%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN386+1 : TPTP v9.2.1. Released v2.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n008.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 09:08:45 AM UTC 2026 % Result : Theorem 219.43s 219.69s % Output : Proof 219.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN386+1 : TPTP v9.2.1. Released v2.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n008.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 23:25:48 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 219.43/219.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 219.43/219.69 --- Run --no-e-matching --full-saturate-quant at 6... % 219.43/219.69 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 219.43/219.69 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 219.43/219.69 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 219.43/219.69 --- Run --trigger-sel=max --full-saturate-quant at 15... % 219.43/219.69 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 219.43/219.69 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 219.43/219.69 --- Run --prenex-quant=none --full-saturate-quant at 30... % 219.43/219.69 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 15... % 219.43/219.69 --- Run --relevant-triggers --full-saturate-quant at 30... % 219.43/219.69 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 15... % 219.43/219.69 --- Run --pre-skolem-quant=on --full-saturate-quant at 15... % 219.43/219.69 % SZS status Theorem % 219.43/219.69 % SZS output start Proof % 219.43/219.69 ( % 219.43/219.69 (declare-sort $$unsorted 0) % 219.43/219.69 (declare-const tptp.big_s (-> $$unsorted $$unsorted Bool)) % 219.43/219.69 (declare-const tptp.big_f (-> $$unsorted $$unsorted Bool)) % 219.43/219.69 (declare-const tptp.big_d (-> $$unsorted $$unsorted $$unsorted Bool)) % 219.43/219.69 (define @t1 () (@var "E" $$unsorted)) % 219.43/219.69 (define @t2 () (@var "Y" $$unsorted)) % 219.43/219.69 (define @t3 () (@var "Z" $$unsorted)) % 219.43/219.69 (define @t4 () (tptp.big_d @t3 @t2 @t1)) % 219.43/219.69 (define @t5 () (@var "W" $$unsorted)) % 219.43/219.69 (define @t6 () (tptp.big_f @t5 @t3)) % 219.43/219.69 (define @t7 () (@list @t3)) % 219.43/219.69 (define @t8 () (forall @t7 (=> @t6 @t4))) % 219.43/219.69 (define @t9 () (@var "M" $$unsorted)) % 219.43/219.69 (define @t10 () (tptp.big_s @t9 @t5)) % 219.43/219.69 (define @t11 () (=> @t10 @t8)) % 219.43/219.69 (define @t12 () (@list @t5)) % 219.43/219.69 (define @t13 () (forall @t12 @t11)) % 219.43/219.69 (define @t14 () (@list @t9)) % 219.43/219.69 (define @t15 () (exists @t14 @t13)) % 219.43/219.69 (define @t16 () (@list @t1)) % 219.43/219.69 (define @t17 () (forall @t16 @t15)) % 219.43/219.69 (define @t18 () (@list @t2)) % 219.43/219.69 (define @t19 () (exists @t18 @t17)) % 219.43/219.69 (define @t20 () (tptp.big_d @t2 @t3 @t1)) % 219.43/219.69 (define @t21 () (@var "B" $$unsorted)) % 219.43/219.69 (define @t22 () (tptp.big_f @t21 @t3)) % 219.43/219.69 (define @t23 () (@var "A" $$unsorted)) % 219.43/219.69 (define @t24 () (tptp.big_f @t23 @t2)) % 219.43/219.69 (define @t25 () (and @t24 @t22)) % 219.43/219.69 (define @t26 () (@list @t2 @t3)) % 219.43/219.69 (define @t27 () (forall @t26 (=> @t25 @t20))) % 219.43/219.69 (define @t28 () (@var "D" $$unsorted)) % 219.43/219.69 (define @t29 () (tptp.big_d @t23 @t21 @t28)) % 219.43/219.69 (define @t30 () (=> @t29 @t27)) % 219.43/219.69 (define @t31 () (@list @t23 @t21)) % 219.43/219.69 (define @t32 () (forall @t31 @t30)) % 219.43/219.69 (define @t33 () (@list @t28)) % 219.43/219.69 (define @t34 () (exists @t33 @t32)) % 219.43/219.69 (define @t35 () (forall @t16 @t34)) % 219.43/219.69 (define @t36 () (@var "X" $$unsorted)) % 219.43/219.69 (define @t37 () (tptp.big_d @t5 @t36 @t1)) % 219.43/219.69 (define @t38 () (@var "N" $$unsorted)) % 219.43/219.69 (define @t39 () (tptp.big_s @t38 @t5)) % 219.43/219.69 (define @t40 () (forall @t12 (=> @t39 @t37))) % 219.43/219.69 (define @t41 () (@list @t38)) % 219.43/219.69 (define @t42 () (exists @t41 @t40)) % 219.43/219.69 (define @t43 () (forall @t16 @t42)) % 219.43/219.69 (define @t44 () (@list @t36)) % 219.43/219.69 (define @t45 () (exists @t44 @t43)) % 219.43/219.69 (define @t46 () (tptp.big_f @t36 @t2)) % 219.43/219.69 (define @t47 () (exists @t18 @t46)) % 219.43/219.69 (define @t48 () (forall @t44 @t47)) % 219.43/219.69 (define @t49 () (and @t48 @t45 @t35)) % 219.43/219.69 (define @t50 () (=> @t49 @t19)) % 219.43/219.69 (define @t51 () (not @t50)) % 219.43/219.69 (define @t52 () (@var "BOUND_VARIABLE_7671" $$unsorted)) % 219.43/219.69 (define @t53 () (@const 0 (-> $$unsorted $$unsorted))) % 219.43/219.69 (define @t54 () (@var "BOUND_VARIABLE_7647" $$unsorted)) % 219.43/219.69 (define @t55 () (@const 1 (-> $$unsorted $$unsorted $$unsorted))) % 219.43/219.69 (define @t56 () (not (tptp.big_d (_ @t55 @t52 @t54) @t52 (_ @t53 @t52)))) % 219.43/219.69 (define @t57 () (@list @t54)) % 219.43/219.69 (define @t58 () (forall (@list @t52) (forall @t57 @t56))) % 219.43/219.69 (define @t59 () (@var "BOUND_VARIABLE_7640" $$unsorted)) % 219.43/219.69 (define @t60 () (@var "BOUND_VARIABLE_7663" $$unsorted)) % 219.43/219.69 (define @t61 () (@const 2 (-> $$unsorted $$unsorted $$unsorted))) % 219.43/219.69 (define @t62 () (tptp.big_f (_ @t61 @t60 @t59) (_ @t55 @t60 @t59))) % 219.43/219.69 (define @t63 () (@list @t59)) % 219.43/219.69 (define @t64 () (forall (@list @t60) (forall @t63 @t62))) % 219.43/219.69 (define @t65 () (@var "BOUND_VARIABLE_7634" $$unsorted)) % 219.43/219.69 (define @t66 () (@var "BOUND_VARIABLE_7656" $$unsorted)) % 219.43/219.69 (define @t67 () (tptp.big_s @t65 (_ @t61 @t66 @t65))) % 219.43/219.69 (define @t68 () (@list @t65)) % 219.43/219.69 (define @t69 () (forall (@list @t66) (forall @t68 @t67))) % 219.43/219.69 (define @t70 () (_ @t53 @t2)) % 219.43/219.69 (define @t71 () (forall @t57 (not (tptp.big_d (_ @t55 @t2 @t54) @t2 @t70)))) % 219.43/219.69 (define @t72 () (forall @t18 @t71)) % 219.43/219.69 (define @t73 () (@list @t2)) % 219.43/219.69 (define @t74 () (forall @t63 (tptp.big_f (_ @t61 @t2 @t59) (_ @t55 @t2 @t59)))) % 219.43/219.69 (define @t75 () (forall @t18 @t74)) % 219.43/219.69 (define @t76 () (forall @t68 (tptp.big_s @t65 (_ @t61 @t2 @t65)))) % 219.43/219.69 (define @t77 () (forall @t18 @t76)) % 219.43/219.69 (define @t78 () (and @t77 @t75 @t72)) % 219.43/219.69 (define @t79 () (_ @t55 @t2 @t9)) % 219.43/219.69 (define @t80 () (tptp.big_d @t79 @t2 @t70)) % 219.43/219.69 (define @t81 () (not @t80)) % 219.43/219.69 (define @t82 () (forall @t14 @t81)) % 219.43/219.69 (define @t83 () (@list @t9)) % 219.43/219.69 (define @t84 () (_ @t61 @t2 @t9)) % 219.43/219.69 (define @t85 () (tptp.big_f @t84 @t79)) % 219.43/219.69 (define @t86 () (forall @t14 @t85)) % 219.43/219.69 (define @t87 () (tptp.big_s @t9 @t84)) % 219.43/219.69 (define @t88 () (forall @t14 @t87)) % 219.43/219.69 (define @t89 () (and @t88 @t86 @t82)) % 219.43/219.69 (define @t90 () (not @t85)) % 219.43/219.69 (define @t91 () (not @t90)) % 219.43/219.69 (define @t92 () (not @t87)) % 219.43/219.69 (define @t93 () (not @t92)) % 219.43/219.69 (define @t94 () (and @t93 @t91 @t81)) % 219.43/219.69 (define @t95 () (forall @t14 (not (or @t92 @t90 @t80)))) % 219.43/219.69 (define @t96 () (forall @t18 (not (not @t95)))) % 219.43/219.69 (define @t97 () (not @t96)) % 219.43/219.69 (define @t98 () (@var "BOUND_VARIABLE_7495" $$unsorted)) % 219.43/219.69 (define @t99 () (@var "BOUND_VARIABLE_7493" $$unsorted)) % 219.43/219.69 (define @t100 () (tptp.big_d @t99 @t98 @t1)) % 219.43/219.69 (define @t101 () (not (tptp.big_f @t21 @t98))) % 219.43/219.69 (define @t102 () (not (tptp.big_f @t23 @t99))) % 219.43/219.69 (define @t103 () (@const 3 (-> $$unsorted $$unsorted))) % 219.43/219.69 (define @t104 () (or (not (tptp.big_d @t23 @t21 (_ @t103 @t1))) @t102 @t101 @t100)) % 219.43/219.69 (define @t105 () (@list @t23 @t21 @t99 @t98)) % 219.43/219.69 (define @t106 () (forall @t105 @t104)) % 219.43/219.69 (define @t107 () (forall @t16 (not (not @t106)))) % 219.43/219.69 (define @t108 () (forall @t12 (or (not @t39) @t37))) % 219.43/219.69 (define @t109 () (not (forall @t41 (not @t108)))) % 219.43/219.69 (define @t110 () (forall @t16 @t109)) % 219.43/219.69 (define @t111 () (forall @t44 (not @t110))) % 219.43/219.69 (define @t112 () (@quantifiers_skolemize @t111 0)) % 219.43/219.69 (define @t113 () (@const 4 (-> $$unsorted $$unsorted))) % 219.43/219.69 (define @t114 () (or (not (tptp.big_s (_ @t113 @t1) @t5)) (tptp.big_d @t5 @t112 @t1))) % 219.43/219.69 (define @t115 () (forall @t12 @t114)) % 219.43/219.69 (define @t116 () (forall @t16 (not (not @t115)))) % 219.43/219.69 (define @t117 () (@const 5 (-> $$unsorted $$unsorted))) % 219.43/219.69 (define @t118 () (tptp.big_f @t36 (_ @t117 @t36))) % 219.43/219.69 (define @t119 () (forall @t44 (not (not @t118)))) % 219.43/219.69 (define @t120 () (and @t119 (not (not @t116)) @t107)) % 219.43/219.69 (define @t121 () (=> @t120 @t97)) % 219.43/219.69 (define @t122 () (not @t121)) % 219.43/219.69 (define @t123 () (@var "BOUND_VARIABLE_7522" $$unsorted)) % 219.43/219.69 (define @t124 () (tptp.big_d @t123 @t2 @t1)) % 219.43/219.69 (define @t125 () (not (tptp.big_f @t5 @t123))) % 219.43/219.69 (define @t126 () (not @t10)) % 219.43/219.69 (define @t127 () (or @t126 @t125 @t124)) % 219.43/219.69 (define @t128 () (@list @t5 @t123)) % 219.43/219.69 (define @t129 () (forall @t128 @t127)) % 219.43/219.69 (define @t130 () (not (forall @t14 (not @t129)))) % 219.43/219.69 (define @t131 () (forall @t16 @t130)) % 219.43/219.69 (define @t132 () (not (forall @t18 (not @t131)))) % 219.43/219.69 (define @t133 () (not @t29)) % 219.43/219.69 (define @t134 () (or @t133 @t102 @t101 @t100)) % 219.43/219.69 (define @t135 () (forall @t105 @t134)) % 219.43/219.69 (define @t136 () (not (forall @t33 (not @t135)))) % 219.43/219.69 (define @t137 () (not @t111)) % 219.43/219.69 (define @t138 () (not (forall @t18 (not @t46)))) % 219.43/219.69 (define @t139 () (or @t125 @t124)) % 219.43/219.69 (define @t140 () (or @t126 @t139)) % 219.43/219.69 (define @t141 () (forall @t128 @t140)) % 219.43/219.69 (define @t142 () (@list @t123)) % 219.43/219.69 (define @t143 () (forall @t142 @t140)) % 219.43/219.69 (define @t144 () (forall @t142 @t139)) % 219.43/219.69 (define @t145 () (or @t126 @t144)) % 219.43/219.69 (define @t146 () (forall @t7 (or (not @t6) @t4))) % 219.43/219.69 (define @t147 () (or @t102 @t101 @t100)) % 219.43/219.69 (define @t148 () (or @t133 @t147)) % 219.43/219.69 (define @t149 () (forall @t105 @t148)) % 219.43/219.69 (define @t150 () (@list @t99 @t98)) % 219.43/219.69 (define @t151 () (forall @t150 @t148)) % 219.43/219.69 (define @t152 () (forall @t150 @t147)) % 219.43/219.69 (define @t153 () (or @t133 @t152)) % 219.43/219.69 (define @t154 () (not @t22)) % 219.43/219.69 (define @t155 () (not @t24)) % 219.43/219.69 (define @t156 () (or @t155 @t154 @t20)) % 219.43/219.69 (define @t157 () (forall @t26 @t156)) % 219.43/219.69 (define @t158 () (_ @t117 @t112)) % 219.43/219.69 (define @t159 () (_ @t53 @t158)) % 219.43/219.69 (define @t160 () (_ @t103 @t159)) % 219.43/219.69 (define @t161 () (_ @t113 @t160)) % 219.43/219.69 (define @t162 () (@list @t158 @t161)) % 219.43/219.69 (define @t163 () (_ @t55 @t158 @t161)) % 219.43/219.69 (define @t164 () (_ @t61 @t158 @t161)) % 219.43/219.69 (define @t165 () (tptp.big_d @t164 @t112 @t160)) % 219.43/219.69 (define @t166 () (tptp.big_s @t161 @t164)) % 219.43/219.69 (define @t167 () (not @t166)) % 219.43/219.69 (define @t168 () (or @t167 @t165)) % 219.43/219.69 (define @t169 () (tptp.big_d @t163 @t158 @t159)) % 219.43/219.69 (define @t170 () (tptp.big_f @t112 @t158)) % 219.43/219.69 (define @t171 () (not @t170)) % 219.43/219.69 (define @t172 () (tptp.big_f @t164 @t163)) % 219.43/219.69 (define @t173 () (not @t172)) % 219.43/219.69 (define @t174 () (not @t165)) % 219.43/219.69 (define @t175 () (or @t174 @t173 @t171 @t169)) % 219.43/219.69 (assume @p1 @t51) % 219.43/219.69 (assume @p2 true) % 219.43/219.69 (step @p3 :rule quant-merge-prenex :args ((= @t58 (forall (@list @t52 @t54) @t56)))) % 219.43/219.69 (step @p4 :rule quant-merge-prenex :args ((= @t64 (forall (@list @t60 @t59) @t62)))) % 219.43/219.69 (step @p5 :rule quant-merge-prenex :args ((= @t69 (forall (@list @t66 @t65) @t67)))) % 219.43/219.69 (step @p6 :rule nary_cong :premises (@p5 @p4 @p3) :args ((and @t69 @t64 @t58))) % 219.43/219.69 (step @p7 :rule alpha_equiv :args (@t72 @t73 (@list @t52))) % 219.43/219.69 (step @p8 :rule alpha_equiv :args (@t75 @t73 (@list @t60))) % 219.43/219.69 (step @p9 :rule alpha_equiv :args (@t77 @t73 (@list @t66))) % 219.43/219.69 (step @p10 :rule nary_cong :premises (@p9 @p8 @p7) :args (@t78)) % 219.43/219.69 (step @p11 :rule quant-miniscope-and :args ((= (forall @t18 (and @t76 @t74 @t71)) @t78))) % 219.43/219.69 (step @p12 :rule trans :premises (@p11 @p10)) % 219.43/219.69 (step @p13 :rule trans :premises (@p12 @p6)) % 219.43/219.69 (step @p14 :rule alpha_equiv :args (@t82 @t83 (@list @t54))) % 219.43/219.69 (step @p15 :rule alpha_equiv :args (@t86 @t83 (@list @t59))) % 219.43/219.69 (step @p16 :rule alpha_equiv :args (@t88 @t83 (@list @t65))) % 219.43/219.69 (step @p17 :rule nary_cong :premises (@p16 @p15 @p14) :args (@t89)) % 219.43/219.69 (step @p18 :rule quant-miniscope-and :args ((= (forall @t14 (and @t87 @t85 @t81)) @t89))) % 219.43/219.69 (step @p19 :rule trans :premises (@p18 @p17)) % 219.43/219.69 (step @p20 :rule refl :args (@t81)) % 219.43/219.69 (step @p21 :rule bool-double-not-elim :args (@t85)) % 219.43/219.69 (step @p22 :rule bool-double-not-elim :args (@t87)) % 219.43/219.69 (step @p23 :rule nary_cong :premises (@p22 @p21 @p20) :args (@t94)) % 219.43/219.69 (step @p24 :rule aci_norm :args ((= (and @t93 (and @t91 @t81)) @t94))) % 219.43/219.69 (step @p25 :rule trans :premises (@p24 @p23)) % 219.43/219.69 (step @p26 :rule bool-or-de-morgan :args (@t90 @t80 false)) % 219.43/219.69 (step @p27 :rule refl :args (@t93)) % 219.43/219.69 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((and @t93 (not (or @t90 @t80))))) % 219.43/219.69 (step @p29 :rule bool-or-de-morgan :args (@t92 @t90 (or @t80))) % 219.43/219.69 (step @p30 :rule trans :premises (@p29 @p28)) % 219.43/219.69 (step @p31 :rule trans :premises (@p30 @p25)) % 219.43/219.69 (step @p32 :rule cong :premises (@p31) :args (@t95)) % 219.43/219.69 (step @p33 :rule trans :premises (@p32 @p19)) % 219.43/219.69 (step @p34 :rule bool-double-not-elim :args (@t95)) % 219.43/219.69 (step @p35 :rule trans :premises (@p34 @p33)) % 219.43/219.69 (step @p36 :rule cong :premises (@p35) :args (@t96)) % 219.43/219.69 (step @p37 :rule trans :premises (@p36 @p13)) % 219.43/219.69 (step @p38 :rule cong :premises (@p37) :args (@t97)) % 219.43/219.69 (step @p39 :rule quant-merge-prenex :args ((= (forall @t16 @t106) (forall (@list @t1 @t23 @t21 @t99 @t98) @t104)))) % 219.43/219.69 (step @p40 :rule bool-double-not-elim :args (@t106)) % 219.43/219.69 (step @p41 :rule cong :premises (@p40) :args (@t107)) % 219.43/219.69 (step @p42 :rule trans :premises (@p41 @p39)) % 219.43/219.69 (step @p43 :rule quant-merge-prenex :args ((= (forall @t16 @t115) (forall (@list @t1 @t5) @t114)))) % 219.43/219.69 (step @p44 :rule bool-double-not-elim :args (@t115)) % 219.43/219.69 (step @p45 :rule cong :premises (@p44) :args (@t116)) % 219.43/219.69 (step @p46 :rule trans :premises (@p45 @p43)) % 219.43/219.69 (step @p47 :rule bool-double-not-elim :args (@t116)) % 219.43/219.69 (step @p48 :rule trans :premises (@p47 @p46)) % 219.43/219.69 (step @p49 :rule bool-double-not-elim :args (@t118)) % 219.43/219.69 (step @p50 :rule cong :premises (@p49) :args (@t119)) % 219.43/219.69 (step @p51 :rule nary_cong :premises (@p50 @p48 @p42) :args (@t120)) % 219.43/219.69 (step @p52 :rule cong :premises (@p51 @p38) :args (@t121)) % 219.43/219.69 (step @p53 :rule cong :premises (@p52) :args (@t122)) % 219.43/219.69 ; WARNING: add trust step for TRUST % 219.43/219.69 ; trust TRUST PREPROCESS_QUANTIFIERS_PP % 219.43/219.69 (step @p54 :rule trust :premises () :args ((= (not (=> (and (forall @t44 @t138) @t137 (forall @t16 @t136)) @t132)) @t122))) % 219.43/219.69 (step @p55 :rule exists-elim :args ((= (exists @t18 @t131) @t132))) % 219.43/219.69 (step @p56 :rule exists-elim :args ((= (exists @t14 @t129) @t130))) % 219.43/219.69 (step @p57 :rule aci_norm :args ((= @t140 @t127))) % 219.43/219.69 (step @p58 :rule cong :premises (@p57) :args (@t141)) % 219.43/219.69 (step @p59 :rule quant-merge-prenex :args ((= (forall @t12 @t143) @t141))) % 219.43/219.69 (step @p60 :rule alpha_equiv :args (@t144 (@list @t123) (@list @t3))) % 219.43/219.69 (step @p61 :rule refl :args (@t126)) % 219.43/219.69 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t145)) % 219.43/219.69 (step @p63 :rule quant-miniscope-or :args ((= @t143 @t145))) % 219.43/219.69 (step @p64 :rule trans :premises (@p63 @p62)) % 219.43/219.69 (step @p65 :rule symm :premises (@p64)) % 219.43/219.69 (step @p66 :rule cong :premises (@p65) :args ((forall @t12 (or @t126 @t146)))) % 219.43/219.69 (step @p67 :rule trans :premises (@p66 @p59)) % 219.43/219.69 (step @p68 :rule trans :premises (@p67 @p58)) % 219.43/219.69 (step @p69 :rule bool-impl-elim :args (@t10 @t146)) % 219.43/219.69 (step @p70 :rule cong :premises (@p69) :args ((forall @t12 (=> @t10 @t146)))) % 219.43/219.69 (step @p71 :rule trans :premises (@p70 @p68)) % 219.43/219.69 (step @p72 :rule bool-impl-elim :args (@t6 @t4)) % 219.43/219.69 (step @p73 :rule cong :premises (@p72) :args (@t8)) % 219.43/219.69 (step @p74 :rule refl :args (@t10)) % 219.43/219.69 (step @p75 :rule cong :premises (@p74 @p73) :args (@t11)) % 219.43/219.69 (step @p76 :rule cong :premises (@p75) :args (@t13)) % 219.43/219.69 (step @p77 :rule trans :premises (@p76 @p71)) % 219.43/219.69 (step @p78 :rule cong :premises (@p77) :args (@t15)) % 219.43/219.69 (step @p79 :rule trans :premises (@p78 @p56)) % 219.43/219.69 (step @p80 :rule cong :premises (@p79) :args (@t17)) % 219.43/219.69 (step @p81 :rule cong :premises (@p80) :args (@t19)) % 219.43/219.69 (step @p82 :rule trans :premises (@p81 @p55)) % 219.43/219.69 (step @p83 :rule exists-elim :args ((= (exists @t33 @t135) @t136))) % 219.43/219.69 (step @p84 :rule aci_norm :args ((= @t148 @t134))) % 219.43/219.69 (step @p85 :rule cong :premises (@p84) :args (@t149)) % 219.43/219.69 (step @p86 :rule quant-merge-prenex :args ((= (forall @t31 @t151) @t149))) % 219.43/219.69 (step @p87 :rule alpha_equiv :args (@t152 (@list @t99 @t98) (@list @t2 @t3))) % 219.43/219.69 (step @p88 :rule refl :args (@t133)) % 219.43/219.69 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t153)) % 219.43/219.69 (step @p90 :rule quant-miniscope-or :args ((= @t151 @t153))) % 219.43/219.69 (step @p91 :rule trans :premises (@p90 @p89)) % 219.43/219.69 (step @p92 :rule symm :premises (@p91)) % 219.43/219.69 (step @p93 :rule cong :premises (@p92) :args ((forall @t31 (or @t133 @t157)))) % 219.43/219.69 (step @p94 :rule trans :premises (@p93 @p86)) % 219.43/219.69 (step @p95 :rule trans :premises (@p94 @p85)) % 219.43/219.69 (step @p96 :rule bool-impl-elim :args (@t29 @t157)) % 219.43/219.69 (step @p97 :rule cong :premises (@p96) :args ((forall @t31 (=> @t29 @t157)))) % 219.43/219.69 (step @p98 :rule trans :premises (@p97 @p95)) % 219.43/219.69 (step @p99 :rule aci_norm :args ((= (or (or @t155 @t154) @t20) @t156))) % 219.43/219.69 (step @p100 :rule refl :args (@t20)) % 219.43/219.69 (step @p101 :rule bool-and-de-morgan :args (@t24 @t22 true)) % 219.43/219.69 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or (not @t25) @t20))) % 219.43/219.69 (step @p103 :rule trans :premises (@p102 @p99)) % 219.43/219.69 (step @p104 :rule bool-impl-elim :args (@t25 @t20)) % 219.43/219.69 (step @p105 :rule trans :premises (@p104 @p103)) % 219.43/219.69 (step @p106 :rule cong :premises (@p105) :args (@t27)) % 219.43/219.69 (step @p107 :rule refl :args (@t29)) % 219.43/219.69 (step @p108 :rule cong :premises (@p107 @p106) :args (@t30)) % 219.43/219.69 (step @p109 :rule cong :premises (@p108) :args (@t32)) % 219.43/219.69 (step @p110 :rule trans :premises (@p109 @p98)) % 219.43/219.69 (step @p111 :rule cong :premises (@p110) :args (@t34)) % 219.43/219.69 (step @p112 :rule trans :premises (@p111 @p83)) % 219.43/219.69 (step @p113 :rule cong :premises (@p112) :args (@t35)) % 219.43/219.69 (step @p114 :rule exists-elim :args ((= (exists @t44 @t110) @t137))) % 219.43/219.69 (step @p115 :rule exists-elim :args ((= (exists @t41 @t108) @t109))) % 219.43/219.69 (step @p116 :rule bool-impl-elim :args (@t39 @t37)) % 219.43/219.69 (step @p117 :rule cong :premises (@p116) :args (@t40)) % 219.43/219.69 (step @p118 :rule cong :premises (@p117) :args (@t42)) % 219.43/219.69 (step @p119 :rule trans :premises (@p118 @p115)) % 219.43/219.69 (step @p120 :rule cong :premises (@p119) :args (@t43)) % 219.43/219.69 (step @p121 :rule cong :premises (@p120) :args (@t45)) % 219.43/219.69 (step @p122 :rule trans :premises (@p121 @p114)) % 219.43/219.69 (step @p123 :rule exists-elim :args ((= @t47 @t138))) % 219.43/219.69 (step @p124 :rule cong :premises (@p123) :args (@t48)) % 219.43/219.69 (step @p125 :rule nary_cong :premises (@p124 @p122 @p113) :args (@t49)) % 219.43/219.69 (step @p126 :rule cong :premises (@p125 @p82) :args (@t50)) % 219.43/219.69 (step @p127 :rule cong :premises (@p126) :args (@t51)) % 219.43/219.69 (step @p128 :rule trans :premises (@p127 @p54 @p53)) % 219.43/219.69 (step @p129 :rule eq_resolve :premises (@p1 @p128)) % 219.43/219.69 (step @p130 :rule not_implies_elim1 :premises (@p129)) % 219.43/219.69 (step @p131 :rule and_elim :premises (@p130) :args (0)) % 219.43/219.69 (step @p132 :rule instantiate :premises (@p131) :args ((@list @t112))) % 219.43/219.69 (step @p133 :rule not_implies_elim2 :premises (@p129)) % 219.43/219.69 (step @p134 :rule not_not_elim :premises (@p133)) % 219.43/219.69 (step @p135 :rule and_elim :premises (@p134) :args (1)) % 219.43/219.69 (step @p136 :rule instantiate :premises (@p135) :args (@t162)) % 219.43/219.69 (step @p137 :rule and_elim :premises (@p134) :args (2)) % 219.43/219.69 (step @p138 :rule instantiate :premises (@p137) :args (@t162)) % 219.43/219.69 (step @p139 :rule and_elim :premises (@p130) :args (2)) % 219.43/219.69 (step @p140 :rule instantiate :premises (@p139) :args ((@list @t159 @t164 @t112 @t163 @t158))) % 219.43/219.69 (step @p141 :rule and_elim :premises (@p130) :args (1)) % 219.43/219.69 (step @p142 :rule instantiate :premises (@p141) :args ((@list @t160 @t164))) % 219.43/219.69 (step @p143 :rule and_elim :premises (@p134) :args (0)) % 219.43/219.69 (step @p144 :rule instantiate :premises (@p143) :args (@t162)) % 219.43/219.69 (step @p145 :rule cnf_or_pos :args (@t168)) % 219.43/219.69 (step @p146 :rule reordering :premises (@p145) :args ((or @t167 @t165 (not @t168)))) % 219.43/219.69 (step @p147 :rule chain_m_resolution :premises (@p146 @p144 @p142) :args (@t165 (@list false false) (@list @t166 @t168))) % 219.43/219.69 (step @p148 :rule cnf_or_pos :args (@t175)) % 219.43/219.69 (step @p149 :rule reordering :premises (@p148) :args ((or @t171 @t169 @t173 @t174 (not @t175)))) % 219.43/219.69 (step @p150 false :rule chain_m_resolution :premises (@p149 @p147 @p140 @p138 @p136 @p132) :args (false (@list false false true false false) (@list @t165 @t175 @t169 @t172 @t170))) % 219.43/219.69 ) % 219.43/219.69 % SZS output end Proof % 219.43/219.69 % cvc5 exiting %------------------------------------------------------------------------------