%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG178+1 : TPTP v9.2.1. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 08:05:25 AM UTC 2026 % Result : Theorem 0.41s 0.60s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ALG178+1 : TPTP v9.2.1. Released v2.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n005.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 01:40:48 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.41/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.41/0.60 % SZS status Theorem % 0.41/0.60 % SZS output start Proof % 0.41/0.60 ( % 0.41/0.60 (declare-sort $$unsorted 0) % 0.41/0.60 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.41/0.60 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.41/0.60 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.41/0.60 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.60 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.41/0.60 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.60 (define @t1 () (@var "V" $$unsorted)) % 0.41/0.60 (define @t2 () (@var "U" $$unsorted)) % 0.41/0.60 (define @t3 () (tptp.op1 @t2 @t1)) % 0.41/0.60 (define @t4 () (tptp.sorti1 @t1)) % 0.41/0.60 (define @t5 () (@list @t1)) % 0.41/0.60 (define @t6 () (tptp.sorti1 @t2)) % 0.41/0.60 (define @t7 () (@list @t2)) % 0.41/0.60 (define @t8 () (tptp.op2 @t2 @t1)) % 0.41/0.60 (define @t9 () (tptp.sorti2 @t8)) % 0.41/0.60 (define @t10 () (tptp.sorti2 @t1)) % 0.41/0.60 (define @t11 () (forall @t5 (=> @t10 @t9))) % 0.41/0.60 (define @t12 () (tptp.sorti2 @t2)) % 0.41/0.60 (define @t13 () (=> @t12 @t11)) % 0.41/0.60 (define @t14 () (forall @t7 @t13)) % 0.41/0.60 (define @t15 () (tptp.op1 @t2 @t3)) % 0.41/0.60 (define @t16 () (=> @t4 (= @t15 @t1))) % 0.41/0.60 (define @t17 () (forall @t5 @t16)) % 0.41/0.60 (define @t18 () (=> @t6 @t17)) % 0.41/0.60 (define @t19 () (forall @t7 @t18)) % 0.41/0.60 (define @t20 () (tptp.op2 @t2 @t8)) % 0.41/0.60 (define @t21 () (=> @t10 (= @t20 @t1))) % 0.41/0.60 (define @t22 () (forall @t5 @t21)) % 0.41/0.60 (define @t23 () (=> @t12 @t22)) % 0.41/0.60 (define @t24 () (forall @t7 @t23)) % 0.41/0.60 (define @t25 () (not @t24)) % 0.41/0.60 (define @t26 () (@var "X2" $$unsorted)) % 0.41/0.60 (define @t27 () (tptp.j (tptp.h @t26))) % 0.41/0.60 (define @t28 () (tptp.sorti1 @t26)) % 0.41/0.60 (define @t29 () (=> @t28 (= @t27 @t26))) % 0.41/0.60 (define @t30 () (@list @t26)) % 0.41/0.60 (define @t31 () (forall @t30 @t29)) % 0.41/0.60 (define @t32 () (@var "X1" $$unsorted)) % 0.41/0.60 (define @t33 () (tptp.h (tptp.j @t32))) % 0.41/0.60 (define @t34 () (tptp.sorti2 @t32)) % 0.41/0.60 (define @t35 () (=> @t34 (= @t33 @t32))) % 0.41/0.60 (define @t36 () (@list @t32)) % 0.41/0.60 (define @t37 () (forall @t36 @t35)) % 0.41/0.60 (define @t38 () (@var "Z" $$unsorted)) % 0.41/0.60 (define @t39 () (@var "Y" $$unsorted)) % 0.41/0.60 (define @t40 () (tptp.j @t39)) % 0.41/0.60 (define @t41 () (= (tptp.j (tptp.op2 @t39 @t38)) (tptp.op1 @t40 (tptp.j @t38)))) % 0.41/0.60 (define @t42 () (tptp.sorti2 @t38)) % 0.41/0.60 (define @t43 () (@list @t38)) % 0.41/0.60 (define @t44 () (forall @t43 (=> @t42 @t41))) % 0.41/0.60 (define @t45 () (tptp.sorti2 @t39)) % 0.41/0.60 (define @t46 () (=> @t45 @t44)) % 0.41/0.60 (define @t47 () (@list @t39)) % 0.41/0.60 (define @t48 () (forall @t47 @t46)) % 0.41/0.60 (define @t49 () (@var "X" $$unsorted)) % 0.41/0.60 (define @t50 () (@var "W" $$unsorted)) % 0.41/0.60 (define @t51 () (tptp.h @t50)) % 0.41/0.60 (define @t52 () (= (tptp.h (tptp.op1 @t50 @t49)) (tptp.op2 @t51 (tptp.h @t49)))) % 0.41/0.60 (define @t53 () (tptp.sorti1 @t49)) % 0.41/0.60 (define @t54 () (@list @t49)) % 0.41/0.60 (define @t55 () (forall @t54 (=> @t53 @t52))) % 0.41/0.60 (define @t56 () (tptp.sorti1 @t50)) % 0.41/0.60 (define @t57 () (=> @t56 @t55)) % 0.41/0.60 (define @t58 () (@list @t50)) % 0.41/0.60 (define @t59 () (forall @t58 @t57)) % 0.41/0.60 (define @t60 () (and @t59 @t48 @t37 @t31)) % 0.41/0.60 (define @t61 () (not @t60)) % 0.41/0.60 (define @t62 () (tptp.sorti1 (tptp.j @t1))) % 0.41/0.60 (define @t63 () (forall @t5 (=> @t10 @t62))) % 0.41/0.60 (define @t64 () (tptp.sorti2 (tptp.h @t2))) % 0.41/0.60 (define @t65 () (forall @t7 (=> @t6 @t64))) % 0.41/0.60 (define @t66 () (and @t65 @t63)) % 0.41/0.60 (define @t67 () (=> @t66 @t61)) % 0.41/0.60 (define @t68 () (not @t67)) % 0.41/0.60 (define @t69 () (@var "BOUND_VARIABLE_7584" $$unsorted)) % 0.41/0.60 (define @t70 () (= @t69 (tptp.op2 @t2 (tptp.op2 @t2 @t69)))) % 0.41/0.60 (define @t71 () (not (tptp.sorti2 @t69))) % 0.41/0.60 (define @t72 () (not @t12)) % 0.41/0.60 (define @t73 () (or @t72 @t71 @t70)) % 0.41/0.60 (define @t74 () (or @t71 @t70)) % 0.41/0.60 (define @t75 () (or @t72 @t74)) % 0.41/0.60 (define @t76 () (@list @t2 @t69)) % 0.41/0.60 (define @t77 () (forall @t76 @t75)) % 0.41/0.60 (define @t78 () (@list @t69)) % 0.41/0.60 (define @t79 () (forall @t78 @t75)) % 0.41/0.60 (define @t80 () (forall @t78 @t74)) % 0.41/0.60 (define @t81 () (@list @t1)) % 0.41/0.60 (define @t82 () (or @t72 @t80)) % 0.41/0.60 (define @t83 () (= @t1 @t20)) % 0.41/0.60 (define @t84 () (not @t10)) % 0.41/0.60 (define @t85 () (forall @t5 (or @t84 @t83))) % 0.41/0.60 (define @t86 () (forall @t76 @t73)) % 0.41/0.60 (define @t87 () (@quantifiers_skolemize @t86 1)) % 0.41/0.60 (define @t88 () (@quantifiers_skolemize @t86 0)) % 0.41/0.60 (define @t89 () (tptp.op2 @t88 @t87)) % 0.41/0.60 (define @t90 () (= @t87 (tptp.op2 @t88 @t89))) % 0.41/0.60 (define @t91 () (tptp.sorti2 @t87)) % 0.41/0.60 (define @t92 () (not @t91)) % 0.41/0.60 (define @t93 () (tptp.sorti2 @t88)) % 0.41/0.60 (define @t94 () (not @t93)) % 0.41/0.60 (define @t95 () (or @t94 @t92 @t90)) % 0.41/0.60 (define @t96 () (not @t90)) % 0.41/0.60 (define @t97 () (@list true)) % 0.41/0.60 (define @t98 () (@list @t95)) % 0.41/0.60 (define @t99 () (= @t26 @t27)) % 0.41/0.60 (define @t100 () (= @t32 @t33)) % 0.41/0.60 (define @t101 () (@var "BOUND_VARIABLE_7635" $$unsorted)) % 0.41/0.60 (define @t102 () (= (tptp.j (tptp.op2 @t39 @t101)) (tptp.op1 @t40 (tptp.j @t101)))) % 0.41/0.60 (define @t103 () (not (tptp.sorti2 @t101))) % 0.41/0.60 (define @t104 () (not @t45)) % 0.41/0.60 (define @t105 () (or @t103 @t102)) % 0.41/0.60 (define @t106 () (or @t104 @t105)) % 0.41/0.60 (define @t107 () (forall (@list @t39 @t101) @t106)) % 0.41/0.60 (define @t108 () (@list @t101)) % 0.41/0.60 (define @t109 () (forall @t108 @t106)) % 0.41/0.60 (define @t110 () (forall @t108 @t105)) % 0.41/0.60 (define @t111 () (or @t104 @t110)) % 0.41/0.60 (define @t112 () (forall @t43 (or (not @t42) @t41))) % 0.41/0.60 (define @t113 () (@var "BOUND_VARIABLE_7612" $$unsorted)) % 0.41/0.60 (define @t114 () (= (tptp.h (tptp.op1 @t50 @t113)) (tptp.op2 @t51 (tptp.h @t113)))) % 0.41/0.60 (define @t115 () (not (tptp.sorti1 @t113))) % 0.41/0.60 (define @t116 () (not @t56)) % 0.41/0.60 (define @t117 () (or @t115 @t114)) % 0.41/0.60 (define @t118 () (or @t116 @t117)) % 0.41/0.60 (define @t119 () (forall (@list @t50 @t113) @t118)) % 0.41/0.60 (define @t120 () (@list @t113)) % 0.41/0.60 (define @t121 () (forall @t120 @t118)) % 0.41/0.60 (define @t122 () (forall @t120 @t117)) % 0.41/0.60 (define @t123 () (or @t116 @t122)) % 0.41/0.60 (define @t124 () (forall @t54 (or (not @t53) @t52))) % 0.41/0.60 (define @t125 () (@list @t88 @t87)) % 0.41/0.60 (define @t126 () (tptp.j @t87)) % 0.41/0.60 (define @t127 () (tptp.j @t88)) % 0.41/0.60 (define @t128 () (tptp.op1 @t127 @t126)) % 0.41/0.60 (define @t129 () (tptp.j @t89)) % 0.41/0.60 (define @t130 () (= @t129 @t128)) % 0.41/0.60 (define @t131 () (or @t94 @t92 @t130)) % 0.41/0.60 (define @t132 () (@list false false false)) % 0.41/0.60 (define @t133 () (@list @t88)) % 0.41/0.60 (define @t134 () (tptp.h @t127)) % 0.41/0.60 (define @t135 () (= @t88 @t134)) % 0.41/0.60 (define @t136 () (or @t94 @t135)) % 0.41/0.60 (define @t137 () (@list false false)) % 0.41/0.60 (define @t138 () (@list @t87)) % 0.41/0.60 (define @t139 () (tptp.h @t126)) % 0.41/0.60 (define @t140 () (= @t87 @t139)) % 0.41/0.60 (define @t141 () (or @t92 @t140)) % 0.41/0.60 (define @t142 () (@var "BOUND_VARIABLE_7561" $$unsorted)) % 0.41/0.60 (define @t143 () (= @t142 (tptp.op1 @t2 (tptp.op1 @t2 @t142)))) % 0.41/0.60 (define @t144 () (not (tptp.sorti1 @t142))) % 0.41/0.60 (define @t145 () (not @t6)) % 0.41/0.60 (define @t146 () (or @t144 @t143)) % 0.41/0.60 (define @t147 () (or @t145 @t146)) % 0.41/0.60 (define @t148 () (forall (@list @t2 @t142) @t147)) % 0.41/0.60 (define @t149 () (@list @t142)) % 0.41/0.60 (define @t150 () (forall @t149 @t147)) % 0.41/0.60 (define @t151 () (forall @t149 @t146)) % 0.41/0.60 (define @t152 () (or @t145 @t151)) % 0.41/0.60 (define @t153 () (= @t1 @t15)) % 0.41/0.60 (define @t154 () (forall @t5 (or (not @t4) @t153))) % 0.41/0.60 (define @t155 () (@list @t127 @t126)) % 0.41/0.60 (define @t156 () (tptp.sorti1 @t126)) % 0.41/0.60 (define @t157 () (or @t92 @t156)) % 0.41/0.60 (define @t158 () (tptp.sorti1 @t127)) % 0.41/0.60 (define @t159 () (or @t94 @t158)) % 0.41/0.60 (define @t160 () (= @t126 (tptp.op1 @t127 @t128))) % 0.41/0.60 (define @t161 () (not @t156)) % 0.41/0.60 (define @t162 () (not @t158)) % 0.41/0.60 (define @t163 () (or @t162 @t161 @t160)) % 0.41/0.60 (define @t164 () (tptp.op2 @t134 @t139)) % 0.41/0.60 (define @t165 () (= (tptp.h @t128) @t164)) % 0.41/0.60 (define @t166 () (or @t162 @t161 @t165)) % 0.41/0.60 (define @t167 () (@var "BOUND_VARIABLE_7539" $$unsorted)) % 0.41/0.60 (define @t168 () (tptp.sorti2 (tptp.op2 @t2 @t167))) % 0.41/0.60 (define @t169 () (not (tptp.sorti2 @t167))) % 0.41/0.60 (define @t170 () (or @t169 @t168)) % 0.41/0.60 (define @t171 () (or @t72 @t170)) % 0.41/0.60 (define @t172 () (forall (@list @t2 @t167) @t171)) % 0.41/0.60 (define @t173 () (@list @t167)) % 0.41/0.60 (define @t174 () (forall @t173 @t171)) % 0.41/0.60 (define @t175 () (forall @t173 @t170)) % 0.41/0.60 (define @t176 () (or @t72 @t175)) % 0.41/0.60 (define @t177 () (forall @t5 (or @t84 @t9))) % 0.41/0.60 (define @t178 () (tptp.sorti2 @t89)) % 0.41/0.60 (define @t179 () (or @t94 @t92 @t178)) % 0.41/0.60 (define @t180 () (tptp.sorti1 @t129)) % 0.41/0.60 (define @t181 () (not @t178)) % 0.41/0.60 (define @t182 () (or @t181 @t180)) % 0.41/0.60 (define @t183 () (tptp.h @t129)) % 0.41/0.60 (define @t184 () (tptp.op2 @t134 @t183)) % 0.41/0.60 (define @t185 () (tptp.op1 @t127 @t129)) % 0.41/0.60 (define @t186 () (tptp.h @t185)) % 0.41/0.60 (define @t187 () (= @t186 @t184)) % 0.41/0.60 (define @t188 () (not @t180)) % 0.41/0.60 (define @t189 () (or @t162 @t188 @t187)) % 0.41/0.60 (define @t190 () (not @t187)) % 0.41/0.60 (define @t191 () (not @t165)) % 0.41/0.60 (define @t192 () (not @t160)) % 0.41/0.60 (define @t193 () (not @t140)) % 0.41/0.60 (define @t194 () (not @t135)) % 0.41/0.60 (define @t195 () (not @t130)) % 0.41/0.60 (define @t196 () (and @t96 @t130 @t135 @t140 @t160 @t165)) % 0.41/0.60 (assume @p1 (forall @t7 (=> @t6 (forall @t5 (=> @t4 (tptp.sorti1 @t3)))))) % 0.41/0.60 (assume @p2 @t14) % 0.41/0.60 (assume @p3 @t19) % 0.41/0.60 (assume @p4 @t25) % 0.41/0.60 (assume @p5 @t68) % 0.41/0.60 (assume @p6 true) % 0.41/0.60 (step @p7 :rule aci_norm :args ((= @t75 @t73))) % 0.41/0.60 (step @p8 :rule cong :premises (@p7) :args (@t77)) % 0.41/0.60 (step @p9 :rule quant-merge-prenex :args ((= (forall @t7 @t79) @t77))) % 0.41/0.60 (step @p10 :rule alpha_equiv :args (@t80 (@list @t69) @t81)) % 0.41/0.60 (step @p11 :rule refl :args (@t72)) % 0.41/0.60 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t82)) % 0.41/0.60 (step @p13 :rule quant-miniscope-or :args ((= @t79 @t82))) % 0.41/0.60 (step @p14 :rule trans :premises (@p13 @p12)) % 0.41/0.60 (step @p15 :rule symm :premises (@p14)) % 0.41/0.60 (step @p16 :rule cong :premises (@p15) :args ((forall @t7 (or @t72 @t85)))) % 0.41/0.60 (step @p17 :rule trans :premises (@p16 @p9)) % 0.41/0.60 (step @p18 :rule trans :premises (@p17 @p8)) % 0.41/0.60 (step @p19 :rule bool-impl-elim :args (@t12 @t85)) % 0.41/0.60 (step @p20 :rule cong :premises (@p19) :args ((forall @t7 (=> @t12 @t85)))) % 0.41/0.60 (step @p21 :rule trans :premises (@p20 @p18)) % 0.41/0.60 (step @p22 :rule bool-impl-elim :args (@t10 @t83)) % 0.41/0.60 (step @p23 :rule cong :premises (@p22) :args ((forall @t5 (=> @t10 @t83)))) % 0.41/0.60 (step @p24 :rule eq-symm :args (@t20 @t1)) % 0.41/0.60 (step @p25 :rule refl :args (@t10)) % 0.41/0.60 (step @p26 :rule cong :premises (@p25 @p24) :args (@t21)) % 0.41/0.60 (step @p27 :rule cong :premises (@p26) :args (@t22)) % 0.41/0.60 (step @p28 :rule trans :premises (@p27 @p23)) % 0.41/0.60 (step @p29 :rule refl :args (@t12)) % 0.41/0.60 (step @p30 :rule cong :premises (@p29 @p28) :args (@t23)) % 0.41/0.60 (step @p31 :rule cong :premises (@p30) :args (@t24)) % 0.41/0.60 (step @p32 :rule trans :premises (@p31 @p21)) % 0.41/0.60 (step @p33 :rule cong :premises (@p32) :args (@t25)) % 0.41/0.60 (step @p34 :rule eq_resolve :premises (@p4 @p33)) % 0.41/0.60 (step @p35 :rule skolemize :premises (@p34)) % 0.41/0.60 (step @p36 :rule cnf_or_neg :args (@t95 2)) % 0.41/0.60 (step @p37 :rule chain_m_resolution :premises (@p36 @p35) :args (@t96 @t97 @t98)) % 0.41/0.60 (step @p38 :rule bool-impl-elim :args (@t28 @t99)) % 0.41/0.60 (step @p39 :rule cong :premises (@p38) :args ((forall @t30 (=> @t28 @t99)))) % 0.41/0.60 (step @p40 :rule eq-symm :args (@t27 @t26)) % 0.41/0.60 (step @p41 :rule refl :args (@t28)) % 0.41/0.60 (step @p42 :rule cong :premises (@p41 @p40) :args (@t29)) % 0.41/0.60 (step @p43 :rule cong :premises (@p42) :args (@t31)) % 0.41/0.60 (step @p44 :rule trans :premises (@p43 @p39)) % 0.41/0.60 (step @p45 :rule bool-impl-elim :args (@t34 @t100)) % 0.41/0.60 (step @p46 :rule cong :premises (@p45) :args ((forall @t36 (=> @t34 @t100)))) % 0.41/0.60 (step @p47 :rule eq-symm :args (@t33 @t32)) % 0.41/0.60 (step @p48 :rule refl :args (@t34)) % 0.41/0.60 (step @p49 :rule cong :premises (@p48 @p47) :args (@t35)) % 0.41/0.60 (step @p50 :rule cong :premises (@p49) :args (@t37)) % 0.41/0.60 (step @p51 :rule trans :premises (@p50 @p46)) % 0.41/0.60 (step @p52 :rule aci_norm :args ((= @t106 (or @t104 @t103 @t102)))) % 0.41/0.60 (step @p53 :rule cong :premises (@p52) :args (@t107)) % 0.41/0.60 (step @p54 :rule quant-merge-prenex :args ((= (forall @t47 @t109) @t107))) % 0.41/0.60 (step @p55 :rule alpha_equiv :args (@t110 (@list @t101) (@list @t38))) % 0.41/0.60 (step @p56 :rule refl :args (@t104)) % 0.41/0.60 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t111)) % 0.41/0.60 (step @p58 :rule quant-miniscope-or :args ((= @t109 @t111))) % 0.41/0.60 (step @p59 :rule trans :premises (@p58 @p57)) % 0.41/0.60 (step @p60 :rule symm :premises (@p59)) % 0.41/0.60 (step @p61 :rule cong :premises (@p60) :args ((forall @t47 (or @t104 @t112)))) % 0.41/0.60 (step @p62 :rule trans :premises (@p61 @p54)) % 0.41/0.60 (step @p63 :rule trans :premises (@p62 @p53)) % 0.41/0.60 (step @p64 :rule bool-impl-elim :args (@t45 @t112)) % 0.41/0.60 (step @p65 :rule cong :premises (@p64) :args ((forall @t47 (=> @t45 @t112)))) % 0.41/0.60 (step @p66 :rule trans :premises (@p65 @p63)) % 0.41/0.60 (step @p67 :rule bool-impl-elim :args (@t42 @t41)) % 0.41/0.60 (step @p68 :rule cong :premises (@p67) :args (@t44)) % 0.41/0.60 (step @p69 :rule refl :args (@t45)) % 0.41/0.60 (step @p70 :rule cong :premises (@p69 @p68) :args (@t46)) % 0.41/0.60 (step @p71 :rule cong :premises (@p70) :args (@t48)) % 0.41/0.60 (step @p72 :rule trans :premises (@p71 @p66)) % 0.41/0.60 (step @p73 :rule aci_norm :args ((= @t118 (or @t116 @t115 @t114)))) % 0.41/0.60 (step @p74 :rule cong :premises (@p73) :args (@t119)) % 0.41/0.60 (step @p75 :rule quant-merge-prenex :args ((= (forall @t58 @t121) @t119))) % 0.41/0.60 (step @p76 :rule alpha_equiv :args (@t122 (@list @t113) (@list @t49))) % 0.41/0.60 (step @p77 :rule refl :args (@t116)) % 0.41/0.60 (step @p78 :rule nary_cong :premises (@p77 @p76) :args (@t123)) % 0.41/0.60 (step @p79 :rule quant-miniscope-or :args ((= @t121 @t123))) % 0.41/0.60 (step @p80 :rule trans :premises (@p79 @p78)) % 0.41/0.60 (step @p81 :rule symm :premises (@p80)) % 0.41/0.60 (step @p82 :rule cong :premises (@p81) :args ((forall @t58 (or @t116 @t124)))) % 0.41/0.60 (step @p83 :rule trans :premises (@p82 @p75)) % 0.41/0.60 (step @p84 :rule trans :premises (@p83 @p74)) % 0.41/0.60 (step @p85 :rule bool-impl-elim :args (@t56 @t124)) % 0.41/0.60 (step @p86 :rule cong :premises (@p85) :args ((forall @t58 (=> @t56 @t124)))) % 0.41/0.60 (step @p87 :rule trans :premises (@p86 @p84)) % 0.41/0.60 (step @p88 :rule bool-impl-elim :args (@t53 @t52)) % 0.41/0.60 (step @p89 :rule cong :premises (@p88) :args (@t55)) % 0.41/0.60 (step @p90 :rule refl :args (@t56)) % 0.41/0.60 (step @p91 :rule cong :premises (@p90 @p89) :args (@t57)) % 0.41/0.60 (step @p92 :rule cong :premises (@p91) :args (@t59)) % 0.41/0.60 (step @p93 :rule trans :premises (@p92 @p87)) % 0.41/0.60 (step @p94 :rule nary_cong :premises (@p93 @p72 @p51 @p44) :args (@t60)) % 0.41/0.60 (step @p95 :rule cong :premises (@p94) :args (@t61)) % 0.41/0.60 (step @p96 :rule bool-impl-elim :args (@t10 @t62)) % 0.41/0.60 (step @p97 :rule cong :premises (@p96) :args (@t63)) % 0.41/0.60 (step @p98 :rule bool-impl-elim :args (@t6 @t64)) % 0.41/0.60 (step @p99 :rule cong :premises (@p98) :args (@t65)) % 0.41/0.60 (step @p100 :rule nary_cong :premises (@p99 @p97) :args (@t66)) % 0.41/0.60 (step @p101 :rule cong :premises (@p100 @p95) :args (@t67)) % 0.41/0.60 (step @p102 :rule cong :premises (@p101) :args (@t68)) % 0.41/0.60 (step @p103 :rule eq_resolve :premises (@p5 @p102)) % 0.41/0.60 (step @p104 :rule not_implies_elim2 :premises (@p103)) % 0.41/0.60 (step @p105 :rule not_not_elim :premises (@p104)) % 0.41/0.60 (step @p106 :rule and_elim :premises (@p105) :args (1)) % 0.41/0.60 (step @p107 :rule instantiate :premises (@p106) :args (@t125)) % 0.41/0.60 (step @p108 :rule bool-double-not-elim :args (@t91)) % 0.41/0.60 (step @p109 :rule refl :args (@t95)) % 0.41/0.60 (step @p110 :rule nary_cong :premises (@p109 @p108) :args ((or @t95 (not @t92)))) % 0.41/0.60 (step @p111 :rule cnf_or_neg :args (@t95 1)) % 0.41/0.60 (step @p112 :rule eq_resolve :premises (@p111 @p110)) % 0.41/0.60 (step @p113 :rule reordering :premises (@p112) :args ((or @t91 @t95))) % 0.41/0.60 (step @p114 :rule chain_m_resolution :premises (@p113 @p35) :args (@t91 @t97 @t98)) % 0.41/0.60 (step @p115 :rule bool-double-not-elim :args (@t93)) % 0.41/0.60 (step @p116 :rule nary_cong :premises (@p109 @p115) :args ((or @t95 (not @t94)))) % 0.41/0.60 (step @p117 :rule cnf_or_neg :args (@t95 0)) % 0.41/0.60 (step @p118 :rule eq_resolve :premises (@p117 @p116)) % 0.41/0.60 (step @p119 :rule reordering :premises (@p118) :args ((or @t93 @t95))) % 0.41/0.60 (step @p120 :rule chain_m_resolution :premises (@p119 @p35) :args (@t93 @t97 @t98)) % 0.41/0.60 (step @p121 :rule cnf_or_pos :args (@t131)) % 0.41/0.60 (step @p122 :rule reordering :premises (@p121) :args ((or @t94 @t92 @t130 (not @t131)))) % 0.41/0.60 (step @p123 :rule chain_m_resolution :premises (@p122 @p120 @p114 @p107) :args (@t130 @t132 (@list @t93 @t91 @t131))) % 0.41/0.60 (step @p124 :rule and_elim :premises (@p105) :args (2)) % 0.41/0.60 (step @p125 :rule instantiate :premises (@p124) :args (@t133)) % 0.41/0.60 (step @p126 :rule cnf_or_pos :args (@t136)) % 0.41/0.60 (step @p127 :rule reordering :premises (@p126) :args ((or @t94 @t135 (not @t136)))) % 0.41/0.60 (step @p128 :rule chain_m_resolution :premises (@p127 @p120 @p125) :args (@t135 @t137 (@list @t93 @t136))) % 0.41/0.60 (step @p129 :rule instantiate :premises (@p124) :args (@t138)) % 0.41/0.60 (step @p130 :rule cnf_or_pos :args (@t141)) % 0.41/0.60 (step @p131 :rule reordering :premises (@p130) :args ((or @t92 @t140 (not @t141)))) % 0.41/0.60 (step @p132 :rule chain_m_resolution :premises (@p131 @p114 @p129) :args (@t140 @t137 (@list @t91 @t141))) % 0.41/0.60 (step @p133 :rule aci_norm :args ((= @t147 (or @t145 @t144 @t143)))) % 0.41/0.60 (step @p134 :rule cong :premises (@p133) :args (@t148)) % 0.41/0.60 (step @p135 :rule quant-merge-prenex :args ((= (forall @t7 @t150) @t148))) % 0.41/0.60 (step @p136 :rule alpha_equiv :args (@t151 (@list @t142) @t81)) % 0.41/0.60 (step @p137 :rule refl :args (@t145)) % 0.41/0.60 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t152)) % 0.41/0.60 (step @p139 :rule quant-miniscope-or :args ((= @t150 @t152))) % 0.41/0.60 (step @p140 :rule trans :premises (@p139 @p138)) % 0.41/0.60 (step @p141 :rule symm :premises (@p140)) % 0.41/0.60 (step @p142 :rule cong :premises (@p141) :args ((forall @t7 (or @t145 @t154)))) % 0.41/0.60 (step @p143 :rule trans :premises (@p142 @p135)) % 0.41/0.60 (step @p144 :rule trans :premises (@p143 @p134)) % 0.41/0.60 (step @p145 :rule bool-impl-elim :args (@t6 @t154)) % 0.41/0.60 (step @p146 :rule cong :premises (@p145) :args ((forall @t7 (=> @t6 @t154)))) % 0.41/0.60 (step @p147 :rule trans :premises (@p146 @p144)) % 0.41/0.60 (step @p148 :rule bool-impl-elim :args (@t4 @t153)) % 0.41/0.60 (step @p149 :rule cong :premises (@p148) :args ((forall @t5 (=> @t4 @t153)))) % 0.41/0.60 (step @p150 :rule eq-symm :args (@t15 @t1)) % 0.41/0.60 (step @p151 :rule refl :args (@t4)) % 0.41/0.60 (step @p152 :rule cong :premises (@p151 @p150) :args (@t16)) % 0.41/0.60 (step @p153 :rule cong :premises (@p152) :args (@t17)) % 0.41/0.60 (step @p154 :rule trans :premises (@p153 @p149)) % 0.41/0.60 (step @p155 :rule refl :args (@t6)) % 0.41/0.60 (step @p156 :rule cong :premises (@p155 @p154) :args (@t18)) % 0.41/0.60 (step @p157 :rule cong :premises (@p156) :args (@t19)) % 0.41/0.60 (step @p158 :rule trans :premises (@p157 @p147)) % 0.41/0.60 (step @p159 :rule eq_resolve :premises (@p3 @p158)) % 0.41/0.60 (step @p160 :rule instantiate :premises (@p159) :args (@t155)) % 0.41/0.60 (step @p161 :rule not_implies_elim1 :premises (@p103)) % 0.41/0.60 (step @p162 :rule and_elim :premises (@p161) :args (1)) % 0.41/0.60 (step @p163 :rule instantiate :premises (@p162) :args (@t138)) % 0.41/0.60 (step @p164 :rule cnf_or_pos :args (@t157)) % 0.41/0.60 (step @p165 :rule reordering :premises (@p164) :args ((or @t92 @t156 (not @t157)))) % 0.41/0.60 (step @p166 :rule chain_m_resolution :premises (@p165 @p114 @p163) :args (@t156 @t137 (@list @t91 @t157))) % 0.41/0.60 (step @p167 :rule instantiate :premises (@p162) :args (@t133)) % 0.41/0.60 (step @p168 :rule cnf_or_pos :args (@t159)) % 0.41/0.60 (step @p169 :rule reordering :premises (@p168) :args ((or @t94 @t158 (not @t159)))) % 0.41/0.60 (step @p170 :rule chain_m_resolution :premises (@p169 @p120 @p167) :args (@t158 @t137 (@list @t93 @t159))) % 0.41/0.60 (step @p171 :rule cnf_or_pos :args (@t163)) % 0.41/0.60 (step @p172 :rule reordering :premises (@p171) :args ((or @t162 @t161 @t160 (not @t163)))) % 0.41/0.60 (step @p173 :rule chain_m_resolution :premises (@p172 @p170 @p166 @p160) :args (@t160 @t132 (@list @t158 @t156 @t163))) % 0.41/0.60 (step @p174 :rule and_elim :premises (@p105) :args (0)) % 0.41/0.60 (step @p175 :rule instantiate :premises (@p174) :args (@t155)) % 0.41/0.60 (step @p176 :rule cnf_or_pos :args (@t166)) % 0.41/0.60 (step @p177 :rule reordering :premises (@p176) :args ((or @t162 @t161 @t165 (not @t166)))) % 0.41/0.60 (step @p178 :rule chain_m_resolution :premises (@p177 @p170 @p166 @p175) :args (@t165 @t132 (@list @t158 @t156 @t166))) % 0.41/0.60 (step @p179 :rule instantiate :premises (@p174) :args ((@list @t127 @t129))) % 0.41/0.60 (step @p180 :rule instantiate :premises (@p162) :args ((@list @t89))) % 0.41/0.60 (step @p181 :rule aci_norm :args ((= @t171 (or @t72 @t169 @t168)))) % 0.41/0.60 (step @p182 :rule cong :premises (@p181) :args (@t172)) % 0.41/0.60 (step @p183 :rule quant-merge-prenex :args ((= (forall @t7 @t174) @t172))) % 0.41/0.60 (step @p184 :rule alpha_equiv :args (@t175 (@list @t167) @t81)) % 0.41/0.60 (step @p185 :rule nary_cong :premises (@p11 @p184) :args (@t176)) % 0.41/0.60 (step @p186 :rule quant-miniscope-or :args ((= @t174 @t176))) % 0.41/0.60 (step @p187 :rule trans :premises (@p186 @p185)) % 0.41/0.60 (step @p188 :rule symm :premises (@p187)) % 0.41/0.60 (step @p189 :rule cong :premises (@p188) :args ((forall @t7 (or @t72 @t177)))) % 0.41/0.60 (step @p190 :rule trans :premises (@p189 @p183)) % 0.41/0.60 (step @p191 :rule trans :premises (@p190 @p182)) % 0.41/0.60 (step @p192 :rule bool-impl-elim :args (@t12 @t177)) % 0.41/0.60 (step @p193 :rule cong :premises (@p192) :args ((forall @t7 (=> @t12 @t177)))) % 0.41/0.60 (step @p194 :rule trans :premises (@p193 @p191)) % 0.41/0.60 (step @p195 :rule bool-impl-elim :args (@t10 @t9)) % 0.41/0.60 (step @p196 :rule cong :premises (@p195) :args (@t11)) % 0.41/0.60 (step @p197 :rule cong :premises (@p29 @p196) :args (@t13)) % 0.41/0.60 (step @p198 :rule cong :premises (@p197) :args (@t14)) % 0.41/0.60 (step @p199 :rule trans :premises (@p198 @p194)) % 0.41/0.60 (step @p200 :rule eq_resolve :premises (@p2 @p199)) % 0.41/0.60 (step @p201 :rule instantiate :premises (@p200) :args (@t125)) % 0.41/0.60 (step @p202 :rule cnf_or_pos :args (@t179)) % 0.41/0.60 (step @p203 :rule reordering :premises (@p202) :args ((or @t94 @t92 @t178 (not @t179)))) % 0.41/0.60 (step @p204 :rule chain_m_resolution :premises (@p203 @p120 @p114 @p201) :args (@t178 @t132 (@list @t93 @t91 @t179))) % 0.41/0.60 (step @p205 :rule cnf_or_pos :args (@t182)) % 0.41/0.60 (step @p206 :rule reordering :premises (@p205) :args ((or @t181 @t180 (not @t182)))) % 0.41/0.60 (step @p207 :rule chain_m_resolution :premises (@p206 @p204 @p180) :args (@t180 @t137 (@list @t178 @t182))) % 0.41/0.60 (step @p208 :rule cnf_or_pos :args (@t189)) % 0.41/0.60 (step @p209 :rule reordering :premises (@p208) :args ((or @t162 @t188 @t187 (not @t189)))) % 0.41/0.60 (step @p210 :rule chain_m_resolution :premises (@p209 @p170 @p207 @p179) :args (@t187 @t132 (@list @t158 @t180 @t189))) % 0.41/0.60 (step @p211 :rule refl :args (@t190)) % 0.41/0.60 (step @p212 :rule refl :args (@t191)) % 0.41/0.60 (step @p213 :rule refl :args (@t192)) % 0.41/0.60 (step @p214 :rule refl :args (@t193)) % 0.41/0.60 (step @p215 :rule refl :args (@t194)) % 0.41/0.60 (step @p216 :rule refl :args (@t195)) % 0.41/0.60 (step @p217 :rule bool-double-not-elim :args (@t90)) % 0.41/0.60 (step @p218 :rule nary_cong :premises (@p217 @p216 @p215 @p214 @p213 @p212 @p211) :args ((or (not @t96) @t195 @t194 @t193 @t192 @t191 @t190))) % 0.41/0.60 (assume-push @p253 @t96) % 0.41/0.60 (assume-push @p254 @t130) % 0.41/0.60 (assume-push @p255 @t135) % 0.41/0.60 (assume-push @p256 @t140) % 0.41/0.60 (assume-push @p257 @t160) % 0.41/0.60 (assume-push @p258 @t165) % 0.41/0.60 (step @p225 :rule false_intro :premises (@p37)) % 0.41/0.60 (step @p226 :rule symm :premises (@p132)) % 0.41/0.60 (step @p227 :rule symm :premises (@p128)) % 0.41/0.60 (step @p228 :rule cong :premises (@p227 @p226) :args (@t164)) % 0.41/0.60 (step @p229 :rule cong :premises (@p123) :args (@t183)) % 0.41/0.60 (step @p230 :rule trans :premises (@p229 @p178 @p228)) % 0.41/0.60 (step @p231 :rule cong :premises (@p227 @p230) :args (@t184)) % 0.41/0.60 (step @p232 :rule symm :premises (@p173)) % 0.41/0.60 (step @p233 :rule refl :args (@t127)) % 0.41/0.60 (step @p234 :rule cong :premises (@p233 @p123) :args (@t185)) % 0.41/0.60 (step @p235 :rule trans :premises (@p234 @p232)) % 0.41/0.60 (step @p236 :rule cong :premises (@p235) :args (@t186)) % 0.41/0.60 (step @p237 :rule trans :premises (@p236 @p226)) % 0.41/0.60 (step @p238 :rule cong :premises (@p237 @p231) :args (@t187)) % 0.41/0.60 (step @p239 :rule trans :premises (@p238 @p225)) % 0.41/0.60 (step @p240 :rule false_elim :premises (@p239)) % 0.41/0.60 (step-pop @p259 :rule scope :premises (@p240)) % 0.41/0.60 (step-pop @p260 :rule scope :premises (@p259)) % 0.41/0.60 (step-pop @p261 :rule scope :premises (@p260)) % 0.41/0.60 (step-pop @p262 :rule scope :premises (@p261)) % 0.41/0.60 (step-pop @p263 :rule scope :premises (@p262)) % 0.41/0.60 (step-pop @p264 :rule scope :premises (@p263)) % 0.41/0.60 (step @p241 :rule process_scope :premises (@p264) :args (@t190)) % 0.41/0.60 (step @p248 :rule implies_elim :premises (@p241)) % 0.41/0.60 (step @p249 :rule cnf_and_neg :args (@t196)) % 0.41/0.60 (step @p250 :rule resolution :premises (@p249 @p248) :args (true @t196)) % 0.41/0.60 (step @p251 :rule eq_resolve :premises (@p250 @p218)) % 0.41/0.60 (step @p252 false :rule chain_m_resolution :premises (@p251 @p210 @p178 @p173 @p132 @p128 @p123 @p37) :args (false (@list false false false false false false true) (@list @t187 @t165 @t160 @t140 @t135 @t130 @t90))) % 0.41/0.60 ) % 0.41/0.60 % SZS output end Proof % 0.41/0.60 % cvc5 exiting %------------------------------------------------------------------------------