % 203.53/203.82 (step @p120 :rule trans :premises (@p119 @p118)) % 203.53/203.82 (step @p121 :rule exists-elim :args ((= @t63 @t122))) % 203.53/203.82 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t64)) % 203.53/203.82 (step @p123 :rule cong :premises (@p122) :args (@t65)) % 203.53/203.82 (step @p124 :rule trans :premises (@p123 @p115)) % 203.53/203.82 (step @p125 :rule trans :premises (@p124 @p96)) % 203.53/203.82 (step @p126 :rule eq_resolve :premises (@p28 @p125)) % 203.53/203.82 (step @p127 :rule skolemize :premises (@p126)) % 203.53/203.82 (step @p128 :rule bool-double-not-elim :args (@t129)) % 203.53/203.82 (step @p129 :rule refl :args (@t133)) % 203.53/203.82 (step @p130 :rule nary_cong :premises (@p129 @p128) :args ((or @t133 (not @t132)))) % 203.53/203.82 (step @p131 :rule cnf_or_neg :args (@t133 0)) % 203.53/203.82 (step @p132 :rule eq_resolve :premises (@p131 @p130)) % 203.53/203.82 (step @p133 :rule reordering :premises (@p132) :args ((or @t129 @t133))) % 203.53/203.82 (step @p134 :rule chain_m_resolution :premises (@p133 @p127) :args (@t129 @t134 @t135)) % 203.53/203.82 (assume-push @p191 @t137) % 203.53/203.82 (step @p136 :rule instantiate :premises (@p191) :args ((@list @t128))) % 203.53/203.82 (step-pop @p192 :rule scope :premises (@p136)) % 203.53/203.82 (step @p137 :rule process_scope :premises (@p192) :args (@t132)) % 203.53/203.82 (step @p139 :rule implies_elim :premises (@p137)) % 203.53/203.82 (step @p140 :rule reordering :premises (@p139) :args ((or @t132 @t138))) % 203.53/203.82 (step @p141 :rule chain_m_resolution :premises (@p140 @p134) :args (@t138 (@list false) (@list @t129))) % 203.53/203.82 (step @p142 :rule alpha_equiv :args (@t137 (@list @t136) (@list @t100))) % 203.53/203.82 (step @p143 :rule equiv_elim2 :premises (@p142)) % 203.53/203.82 (step @p144 :rule chain_m_resolution :premises (@p143 @p141) :args (@t140 @t134 (@list @t137))) % 203.53/203.82 (step @p145 :rule bool-double-not-elim :args (@t139)) % 203.53/203.82 (step @p146 :rule refl :args (@t141)) % 203.53/203.82 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or @t141 (not @t140)))) % 203.53/203.82 (step @p148 :rule cnf_or_neg :args (@t141 1)) % 203.53/203.82 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 203.53/203.82 (step @p150 :rule reordering :premises (@p149) :args ((or @t139 @t141))) % 203.53/203.82 (step @p151 :rule chain_m_resolution :premises (@p150 @p144) :args (@t141 @t134 (@list @t139))) % 203.53/203.82 (step @p152 :rule cnf_equiv_pos2 :args (@t143)) % 203.53/203.82 (step @p153 :rule reordering :premises (@p152) :args ((or @t142 (not @t141) (not @t143)))) % 203.53/203.82 (step @p154 :rule chain_m_resolution :premises (@p153 @p151 @p95) :args (@t142 @t144 (@list @t141 @t143))) % 203.53/203.82 (step @p155 :rule cnf_or_pos :args (@t147)) % 203.53/203.82 (step @p156 :rule reordering :premises (@p155) :args ((or @t145 @t146 (not @t147)))) % 203.53/203.82 (step @p157 :rule chain_m_resolution :premises (@p156 @p154 @p74) :args (@t145 @t144 (@list @t142 @t147))) % 203.53/203.82 (step @p158 :rule cnf_equiv_pos1 :args (@t149)) % 203.53/203.82 (step @p159 :rule reordering :premises (@p158) :args ((or @t148 (not @t145) (not @t149)))) % 203.53/203.82 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p45) :args (@t148 @t144 (@list @t145 @t149))) % 203.53/203.82 ; trust TRUST PREPROCESS_SORT_INFER % 203.53/203.82 (step @p161 :rule trust :premises () :args ((= @t151 @t150))) % 203.53/203.82 (step @p162 :rule exists-elim :args ((= @t58 @t151))) % 203.53/203.82 (step @p163 :rule trans :premises (@p162 @p161)) % 203.53/203.82 (step @p164 :rule eq_resolve :premises (@p27 @p163)) % 203.53/203.82 (step @p165 :rule refl :args (@t152)) % 203.53/203.82 (step @p166 :rule bool-double-not-elim :args (@t82)) % 203.53/203.82 (step @p167 :rule nary_cong :premises (@p166 @p165) :args ((or (not @t150) @t152))) % 203.53/203.82 (step @p168 :rule bool-double-not-elim :args (@t152)) % 203.53/203.82 (step @p169 :rule refl :args (@t150)) % 203.53/203.82 (step @p170 :rule cong :premises (@p169 @p168) :args ((=> @t150 @t153))) % 203.53/203.82 (assume-push @p193 @t150) % 203.53/203.82 (step @p172 :rule skolemize :premises (@p164)) % 203.53/203.82 (step-pop @p194 :rule scope :premises (@p172)) % 203.53/203.82 (step @p173 :rule process_scope :premises (@p194) :args (@t153)) % 203.53/203.82 (step @p175 :rule eq_resolve :premises (@p173 @p170)) % 203.53/203.82 (step @p176 :rule implies_elim :premises (@p175)) % 203.53/203.82 (step @p177 :rule eq_resolve :premises (@p176 @p167)) % 203.53/203.82 (step @p178 :rule chain_m_resolution :premises (@p177 @p164) :args (@t152 @t134 (@list @t82))) % 203.53/203.82 (step @p179 :rule instantiate :premises (@p178) :args (@t154)) % 203.53/203.82 (step @p180 :rule cnf_or_neg :args (@t133 1)) % 203.53/203.82 (step @p181 :rule chain_m_resolution :premises (@p180 @p127) :args ((not @t131) @t134 @t135)) % 203.53/203.82 (step @p182 :rule cnf_or_pos :args (@t157)) % 203.53/203.82 (step @p183 :rule reordering :premises (@p182) :args ((or @t131 @t156 @t158))) % 203.53/203.82 (step @p184 :rule chain_m_resolution :premises (@p183 @p181 @p179) :args (@t158 @t99 (@list @t131 @t155))) % 203.53/203.82 (assume-push @p195 @t148) % 203.53/203.82 (step @p186 :rule instantiate :premises (@p195) :args (@t154)) % 203.53/203.82 (step-pop @p196 :rule scope :premises (@p186)) % 203.53/203.82 (step @p187 :rule process_scope :premises (@p196) :args (@t157)) % 203.53/203.82 (step @p189 :rule implies_elim :premises (@p187)) % 203.53/203.82 (step @p190 false :rule chain_m_resolution :premises (@p189 @p184 @p160) :args (false @t99 (@list @t157 @t148))) % 203.53/203.83 ) % 203.53/203.83 % SZS output end Proof % 203.53/203.83 % cvc5 exiting %------------------------------------------------------------------------------