%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KRS261+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:29:11 AM UTC 2026 % Result : Theorem 28.52s 28.75s % Output : Proof 28.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS261+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n019.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 05:36:34 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 28.52/28.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 28.52/28.75 --- Run --no-e-matching --full-saturate-quant at 6... % 28.52/28.75 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 28.52/28.75 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 28.52/28.75 % SZS status Theorem % 28.52/28.75 % SZS output start Proof % 28.52/28.75 ( % 28.52/28.75 (declare-sort $$unsorted 0) % 28.52/28.75 (declare-const tptp.xora (-> $$unsorted $$unsorted Bool)) % 28.52/28.75 (declare-const tptp.nevera (-> $$unsorted $$unsorted Bool)) % 28.52/28.75 (declare-const tptp.nota (-> $$unsorted $$unsorted Bool)) % 28.52/28.75 (declare-const tptp.mighta (-> $$unsorted $$unsorted Bool)) % 28.52/28.75 (declare-const tptp.noc $$unsorted) % 28.52/28.75 (declare-const tptp.uns $$unsorted) % 28.52/28.75 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 28.52/28.75 (declare-const tptp.tca $$unsorted) % 28.52/28.75 (declare-const tptp.sca $$unsorted) % 28.52/28.75 (declare-const tptp.wth $$unsorted) % 28.52/28.75 (declare-const tptp.unp $$unsorted) % 28.52/28.75 (declare-const tptp.wca $$unsorted) % 28.52/28.75 (declare-const tptp.wec $$unsorted) % 28.52/28.75 (declare-const tptp.sap $$unsorted) % 28.52/28.75 (declare-const tptp.wtc $$unsorted) % 28.52/28.75 (declare-const tptp.model (-> $$unsorted $$unsorted Bool)) % 28.52/28.75 (declare-const tptp.sat $$unsorted) % 28.52/28.75 (declare-const tptp.cax $$unsorted) % 28.52/28.75 (declare-const tptp.eqv $$unsorted) % 28.52/28.75 (declare-const tptp.esa $$unsorted) % 28.52/28.75 (declare-const tptp.csa $$unsorted) % 28.52/28.75 (declare-const tptp.status (-> $$unsorted $$unsorted $$unsorted Bool)) % 28.52/28.75 (declare-const tptp.thm $$unsorted) % 28.52/28.75 (declare-const tptp.isa (-> $$unsorted $$unsorted Bool)) % 28.52/28.75 (declare-const tptp.eth $$unsorted) % 28.52/28.75 (declare-const tptp.tac $$unsorted) % 28.52/28.75 (declare-const tptp.tau $$unsorted) % 28.52/28.75 (define @t1 () (@var "C" $$unsorted)) % 28.52/28.75 (define @t2 () (@var "Ax" $$unsorted)) % 28.52/28.75 (define @t3 () (@var "I2" $$unsorted)) % 28.52/28.75 (define @t4 () (tptp.model @t3 @t1)) % 28.52/28.75 (define @t5 () (@list @t3)) % 28.52/28.75 (define @t6 () (exists @t5 @t4)) % 28.52/28.75 (define @t7 () (@var "I1" $$unsorted)) % 28.52/28.75 (define @t8 () (tptp.model @t7 @t2)) % 28.52/28.75 (define @t9 () (@list @t7)) % 28.52/28.75 (define @t10 () (exists @t9 @t8)) % 28.52/28.75 (define @t11 () (not @t10)) % 28.52/28.75 (define @t12 () (@list @t2 @t1)) % 28.52/28.75 (define @t13 () (tptp.model @t7 @t1)) % 28.52/28.75 (define @t14 () (and @t8 @t13)) % 28.52/28.75 (define @t15 () (exists @t9 @t14)) % 28.52/28.75 (define @t16 () (tptp.status @t2 @t1 tptp.thm)) % 28.52/28.75 (define @t17 () (forall @t9 (=> @t8 @t13))) % 28.52/28.75 (define @t18 () (= @t17 @t16)) % 28.52/28.75 (define @t19 () (forall @t12 @t18)) % 28.52/28.75 (define @t20 () (tptp.model @t3 @t2)) % 28.52/28.75 (define @t21 () (forall @t5 @t4)) % 28.52/28.75 (define @t22 () (@var "I3" $$unsorted)) % 28.52/28.75 (define @t23 () (tptp.model @t22 @t2)) % 28.52/28.75 (define @t24 () (not @t23)) % 28.52/28.75 (define @t25 () (tptp.model @t22 @t1)) % 28.52/28.75 (define @t26 () (@list @t22)) % 28.52/28.75 (define @t27 () (exists @t26 (and @t25 @t24))) % 28.52/28.75 (define @t28 () (forall @t5 (=> @t20 @t4))) % 28.52/28.75 (define @t29 () (tptp.status @t2 @t1 tptp.eth)) % 28.52/28.75 (define @t30 () (forall @t26 (= @t23 @t25))) % 28.52/28.75 (define @t31 () (not @t20)) % 28.52/28.75 (define @t32 () (exists @t5 @t31)) % 28.52/28.75 (define @t33 () (and @t10 @t32 @t30)) % 28.52/28.75 (define @t34 () (= @t33 @t29)) % 28.52/28.75 (define @t35 () (forall @t12 @t34)) % 28.52/28.75 (define @t36 () (@var "I4" $$unsorted)) % 28.52/28.75 (define @t37 () (tptp.model @t36 @t1)) % 28.52/28.75 (define @t38 () (not @t37)) % 28.52/28.75 (define @t39 () (@list @t36)) % 28.52/28.75 (define @t40 () (exists @t39 @t38)) % 28.52/28.75 (define @t41 () (not @t25)) % 28.52/28.75 (define @t42 () (tptp.not @t1)) % 28.52/28.75 (define @t43 () (tptp.model @t3 @t42)) % 28.52/28.75 (define @t44 () (@var "S2" $$unsorted)) % 28.52/28.75 (define @t45 () (@var "S1" $$unsorted)) % 28.52/28.75 (define @t46 () (tptp.mighta @t45 @t44)) % 28.52/28.75 (define @t47 () (tptp.status @t2 @t1 @t44)) % 28.52/28.75 (define @t48 () (tptp.status @t2 @t1 @t45)) % 28.52/28.75 (define @t49 () (and @t48 @t47)) % 28.52/28.75 (define @t50 () (exists @t12 @t49)) % 28.52/28.75 (define @t51 () (= @t50 @t46)) % 28.52/28.75 (define @t52 () (@list @t45 @t44)) % 28.52/28.75 (define @t53 () (forall @t52 @t51)) % 28.52/28.75 (define @t54 () (not @t47)) % 28.52/28.75 (define @t55 () (@var "F" $$unsorted)) % 28.52/28.75 (define @t56 () (@var "I" $$unsorted)) % 28.52/28.75 (define @t57 () (tptp.model @t56 (tptp.not @t55))) % 28.52/28.75 (define @t58 () (tptp.model @t56 @t55)) % 28.52/28.75 (define @t59 () (@list @t56 @t55)) % 28.52/28.75 (define @t60 () (@list @t56)) % 28.52/28.75 (define @t61 () (@list @t55)) % 28.52/28.75 (define @t62 () (and @t24 @t25)) % 28.52/28.75 (define @t63 () (exists @t26 @t62)) % 28.52/28.75 (define @t64 () (and @t10 @t28 @t63 @t40)) % 28.52/28.75 (define @t65 () (exists @t12 @t64)) % 28.52/28.75 (define @t66 () (tptp.mighta tptp.eth tptp.thm)) % 28.52/28.75 (define @t67 () (@var "BOUND_VARIABLE_7929" $$unsorted)) % 28.52/28.75 (define @t68 () (not (tptp.model @t67 @t1))) % 28.52/28.75 (define @t69 () (tptp.model @t67 @t2)) % 28.52/28.75 (define @t70 () (@var "BOUND_VARIABLE_7935" $$unsorted)) % 28.52/28.75 (define @t71 () (tptp.model @t70 @t1)) % 28.52/28.75 (define @t72 () (forall @t5 (or @t31 @t4))) % 28.52/28.75 (define @t73 () (not @t72)) % 28.52/28.75 (define @t74 () (@var "BOUND_VARIABLE_7925" $$unsorted)) % 28.52/28.75 (define @t75 () (not (tptp.model @t74 @t2))) % 28.52/28.75 (define @t76 () (or @t75 @t73 @t71 @t69 @t68)) % 28.52/28.75 (define @t77 () (or @t69 @t68)) % 28.52/28.75 (define @t78 () (or @t75 @t73 @t77 @t71)) % 28.52/28.75 (define @t79 () (@list @t2 @t1 @t74 @t67 @t70)) % 28.52/28.75 (define @t80 () (forall @t79 @t78)) % 28.52/28.75 (define @t81 () (forall (@list @t74 @t67 @t70) @t78)) % 28.52/28.75 (define @t82 () (forall (@list @t70) @t71)) % 28.52/28.75 (define @t83 () (forall (@list @t67) @t77)) % 28.52/28.75 (define @t84 () (forall (@list @t74) @t75)) % 28.52/28.75 (define @t85 () (@list @t7)) % 28.52/28.75 (define @t86 () (or @t84 @t73 @t83 @t82)) % 28.52/28.75 (define @t87 () (forall @t39 @t37)) % 28.52/28.75 (define @t88 () (forall @t26 (or @t23 @t41))) % 28.52/28.75 (define @t89 () (not @t8)) % 28.52/28.75 (define @t90 () (forall @t9 @t89)) % 28.52/28.75 (define @t91 () (not @t87)) % 28.52/28.75 (define @t92 () (not @t91)) % 28.52/28.75 (define @t93 () (not @t88)) % 28.52/28.75 (define @t94 () (not @t93)) % 28.52/28.75 (define @t95 () (not @t90)) % 28.52/28.75 (define @t96 () (not @t95)) % 28.52/28.76 (define @t97 () (or @t96 @t73 @t94 @t92)) % 28.52/28.76 (define @t98 () (and @t95 @t72 @t93 @t91)) % 28.52/28.76 (define @t99 () (forall @t12 (not @t98))) % 28.52/28.76 (define @t100 () (not @t99)) % 28.52/28.76 (define @t101 () (forall @t39 (not @t38))) % 28.52/28.76 (define @t102 () (not @t101)) % 28.52/28.76 (define @t103 () (forall @t26 (not @t62))) % 28.52/28.76 (define @t104 () (not @t103)) % 28.52/28.76 (define @t105 () (forall @t79 @t76)) % 28.52/28.76 (define @t106 () (@quantifiers_skolemize @t105 0)) % 28.52/28.76 (define @t107 () (@quantifiers_skolemize @t105 2)) % 28.52/28.76 (define @t108 () (tptp.model @t107 @t106)) % 28.52/28.76 (define @t109 () (@quantifiers_skolemize @t105 1)) % 28.52/28.76 (define @t110 () (@quantifiers_skolemize @t105 3)) % 28.52/28.76 (define @t111 () (tptp.model @t110 @t106)) % 28.52/28.76 (define @t112 () (tptp.model @t3 @t106)) % 28.52/28.76 (define @t113 () (not @t112)) % 28.52/28.76 (define @t114 () (not @t108)) % 28.52/28.76 (define @t115 () (or @t114 (not (forall @t5 (or @t113 (tptp.model @t3 @t109)))) (tptp.model (@quantifiers_skolemize @t105 4) @t109) @t111 (not (tptp.model @t110 @t109)))) % 28.52/28.76 (define @t116 () (@list true)) % 28.52/28.76 (define @t117 () (@list @t115)) % 28.52/28.76 (define @t118 () (and @t95 (not (forall @t5 @t20)) (forall @t26 (= @t25 @t23)))) % 28.52/28.76 (define @t119 () (forall @t5 (not @t31))) % 28.52/28.76 (define @t120 () (not @t119)) % 28.52/28.76 (define @t121 () (forall @t5 @t112)) % 28.52/28.76 (define @t122 () (not @t121)) % 28.52/28.76 (define @t123 () (tptp.model @t7 @t106)) % 28.52/28.76 (define @t124 () (not @t123)) % 28.52/28.76 (define @t125 () (forall @t9 @t124)) % 28.52/28.76 (define @t126 () (not @t125)) % 28.52/28.76 (define @t127 () (and @t126 @t122)) % 28.52/28.76 (define @t128 () (tptp.model @t22 @t106)) % 28.52/28.76 (define @t129 () (forall @t26 (= @t128 @t128))) % 28.52/28.76 (define @t130 () (and @t126 @t122 @t129)) % 28.52/28.76 (define @t131 () (tptp.status @t106 @t106 tptp.eth)) % 28.52/28.76 (define @t132 () (= @t131 @t130)) % 28.52/28.76 (define @t133 () (forall @t12 (= @t29 @t118))) % 28.52/28.76 (define @t134 () (@list @t106 @t106)) % 28.52/28.76 (define @t135 () (= @t131 @t127)) % 28.52/28.76 (define @t136 () (@list false)) % 28.52/28.76 (define @t137 () (forall @t12 (not @t49))) % 28.52/28.76 (define @t138 () (not @t137)) % 28.52/28.76 (define @t139 () (forall @t12 (or (not @t29) (not @t16)))) % 28.52/28.76 (define @t140 () (not @t139)) % 28.52/28.76 (define @t141 () (= @t66 @t140)) % 28.52/28.76 (define @t142 () (not @t141)) % 28.52/28.76 (define @t143 () (@list true false)) % 28.52/28.76 (define @t144 () (forall @t9 (or @t89 @t13))) % 28.52/28.76 (define @t145 () (tptp.status @t106 @t106 tptp.thm)) % 28.52/28.76 (define @t146 () (forall @t9 (or @t124 @t123))) % 28.52/28.76 (define @t147 () (= @t145 @t146)) % 28.52/28.76 (define @t148 () (forall @t12 (= @t16 @t144))) % 28.52/28.76 (define @t149 () (not @t145)) % 28.52/28.76 (define @t150 () (not @t131)) % 28.52/28.76 (define @t151 () (or @t150 @t149)) % 28.52/28.76 (define @t152 () (@list false false)) % 28.52/28.76 (define @t153 () (not @t127)) % 28.52/28.76 (define @t154 () (forall @t5 @t113)) % 28.52/28.76 (assume @p1 (forall @t12 (= (=> @t11 (not @t6)) (tptp.status @t2 @t1 tptp.unp)))) % 28.52/28.76 (assume @p2 (forall @t12 (= (=> @t10 @t6) (tptp.status @t2 @t1 tptp.sap)))) % 28.52/28.76 (assume @p3 (forall @t12 (= (= @t10 @t6) (tptp.status @t2 @t1 tptp.esa)))) % 28.52/28.76 (assume @p4 (forall @t12 (= @t15 (tptp.status @t2 @t1 tptp.sat)))) % 28.52/28.76 (assume @p5 @t19) % 28.52/28.76 (assume @p6 (forall @t12 (= (and @t10 (forall @t5 (= @t20 @t4))) (tptp.status @t2 @t1 tptp.eqv)))) % 28.52/28.76 (assume @p7 (forall @t12 (= (and @t10 @t21) (tptp.status @t2 @t1 tptp.tac)))) % 28.52/28.76 (assume @p8 (forall @t12 (= (and @t10 @t28 @t27) (tptp.status @t2 @t1 tptp.wec)))) % 28.52/28.76 (assume @p9 @t35) % 28.52/28.76 (assume @p10 (forall @t12 (= (forall @t9 @t14) (tptp.status @t2 @t1 tptp.tau)))) % 28.52/28.76 (assume @p11 (forall @t12 (= (and @t10 @t32 (forall @t26 @t25)) (tptp.status @t2 @t1 tptp.wtc)))) % 28.52/28.76 (assume @p12 (forall @t12 (= (and @t10 @t28 @t27 @t40) (tptp.status @t2 @t1 tptp.wth)))) % 28.52/28.76 (assume @p13 (forall @t12 (= @t11 (tptp.status @t2 @t1 tptp.cax)))) % 28.52/28.76 (assume @p14 (forall @t12 (= (and @t11 @t6) (tptp.status @t2 @t1 tptp.sca)))) % 28.52/28.76 (assume @p15 (forall @t12 (= (and @t11 @t21) (tptp.status @t2 @t1 tptp.tca)))) % 28.52/28.76 (assume @p16 (forall @t12 (= (and @t11 @t6 (exists @t26 @t41)) (tptp.status @t2 @t1 tptp.wca)))) % 28.52/28.76 (assume @p17 (forall @t12 (= (exists @t9 (and @t8 (tptp.model @t7 @t42))) (tptp.status @t2 @t1 tptp.csa)))) % 28.52/28.76 (assume @p18 (forall @t12 (= (and (forall @t9 @t8) (forall @t5 @t43)) (tptp.status @t2 @t1 tptp.uns)))) % 28.52/28.76 (assume @p19 (forall @t12 (= (and @t15 (exists @t5 (and @t20 @t43))) (tptp.status @t2 @t1 tptp.noc)))) % 28.52/28.76 (assume @p20 @t53) % 28.52/28.76 (assume @p21 (forall @t52 (= (forall @t12 (=> @t48 @t47)) (tptp.isa @t45 @t44)))) % 28.52/28.76 (assume @p22 (forall @t52 (= (exists @t12 (and @t48 @t54)) (tptp.nota @t45 @t44)))) % 28.52/28.76 (assume @p23 (forall @t52 (= (forall @t12 (=> @t48 @t54)) (tptp.nevera @t45 @t44)))) % 28.52/28.76 (assume @p24 (forall @t52 (= (forall @t12 (xor @t48 @t47)) (tptp.xora @t45 @t44)))) % 28.52/28.76 (assume @p25 (forall @t59 (xor @t58 @t57))) % 28.52/28.76 (assume @p26 (forall @t59 (= @t58 (not @t57)))) % 28.52/28.76 (assume @p27 (exists @t61 (forall @t60 @t58))) % 28.52/28.76 (assume @p28 (exists @t61 (and (exists @t9 (tptp.model @t7 @t55)) (exists @t5 (not (tptp.model @t3 @t55)))))) % 28.52/28.76 (assume @p29 (exists @t61 (forall @t60 (not @t58)))) % 28.52/28.76 (assume @p30 (exists @t12 (and @t15 (exists @t5 (or @t31 (not @t4)))))) % 28.52/28.76 (assume @p31 @t65) % 28.52/28.76 (assume @p32 (exists (@list @t7 @t2 @t1) (and @t8 (not @t13) @t6))) % 28.52/28.76 (assume @p33 (not @t66)) % 28.52/28.76 (assume @p34 true) % 28.52/28.76 (step @p35 :rule aci_norm :args ((= @t78 @t76))) % 28.52/28.76 (step @p36 :rule cong :premises (@p35) :args (@t80)) % 28.52/28.76 (step @p37 :rule quant-merge-prenex :args ((= (forall @t12 @t81) @t80))) % 28.52/28.76 (step @p38 :rule alpha_equiv :args (@t82 (@list @t70) (@list @t36))) % 28.52/28.76 (step @p39 :rule alpha_equiv :args (@t83 (@list @t67) (@list @t22))) % 28.52/28.76 (step @p40 :rule refl :args (@t73)) % 28.52/28.76 (step @p41 :rule alpha_equiv :args (@t84 (@list @t74) @t85)) % 28.52/28.76 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39 @p38) :args (@t86)) % 28.52/28.76 (step @p43 :rule quant-miniscope-or :args ((= @t81 @t86))) % 28.52/28.76 (step @p44 :rule trans :premises (@p43 @p42)) % 28.52/28.76 (step @p45 :rule symm :premises (@p44)) % 28.52/28.76 (step @p46 :rule cong :premises (@p45) :args ((forall @t12 (or @t90 @t73 @t88 @t87)))) % 28.52/28.76 (step @p47 :rule trans :premises (@p46 @p37)) % 28.52/28.76 (step @p48 :rule trans :premises (@p47 @p36)) % 28.52/28.76 (step @p49 :rule bool-double-not-elim :args (@t87)) % 28.52/28.76 (step @p50 :rule bool-double-not-elim :args (@t88)) % 28.52/28.76 (step @p51 :rule bool-double-not-elim :args (@t90)) % 28.52/28.76 (step @p52 :rule nary_cong :premises (@p51 @p40 @p50 @p49) :args (@t97)) % 28.52/28.76 (step @p53 :rule aci_norm :args ((= (or @t96 (or @t73 (or @t94 @t92))) @t97))) % 28.52/28.76 (step @p54 :rule trans :premises (@p53 @p52)) % 28.52/28.76 (step @p55 :rule bool-and-de-morgan :args (@t93 @t91 true)) % 28.52/28.76 (step @p56 :rule nary_cong :premises (@p40 @p55) :args ((or @t73 (not (and @t93 @t91))))) % 28.52/28.76 (step @p57 :rule bool-and-de-morgan :args (@t72 @t93 (and @t91))) % 28.52/28.76 (step @p58 :rule trans :premises (@p57 @p56)) % 28.52/28.76 (step @p59 :rule refl :args (@t96)) % 28.52/28.76 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or @t96 (not (and @t72 @t93 @t91))))) % 28.52/28.76 (step @p61 :rule bool-and-de-morgan :args (@t95 @t72 (and @t93 @t91))) % 28.52/28.76 (step @p62 :rule trans :premises (@p61 @p60)) % 28.52/28.76 (step @p63 :rule trans :premises (@p62 @p54)) % 28.52/28.76 (step @p64 :rule cong :premises (@p63) :args (@t99)) % 28.52/28.76 (step @p65 :rule trans :premises (@p64 @p48)) % 28.52/28.76 (step @p66 :rule cong :premises (@p65) :args (@t100)) % 28.52/28.76 (step @p67 :rule exists-elim :args ((= (exists @t12 @t98) @t100))) % 28.52/28.76 (step @p68 :rule trans :premises (@p67 @p66)) % 28.52/28.76 (step @p69 :rule bool-double-not-elim :args (@t37)) % 28.52/28.76 (step @p70 :rule cong :premises (@p69) :args (@t101)) % 28.52/28.76 (step @p71 :rule cong :premises (@p70) :args (@t102)) % 28.52/28.76 (step @p72 :rule exists-elim :args ((= @t40 @t102))) % 28.52/28.76 (step @p73 :rule trans :premises (@p72 @p71)) % 28.52/28.76 (step @p74 :rule refl :args (@t41)) % 28.52/28.76 (step @p75 :rule bool-double-not-elim :args (@t23)) % 28.52/28.76 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((or (not @t24) @t41))) % 28.52/28.76 (step @p77 :rule bool-and-de-morgan :args (@t24 @t25 true)) % 28.52/28.76 (step @p78 :rule trans :premises (@p77 @p76)) % 28.52/28.76 (step @p79 :rule cong :premises (@p78) :args (@t103)) % 28.52/28.76 (step @p80 :rule cong :premises (@p79) :args (@t104)) % 28.52/28.76 (step @p81 :rule exists-elim :args ((= @t63 @t104))) % 28.52/28.76 (step @p82 :rule trans :premises (@p81 @p80)) % 28.52/28.76 (step @p83 :rule bool-impl-elim :args (@t20 @t4)) % 28.52/28.76 (step @p84 :rule cong :premises (@p83) :args (@t28)) % 28.52/28.76 (step @p85 :rule exists-elim :args ((= @t10 @t95))) % 28.52/28.76 (step @p86 :rule nary_cong :premises (@p85 @p84 @p82 @p73) :args (@t64)) % 28.52/28.76 (step @p87 :rule cong :premises (@p86) :args (@t65)) % 28.52/28.76 (step @p88 :rule trans :premises (@p87 @p68)) % 28.52/28.76 (step @p89 :rule eq_resolve :premises (@p31 @p88)) % 28.52/28.76 (step @p90 :rule skolemize :premises (@p89)) % 28.52/28.76 (step @p91 :rule bool-double-not-elim :args (@t108)) % 28.52/28.76 (step @p92 :rule refl :args (@t115)) % 28.52/28.76 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t115 (not @t114)))) % 28.52/28.76 (step @p94 :rule cnf_or_neg :args (@t115 0)) % 28.52/28.76 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 28.52/28.76 (step @p96 :rule reordering :premises (@p95) :args ((or @t108 @t115))) % 28.52/28.76 (step @p97 :rule chain_m_resolution :premises (@p96 @p90) :args (@t108 @t116 @t117)) % 28.52/28.76 (step @p98 :rule eq-symm :args (@t118 @t29)) % 28.52/28.76 (step @p99 :rule refl :args (@t29)) % 28.52/28.76 (step @p100 :rule eq-symm :args (@t23 @t25)) % 28.52/28.76 (step @p101 :rule cong :premises (@p100) :args (@t30)) % 28.52/28.76 (step @p102 :rule bool-double-not-elim :args (@t20)) % 28.52/28.76 (step @p103 :rule cong :premises (@p102) :args (@t119)) % 28.52/28.76 (step @p104 :rule cong :premises (@p103) :args (@t120)) % 28.52/28.76 (step @p105 :rule exists-elim :args ((= @t32 @t120))) % 28.52/28.76 (step @p106 :rule trans :premises (@p105 @p104)) % 28.52/28.76 (step @p107 :rule nary_cong :premises (@p85 @p106 @p101) :args (@t33)) % 28.52/28.76 (step @p108 :rule cong :premises (@p107 @p99) :args (@t34)) % 28.52/28.76 (step @p109 :rule trans :premises (@p108 @p98)) % 28.52/28.76 (step @p110 :rule cong :premises (@p109) :args (@t35)) % 28.52/28.76 (step @p111 :rule eq_resolve :premises (@p9 @p110)) % 28.52/28.76 (step @p112 :rule aci_norm :args ((= (and @t126 @t122 true) @t127))) % 28.52/28.76 (step @p113 :rule quant-unused-vars :args ((= (forall @t26 true) true))) % 28.52/28.76 (step @p114 :rule eq-refl :args (@t128)) % 28.52/28.76 (step @p115 :rule cong :premises (@p114) :args (@t129)) % 28.52/28.76 (step @p116 :rule trans :premises (@p115 @p113)) % 28.52/28.76 (step @p117 :rule refl :args (@t122)) % 28.52/28.76 (step @p118 :rule refl :args (@t126)) % 28.52/28.76 (step @p119 :rule nary_cong :premises (@p118 @p117 @p116) :args (@t130)) % 28.52/28.76 (step @p120 :rule trans :premises (@p119 @p112)) % 28.52/28.76 (step @p121 :rule refl :args (@t131)) % 28.52/28.76 (step @p122 :rule cong :premises (@p121 @p120) :args (@t132)) % 28.52/28.76 (step @p123 :rule refl :args (@t133)) % 28.52/28.76 (step @p124 :rule cong :premises (@p123 @p122) :args ((=> @t133 @t132))) % 28.52/28.76 (assume-push @p211 @t133) % 28.52/28.76 (step @p126 :rule instantiate :premises (@p111) :args (@t134)) % 28.52/28.76 (step-pop @p212 :rule scope :premises (@p126)) % 28.52/28.76 (step @p127 :rule process_scope :premises (@p212) :args (@t132)) % 28.52/28.76 (step @p129 :rule eq_resolve :premises (@p127 @p124)) % 28.52/28.76 (step @p130 :rule implies_elim :premises (@p129)) % 28.52/28.76 (step @p131 :rule chain_m_resolution :premises (@p130 @p111) :args (@t135 @t136 (@list @t133))) % 28.52/28.76 (step @p132 :rule eq-symm :args ((not (forall @t12 (or (not @t48) @t54))) @t46)) % 28.52/28.76 (step @p133 :rule refl :args (@t46)) % 28.52/28.76 (step @p134 :rule bool-and-de-morgan :args (@t48 @t47 true)) % 28.52/28.76 (step @p135 :rule cong :premises (@p134) :args (@t137)) % 28.52/28.76 (step @p136 :rule cong :premises (@p135) :args (@t138)) % 28.52/28.76 (step @p137 :rule exists-elim :args ((= @t50 @t138))) % 28.52/28.76 (step @p138 :rule trans :premises (@p137 @p136)) % 28.52/28.76 (step @p139 :rule cong :premises (@p138 @p133) :args (@t51)) % 28.52/28.76 (step @p140 :rule trans :premises (@p139 @p132)) % 28.52/28.76 (step @p141 :rule cong :premises (@p140) :args (@t53)) % 28.52/28.76 (step @p142 :rule eq_resolve :premises (@p20 @p141)) % 28.52/28.76 (step @p143 :rule instantiate :premises (@p142) :args ((@list tptp.eth tptp.thm))) % 28.52/28.76 (step @p144 :rule bool-double-not-elim :args (@t139)) % 28.52/28.76 (step @p145 :rule refl :args (@t66)) % 28.52/28.76 (step @p146 :rule refl :args (@t142)) % 28.52/28.76 (step @p147 :rule nary_cong :premises (@p146 @p145 @p144) :args ((or @t142 @t66 (not @t140)))) % 28.52/28.76 (step @p148 :rule cnf_equiv_pos2 :args (@t141)) % 28.52/28.76 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 28.52/28.76 (step @p150 :rule reordering :premises (@p149) :args ((or @t66 @t139 @t142))) % 28.52/28.76 (step @p151 :rule chain_m_resolution :premises (@p150 @p33 @p143) :args (@t139 @t143 (@list @t66 @t141))) % 28.52/28.76 (step @p152 :rule instantiate :premises (@p151) :args (@t134)) % 28.52/28.76 (step @p153 :rule eq-symm :args (@t144 @t16)) % 28.52/28.76 (step @p154 :rule refl :args (@t16)) % 28.52/28.76 (step @p155 :rule bool-impl-elim :args (@t8 @t13)) % 28.52/28.76 (step @p156 :rule cong :premises (@p155) :args (@t17)) % 28.52/28.76 (step @p157 :rule cong :premises (@p156 @p154) :args (@t18)) % 28.52/28.76 (step @p158 :rule trans :premises (@p157 @p153)) % 28.52/28.76 (step @p159 :rule cong :premises (@p158) :args (@t19)) % 28.52/28.76 (step @p160 :rule eq_resolve :premises (@p5 @p159)) % 28.52/28.76 (step @p161 :rule bool-eq-true :args (@t145)) % 28.52/28.76 (step @p162 :rule quant-unused-vars :args ((= (forall @t9 true) true))) % 28.52/28.76 (step @p163 :rule bool-or-taut2 :args (false @t123 false false)) % 28.52/28.76 (step @p164 :rule cong :premises (@p163) :args (@t146)) % 28.52/28.76 (step @p165 :rule trans :premises (@p164 @p162)) % 28.52/28.76 (step @p166 :rule refl :args (@t145)) % 28.52/28.76 (step @p167 :rule cong :premises (@p166 @p165) :args (@t147)) % 28.52/28.76 (step @p168 :rule trans :premises (@p167 @p161)) % 28.52/28.76 (step @p169 :rule refl :args (@t148)) % 28.52/28.76 (step @p170 :rule cong :premises (@p169 @p168) :args ((=> @t148 @t147))) % 28.52/28.76 (assume-push @p213 @t148) % 28.52/28.76 (step @p172 :rule instantiate :premises (@p160) :args (@t134)) % 28.52/28.76 (step-pop @p214 :rule scope :premises (@p172)) % 28.52/28.76 (step @p173 :rule process_scope :premises (@p214) :args (@t147)) % 28.52/28.76 (step @p175 :rule eq_resolve :premises (@p173 @p170)) % 28.52/28.76 (step @p176 :rule implies_elim :premises (@p175)) % 28.52/28.76 (step @p177 :rule chain_m_resolution :premises (@p176 @p160) :args (@t145 @t136 (@list @t148))) % 28.52/28.76 (step @p178 :rule cnf_or_pos :args (@t151)) % 28.52/28.76 (step @p179 :rule reordering :premises (@p178) :args ((or @t149 @t150 (not @t151)))) % 28.52/28.76 (step @p180 :rule chain_m_resolution :premises (@p179 @p177 @p152) :args (@t150 @t152 (@list @t145 @t151))) % 28.52/28.76 (step @p181 :rule cnf_equiv_pos2 :args (@t135)) % 28.52/28.76 (step @p182 :rule reordering :premises (@p181) :args ((or @t131 @t153 (not @t135)))) % 28.52/28.76 (step @p183 :rule chain_m_resolution :premises (@p182 @p180 @p131) :args (@t153 @t143 (@list @t131 @t135))) % 28.52/28.76 (step @p184 :rule cnf_or_neg :args (@t115 3)) % 28.52/28.76 (step @p185 :rule chain_m_resolution :premises (@p184 @p90) :args ((not @t111) @t116 @t117)) % 28.52/28.76 (assume-push @p215 @t121) % 28.52/28.76 (step @p187 :rule instantiate :premises (@p215) :args ((@list @t110))) % 28.52/28.76 (step-pop @p216 :rule scope :premises (@p187)) % 28.52/28.76 (step @p188 :rule process_scope :premises (@p216) :args (@t111)) % 28.52/28.76 (step @p190 :rule implies_elim :premises (@p188)) % 28.52/28.76 (step @p191 :rule reordering :premises (@p190) :args ((or @t111 @t122))) % 28.52/28.76 (step @p192 :rule chain_m_resolution :premises (@p191 @p185) :args (@t122 @t116 (@list @t111))) % 28.52/28.76 (step @p193 :rule bool-double-not-elim :args (@t121)) % 28.52/28.76 (step @p194 :rule bool-double-not-elim :args (@t125)) % 28.52/28.76 (step @p195 :rule refl :args (@t127)) % 28.52/28.76 (step @p196 :rule nary_cong :premises (@p195 @p194 @p193) :args ((or @t127 (not @t126) (not @t122)))) % 28.52/28.76 (step @p197 :rule cnf_and_neg :args (@t127)) % 28.52/28.76 (step @p198 :rule eq_resolve :premises (@p197 @p196)) % 28.52/28.76 (step @p199 :rule reordering :premises (@p198) :args ((or @t125 @t121 @t127))) % 28.52/28.76 (step @p200 :rule chain_m_resolution :premises (@p199 @p192 @p183) :args (@t125 (@list true true) (@list @t121 @t127))) % 28.52/28.76 (step @p201 :rule alpha_equiv :args (@t154 (@list @t3) @t85)) % 28.52/28.76 (step @p202 :rule equiv_elim2 :premises (@p201)) % 28.52/28.76 (step @p203 :rule chain_m_resolution :premises (@p202 @p200) :args (@t154 @t136 (@list @t125))) % 28.52/28.76 (assume-push @p217 @t154) % 28.52/28.76 (step @p205 :rule instantiate :premises (@p217) :args ((@list @t107))) % 28.52/28.76 (step-pop @p218 :rule scope :premises (@p205)) % 28.52/28.76 (step @p206 :rule process_scope :premises (@p218) :args (@t114)) % 28.52/28.76 (step @p208 :rule implies_elim :premises (@p206)) % 28.52/28.76 (step @p209 :rule reordering :premises (@p208) :args ((or @t114 (not @t154)))) % 28.52/28.76 (step @p210 false :rule chain_m_resolution :premises (@p209 @p203 @p97) :args (false @t152 (@list @t154 @t108))) % 28.52/28.76 ) % 28.52/28.76 % SZS output end Proof % 28.52/28.76 % cvc5 exiting %------------------------------------------------------------------------------