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cvc5---1.3.4.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cvc5---1.3.4
% Problem  : NUM536+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n009.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 08:39:45 AM UTC 2026

% Result   : Theorem 0.46s 0.68s
% Output   : Proof 0.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM536+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13  % Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.34  % Computer : n009.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 11:28:14 EDT 2026
% 0.16/0.34  % CPUTime  : 
% 0.31/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.46/0.68  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.46/0.68  % SZS status Theorem
% 0.46/0.68  % SZS output start Proof
% 0.46/0.68  (
% 0.46/0.68  (declare-sort $$unsorted 0)
% 0.46/0.68  (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted))
% 0.46/0.68  (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted))
% 0.46/0.68  (declare-const tptp.slcrc0 $$unsorted)
% 0.46/0.68  (declare-const tptp.xS $$unsorted)
% 0.46/0.68  (declare-const tptp.isCountable0 (-> $$unsorted Bool))
% 0.46/0.68  (declare-const tptp.isFinite0 (-> $$unsorted Bool))
% 0.46/0.68  (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool))
% 0.46/0.68  (declare-const tptp.xx $$unsorted)
% 0.46/0.68  (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool))
% 0.46/0.68  (declare-const tptp.aElement0 (-> $$unsorted Bool))
% 0.46/0.68  (declare-const tptp.aSet0 (-> $$unsorted Bool))
% 0.46/0.68  (define @t1 () (@var "W0" $$unsorted))
% 0.46/0.68  (define @t2 () (tptp.aSet0 @t1))
% 0.46/0.68  (define @t3 () (@list @t1))
% 0.46/0.68  (define @t4 () (@var "W1" $$unsorted))
% 0.46/0.68  (define @t5 () (tptp.aElement0 @t4))
% 0.46/0.68  (define @t6 () (tptp.aElementOf0 @t4 @t1))
% 0.46/0.68  (define @t7 () (@list @t4))
% 0.46/0.68  (define @t8 () (forall @t7 (=> @t6 @t5)))
% 0.46/0.68  (define @t9 () (=> @t2 @t8))
% 0.46/0.68  (define @t10 () (forall @t3 @t9))
% 0.46/0.68  (define @t11 () (tptp.isFinite0 @t1))
% 0.46/0.68  (define @t12 () (= @t1 tptp.slcrc0))
% 0.46/0.68  (define @t13 () (tptp.isCountable0 @t1))
% 0.46/0.68  (define @t14 () (and @t2 @t13))
% 0.46/0.68  (define @t15 () (@var "W2" $$unsorted))
% 0.46/0.68  (define @t16 () (@list @t15))
% 0.46/0.68  (define @t17 () (tptp.aSet0 @t4))
% 0.46/0.68  (define @t18 () (tptp.aSubsetOf0 @t4 @t1))
% 0.46/0.68  (define @t19 () (tptp.aSubsetOf0 @t1 @t4))
% 0.46/0.68  (define @t20 () (@list @t1 @t4))
% 0.46/0.68  (define @t21 () (tptp.aSet0 @t15))
% 0.46/0.68  (define @t22 () (@var "W3" $$unsorted))
% 0.46/0.68  (define @t23 () (= @t22 @t4))
% 0.46/0.68  (define @t24 () (tptp.aElementOf0 @t22 @t1))
% 0.46/0.68  (define @t25 () (or @t24 @t23))
% 0.46/0.68  (define @t26 () (tptp.aElement0 @t22))
% 0.46/0.68  (define @t27 () (and @t26 @t25))
% 0.46/0.68  (define @t28 () (tptp.aElementOf0 @t22 @t15))
% 0.46/0.68  (define @t29 () (= @t28 @t27))
% 0.46/0.68  (define @t30 () (@list @t22))
% 0.46/0.68  (define @t31 () (forall @t30 @t29))
% 0.46/0.68  (define @t32 () (and @t21 @t31))
% 0.46/0.68  (define @t33 () (tptp.sdtpldt0 @t1 @t4))
% 0.46/0.68  (define @t34 () (= @t15 @t33))
% 0.46/0.68  (define @t35 () (= @t34 @t32))
% 0.46/0.68  (define @t36 () (forall @t16 @t35))
% 0.46/0.68  (define @t37 () (and @t2 @t5))
% 0.46/0.68  (define @t38 () (=> @t37 @t36))
% 0.46/0.68  (define @t39 () (forall @t20 @t38))
% 0.46/0.68  (define @t40 () (not @t23))
% 0.46/0.68  (define @t41 () (and @t26 @t24 @t40))
% 0.46/0.68  (define @t42 () (= @t28 @t41))
% 0.46/0.68  (define @t43 () (forall @t30 @t42))
% 0.46/0.68  (define @t44 () (and @t21 @t43))
% 0.46/0.68  (define @t45 () (tptp.sdtmndt0 @t1 @t4))
% 0.46/0.68  (define @t46 () (= @t15 @t45))
% 0.46/0.68  (define @t47 () (= @t46 @t44))
% 0.46/0.68  (define @t48 () (forall @t16 @t47))
% 0.46/0.68  (define @t49 () (=> @t37 @t48))
% 0.46/0.68  (define @t50 () (forall @t20 @t49))
% 0.46/0.68  (define @t51 () (tptp.aSet0 tptp.xS))
% 0.46/0.68  (define @t52 () (tptp.aElement0 tptp.xx))
% 0.46/0.68  (define @t53 () (tptp.aElementOf0 tptp.xx tptp.xS))
% 0.46/0.68  (define @t54 () (not @t53))
% 0.46/0.68  (define @t55 () (tptp.sdtpldt0 tptp.xS tptp.xx))
% 0.46/0.68  (define @t56 () (tptp.sdtmndt0 @t55 tptp.xx))
% 0.46/0.68  (define @t57 () (= @t56 tptp.xS))
% 0.46/0.68  (define @t58 () (@var "BOUND_VARIABLE_7706" $$unsorted))
% 0.46/0.68  (define @t59 () (tptp.aElementOf0 @t22 @t58))
% 0.46/0.68  (define @t60 () (= @t4 @t22))
% 0.46/0.68  (define @t61 () (and @t26 @t24 (not @t60)))
% 0.46/0.68  (define @t62 () (forall @t30 (= @t59 @t61)))
% 0.46/0.68  (define @t63 () (tptp.aSet0 @t58))
% 0.46/0.68  (define @t64 () (and @t63 @t62))
% 0.46/0.68  (define @t65 () (= (= @t58 @t45) @t64))
% 0.46/0.68  (define @t66 () (not @t5))
% 0.46/0.68  (define @t67 () (not @t2))
% 0.46/0.68  (define @t68 () (or @t67 @t66 @t65))
% 0.46/0.68  (define @t69 () (@list @t1 @t4 @t58))
% 0.46/0.68  (define @t70 () (forall @t69 @t68))
% 0.46/0.68  (define @t71 () (@list @t58))
% 0.46/0.68  (define @t72 () (forall @t71 @t68))
% 0.46/0.68  (define @t73 () (forall @t71 @t65))
% 0.46/0.68  (define @t74 () (@list @t15))
% 0.46/0.68  (define @t75 () (or @t67 @t66 @t73))
% 0.46/0.68  (define @t76 () (forall @t16 (= @t46 (and @t21 (forall @t30 (= @t28 @t61))))))
% 0.46/0.68  (define @t77 () (or @t67 @t66 @t76))
% 0.46/0.68  (define @t78 () (or @t67 @t66))
% 0.46/0.68  (define @t79 () (not @t37))
% 0.46/0.68  (define @t80 () (= tptp.xx @t22))
% 0.46/0.68  (define @t81 () (not @t80))
% 0.46/0.68  (define @t82 () (tptp.aElementOf0 @t22 @t55))
% 0.46/0.68  (define @t83 () (and @t26 @t82 @t81))
% 0.46/0.68  (define @t84 () (tptp.aElementOf0 @t22 tptp.xS))
% 0.46/0.68  (define @t85 () (forall @t30 (= @t83 @t84)))
% 0.46/0.68  (define @t86 () (and @t51 @t85))
% 0.46/0.68  (define @t87 () (= @t57 @t86))
% 0.46/0.68  (define @t88 () (not @t52))
% 0.46/0.68  (define @t89 () (tptp.aSet0 @t55))
% 0.46/0.68  (define @t90 () (not @t89))
% 0.46/0.68  (define @t91 () (or @t90 @t88 @t87))
% 0.46/0.68  (define @t92 () (forall @t69 (or @t67 @t66 (= (= @t45 @t58) (and @t63 (forall @t30 (= @t61 @t59)))))))
% 0.46/0.68  (define @t93 () (= @t22 tptp.xx))
% 0.46/0.68  (define @t94 () (forall @t30 (= @t84 (and @t26 @t82 (not @t93)))))
% 0.46/0.68  (define @t95 () (and @t51 @t94))
% 0.46/0.68  (define @t96 () (= tptp.xS @t56))
% 0.46/0.68  (define @t97 () (= @t96 @t95))
% 0.46/0.68  (define @t98 () (or @t90 @t88 @t97))
% 0.46/0.68  (define @t99 () (@list false))
% 0.46/0.68  (define @t100 () (@var "BOUND_VARIABLE_7675" $$unsorted))
% 0.46/0.68  (define @t101 () (tptp.aElementOf0 @t22 @t100))
% 0.46/0.68  (define @t102 () (and @t26 (or @t24 @t60)))
% 0.46/0.68  (define @t103 () (forall @t30 (= @t101 @t102)))
% 0.46/0.68  (define @t104 () (tptp.aSet0 @t100))
% 0.46/0.68  (define @t105 () (and @t104 @t103))
% 0.46/0.68  (define @t106 () (= (= @t100 @t33) @t105))
% 0.46/0.68  (define @t107 () (or @t67 @t66 @t106))
% 0.46/0.68  (define @t108 () (@list @t1 @t4 @t100))
% 0.46/0.68  (define @t109 () (forall @t108 @t107))
% 0.46/0.68  (define @t110 () (@list @t100))
% 0.46/0.68  (define @t111 () (forall @t110 @t107))
% 0.46/0.68  (define @t112 () (forall @t110 @t106))
% 0.46/0.68  (define @t113 () (or @t67 @t66 @t112))
% 0.46/0.68  (define @t114 () (forall @t16 (= @t34 (and @t21 (forall @t30 (= @t28 @t102))))))
% 0.46/0.68  (define @t115 () (or @t67 @t66 @t114))
% 0.46/0.68  (define @t116 () (forall @t30 (= (and @t26 (or @t84 @t93)) @t82)))
% 0.46/0.68  (define @t117 () (and @t89 @t116))
% 0.46/0.68  (define @t118 () (or @t84 @t80))
% 0.46/0.68  (define @t119 () (and @t26 @t118))
% 0.46/0.68  (define @t120 () (= @t119 @t82))
% 0.46/0.68  (define @t121 () (forall @t30 @t120))
% 0.46/0.68  (define @t122 () (and @t89 @t121))
% 0.46/0.68  (define @t123 () (= (= @t55 @t55) @t122))
% 0.46/0.68  (define @t124 () (not @t51))
% 0.46/0.68  (define @t125 () (or @t124 @t88 @t123))
% 0.46/0.68  (define @t126 () (forall @t108 (or @t67 @t66 (= (= @t33 @t100) (and @t104 (forall @t30 (= @t102 @t101)))))))
% 0.46/0.68  (define @t127 () (or @t124 @t88 @t117))
% 0.46/0.68  (define @t128 () (@list false false false))
% 0.46/0.68  (define @t129 () (not @t117))
% 0.46/0.68  (define @t130 () (@list @t117))
% 0.46/0.68  (define @t131 () (not @t95))
% 0.46/0.68  (define @t132 () (not @t94))
% 0.46/0.68  (define @t133 () (@quantifiers_skolemize @t94 0))
% 0.46/0.68  (define @t134 () (= tptp.xx @t133))
% 0.46/0.68  (define @t135 () (not @t134))
% 0.46/0.68  (define @t136 () (tptp.aElementOf0 @t133 @t55))
% 0.46/0.68  (define @t137 () (tptp.aElement0 @t133))
% 0.46/0.68  (define @t138 () (and @t137 @t136 @t135))
% 0.46/0.68  (define @t139 () (tptp.aElementOf0 @t133 tptp.xS))
% 0.46/0.68  (define @t140 () (= @t139 @t138))
% 0.46/0.68  (define @t141 () (not @t140))
% 0.46/0.68  (define @t142 () (= @t133 tptp.xx))
% 0.46/0.68  (define @t143 () (not @t142))
% 0.46/0.68  (define @t144 () (and @t137 @t136 @t143))
% 0.46/0.68  (define @t145 () (= @t139 @t144))
% 0.46/0.68  (define @t146 () (not @t145))
% 0.46/0.68  (define @t147 () (@var "BOUND_VARIABLE_7553" $$unsorted))
% 0.46/0.68  (define @t148 () (tptp.aElement0 @t147))
% 0.46/0.68  (define @t149 () (not (tptp.aElementOf0 @t147 @t1)))
% 0.46/0.68  (define @t150 () (or @t149 @t148))
% 0.46/0.68  (define @t151 () (or @t67 @t150))
% 0.46/0.68  (define @t152 () (forall (@list @t1 @t147) @t151))
% 0.46/0.68  (define @t153 () (@list @t147))
% 0.46/0.68  (define @t154 () (forall @t153 @t151))
% 0.46/0.68  (define @t155 () (forall @t153 @t150))
% 0.46/0.68  (define @t156 () (or @t67 @t155))
% 0.46/0.68  (define @t157 () (forall @t7 (or (not @t6) @t5)))
% 0.46/0.68  (define @t158 () (not @t139))
% 0.46/0.68  (define @t159 () (or @t124 @t158 @t137))
% 0.46/0.68  (define @t160 () (or @t139 @t134))
% 0.46/0.68  (define @t161 () (not @t136))
% 0.46/0.68  (define @t162 () (not @t137))
% 0.46/0.68  (define @t163 () (and @t137 @t160))
% 0.46/0.68  (define @t164 () (not @t160))
% 0.46/0.68  (define @t165 () (or @t139 @t142))
% 0.46/0.68  (define @t166 () (and @t137 @t165))
% 0.46/0.68  (define @t167 () (= @t166 @t136))
% 0.46/0.68  (define @t168 () (= @t136 @t163))
% 0.46/0.68  (define @t169 () (not @t168))
% 0.46/0.68  (define @t170 () (not @t163))
% 0.46/0.68  (define @t171 () (not @t138))
% 0.46/0.68  (define @t172 () (and @t54 @t134))
% 0.46/0.68  (assume @p1 (forall @t3 (=> @t2 true)))
% 0.46/0.68  (assume @p2 (forall @t3 (=> (tptp.aElement0 @t1) true)))
% 0.46/0.68  (assume @p3 @t10)
% 0.46/0.68  (assume @p4 (forall @t3 (=> @t2 (=> @t11 true))))
% 0.46/0.68  (assume @p5 (forall @t3 (= @t12 (and @t2 (not (exists @t7 @t6))))))
% 0.46/0.68  (assume @p6 (tptp.isFinite0 tptp.slcrc0))
% 0.46/0.68  (assume @p7 (forall @t3 (=> @t2 (=> @t13 true))))
% 0.46/0.68  (assume @p8 (forall @t3 (=> @t14 (not @t11))))
% 0.46/0.68  (assume @p9 (forall @t3 (=> @t14 (not @t12))))
% 0.46/0.68  (assume @p10 (forall @t3 (=> @t2 (forall @t7 (= @t18 (and @t17 (forall @t16 (=> (tptp.aElementOf0 @t15 @t4) (tptp.aElementOf0 @t15 @t1)))))))))
% 0.46/0.68  (assume @p11 (forall @t3 (=> (and @t2 @t11) (forall @t7 (=> @t18 (tptp.isFinite0 @t4))))))
% 0.46/0.68  (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1))))
% 0.46/0.68  (assume @p13 (forall @t20 (=> (and @t2 @t17) (=> (and @t19 @t18) (= @t1 @t4)))))
% 0.46/0.68  (assume @p14 (forall (@list @t1 @t4 @t15) (=> (and @t2 @t17 @t21) (=> (and @t19 (tptp.aSubsetOf0 @t4 @t15)) (tptp.aSubsetOf0 @t1 @t15)))))
% 0.46/0.68  (assume @p15 @t39)
% 0.46/0.68  (assume @p16 @t50)
% 0.46/0.68  (assume @p17 (forall @t3 (=> @t2 (forall @t7 (=> @t6 (= (tptp.sdtpldt0 @t45 @t4) @t1))))))
% 0.46/0.68  (assume @p18 (and @t52 @t51))
% 0.46/0.68  (assume @p19 @t54)
% 0.46/0.68  (assume @p20 (not @t57))
% 0.46/0.68  (assume @p21 true)
% 0.46/0.68  (step @p22 :rule eq-symm :args (@t59 @t61))
% 0.46/0.68  (step @p23 :rule cong :premises (@p22) :args (@t62))
% 0.46/0.68  (step @p24 :rule refl :args (@t63))
% 0.46/0.68  (step @p25 :rule nary_cong :premises (@p24 @p23) :args (@t64))
% 0.46/0.68  (step @p26 :rule eq-symm :args (@t58 @t45))
% 0.46/0.68  (step @p27 :rule cong :premises (@p26 @p25) :args (@t65))
% 0.46/0.68  (step @p28 :rule refl :args (@t66))
% 0.46/0.68  (step @p29 :rule refl :args (@t67))
% 0.46/0.68  (step @p30 :rule nary_cong :premises (@p29 @p28 @p27) :args (@t68))
% 0.46/0.68  (step @p31 :rule cong :premises (@p30) :args (@t70))
% 0.46/0.68  (step @p32 :rule quant-merge-prenex :args ((= (forall @t20 @t72) @t70)))
% 0.46/0.68  (step @p33 :rule alpha_equiv :args (@t73 (@list @t58) @t74))
% 0.46/0.68  (step @p34 :rule refl :args (@t66))
% 0.46/0.68  (step @p35 :rule refl :args (@t67))
% 0.46/0.68  (step @p36 :rule nary_cong :premises (@p35 @p34 @p33) :args (@t75))
% 0.46/0.68  (step @p37 :rule quant-miniscope-or :args ((= @t72 @t75)))
% 0.46/0.68  (step @p38 :rule trans :premises (@p37 @p36))
% 0.46/0.68  (step @p39 :rule symm :premises (@p38))
% 0.46/0.68  (step @p40 :rule cong :premises (@p39) :args ((forall @t20 @t77)))
% 0.46/0.68  (step @p41 :rule trans :premises (@p40 @p32))
% 0.46/0.68  (step @p42 :rule trans :premises (@p41 @p31))
% 0.46/0.68  (step @p43 :rule aci_norm :args ((= (or @t78 @t76) @t77)))
% 0.46/0.68  (step @p44 :rule refl :args (@t76))
% 0.46/0.68  (step @p45 :rule bool-and-de-morgan :args (@t2 @t5 true))
% 0.46/0.68  (step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or @t79 @t76)))
% 0.46/0.68  (step @p47 :rule trans :premises (@p46 @p43))
% 0.46/0.68  (step @p48 :rule bool-impl-elim :args (@t37 @t76))
% 0.46/0.68  (step @p49 :rule trans :premises (@p48 @p47))
% 0.46/0.68  (step @p50 :rule cong :premises (@p49) :args ((forall @t20 (=> @t37 @t76))))
% 0.46/0.68  (step @p51 :rule trans :premises (@p50 @p42))
% 0.46/0.68  (step @p52 :rule eq-symm :args (@t22 @t4))
% 0.46/0.68  (step @p53 :rule cong :premises (@p52) :args (@t40))
% 0.46/0.68  (step @p54 :rule refl :args (@t24))
% 0.46/0.68  (step @p55 :rule refl :args (@t26))
% 0.46/0.68  (step @p56 :rule nary_cong :premises (@p55 @p54 @p53) :args (@t41))
% 0.46/0.68  (step @p57 :rule refl :args (@t28))
% 0.46/0.68  (step @p58 :rule cong :premises (@p57 @p56) :args (@t42))
% 0.46/0.68  (step @p59 :rule cong :premises (@p58) :args (@t43))
% 0.46/0.68  (step @p60 :rule refl :args (@t21))
% 0.46/0.68  (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t44))
% 0.46/0.68  (step @p62 :rule refl :args (@t46))
% 0.46/0.68  (step @p63 :rule cong :premises (@p62 @p61) :args (@t47))
% 0.46/0.68  (step @p64 :rule cong :premises (@p63) :args (@t48))
% 0.46/0.68  (step @p65 :rule refl :args (@t37))
% 0.46/0.68  (step @p66 :rule cong :premises (@p65 @p64) :args (@t49))
% 0.46/0.68  (step @p67 :rule cong :premises (@p66) :args (@t50))
% 0.46/0.68  (step @p68 :rule trans :premises (@p67 @p51))
% 0.46/0.68  (step @p69 :rule eq_resolve :premises (@p16 @p68))
% 0.46/0.68  (step @p70 :rule eq-symm :args (tptp.xx @t22))
% 0.46/0.68  (step @p71 :rule cong :premises (@p70) :args (@t81))
% 0.46/0.68  (step @p72 :rule refl :args (@t82))
% 0.46/0.68  (step @p73 :rule nary_cong :premises (@p55 @p72 @p71) :args (@t83))
% 0.46/0.68  (step @p74 :rule refl :args (@t84))
% 0.46/0.68  (step @p75 :rule cong :premises (@p74 @p73) :args ((= @t84 @t83)))
% 0.46/0.68  (step @p76 :rule eq-symm :args (@t83 @t84))
% 0.46/0.68  (step @p77 :rule trans :premises (@p76 @p75))
% 0.46/0.68  (step @p78 :rule cong :premises (@p77) :args (@t85))
% 0.46/0.68  (step @p79 :rule refl :args (@t51))
% 0.46/0.68  (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t86))
% 0.46/0.68  (step @p81 :rule eq-symm :args (@t56 tptp.xS))
% 0.46/0.68  (step @p82 :rule cong :premises (@p81 @p80) :args (@t87))
% 0.46/0.68  (step @p83 :rule refl :args (@t88))
% 0.46/0.68  (step @p84 :rule refl :args (@t90))
% 0.46/0.68  (step @p85 :rule nary_cong :premises (@p84 @p83 @p82) :args (@t91))
% 0.46/0.68  (step @p86 :rule refl :args (@t92))
% 0.46/0.68  (step @p87 :rule cong :premises (@p86 @p85) :args ((=> @t92 @t91)))
% 0.46/0.68  (assume-push @p286 @t92)
% 0.46/0.68  (step @p89 :rule instantiate :premises (@p69) :args ((@list @t55 tptp.xx tptp.xS)))
% 0.46/0.68  (step-pop @p287 :rule scope :premises (@p89))
% 0.46/0.68  (step @p90 :rule process_scope :premises (@p287) :args (@t91))
% 0.46/0.68  (step @p92 :rule eq_resolve :premises (@p90 @p87))
% 0.46/0.68  (step @p93 :rule implies_elim :premises (@p92))
% 0.46/0.68  (step @p94 :rule chain_m_resolution :premises (@p93 @p69) :args (@t98 @t99 (@list @t92)))
% 0.46/0.68  (step @p95 :rule eq-symm :args (@t101 @t102))
% 0.46/0.68  (step @p96 :rule cong :premises (@p95) :args (@t103))
% 0.46/0.68  (step @p97 :rule refl :args (@t104))
% 0.46/0.68  (step @p98 :rule nary_cong :premises (@p97 @p96) :args (@t105))
% 0.46/0.68  (step @p99 :rule eq-symm :args (@t100 @t33))
% 0.46/0.68  (step @p100 :rule cong :premises (@p99 @p98) :args (@t106))
% 0.46/0.68  (step @p101 :rule nary_cong :premises (@p29 @p28 @p100) :args (@t107))
% 0.46/0.68  (step @p102 :rule cong :premises (@p101) :args (@t109))
% 0.46/0.68  (step @p103 :rule quant-merge-prenex :args ((= (forall @t20 @t111) @t109)))
% 0.46/0.68  (step @p104 :rule alpha_equiv :args (@t112 (@list @t100) @t74))
% 0.46/0.68  (step @p105 :rule nary_cong :premises (@p35 @p34 @p104) :args (@t113))
% 0.46/0.68  (step @p106 :rule quant-miniscope-or :args ((= @t111 @t113)))
% 0.46/0.68  (step @p107 :rule trans :premises (@p106 @p105))
% 0.46/0.68  (step @p108 :rule symm :premises (@p107))
% 0.46/0.68  (step @p109 :rule cong :premises (@p108) :args ((forall @t20 @t115)))
% 0.46/0.68  (step @p110 :rule trans :premises (@p109 @p103))
% 0.46/0.68  (step @p111 :rule trans :premises (@p110 @p102))
% 0.46/0.68  (step @p112 :rule aci_norm :args ((= (or @t78 @t114) @t115)))
% 0.46/0.68  (step @p113 :rule refl :args (@t114))
% 0.46/0.68  (step @p114 :rule nary_cong :premises (@p45 @p113) :args ((or @t79 @t114)))
% 0.46/0.68  (step @p115 :rule trans :premises (@p114 @p112))
% 0.46/0.68  (step @p116 :rule bool-impl-elim :args (@t37 @t114))
% 0.46/0.68  (step @p117 :rule trans :premises (@p116 @p115))
% 0.46/0.68  (step @p118 :rule cong :premises (@p117) :args ((forall @t20 (=> @t37 @t114))))
% 0.46/0.68  (step @p119 :rule trans :premises (@p118 @p111))
% 0.46/0.68  (step @p120 :rule nary_cong :premises (@p54 @p52) :args (@t25))
% 0.46/0.68  (step @p121 :rule nary_cong :premises (@p55 @p120) :args (@t27))
% 0.46/0.68  (step @p122 :rule cong :premises (@p57 @p121) :args (@t29))
% 0.46/0.68  (step @p123 :rule cong :premises (@p122) :args (@t31))
% 0.46/0.68  (step @p124 :rule nary_cong :premises (@p60 @p123) :args (@t32))
% 0.46/0.68  (step @p125 :rule refl :args (@t34))
% 0.46/0.68  (step @p126 :rule cong :premises (@p125 @p124) :args (@t35))
% 0.46/0.68  (step @p127 :rule cong :premises (@p126) :args (@t36))
% 0.46/0.68  (step @p128 :rule cong :premises (@p65 @p127) :args (@t38))
% 0.46/0.68  (step @p129 :rule cong :premises (@p128) :args (@t39))
% 0.46/0.68  (step @p130 :rule trans :premises (@p129 @p119))
% 0.46/0.68  (step @p131 :rule eq_resolve :premises (@p15 @p130))
% 0.46/0.68  (step @p132 :rule bool-eq-true :args (@t117))
% 0.46/0.68  (step @p133 :rule eq-symm :args (true @t117))
% 0.46/0.68  (step @p134 :rule trans :premises (@p133 @p132))
% 0.46/0.68  (step @p135 :rule nary_cong :premises (@p74 @p70) :args (@t118))
% 0.46/0.68  (step @p136 :rule nary_cong :premises (@p55 @p135) :args (@t119))
% 0.46/0.68  (step @p137 :rule cong :premises (@p136 @p72) :args (@t120))
% 0.46/0.68  (step @p138 :rule cong :premises (@p137) :args (@t121))
% 0.46/0.68  (step @p139 :rule refl :args (@t89))
% 0.46/0.68  (step @p140 :rule nary_cong :premises (@p139 @p138) :args (@t122))
% 0.46/0.68  (step @p141 :rule eq-refl :args (@t55))
% 0.46/0.68  (step @p142 :rule cong :premises (@p141 @p140) :args (@t123))
% 0.46/0.68  (step @p143 :rule trans :premises (@p142 @p134))
% 0.46/0.68  (step @p144 :rule refl :args (@t124))
% 0.46/0.68  (step @p145 :rule nary_cong :premises (@p144 @p83 @p143) :args (@t125))
% 0.46/0.68  (step @p146 :rule refl :args (@t126))
% 0.46/0.68  (step @p147 :rule cong :premises (@p146 @p145) :args ((=> @t126 @t125)))
% 0.46/0.68  (assume-push @p288 @t126)
% 0.46/0.68  (step @p149 :rule instantiate :premises (@p131) :args ((@list tptp.xS tptp.xx @t55)))
% 0.46/0.68  (step-pop @p289 :rule scope :premises (@p149))
% 0.46/0.68  (step @p150 :rule process_scope :premises (@p289) :args (@t125))
% 0.46/0.68  (step @p152 :rule eq_resolve :premises (@p150 @p147))
% 0.46/0.68  (step @p153 :rule implies_elim :premises (@p152))
% 0.46/0.68  (step @p154 :rule chain_m_resolution :premises (@p153 @p131) :args (@t127 @t99 (@list @t126)))
% 0.46/0.68  (step @p155 :rule and_elim :premises (@p18) :args (1))
% 0.46/0.68  (step @p156 :rule and_elim :premises (@p18) :args (0))
% 0.46/0.68  (step @p157 :rule cnf_or_pos :args (@t127))
% 0.46/0.68  (step @p158 :rule reordering :premises (@p157) :args ((or @t88 @t124 @t117 (not @t127))))
% 0.46/0.68  (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p155 @p154) :args (@t117 @t128 (@list @t52 @t51 @t127)))
% 0.46/0.68  (step @p160 :rule cnf_and_pos :args (@t117 0))
% 0.46/0.68  (step @p161 :rule reordering :premises (@p160) :args ((or @t89 @t129)))
% 0.46/0.68  (step @p162 :rule chain_m_resolution :premises (@p161 @p159) :args (@t89 @t99 @t130))
% 0.46/0.68  (step @p163 :rule cnf_or_pos :args (@t98))
% 0.46/0.68  (step @p164 :rule reordering :premises (@p163) :args ((or @t88 @t90 @t97 (not @t98))))
% 0.46/0.68  (step @p165 :rule chain_m_resolution :premises (@p164 @p156 @p162 @p94) :args (@t97 @t128 (@list @t52 @t89 @t98)))
% 0.46/0.68  (step @p166 :rule symm :premises (@p20))
% 0.46/0.68  (step @p167 :rule cnf_equiv_pos2 :args (@t97))
% 0.46/0.68  (step @p168 :rule reordering :premises (@p167) :args ((or @t96 @t131 (not @t97))))
% 0.46/0.68  (step @p169 :rule chain_m_resolution :premises (@p168 @p166 @p165) :args (@t131 (@list true false) (@list @t96 @t97)))
% 0.46/0.68  (step @p170 :rule cnf_and_neg :args (@t95))
% 0.46/0.68  (step @p171 :rule reordering :premises (@p170) :args ((or @t124 @t95 @t132)))
% 0.46/0.68  (step @p172 :rule chain_m_resolution :premises (@p171 @p155 @p169) :args (@t132 (@list false true) (@list @t51 @t95)))
% 0.46/0.68  (step @p173 :rule refl :args (@t141))
% 0.46/0.68  (step @p174 :rule bool-double-not-elim :args (@t94))
% 0.46/0.68  (step @p175 :rule nary_cong :premises (@p174 @p173) :args ((or (not @t132) @t141)))
% 0.46/0.68  (step @p176 :rule eq-symm :args (@t133 tptp.xx))
% 0.46/0.68  (step @p177 :rule cong :premises (@p176) :args (@t143))
% 0.46/0.68  (step @p178 :rule refl :args (@t136))
% 0.46/0.68  (step @p179 :rule refl :args (@t137))
% 0.46/0.68  (step @p180 :rule nary_cong :premises (@p179 @p178 @p177) :args (@t144))
% 0.46/0.68  (step @p181 :rule refl :args (@t139))
% 0.46/0.68  (step @p182 :rule cong :premises (@p181 @p180) :args (@t145))
% 0.46/0.68  (step @p183 :rule cong :premises (@p182) :args (@t146))
% 0.46/0.68  (step @p184 :rule refl :args (@t132))
% 0.46/0.68  (step @p185 :rule cong :premises (@p184 @p183) :args ((=> @t132 @t146)))
% 0.46/0.68  (assume-push @p290 @t132)
% 0.46/0.68  (step @p187 :rule skolemize :premises (@p172))
% 0.46/0.68  (step-pop @p291 :rule scope :premises (@p187))
% 0.46/0.68  (step @p188 :rule process_scope :premises (@p291) :args (@t146))
% 0.46/0.68  (step @p190 :rule eq_resolve :premises (@p188 @p185))
% 0.46/0.68  (step @p191 :rule implies_elim :premises (@p190))
% 0.46/0.68  (step @p192 :rule eq_resolve :premises (@p191 @p175))
% 0.46/0.68  (step @p193 :rule chain_m_resolution :premises (@p192 @p172) :args (@t141 (@list true) (@list @t94)))
% 0.46/0.68  (step @p194 :rule cnf_equiv_neg1 :args (@t140))
% 0.46/0.68  (step @p195 :rule reordering :premises (@p194) :args ((or @t139 @t138 @t140)))
% 0.46/0.68  (step @p196 :rule aci_norm :args ((= @t151 (or @t67 @t149 @t148))))
% 0.46/0.68  (step @p197 :rule cong :premises (@p196) :args (@t152))
% 0.46/0.68  (step @p198 :rule quant-merge-prenex :args ((= (forall @t3 @t154) @t152)))
% 0.46/0.68  (step @p199 :rule alpha_equiv :args (@t155 (@list @t147) (@list @t4)))
% 0.46/0.68  (step @p200 :rule nary_cong :premises (@p35 @p199) :args (@t156))
% 0.46/0.68  (step @p201 :rule quant-miniscope-or :args ((= @t154 @t156)))
% 0.46/0.68  (step @p202 :rule trans :premises (@p201 @p200))
% 0.46/0.68  (step @p203 :rule symm :premises (@p202))
% 0.46/0.68  (step @p204 :rule cong :premises (@p203) :args ((forall @t3 (or @t67 @t157))))
% 0.46/0.68  (step @p205 :rule trans :premises (@p204 @p198))
% 0.46/0.68  (step @p206 :rule trans :premises (@p205 @p197))
% 0.46/0.68  (step @p207 :rule bool-impl-elim :args (@t2 @t157))
% 0.46/0.68  (step @p208 :rule cong :premises (@p207) :args ((forall @t3 (=> @t2 @t157))))
% 0.46/0.68  (step @p209 :rule trans :premises (@p208 @p206))
% 0.46/0.68  (step @p210 :rule bool-impl-elim :args (@t6 @t5))
% 0.46/0.68  (step @p211 :rule cong :premises (@p210) :args (@t8))
% 0.46/0.68  (step @p212 :rule refl :args (@t2))
% 0.46/0.68  (step @p213 :rule cong :premises (@p212 @p211) :args (@t9))
% 0.46/0.68  (step @p214 :rule cong :premises (@p213) :args (@t10))
% 0.46/0.68  (step @p215 :rule trans :premises (@p214 @p209))
% 0.46/0.68  (step @p216 :rule eq_resolve :premises (@p3 @p215))
% 0.46/0.68  (step @p217 :rule instantiate :premises (@p216) :args ((@list tptp.xS @t133)))
% 0.46/0.68  (step @p218 :rule cnf_or_pos :args (@t159))
% 0.46/0.68  (step @p219 :rule reordering :premises (@p218) :args ((or @t124 @t137 @t158 (not @t159))))
% 0.46/0.68  (step @p220 :rule cnf_or_neg :args (@t160 0))
% 0.46/0.68  (step @p221 :rule reordering :premises (@p220) :args ((or @t158 @t160)))
% 0.46/0.68  (step @p222 :rule bool-double-not-elim :args (@t134))
% 0.46/0.68  (step @p223 :rule refl :args (@t161))
% 0.46/0.68  (step @p224 :rule refl :args (@t162))
% 0.46/0.68  (step @p225 :rule refl :args (@t138))
% 0.46/0.68  (step @p226 :rule nary_cong :premises (@p225 @p224 @p223 @p222) :args ((or @t138 @t162 @t161 (not @t135))))
% 0.46/0.68  (step @p227 :rule cnf_and_neg :args (@t138))
% 0.46/0.68  (step @p228 :rule eq_resolve :premises (@p227 @p226))
% 0.46/0.68  (step @p229 :rule reordering :premises (@p228) :args ((or @t134 @t138 @t162 @t161)))
% 0.46/0.68  (step @p230 :rule cnf_and_neg :args (@t163))
% 0.46/0.68  (step @p231 :rule reordering :premises (@p230) :args ((or @t162 @t163 @t164)))
% 0.46/0.68  (step @p232 :rule cnf_and_pos :args (@t117 1))
% 0.46/0.68  (step @p233 :rule reordering :premises (@p232) :args ((or @t116 @t129)))
% 0.46/0.68  (step @p234 :rule chain_m_resolution :premises (@p233 @p159) :args (@t116 @t99 @t130))
% 0.46/0.68  (step @p235 :rule nary_cong :premises (@p181 @p176) :args (@t165))
% 0.46/0.68  (step @p236 :rule nary_cong :premises (@p179 @p235) :args (@t166))
% 0.46/0.68  (step @p237 :rule cong :premises (@p178 @p236) :args ((= @t136 @t166)))
% 0.46/0.68  (step @p238 :rule eq-symm :args (@t166 @t136))
% 0.46/0.68  (step @p239 :rule trans :premises (@p238 @p237))
% 0.46/0.68  (step @p240 :rule refl :args (@t116))
% 0.46/0.68  (step @p241 :rule cong :premises (@p240 @p239) :args ((=> @t116 @t167)))
% 0.46/0.68  (assume-push @p292 @t116)
% 0.46/0.68  (step @p243 :rule instantiate :premises (@p234) :args ((@list @t133)))
% 0.46/0.68  (step-pop @p293 :rule scope :premises (@p243))
% 0.46/0.68  (step @p244 :rule process_scope :premises (@p293) :args (@t167))
% 0.46/0.68  (step @p246 :rule eq_resolve :premises (@p244 @p241))
% 0.46/0.68  (step @p247 :rule implies_elim :premises (@p246))
% 0.46/0.68  (step @p248 :rule chain_m_resolution :premises (@p247 @p234) :args (@t168 @t99 (@list @t116)))
% 0.46/0.68  (step @p249 :rule cnf_equiv_pos2 :args (@t168))
% 0.46/0.68  (step @p250 :rule reordering :premises (@p249) :args ((or @t136 @t170 @t169)))
% 0.46/0.68  (step @p251 :rule chain_m_resolution :premises (@p250 @p248 @p231 @p229 @p221 @p219 @p217 @p155 @p195 @p193) :args ((or @t134 @t138) (@list false false true false false false false false true) (@list @t168 @t163 @t136 @t160 @t137 @t159 @t51 @t139 @t140)))
% 0.46/0.68  (step @p252 :rule cnf_and_pos :args (@t138 1))
% 0.46/0.68  (step @p253 :rule reordering :premises (@p252) :args ((or @t136 @t171)))
% 0.46/0.68  (step @p254 :rule cnf_equiv_neg2 :args (@t140))
% 0.46/0.68  (step @p255 :rule cnf_equiv_pos1 :args (@t168))
% 0.46/0.68  (step @p256 :rule reordering :premises (@p255) :args ((or @t161 @t163 @t169)))
% 0.46/0.68  (step @p257 :rule cnf_or_pos :args (@t160))
% 0.46/0.68  (step @p258 :rule reordering :premises (@p257) :args ((or @t139 @t134 @t164)))
% 0.46/0.68  (step @p259 :rule cnf_and_pos :args (@t163 1))
% 0.46/0.68  (step @p260 :rule reordering :premises (@p259) :args ((or @t160 @t170)))
% 0.46/0.68  (step @p261 :rule chain_m_resolution :premises (@p260 @p258 @p256 @p248 @p254 @p193 @p253 @p251) :args (@t134 (@list true false false true true false false) (@list @t160 @t163 @t168 @t139 @t140 @t136 @t138)))
% 0.46/0.68  (step @p262 :rule cnf_and_pos :args (@t138 2))
% 0.46/0.68  (step @p263 :rule reordering :premises (@p262) :args ((or @t135 @t171)))
% 0.46/0.68  (step @p264 :rule chain_m_resolution :premises (@p263 @p261) :args (@t171 @t99 (@list @t134)))
% 0.46/0.68  (step @p265 :rule chain_m_resolution :premises (@p195 @p264 @p193) :args (@t139 (@list true true) (@list @t138 @t140)))
% 0.46/0.68  (step @p266 :rule refl :args (@t158))
% 0.46/0.68  (step @p267 :rule refl :args (@t135))
% 0.46/0.68  (step @p268 :rule bool-double-not-elim :args (@t53))
% 0.46/0.68  (step @p269 :rule nary_cong :premises (@p268 @p267 @p266) :args ((or (not @t54) @t135 @t158)))
% 0.46/0.68  (assume-push @p294 @t54)
% 0.46/0.68  (assume-push @p295 @t134)
% 0.46/0.68  (step @p272 :rule false_intro :premises (@p19))
% 0.46/0.68  (step @p273 :rule refl :args (tptp.xS))
% 0.46/0.68  (step @p274 :rule symm :premises (@p261))
% 0.46/0.68  (step @p275 :rule cong :premises (@p274 @p273) :args (@t139))
% 0.46/0.68  (step @p276 :rule trans :premises (@p275 @p272))
% 0.46/0.68  (step @p277 :rule false_elim :premises (@p276))
% 0.46/0.68  (step-pop @p296 :rule scope :premises (@p277))
% 0.46/0.68  (step-pop @p297 :rule scope :premises (@p296))
% 0.46/0.68  (step @p278 :rule process_scope :premises (@p297) :args (@t158))
% 0.46/0.68  (step @p281 :rule implies_elim :premises (@p278))
% 0.46/0.68  (step @p282 :rule cnf_and_neg :args (@t172))
% 0.46/0.68  (step @p283 :rule resolution :premises (@p282 @p281) :args (true @t172))
% 0.46/0.68  (step @p284 :rule eq_resolve :premises (@p283 @p269))
% 0.46/0.68  (step @p285 false :rule chain_m_resolution :premises (@p284 @p265 @p261 @p19) :args (false (@list false false true) (@list @t139 @t134 @t53)))
% 0.46/0.68  )
% 0.46/0.68  % SZS output end Proof
% 0.46/0.68  % cvc5 exiting
%------------------------------------------------------------------------------