%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG070+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 : n006.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 08:05:09 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG070+1 : TPTP v9.2.1. Released v2.7.0. % 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 : n006.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 : Wed Jun 3 01:38:49 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.58 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.58 (define @t3 () (tptp.op1 @t2 @t1)) % 0.37/0.58 (define @t4 () (tptp.sorti1 @t1)) % 0.37/0.58 (define @t5 () (@list @t1)) % 0.37/0.58 (define @t6 () (tptp.sorti1 @t2)) % 0.37/0.58 (define @t7 () (@list @t2)) % 0.37/0.58 (define @t8 () (tptp.op2 @t2 @t1)) % 0.37/0.58 (define @t9 () (tptp.sorti2 @t1)) % 0.37/0.58 (define @t10 () (tptp.sorti2 @t2)) % 0.37/0.58 (define @t11 () (tptp.op1 @t2 @t2)) % 0.37/0.58 (define @t12 () (not (= @t11 @t1))) % 0.37/0.58 (define @t13 () (or @t12 (= @t3 @t2))) % 0.37/0.58 (define @t14 () (=> @t4 @t13)) % 0.37/0.58 (define @t15 () (forall @t5 @t14)) % 0.37/0.58 (define @t16 () (=> @t6 @t15)) % 0.37/0.58 (define @t17 () (forall @t7 @t16)) % 0.37/0.58 (define @t18 () (tptp.op2 @t2 @t2)) % 0.37/0.58 (define @t19 () (not (= @t18 @t1))) % 0.37/0.58 (define @t20 () (or @t19 (= @t8 @t2))) % 0.37/0.58 (define @t21 () (=> @t9 @t20)) % 0.37/0.58 (define @t22 () (forall @t5 @t21)) % 0.37/0.58 (define @t23 () (=> @t10 @t22)) % 0.37/0.58 (define @t24 () (forall @t7 @t23)) % 0.37/0.58 (define @t25 () (not @t24)) % 0.37/0.58 (define @t26 () (@var "X2" $$unsorted)) % 0.37/0.58 (define @t27 () (tptp.j (tptp.h @t26))) % 0.37/0.58 (define @t28 () (tptp.sorti1 @t26)) % 0.37/0.58 (define @t29 () (=> @t28 (= @t27 @t26))) % 0.37/0.58 (define @t30 () (@list @t26)) % 0.37/0.58 (define @t31 () (forall @t30 @t29)) % 0.37/0.58 (define @t32 () (@var "X1" $$unsorted)) % 0.37/0.58 (define @t33 () (tptp.h (tptp.j @t32))) % 0.37/0.58 (define @t34 () (tptp.sorti2 @t32)) % 0.37/0.58 (define @t35 () (=> @t34 (= @t33 @t32))) % 0.37/0.58 (define @t36 () (@list @t32)) % 0.37/0.58 (define @t37 () (forall @t36 @t35)) % 0.37/0.58 (define @t38 () (@var "Z" $$unsorted)) % 0.37/0.58 (define @t39 () (@var "Y" $$unsorted)) % 0.37/0.58 (define @t40 () (tptp.j @t39)) % 0.37/0.58 (define @t41 () (= (tptp.j (tptp.op2 @t39 @t38)) (tptp.op1 @t40 (tptp.j @t38)))) % 0.37/0.58 (define @t42 () (tptp.sorti2 @t38)) % 0.37/0.58 (define @t43 () (@list @t38)) % 0.37/0.58 (define @t44 () (forall @t43 (=> @t42 @t41))) % 0.37/0.58 (define @t45 () (tptp.sorti2 @t39)) % 0.37/0.58 (define @t46 () (=> @t45 @t44)) % 0.37/0.58 (define @t47 () (@list @t39)) % 0.37/0.58 (define @t48 () (forall @t47 @t46)) % 0.37/0.58 (define @t49 () (@var "X" $$unsorted)) % 0.37/0.58 (define @t50 () (@var "W" $$unsorted)) % 0.37/0.58 (define @t51 () (tptp.h @t50)) % 0.37/0.58 (define @t52 () (= (tptp.h (tptp.op1 @t50 @t49)) (tptp.op2 @t51 (tptp.h @t49)))) % 0.37/0.58 (define @t53 () (tptp.sorti1 @t49)) % 0.37/0.58 (define @t54 () (@list @t49)) % 0.37/0.58 (define @t55 () (forall @t54 (=> @t53 @t52))) % 0.37/0.58 (define @t56 () (tptp.sorti1 @t50)) % 0.37/0.58 (define @t57 () (=> @t56 @t55)) % 0.37/0.58 (define @t58 () (@list @t50)) % 0.37/0.58 (define @t59 () (forall @t58 @t57)) % 0.37/0.58 (define @t60 () (and @t59 @t48 @t37 @t31)) % 0.37/0.58 (define @t61 () (not @t60)) % 0.37/0.58 (define @t62 () (tptp.sorti1 (tptp.j @t1))) % 0.37/0.58 (define @t63 () (forall @t5 (=> @t9 @t62))) % 0.37/0.58 (define @t64 () (tptp.sorti2 (tptp.h @t2))) % 0.37/0.58 (define @t65 () (forall @t7 (=> @t6 @t64))) % 0.37/0.58 (define @t66 () (and @t65 @t63)) % 0.37/0.58 (define @t67 () (=> @t66 @t61)) % 0.37/0.58 (define @t68 () (not @t67)) % 0.37/0.58 (define @t69 () (= @t2 (tptp.op2 @t2 @t18))) % 0.37/0.58 (define @t70 () (not (tptp.sorti2 @t18))) % 0.37/0.58 (define @t71 () (not @t10)) % 0.37/0.58 (define @t72 () (or @t71 @t70 @t69)) % 0.37/0.58 (define @t73 () (or @t70 @t69)) % 0.37/0.58 (define @t74 () (not (= @t18 @t18))) % 0.37/0.58 (define @t75 () (or @t70 @t74 @t69)) % 0.37/0.58 (define @t76 () (= @t2 @t8)) % 0.37/0.58 (define @t77 () (not (= @t1 @t18))) % 0.37/0.58 (define @t78 () (not @t9)) % 0.37/0.58 (define @t79 () (or @t77 @t78 @t77 @t76)) % 0.37/0.58 (define @t80 () (or @t78 @t77 @t76)) % 0.37/0.58 (define @t81 () (or @t77 @t76)) % 0.37/0.58 (define @t82 () (@quantifiers_skolemize (forall @t7 @t72) 0)) % 0.37/0.58 (define @t83 () (tptp.op2 @t82 @t82)) % 0.37/0.58 (define @t84 () (= @t82 (tptp.op2 @t82 @t83))) % 0.37/0.58 (define @t85 () (tptp.sorti2 @t83)) % 0.37/0.58 (define @t86 () (not @t85)) % 0.37/0.58 (define @t87 () (tptp.sorti2 @t82)) % 0.37/0.58 (define @t88 () (not @t87)) % 0.37/0.58 (define @t89 () (or @t88 @t86 @t84)) % 0.37/0.58 (define @t90 () (not @t84)) % 0.37/0.58 (define @t91 () (@list true)) % 0.37/0.58 (define @t92 () (@list @t89)) % 0.37/0.58 (define @t93 () (= @t26 @t27)) % 0.37/0.58 (define @t94 () (= @t32 @t33)) % 0.37/0.58 (define @t95 () (@var "BOUND_VARIABLE_7639" $$unsorted)) % 0.37/0.58 (define @t96 () (= (tptp.j (tptp.op2 @t39 @t95)) (tptp.op1 @t40 (tptp.j @t95)))) % 0.37/0.58 (define @t97 () (not (tptp.sorti2 @t95))) % 0.37/0.58 (define @t98 () (not @t45)) % 0.37/0.58 (define @t99 () (or @t97 @t96)) % 0.37/0.58 (define @t100 () (or @t98 @t99)) % 0.37/0.58 (define @t101 () (forall (@list @t39 @t95) @t100)) % 0.37/0.58 (define @t102 () (@list @t95)) % 0.37/0.58 (define @t103 () (forall @t102 @t100)) % 0.37/0.58 (define @t104 () (forall @t102 @t99)) % 0.37/0.58 (define @t105 () (or @t98 @t104)) % 0.37/0.58 (define @t106 () (forall @t43 (or (not @t42) @t41))) % 0.37/0.58 (define @t107 () (@var "BOUND_VARIABLE_7616" $$unsorted)) % 0.37/0.58 (define @t108 () (= (tptp.h (tptp.op1 @t50 @t107)) (tptp.op2 @t51 (tptp.h @t107)))) % 0.37/0.58 (define @t109 () (not (tptp.sorti1 @t107))) % 0.37/0.58 (define @t110 () (not @t56)) % 0.37/0.58 (define @t111 () (or @t109 @t108)) % 0.37/0.58 (define @t112 () (or @t110 @t111)) % 0.37/0.58 (define @t113 () (forall (@list @t50 @t107) @t112)) % 0.37/0.58 (define @t114 () (@list @t107)) % 0.37/0.58 (define @t115 () (forall @t114 @t112)) % 0.37/0.58 (define @t116 () (forall @t114 @t111)) % 0.37/0.58 (define @t117 () (or @t110 @t116)) % 0.37/0.58 (define @t118 () (forall @t54 (or (not @t53) @t52))) % 0.37/0.58 (define @t119 () (tptp.j @t82)) % 0.37/0.58 (define @t120 () (tptp.op1 @t119 @t119)) % 0.37/0.58 (define @t121 () (tptp.j @t83)) % 0.37/0.58 (define @t122 () (= @t121 @t120)) % 0.37/0.58 (define @t123 () (or @t88 @t88 @t122)) % 0.37/0.58 (define @t124 () (@list false false)) % 0.37/0.58 (define @t125 () (@list @t82)) % 0.37/0.58 (define @t126 () (tptp.h @t119)) % 0.37/0.58 (define @t127 () (= @t82 @t126)) % 0.37/0.58 (define @t128 () (or @t88 @t127)) % 0.37/0.58 (define @t129 () (@list @t83)) % 0.37/0.58 (define @t130 () (tptp.h @t121)) % 0.37/0.58 (define @t131 () (= @t83 @t130)) % 0.37/0.58 (define @t132 () (or @t86 @t131)) % 0.37/0.58 (define @t133 () (= @t2 (tptp.op1 @t2 @t11))) % 0.37/0.58 (define @t134 () (not (tptp.sorti1 @t11))) % 0.37/0.58 (define @t135 () (not @t6)) % 0.37/0.58 (define @t136 () (or @t134 @t133)) % 0.37/0.58 (define @t137 () (not (= @t11 @t11))) % 0.37/0.58 (define @t138 () (or @t134 @t137 @t133)) % 0.37/0.58 (define @t139 () (= @t2 @t3)) % 0.37/0.58 (define @t140 () (not (= @t1 @t11))) % 0.37/0.58 (define @t141 () (not @t4)) % 0.37/0.58 (define @t142 () (or @t140 @t141 @t140 @t139)) % 0.37/0.58 (define @t143 () (or @t141 @t140 @t139)) % 0.37/0.58 (define @t144 () (or @t140 @t139)) % 0.37/0.58 (define @t145 () (tptp.sorti1 @t121)) % 0.37/0.58 (define @t146 () (or @t86 @t145)) % 0.37/0.58 (define @t147 () (tptp.sorti1 @t120)) % 0.37/0.58 (define @t148 () (tptp.sorti1 @t119)) % 0.37/0.58 (define @t149 () (or @t88 @t148)) % 0.37/0.58 (define @t150 () (= @t119 (tptp.op1 @t119 @t120))) % 0.37/0.58 (define @t151 () (not @t147)) % 0.37/0.58 (define @t152 () (not @t148)) % 0.37/0.58 (define @t153 () (or @t152 @t151 @t150)) % 0.37/0.58 (define @t154 () (@list false false false)) % 0.37/0.58 (define @t155 () (tptp.op2 @t126 @t130)) % 0.37/0.58 (define @t156 () (tptp.op1 @t119 @t121)) % 0.37/0.58 (define @t157 () (tptp.h @t156)) % 0.37/0.58 (define @t158 () (= @t157 @t155)) % 0.37/0.58 (define @t159 () (not @t145)) % 0.37/0.58 (define @t160 () (or @t152 @t159 @t158)) % 0.37/0.58 (define @t161 () (not @t158)) % 0.37/0.58 (define @t162 () (not @t150)) % 0.37/0.58 (define @t163 () (not @t131)) % 0.37/0.58 (define @t164 () (not @t127)) % 0.37/0.58 (define @t165 () (not @t122)) % 0.37/0.58 (define @t166 () (and @t90 @t122 @t127 @t131 @t150)) % 0.37/0.58 (assume @p1 (forall @t7 (=> @t6 (forall @t5 (=> @t4 (tptp.sorti1 @t3)))))) % 0.37/0.58 (assume @p2 (forall @t7 (=> @t10 (forall @t5 (=> @t9 (tptp.sorti2 @t8)))))) % 0.37/0.58 (assume @p3 @t17) % 0.37/0.58 (assume @p4 @t25) % 0.37/0.58 (assume @p5 @t68) % 0.37/0.58 (assume @p6 true) % 0.37/0.58 (step @p7 :rule aci_norm :args ((= (or @t71 @t73) @t72))) % 0.37/0.58 (step @p8 :rule bool-impl-elim :args (@t10 @t73)) % 0.37/0.58 (step @p9 :rule trans :premises (@p8 @p7)) % 0.37/0.58 (step @p10 :rule cong :premises (@p9) :args ((forall @t7 (=> @t10 @t73)))) % 0.37/0.58 (step @p11 :rule aci_norm :args ((= (or @t70 false @t69) @t73))) % 0.37/0.58 (step @p12 :rule refl :args (@t69)) % 0.37/0.58 (step @p13 :rule evaluate :args ((not true))) % 0.37/0.58 (step @p14 :rule eq-refl :args (@t18)) % 0.37/0.58 (step @p15 :rule cong :premises (@p14) :args (@t74)) % 0.37/0.58 (step @p16 :rule trans :premises (@p15 @p13)) % 0.37/0.58 (step @p17 :rule refl :args (@t70)) % 0.37/0.58 (step @p18 :rule nary_cong :premises (@p17 @p16 @p12) :args (@t75)) % 0.37/0.58 (step @p19 :rule trans :premises (@p18 @p11)) % 0.37/0.58 (step @p20 :rule quant-var-elim-eq :args ((= (forall @t5 @t79) @t75))) % 0.37/0.58 (step @p21 :rule aci_norm :args ((= @t80 @t79))) % 0.37/0.58 (step @p22 :rule cong :premises (@p21) :args ((forall @t5 @t80))) % 0.37/0.58 (step @p23 :rule trans :premises (@p22 @p20)) % 0.37/0.58 (step @p24 :rule trans :premises (@p23 @p19)) % 0.37/0.58 (step @p25 :rule aci_norm :args ((= (or @t78 @t81) @t80))) % 0.37/0.58 (step @p26 :rule bool-impl-elim :args (@t9 @t81)) % 0.37/0.58 (step @p27 :rule trans :premises (@p26 @p25)) % 0.37/0.58 (step @p28 :rule cong :premises (@p27) :args ((forall @t5 (=> @t9 @t81)))) % 0.37/0.58 (step @p29 :rule trans :premises (@p28 @p24)) % 0.37/0.58 (step @p30 :rule eq-symm :args (@t8 @t2)) % 0.37/0.58 (step @p31 :rule eq-symm :args (@t18 @t1)) % 0.37/0.58 (step @p32 :rule cong :premises (@p31) :args (@t19)) % 0.37/0.58 (step @p33 :rule nary_cong :premises (@p32 @p30) :args (@t20)) % 0.37/0.58 (step @p34 :rule refl :args (@t9)) % 0.37/0.58 (step @p35 :rule cong :premises (@p34 @p33) :args (@t21)) % 0.37/0.58 (step @p36 :rule cong :premises (@p35) :args (@t22)) % 0.37/0.58 (step @p37 :rule trans :premises (@p36 @p29)) % 0.37/0.58 (step @p38 :rule refl :args (@t10)) % 0.37/0.58 (step @p39 :rule cong :premises (@p38 @p37) :args (@t23)) % 0.37/0.58 (step @p40 :rule cong :premises (@p39) :args (@t24)) % 0.37/0.58 (step @p41 :rule trans :premises (@p40 @p10)) % 0.37/0.58 (step @p42 :rule cong :premises (@p41) :args (@t25)) % 0.37/0.58 (step @p43 :rule eq_resolve :premises (@p4 @p42)) % 0.37/0.58 (step @p44 :rule skolemize :premises (@p43)) % 0.37/0.58 (step @p45 :rule cnf_or_neg :args (@t89 2)) % 0.37/0.58 (step @p46 :rule chain_m_resolution :premises (@p45 @p44) :args (@t90 @t91 @t92)) % 0.37/0.58 (step @p47 :rule bool-impl-elim :args (@t28 @t93)) % 0.37/0.58 (step @p48 :rule cong :premises (@p47) :args ((forall @t30 (=> @t28 @t93)))) % 0.37/0.58 (step @p49 :rule eq-symm :args (@t27 @t26)) % 0.37/0.58 (step @p50 :rule refl :args (@t28)) % 0.37/0.58 (step @p51 :rule cong :premises (@p50 @p49) :args (@t29)) % 0.37/0.58 (step @p52 :rule cong :premises (@p51) :args (@t31)) % 0.37/0.58 (step @p53 :rule trans :premises (@p52 @p48)) % 0.37/0.58 (step @p54 :rule bool-impl-elim :args (@t34 @t94)) % 0.37/0.58 (step @p55 :rule cong :premises (@p54) :args ((forall @t36 (=> @t34 @t94)))) % 0.37/0.58 (step @p56 :rule eq-symm :args (@t33 @t32)) % 0.37/0.58 (step @p57 :rule refl :args (@t34)) % 0.37/0.58 (step @p58 :rule cong :premises (@p57 @p56) :args (@t35)) % 0.37/0.58 (step @p59 :rule cong :premises (@p58) :args (@t37)) % 0.37/0.58 (step @p60 :rule trans :premises (@p59 @p55)) % 0.37/0.58 (step @p61 :rule aci_norm :args ((= @t100 (or @t98 @t97 @t96)))) % 0.37/0.58 (step @p62 :rule cong :premises (@p61) :args (@t101)) % 0.37/0.58 (step @p63 :rule quant-merge-prenex :args ((= (forall @t47 @t103) @t101))) % 0.37/0.58 (step @p64 :rule alpha_equiv :args (@t104 (@list @t95) (@list @t38))) % 0.37/0.58 (step @p65 :rule refl :args (@t98)) % 0.37/0.58 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t105)) % 0.37/0.58 (step @p67 :rule quant-miniscope-or :args ((= @t103 @t105))) % 0.37/0.58 (step @p68 :rule trans :premises (@p67 @p66)) % 0.37/0.58 (step @p69 :rule symm :premises (@p68)) % 0.37/0.58 (step @p70 :rule cong :premises (@p69) :args ((forall @t47 (or @t98 @t106)))) % 0.37/0.58 (step @p71 :rule trans :premises (@p70 @p63)) % 0.37/0.58 (step @p72 :rule trans :premises (@p71 @p62)) % 0.37/0.58 (step @p73 :rule bool-impl-elim :args (@t45 @t106)) % 0.37/0.58 (step @p74 :rule cong :premises (@p73) :args ((forall @t47 (=> @t45 @t106)))) % 0.37/0.58 (step @p75 :rule trans :premises (@p74 @p72)) % 0.37/0.58 (step @p76 :rule bool-impl-elim :args (@t42 @t41)) % 0.37/0.58 (step @p77 :rule cong :premises (@p76) :args (@t44)) % 0.37/0.58 (step @p78 :rule refl :args (@t45)) % 0.37/0.58 (step @p79 :rule cong :premises (@p78 @p77) :args (@t46)) % 0.37/0.58 (step @p80 :rule cong :premises (@p79) :args (@t48)) % 0.37/0.58 (step @p81 :rule trans :premises (@p80 @p75)) % 0.37/0.58 (step @p82 :rule aci_norm :args ((= @t112 (or @t110 @t109 @t108)))) % 0.37/0.58 (step @p83 :rule cong :premises (@p82) :args (@t113)) % 0.37/0.58 (step @p84 :rule quant-merge-prenex :args ((= (forall @t58 @t115) @t113))) % 0.37/0.58 (step @p85 :rule alpha_equiv :args (@t116 (@list @t107) (@list @t49))) % 0.37/0.58 (step @p86 :rule refl :args (@t110)) % 0.37/0.58 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t117)) % 0.37/0.58 (step @p88 :rule quant-miniscope-or :args ((= @t115 @t117))) % 0.37/0.58 (step @p89 :rule trans :premises (@p88 @p87)) % 0.37/0.58 (step @p90 :rule symm :premises (@p89)) % 0.37/0.58 (step @p91 :rule cong :premises (@p90) :args ((forall @t58 (or @t110 @t118)))) % 0.37/0.58 (step @p92 :rule trans :premises (@p91 @p84)) % 0.37/0.58 (step @p93 :rule trans :premises (@p92 @p83)) % 0.37/0.58 (step @p94 :rule bool-impl-elim :args (@t56 @t118)) % 0.37/0.58 (step @p95 :rule cong :premises (@p94) :args ((forall @t58 (=> @t56 @t118)))) % 0.37/0.58 (step @p96 :rule trans :premises (@p95 @p93)) % 0.37/0.58 (step @p97 :rule bool-impl-elim :args (@t53 @t52)) % 0.37/0.58 (step @p98 :rule cong :premises (@p97) :args (@t55)) % 0.37/0.58 (step @p99 :rule refl :args (@t56)) % 0.37/0.58 (step @p100 :rule cong :premises (@p99 @p98) :args (@t57)) % 0.37/0.58 (step @p101 :rule cong :premises (@p100) :args (@t59)) % 0.37/0.58 (step @p102 :rule trans :premises (@p101 @p96)) % 0.37/0.58 (step @p103 :rule nary_cong :premises (@p102 @p81 @p60 @p53) :args (@t60)) % 0.37/0.58 (step @p104 :rule cong :premises (@p103) :args (@t61)) % 0.37/0.58 (step @p105 :rule bool-impl-elim :args (@t9 @t62)) % 0.37/0.58 (step @p106 :rule cong :premises (@p105) :args (@t63)) % 0.37/0.58 (step @p107 :rule bool-impl-elim :args (@t6 @t64)) % 0.37/0.58 (step @p108 :rule cong :premises (@p107) :args (@t65)) % 0.37/0.58 (step @p109 :rule nary_cong :premises (@p108 @p106) :args (@t66)) % 0.37/0.58 (step @p110 :rule cong :premises (@p109 @p104) :args (@t67)) % 0.37/0.58 (step @p111 :rule cong :premises (@p110) :args (@t68)) % 0.37/0.58 (step @p112 :rule eq_resolve :premises (@p5 @p111)) % 0.37/0.58 (step @p113 :rule not_implies_elim2 :premises (@p112)) % 0.37/0.58 (step @p114 :rule not_not_elim :premises (@p113)) % 0.37/0.58 (step @p115 :rule and_elim :premises (@p114) :args (1)) % 0.37/0.58 (step @p116 :rule instantiate :premises (@p115) :args ((@list @t82 @t82))) % 0.37/0.58 (step @p117 :rule bool-double-not-elim :args (@t87)) % 0.37/0.58 (step @p118 :rule refl :args (@t89)) % 0.37/0.58 (step @p119 :rule nary_cong :premises (@p118 @p117) :args ((or @t89 (not @t88)))) % 0.37/0.58 (step @p120 :rule cnf_or_neg :args (@t89 0)) % 0.37/0.58 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.37/0.58 (step @p122 :rule reordering :premises (@p121) :args ((or @t87 @t89))) % 0.37/0.58 (step @p123 :rule chain_m_resolution :premises (@p122 @p44) :args (@t87 @t91 @t92)) % 0.37/0.58 (step @p124 :rule cnf_or_pos :args (@t123)) % 0.37/0.58 (step @p125 :rule factoring :premises (@p124)) % 0.37/0.58 (step @p126 :rule reordering :premises (@p125) :args ((or @t88 @t122 (not @t123)))) % 0.37/0.58 (step @p127 :rule chain_m_resolution :premises (@p126 @p123 @p116) :args (@t122 @t124 (@list @t87 @t123))) % 0.37/0.58 (step @p128 :rule and_elim :premises (@p114) :args (2)) % 0.37/0.58 (step @p129 :rule instantiate :premises (@p128) :args (@t125)) % 0.37/0.58 (step @p130 :rule cnf_or_pos :args (@t128)) % 0.37/0.58 (step @p131 :rule reordering :premises (@p130) :args ((or @t88 @t127 (not @t128)))) % 0.37/0.58 (step @p132 :rule chain_m_resolution :premises (@p131 @p123 @p129) :args (@t127 @t124 (@list @t87 @t128))) % 0.37/0.58 (step @p133 :rule instantiate :premises (@p128) :args (@t129)) % 0.37/0.58 (step @p134 :rule bool-double-not-elim :args (@t85)) % 0.37/0.58 (step @p135 :rule nary_cong :premises (@p118 @p134) :args ((or @t89 (not @t86)))) % 0.37/0.58 (step @p136 :rule cnf_or_neg :args (@t89 1)) % 0.37/0.58 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 0.37/0.58 (step @p138 :rule reordering :premises (@p137) :args ((or @t85 @t89))) % 0.37/0.58 (step @p139 :rule chain_m_resolution :premises (@p138 @p44) :args (@t85 @t91 @t92)) % 0.37/0.58 (step @p140 :rule cnf_or_pos :args (@t132)) % 0.37/0.58 (step @p141 :rule reordering :premises (@p140) :args ((or @t86 @t131 (not @t132)))) % 0.37/0.58 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p133) :args (@t131 @t124 (@list @t85 @t132))) % 0.37/0.58 (step @p143 :rule aci_norm :args ((= (or @t135 @t136) (or @t135 @t134 @t133)))) % 0.37/0.58 (step @p144 :rule bool-impl-elim :args (@t6 @t136)) % 0.37/0.58 (step @p145 :rule trans :premises (@p144 @p143)) % 0.37/0.58 (step @p146 :rule cong :premises (@p145) :args ((forall @t7 (=> @t6 @t136)))) % 0.37/0.58 (step @p147 :rule aci_norm :args ((= (or @t134 false @t133) @t136))) % 0.37/0.58 (step @p148 :rule refl :args (@t133)) % 0.37/0.58 (step @p149 :rule eq-refl :args (@t11)) % 0.37/0.58 (step @p150 :rule cong :premises (@p149) :args (@t137)) % 0.37/0.58 (step @p151 :rule trans :premises (@p150 @p13)) % 0.37/0.58 (step @p152 :rule refl :args (@t134)) % 0.37/0.58 (step @p153 :rule nary_cong :premises (@p152 @p151 @p148) :args (@t138)) % 0.37/0.58 (step @p154 :rule trans :premises (@p153 @p147)) % 0.37/0.58 (step @p155 :rule quant-var-elim-eq :args ((= (forall @t5 @t142) @t138))) % 0.37/0.58 (step @p156 :rule aci_norm :args ((= @t143 @t142))) % 0.37/0.58 (step @p157 :rule cong :premises (@p156) :args ((forall @t5 @t143))) % 0.37/0.58 (step @p158 :rule trans :premises (@p157 @p155)) % 0.37/0.58 (step @p159 :rule trans :premises (@p158 @p154)) % 0.37/0.58 (step @p160 :rule aci_norm :args ((= (or @t141 @t144) @t143))) % 0.37/0.58 (step @p161 :rule bool-impl-elim :args (@t4 @t144)) % 0.37/0.58 (step @p162 :rule trans :premises (@p161 @p160)) % 0.37/0.58 (step @p163 :rule cong :premises (@p162) :args ((forall @t5 (=> @t4 @t144)))) % 0.37/0.58 (step @p164 :rule trans :premises (@p163 @p159)) % 0.37/0.58 (step @p165 :rule eq-symm :args (@t3 @t2)) % 0.37/0.58 (step @p166 :rule eq-symm :args (@t11 @t1)) % 0.37/0.58 (step @p167 :rule cong :premises (@p166) :args (@t12)) % 0.37/0.58 (step @p168 :rule nary_cong :premises (@p167 @p165) :args (@t13)) % 0.37/0.58 (step @p169 :rule refl :args (@t4)) % 0.37/0.58 (step @p170 :rule cong :premises (@p169 @p168) :args (@t14)) % 0.37/0.58 (step @p171 :rule cong :premises (@p170) :args (@t15)) % 0.37/0.58 (step @p172 :rule trans :premises (@p171 @p164)) % 0.37/0.58 (step @p173 :rule refl :args (@t6)) % 0.37/0.58 (step @p174 :rule cong :premises (@p173 @p172) :args (@t16)) % 0.37/0.58 (step @p175 :rule cong :premises (@p174) :args (@t17)) % 0.37/0.58 (step @p176 :rule trans :premises (@p175 @p146)) % 0.37/0.58 (step @p177 :rule eq_resolve :premises (@p3 @p176)) % 0.37/0.58 (step @p178 :rule instantiate :premises (@p177) :args ((@list @t119))) % 0.37/0.58 (step @p179 :rule not_implies_elim1 :premises (@p112)) % 0.37/0.58 (step @p180 :rule and_elim :premises (@p179) :args (1)) % 0.37/0.58 (step @p181 :rule instantiate :premises (@p180) :args (@t129)) % 0.37/0.58 (step @p182 :rule cnf_or_pos :args (@t146)) % 0.37/0.58 (step @p183 :rule reordering :premises (@p182) :args ((or @t86 @t145 (not @t146)))) % 0.37/0.58 (step @p184 :rule chain_m_resolution :premises (@p183 @p139 @p181) :args (@t145 @t124 (@list @t85 @t146))) % 0.37/0.58 (step @p185 :rule true_intro :premises (@p184)) % 0.37/0.58 (step @p186 :rule symm :premises (@p127)) % 0.37/0.58 (step @p187 :rule cong :premises (@p186) :args (@t147)) % 0.37/0.58 (step @p188 :rule trans :premises (@p187 @p185)) % 0.37/0.58 (step @p189 :rule true_elim :premises (@p188)) % 0.37/0.58 (step @p190 :rule instantiate :premises (@p180) :args (@t125)) % 0.37/0.58 (step @p191 :rule cnf_or_pos :args (@t149)) % 0.37/0.58 (step @p192 :rule reordering :premises (@p191) :args ((or @t88 @t148 (not @t149)))) % 0.37/0.58 (step @p193 :rule chain_m_resolution :premises (@p192 @p123 @p190) :args (@t148 @t124 (@list @t87 @t149))) % 0.37/0.58 (step @p194 :rule cnf_or_pos :args (@t153)) % 0.37/0.58 (step @p195 :rule reordering :premises (@p194) :args ((or @t152 @t151 @t150 (not @t153)))) % 0.37/0.58 (step @p196 :rule chain_m_resolution :premises (@p195 @p193 @p189 @p178) :args (@t150 @t154 (@list @t148 @t147 @t153))) % 0.37/0.58 (step @p197 :rule and_elim :premises (@p114) :args (0)) % 0.37/0.58 (step @p198 :rule instantiate :premises (@p197) :args ((@list @t119 @t121))) % 0.37/0.58 (step @p199 :rule cnf_or_pos :args (@t160)) % 0.37/0.58 (step @p200 :rule reordering :premises (@p199) :args ((or @t152 @t159 @t158 (not @t160)))) % 0.37/0.58 (step @p201 :rule chain_m_resolution :premises (@p200 @p193 @p184 @p198) :args (@t158 @t154 (@list @t148 @t145 @t160))) % 0.37/0.58 (step @p202 :rule refl :args (@t161)) % 0.37/0.58 (step @p203 :rule refl :args (@t162)) % 0.37/0.58 (step @p204 :rule refl :args (@t163)) % 0.37/0.58 (step @p205 :rule refl :args (@t164)) % 0.37/0.58 (step @p206 :rule refl :args (@t165)) % 0.37/0.58 (step @p207 :rule bool-double-not-elim :args (@t84)) % 0.37/0.58 (step @p208 :rule nary_cong :premises (@p207 @p206 @p205 @p204 @p203 @p202) :args ((or (not @t90) @t165 @t164 @t163 @t162 @t161))) % 0.37/0.58 (assume-push @p238 @t90) % 0.37/0.58 (assume-push @p239 @t122) % 0.37/0.58 (assume-push @p240 @t127) % 0.37/0.58 (assume-push @p241 @t131) % 0.37/0.58 (assume-push @p242 @t150) % 0.37/0.58 (step @p214 :rule false_intro :premises (@p46)) % 0.37/0.58 (step @p215 :rule symm :premises (@p142)) % 0.37/0.58 (step @p216 :rule symm :premises (@p132)) % 0.37/0.58 (step @p217 :rule cong :premises (@p216 @p215) :args (@t155)) % 0.37/0.58 (step @p218 :rule symm :premises (@p196)) % 0.37/0.58 (step @p219 :rule refl :args (@t119)) % 0.37/0.58 (step @p220 :rule cong :premises (@p219 @p127) :args (@t156)) % 0.37/0.58 (step @p221 :rule trans :premises (@p220 @p218)) % 0.37/0.58 (step @p222 :rule cong :premises (@p221) :args (@t157)) % 0.37/0.58 (step @p223 :rule trans :premises (@p222 @p216)) % 0.37/0.58 (step @p224 :rule cong :premises (@p223 @p217) :args (@t158)) % 0.37/0.58 (step @p225 :rule trans :premises (@p224 @p214)) % 0.37/0.58 (step @p226 :rule false_elim :premises (@p225)) % 0.37/0.58 (step-pop @p243 :rule scope :premises (@p226)) % 0.37/0.58 (step-pop @p244 :rule scope :premises (@p243)) % 0.37/0.58 (step-pop @p245 :rule scope :premises (@p244)) % 0.37/0.58 (step-pop @p246 :rule scope :premises (@p245)) % 0.37/0.58 (step-pop @p247 :rule scope :premises (@p246)) % 0.37/0.58 (step @p227 :rule process_scope :premises (@p247) :args (@t161)) % 0.37/0.58 (step @p233 :rule implies_elim :premises (@p227)) % 0.37/0.58 (step @p234 :rule cnf_and_neg :args (@t166)) % 0.37/0.58 (step @p235 :rule resolution :premises (@p234 @p233) :args (true @t166)) % 0.37/0.58 (step @p236 :rule eq_resolve :premises (@p235 @p208)) % 0.37/0.58 (step @p237 false :rule chain_m_resolution :premises (@p236 @p201 @p196 @p142 @p132 @p127 @p46) :args (false (@list false false false false false true) (@list @t158 @t150 @t131 @t127 @t122 @t84))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------