%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO530^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n020.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 09:13:04 AM UTC 2026 % Result : Theorem 0.82s 1.11s % Output : Proof 0.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SYO530^1 : TPTP v9.2.1. Released v5.2.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.36 % Computer : n020.cluster.edu % 0.18/0.36 % Model : x86_64 x86_64 % 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.36 % Memory : 8042.1875MB % 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.36 % CPULimit : 300 % 0.18/0.36 % WCLimit : 300 % 0.18/0.36 % DateTime : Wed Jun 3 00:19:26 EDT 2026 % 0.18/0.36 % CPUTime : % 0.28/0.52 %----Proving TH0 % 0.82/1.11 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.82/1.11 % SZS status Theorem % 0.82/1.11 % SZS output start Proof % 0.82/1.11 ( % 0.82/1.11 (declare-sort $$unsorted 0) % 0.82/1.11 (declare-const tptp.eps (-> (-> $$unsorted Bool) $$unsorted)) % 0.82/1.11 (define tptp.epsa () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (_ tptp.eps (lambda (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.82/1.11 (define tptp.epsb () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (_ tptp.eps (lambda (@list _let_1) (_ (_ _let_2 (_ tptp.epsa _let_2)) _let_1))))))) % 0.82/1.11 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 0.82/1.11 (define @t2 () (_ tptp.eps @t1)) % 0.82/1.11 (define @t3 () (_ @t1 @t2)) % 0.82/1.11 (define @t4 () (@var "X" $$unsorted)) % 0.82/1.11 (define @t5 () (_ @t1 @t4)) % 0.82/1.11 (define @t6 () (@list @t4)) % 0.82/1.11 (define @t7 () (exists @t6 @t5)) % 0.82/1.11 (define @t8 () (=> @t7 @t3)) % 0.82/1.11 (define @t9 () (@list @t1)) % 0.82/1.11 (define @t10 () (forall @t9 @t8)) % 0.82/1.11 (define @t11 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.82/1.11 (define @t12 () (_ @t11 (_ tptp.epsa @t11))) % 0.82/1.11 (define @t13 () (@var "Y" $$unsorted)) % 0.82/1.11 (define @t14 () (_ @t11 @t4)) % 0.82/1.11 (define @t15 () (_ @t14 @t13)) % 0.82/1.11 (define @t16 () (@list @t4 @t13)) % 0.82/1.11 (define @t17 () (exists @t16 @t15)) % 0.82/1.11 (define @t18 () (=> @t17 (_ @t12 (_ tptp.epsb @t11)))) % 0.82/1.11 (define @t19 () (@list @t11)) % 0.82/1.11 (define @t20 () (forall @t19 @t18)) % 0.82/1.11 (define @t21 () (not @t20)) % 0.82/1.11 (define @t22 () (@list @t13)) % 0.82/1.11 (define @t23 () (exists @t22 @t15)) % 0.82/1.11 (define @t24 () (lambda @t6 @t23)) % 0.82/1.11 (define @t25 () (lambda @t19 (_ tptp.eps @t24))) % 0.82/1.11 (define @t26 () (lambda @t22 (_ @t12 @t13))) % 0.82/1.11 (define @t27 () (lambda @t19 (_ tptp.eps @t26))) % 0.82/1.11 (define @t28 () (tptp.eps @t1)) % 0.82/1.11 (define @t29 () (_ @t1 @t28)) % 0.82/1.11 (define @t30 () (@var "BOUND_VARIABLE_7510" $$unsorted)) % 0.82/1.11 (define @t31 () (not (_ @t1 @t30))) % 0.82/1.11 (define @t32 () (or @t31 @t29)) % 0.82/1.11 (define @t33 () (forall (@list @t1 @t30) @t32)) % 0.82/1.11 (define @t34 () (@list @t30)) % 0.82/1.11 (define @t35 () (forall @t34 @t32)) % 0.82/1.11 (define @t36 () (forall @t34 @t31)) % 0.82/1.11 (define @t37 () (or @t36 @t29)) % 0.82/1.11 (define @t38 () (_ @t1 @t4)) % 0.82/1.11 (define @t39 () (forall @t6 (not @t38))) % 0.82/1.11 (define @t40 () (or @t39 @t3)) % 0.82/1.11 (define @t41 () (not @t39)) % 0.82/1.11 (define @t42 () (not @t5)) % 0.82/1.11 (define @t43 () (forall @t6 @t42)) % 0.82/1.11 (define @t44 () (not @t43)) % 0.82/1.11 (define @t45 () (@var "BOUND_VARIABLE_7465" $$unsorted)) % 0.82/1.11 (define @t46 () (_ @t11 @t4 @t45)) % 0.82/1.11 (define @t47 () (not @t46)) % 0.82/1.11 (define @t48 () (@list @t45)) % 0.82/1.11 (define @t49 () (forall @t48 @t47)) % 0.82/1.11 (define @t50 () (not @t49)) % 0.82/1.11 (define @t51 () (lambda @t6 @t50)) % 0.82/1.11 (define @t52 () (tptp.eps @t51)) % 0.82/1.11 (define @t53 () (_ @t11 @t52 @t13)) % 0.82/1.11 (define @t54 () (lambda @t22 @t53)) % 0.82/1.11 (define @t55 () (tptp.eps @t54)) % 0.82/1.11 (define @t56 () (_ @t11 @t4 @t13)) % 0.82/1.11 (define @t57 () (not @t56)) % 0.82/1.11 (define @t58 () (forall @t22 @t57)) % 0.82/1.11 (define @t59 () (not @t58)) % 0.82/1.11 (define @t60 () (lambda @t6 @t59)) % 0.82/1.11 (define @t61 () (tptp.eps @t60)) % 0.82/1.11 (define @t62 () (_ @t11 @t61 @t55)) % 0.82/1.11 (define @t63 () (@var "BOUND_VARIABLE_7553" $$unsorted)) % 0.82/1.11 (define @t64 () (@var "BOUND_VARIABLE_7551" $$unsorted)) % 0.82/1.11 (define @t65 () (not (_ @t11 @t64 @t63))) % 0.82/1.11 (define @t66 () (or @t65 @t62)) % 0.82/1.11 (define @t67 () (forall (@list @t11 @t64 @t63) @t66)) % 0.82/1.11 (define @t68 () (@quantifiers_skolemize @t67 0)) % 0.82/1.11 (define @t69 () (not (forall @t48 (not (_ @t68 @t4 @t45))))) % 0.82/1.11 (define @t70 () (lambda @t6 @t69)) % 0.82/1.11 (define @t71 () (@purify @t70)) % 0.82/1.11 (define @t72 () (_ @t71 @t4)) % 0.82/1.11 (define @t73 () (_ @t70 @t4)) % 0.82/1.11 (define @t74 () (= @t72 @t73)) % 0.82/1.11 (define @t75 () (forall @t6 @t74)) % 0.82/1.11 (define @t76 () (tptp.eps @t71)) % 0.82/1.11 (define @t77 () (forall @t48 (not (_ @t68 @t76 @t45)))) % 0.82/1.11 (define @t78 () (not @t77)) % 0.82/1.11 (define @t79 () (_ @t71 @t76)) % 0.82/1.11 (define @t80 () (forall @t6 (= @t69 @t72))) % 0.82/1.11 (define @t81 () (= @t78 @t79)) % 0.82/1.11 (define @t82 () (= @t79 @t78)) % 0.82/1.11 (define @t83 () (@list false)) % 0.82/1.11 (define @t84 () (@list @t80)) % 0.82/1.11 (define @t85 () (@quantifiers_skolemize @t67 1)) % 0.82/1.11 (define @t86 () (@list @t64 @t63)) % 0.82/1.11 (define @t87 () (forall @t86 @t66)) % 0.82/1.11 (define @t88 () (forall @t86 @t65)) % 0.82/1.11 (define @t89 () (or @t88 @t62)) % 0.82/1.11 (define @t90 () (forall @t16 @t57)) % 0.82/1.11 (define @t91 () (lambda @t6 (not (forall @t48 (not (_ @t14 @t45)))))) % 0.82/1.11 (define @t92 () (_ tptp.eps @t91)) % 0.82/1.11 (define @t93 () (_ (_ @t11 @t92) @t13)) % 0.82/1.11 (define @t94 () (lambda @t22 @t93)) % 0.82/1.11 (define @t95 () (_ tptp.eps @t94)) % 0.82/1.11 (define @t96 () (not @t15)) % 0.82/1.11 (define @t97 () (forall @t22 @t96)) % 0.82/1.11 (define @t98 () (not @t97)) % 0.82/1.11 (define @t99 () (lambda @t6 @t98)) % 0.82/1.11 (define @t100 () (_ tptp.eps @t99)) % 0.82/1.11 (define @t101 () (_ tptp.eps @t51)) % 0.82/1.11 (define @t102 () (lambda @t22 (_ (_ @t11 @t101) @t13))) % 0.82/1.11 (define @t103 () (_ tptp.eps @t60)) % 0.82/1.11 (define @t104 () (_ tptp.eps @t102)) % 0.82/1.11 (define @t105 () (_ @t11 @t103)) % 0.82/1.11 (define @t106 () (_ @t105 @t104)) % 0.82/1.11 (define @t107 () (or @t90 @t106)) % 0.82/1.11 (define @t108 () (not @t90)) % 0.82/1.11 (define @t109 () (_ (lambda @t19 @t104) @t11)) % 0.82/1.11 (define @t110 () (_ (lambda @t19 @t103) @t11)) % 0.82/1.11 (define @t111 () (forall @t16 @t96)) % 0.82/1.11 (define @t112 () (not @t111)) % 0.82/1.11 (define @t113 () (_ @t11 @t110)) % 0.82/1.11 (define @t114 () (=> @t17 (_ @t113 @t109))) % 0.82/1.11 (define @t115 () (forall @t19 @t114)) % 0.82/1.11 (define @t116 () (_ @t68 @t76)) % 0.82/1.11 (define @t117 () (tptp.eps @t116)) % 0.82/1.11 (define @t118 () (not (forall @t22 (not (_ @t68 @t4 @t13))))) % 0.82/1.11 (define @t119 () (lambda @t6 @t118)) % 0.82/1.11 (define @t120 () (@purify @t119)) % 0.82/1.11 (define @t121 () (_ @t68 (tptp.eps @t120) @t117)) % 0.82/1.11 (define @t122 () (@quantifiers_skolemize @t67 2)) % 0.82/1.11 (define @t123 () (_ @t68 @t85 @t122)) % 0.82/1.11 (define @t124 () (not @t123)) % 0.82/1.11 (define @t125 () (or @t124 @t121)) % 0.82/1.11 (define @t126 () (not @t125)) % 0.82/1.11 (define @t127 () (not @t67)) % 0.82/1.11 (define @t128 () (tptp.eps @t70)) % 0.82/1.11 (define @t129 () (lambda @t22 (_ @t68 @t128 @t13))) % 0.82/1.11 (define @t130 () (tptp.eps @t129)) % 0.82/1.11 (define @t131 () (tptp.eps @t119)) % 0.82/1.11 (define @t132 () (_ @t68 @t131 @t130)) % 0.82/1.11 (define @t133 () (or @t124 @t132)) % 0.82/1.11 (define @t134 () (not @t133)) % 0.82/1.11 (define @t135 () (@list true)) % 0.82/1.11 (define @t136 () (@list @t125)) % 0.82/1.11 (define @t137 () (forall @t48 (not (_ @t68 @t85 @t45)))) % 0.82/1.11 (define @t138 () (not @t137)) % 0.82/1.11 (define @t139 () (_ @t71 @t85)) % 0.82/1.11 (define @t140 () (= @t138 @t139)) % 0.82/1.11 (define @t141 () (not @t140)) % 0.82/1.11 (define @t142 () (@list true false)) % 0.82/1.11 (define @t143 () (not @t139)) % 0.82/1.11 (define @t144 () (or @t143 @t79)) % 0.82/1.11 (define @t145 () (@list false false)) % 0.82/1.11 (define @t146 () (@quantifiers_skolemize @t77 0)) % 0.82/1.11 (define @t147 () (_ @t68 @t76 @t146)) % 0.82/1.11 (define @t148 () (not @t147)) % 0.82/1.11 (define @t149 () (not @t148)) % 0.82/1.11 (define @t150 () (@const 0 $$unsorted)) % 0.82/1.11 (define @t151 () (_ @t120 @t150)) % 0.82/1.11 (define @t152 () (_ @t71 @t150)) % 0.82/1.11 (define @t153 () (= @t152 @t151)) % 0.82/1.11 (define @t154 () (forall @t48 (not (_ @t68 @t150 @t45)))) % 0.82/1.11 (define @t155 () (not @t154)) % 0.82/1.11 (define @t156 () (= @t155 @t152)) % 0.82/1.11 (define @t157 () (@list @t150)) % 0.82/1.11 (define @t158 () (= @t152 @t155)) % 0.82/1.11 (define @t159 () (not @t158)) % 0.82/1.11 (define @t160 () (not @t152)) % 0.82/1.11 (define @t161 () (_ @t120 @t4)) % 0.82/1.11 (define @t162 () (_ @t119 @t4)) % 0.82/1.11 (define @t163 () (= @t161 @t162)) % 0.82/1.11 (define @t164 () (forall @t6 @t163)) % 0.82/1.11 (define @t165 () (forall @t22 (not (_ @t68 @t150 @t13)))) % 0.82/1.11 (define @t166 () (not @t165)) % 0.82/1.11 (define @t167 () (forall @t6 (= @t118 @t161))) % 0.82/1.11 (define @t168 () (= @t166 @t151)) % 0.82/1.11 (define @t169 () (= @t151 @t166)) % 0.82/1.11 (define @t170 () (not @t169)) % 0.82/1.11 (define @t171 () (= @t71 @t120)) % 0.82/1.11 (define @t172 () (_ @t68 @t76 @t117)) % 0.82/1.11 (define @t173 () (or @t148 @t172)) % 0.82/1.11 (define @t174 () (not @t173)) % 0.82/1.11 (define @t175 () (_ tptp.eps @t71)) % 0.82/1.11 (define @t176 () (_ @t68 @t175)) % 0.82/1.11 (define @t177 () (_ tptp.eps @t176)) % 0.82/1.11 (define @t178 () (_ @t116 @t117)) % 0.82/1.11 (define @t179 () (_ @t116 @t146)) % 0.82/1.11 (define @t180 () (not @t179)) % 0.82/1.11 (define @t181 () (or @t180 @t178)) % 0.82/1.11 (define @t182 () (_ @t116 @t117)) % 0.82/1.11 (define @t183 () (_ @t116 @t146)) % 0.82/1.11 (define @t184 () (not @t183)) % 0.82/1.11 (define @t185 () (or @t184 @t182)) % 0.82/1.11 (assume @p1 @t10) % 0.82/1.11 (assume @p2 @t21) % 0.82/1.11 (assume @p3 true) % 0.82/1.11 (step @p4 (= tptp.epsa @t25) :rule refl :args (@t25)) % 0.82/1.11 (step @p5 (= tptp.epsb @t27) :rule refl :args (@t27)) % 0.82/1.11 (step @p6 :rule quant-merge-prenex :args ((= (forall @t9 @t35) @t33))) % 0.82/1.11 (step @p7 :rule refl :args (@t29)) % 0.82/1.11 (step @p8 :rule alpha_equiv :args (@t36 (@list @t30) (@list @t4))) % 0.82/1.11 (step @p9 :rule nary_cong :premises (@p8 @p7) :args (@t37)) % 0.82/1.11 (step @p10 :rule quant-miniscope-or :args ((= @t35 @t37))) % 0.82/1.11 (step @p11 :rule trans :premises (@p10 @p9)) % 0.82/1.11 (step @p12 :rule symm :premises (@p11)) % 0.82/1.11 (step @p13 :rule cong :premises (@p12) :args ((forall @t9 (or @t39 @t29)))) % 0.82/1.11 (step @p14 :rule trans :premises (@p13 @p6)) % 0.82/1.11 (step @p15 :rule refl :args ((_ @t1 @t2))) % 0.82/1.11 (step @p16 :rule refl :args (@t28)) % 0.82/1.11 (step @p17 :rule cong :premises (@p16) :args (@t29)) % 0.82/1.11 (step @p18 :rule trans :premises (@p17 @p15)) % 0.82/1.11 (step @p19 :rule refl :args (@t1)) % 0.82/1.11 (step @p20 :rule ho_cong :premises (@p19 @p16)) % 0.82/1.11 (step @p21 :rule cong :premises (@p20 @p18) :args ((= (_ @t1 @t28) @t29))) % 0.82/1.11 (step @p22 :rule symm :premises (@p21)) % 0.82/1.11 (step @p23 :rule refl :args (@t3)) % 0.82/1.11 (step @p24 :rule eq_resolve :premises (@p23 @p22)) % 0.82/1.11 (step @p25 :rule refl :args (@t2)) % 0.82/1.11 (step @p26 :rule cong :premises (@p25 @p16) :args ((= @t2 @t28))) % 0.82/1.11 (step @p27 :rule symm :premises (@p26)) % 0.82/1.11 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.82/1.11 (step @p29 :rule ho_cong :premises (@p19 @p28)) % 0.82/1.11 (step @p30 :rule trans :premises (@p29 @p24)) % 0.82/1.11 (step @p31 :rule refl :args (@t39)) % 0.82/1.11 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t40)) % 0.82/1.11 (step @p33 :rule cong :premises (@p32) :args ((forall @t9 @t40))) % 0.82/1.11 (step @p34 :rule trans :premises (@p33 @p14)) % 0.82/1.11 (step @p35 :rule bool-double-not-elim :args (@t39)) % 0.82/1.11 (step @p36 :rule nary_cong :premises (@p35 @p23) :args ((or (not @t41) @t3))) % 0.82/1.11 (step @p37 :rule bool-impl-elim :args (@t41 @t3)) % 0.82/1.11 (step @p38 :rule trans :premises (@p37 @p36)) % 0.82/1.11 (step @p39 :rule cong :premises (@p38) :args ((forall @t9 (=> @t41 @t3)))) % 0.82/1.11 (step @p40 :rule trans :premises (@p39 @p34)) % 0.82/1.11 (step @p41 :rule refl :args (@t3)) % 0.82/1.11 (step @p42 :rule refl :args (@t38)) % 0.82/1.11 (step @p43 :rule refl :args (@t5)) % 0.82/1.11 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t5 @t38))) % 0.82/1.11 (step @p45 :rule symm :premises (@p44)) % 0.82/1.11 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.82/1.11 (step @p47 :rule cong :premises (@p46) :args (@t42)) % 0.82/1.11 (step @p48 :rule cong :premises (@p47) :args (@t43)) % 0.82/1.11 (step @p49 :rule cong :premises (@p48) :args (@t44)) % 0.82/1.11 (step @p50 :rule exists-elim :args ((= @t7 @t44))) % 0.82/1.11 (step @p51 :rule trans :premises (@p50 @p49)) % 0.82/1.11 (step @p52 :rule cong :premises (@p51 @p41) :args (@t8)) % 0.82/1.11 (step @p53 :rule cong :premises (@p52) :args (@t10)) % 0.82/1.11 (step @p54 :rule trans :premises (@p53 @p40)) % 0.82/1.11 (step @p55 :rule eq_resolve :premises (@p1 @p54)) % 0.82/1.11 (step @p56 :rule eq-symm :args (@t72 @t69)) % 0.82/1.11 (step @p57 :rule beta-reduce :args ((= @t73 @t69))) % 0.82/1.11 (step @p58 :rule refl :args (@t72)) % 0.82/1.11 (step @p59 :rule cong :premises (@p58 @p57) :args (@t74)) % 0.82/1.11 (step @p60 :rule trans :premises (@p59 @p56)) % 0.82/1.11 (step @p61 :rule cong :premises (@p60) :args (@t75)) % 0.82/1.11 (step @p62 :rule quant-unused-vars :args ((= (forall @t6 true) true))) % 0.82/1.11 (step @p63 :rule eq-refl :args (@t73)) % 0.82/1.11 (step @p64 :rule cong :premises (@p63) :args ((forall @t6 (= @t73 @t73)))) % 0.82/1.11 (step @p65 :rule trans :premises (@p64 @p62)) % 0.82/1.11 (step @p66 :rule refl :args (@t73)) % 0.82/1.11 (step @p67 :rule refl :args (@t4)) % 0.82/1.11 (step @p68 :rule skolem_intro :args (@t71)) % 0.82/1.11 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 0.82/1.11 (step @p70 :rule cong :premises (@p69 @p66) :args (@t74)) % 0.82/1.11 (step @p71 :rule cong :premises (@p70) :args (@t75)) % 0.82/1.11 (step @p72 :rule trans :premises (@p71 @p65)) % 0.82/1.11 (step @p73 :rule true_elim :premises (@p72)) % 0.82/1.11 (step @p74 :rule eq_resolve :premises (@p73 @p61)) % 0.82/1.11 (step @p75 :rule eq-symm :args (@t78 @t79)) % 0.82/1.11 (step @p76 :rule refl :args (@t80)) % 0.82/1.11 (step @p77 :rule cong :premises (@p76 @p75) :args ((=> @t80 @t81))) % 0.82/1.11 (assume-push @p422 @t80) % 0.82/1.11 (step @p79 :rule instantiate :premises (@p74) :args ((@list @t76))) % 0.82/1.11 (step-pop @p423 :rule scope :premises (@p79)) % 0.82/1.11 (step @p80 :rule process_scope :premises (@p423) :args (@t81)) % 0.82/1.11 (step @p82 :rule eq_resolve :premises (@p80 @p77)) % 0.82/1.11 (step @p83 :rule implies_elim :premises (@p82)) % 0.82/1.11 (step @p84 :rule chain_m_resolution :premises (@p83 @p74) :args (@t82 @t83 @t84)) % 0.82/1.11 (step @p85 :rule instantiate :premises (@p55) :args ((@list @t71 @t85))) % 0.82/1.11 (step @p86 :rule instantiate :premises (@p74) :args ((@list @t85))) % 0.82/1.11 (step @p87 :rule quant-merge-prenex :args ((= (forall @t19 @t87) @t67))) % 0.82/1.11 (step @p88 :rule refl :args (@t62)) % 0.82/1.11 (step @p89 :rule alpha_equiv :args (@t88 (@list @t64 @t63) (@list @t4 @t13))) % 0.82/1.11 (step @p90 :rule 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(step @p328 :rule true_elim :premises (@p327)) % 0.82/1.11 (step @p329 :rule eq_resolve :premises (@p328 @p319)) % 0.82/1.11 (step @p330 :rule eq-symm :args (@t166 @t151)) % 0.82/1.11 (step @p331 :rule refl :args (@t167)) % 0.82/1.11 (step @p332 :rule cong :premises (@p331 @p330) :args ((=> @t167 @t168))) % 0.82/1.11 (assume-push @p432 @t167) % 0.82/1.11 (step @p334 :rule instantiate :premises (@p329) :args (@t157)) % 0.82/1.11 (step-pop @p433 :rule scope :premises (@p334)) % 0.82/1.11 (step @p335 :rule process_scope :premises (@p433) :args (@t168)) % 0.82/1.11 (step @p337 :rule eq_resolve :premises (@p335 @p332)) % 0.82/1.11 (step @p338 :rule implies_elim :premises (@p337)) % 0.82/1.11 (step @p339 :rule chain_m_resolution :premises (@p338 @p329) :args (@t169 @t83 (@list @t167))) % 0.82/1.11 (step @p340 :rule bool-double-not-elim :args (@t165)) % 0.82/1.11 (step @p341 :rule refl :args (@t151)) % 0.82/1.11 (step @p342 :rule refl :args (@t170)) % 0.82/1.11 (step @p343 :rule nary_cong :premises (@p342 @p341 @p340) :args ((or @t170 @t151 (not @t166)))) % 0.82/1.11 (step @p344 :rule cnf_equiv_pos2 :args (@t169)) % 0.82/1.11 (step @p345 :rule eq_resolve :premises (@p344 @p343)) % 0.82/1.11 (step @p346 :rule reordering :premises (@p345) :args ((or @t151 @t165 @t170))) % 0.82/1.11 (step @p347 :rule alpha_equiv :args (@t154 (@list @t45) (@list @t13))) % 0.82/1.11 (step @p348 :rule equiv_elim2 :premises (@p347)) % 0.82/1.11 (step @p349 :rule chain_m_resolution :premises (@p348 @p346 @p339 @p313 @p311 @p302) :args ((or @t153 @t160) (@list false false true false true) (@list @t165 @t169 @t154 @t158 @t151))) % 0.82/1.11 (step @p350 :rule cnf_equiv_neg1 :args (@t153)) % 0.82/1.11 (step @p351 :rule reordering :premises (@p350) :args ((or @t152 @t151 @t153))) % 0.82/1.11 (step @p352 :rule bool-double-not-elim :args (@t154)) % 0.82/1.11 (step @p353 :rule refl :args (@t152)) % 0.82/1.11 (step @p354 :rule refl :args (@t159)) % 0.82/1.11 (step @p355 :rule nary_cong :premises (@p354 @p353 @p352) :args ((or @t159 @t152 (not @t155)))) % 0.82/1.11 (step @p356 :rule cnf_equiv_pos2 :args (@t158)) % 0.82/1.11 (step @p357 :rule eq_resolve :premises (@p356 @p355)) % 0.82/1.11 (step @p358 :rule reordering :premises (@p357) :args ((or @t152 @t154 @t159))) % 0.82/1.11 (step @p359 :rule cnf_equiv_pos1 :args (@t169)) % 0.82/1.11 (step @p360 :rule reordering :premises (@p359) :args ((or (not @t151) @t166 @t170))) % 0.82/1.11 (step @p361 :rule equiv_elim1 :premises (@p347)) % 0.82/1.11 (step @p362 :rule chain_m_resolution :premises (@p361 @p360 @p339 @p358 @p311 @p351 @p349) :args (@t153 (@list true false false false false true) (@list @t165 @t169 @t154 @t158 @t151 @t152))) % 0.82/1.11 ; WARNING: add trust step for TRUST % 0.82/1.11 ; trust TRUST THEORY_LEMMA % 0.82/1.11 (step @p363 :rule trust :premises () :args ((or @t171 (not @t153)))) % 0.82/1.11 (step @p364 :rule chain_m_resolution :premises (@p363 @p362) :args (@t171 @t83 (@list @t153))) % 0.82/1.11 (step @p365 :rule cong :premises (@p364) :args (@t76)) % 0.82/1.11 (step @p366 :rule cong :premises (@p365 @p301) :args (@t172)) % 0.82/1.11 (step @p367 :rule trans :premises (@p366 @p300)) % 0.82/1.11 (step @p368 :rule false_elim :premises (@p367)) % 0.82/1.11 (step @p369 :rule cnf_or_pos :args (@t173)) % 0.82/1.11 (step @p370 :rule reordering :premises (@p369) :args ((or @t172 @t148 @t174))) % 0.82/1.11 (step @p371 :rule chain_m_resolution :premises (@p370 @p368 @p297) :args (@t174 @t142 (@list @t172 @t147))) % 0.82/1.11 (step @p372 :rule refl :args ((_ @t68 @t175 @t177))) % 0.82/1.11 (step @p373 :rule refl :args ((tptp.eps @t176))) % 0.82/1.11 (step @p374 :rule refl :args (@t76)) % 0.82/1.11 (step @p375 :rule refl :args (@t68)) % 0.82/1.11 (step @p376 :rule ho_cong :premises (@p375 @p374)) % 0.82/1.11 (step @p377 :rule cong :premises (@p376) :args (@t117)) % 0.82/1.11 (step @p378 :rule trans :premises (@p377 @p373)) % 0.82/1.11 (step @p379 :rule cong :premises (@p374 @p378) :args (@t172)) % 0.82/1.11 (step @p380 :rule trans :premises (@p379 @p372)) % 0.82/1.11 (step @p381 :rule ho_cong :premises (@p376 @p378)) % 0.82/1.11 (step @p382 :rule cong :premises (@p381 @p380) :args ((= @t178 @t172))) % 0.82/1.11 (step @p383 :rule symm :premises (@p382)) % 0.82/1.11 (step @p384 :rule refl :args ((_ @t176 @t177))) % 0.82/1.11 (step @p385 :rule eq_resolve :premises (@p384 @p383)) % 0.82/1.11 (step @p386 :rule refl :args ((_ @t68 @t175 @t146))) % 0.82/1.11 (step @p387 :rule refl :args (@t146)) % 0.82/1.11 (step @p388 :rule cong :premises (@p374 @p387) :args (@t147)) % 0.82/1.11 (step @p389 :rule trans :premises (@p388 @p386)) % 0.82/1.11 (step @p390 :rule ho_cong :premises (@p376 @p387)) % 0.82/1.11 (step @p391 :rule cong :premises (@p390 @p389) :args ((= @t179 @t147))) % 0.82/1.11 (step @p392 :rule symm :premises (@p391)) % 0.82/1.11 (step @p393 :rule refl :args ((_ @t176 @t146))) % 0.82/1.11 (step @p394 :rule eq_resolve :premises (@p393 @p392)) % 0.82/1.11 (step @p395 :rule cong :premises (@p394) :args (@t180)) % 0.82/1.11 (step @p396 :rule nary_cong :premises (@p395 @p385) :args (@t181)) % 0.82/1.11 (step @p397 :rule refl :args (@t33)) % 0.82/1.11 (step @p398 :rule cong :premises (@p397 @p396) :args ((=> @t33 @t181))) % 0.82/1.11 (step @p399 :rule refl :args ((_ @t176 @t177))) % 0.82/1.11 (step @p400 :rule ho_cong :premises (@p376 @p378)) % 0.82/1.11 (step @p401 :rule trans :premises (@p400 @p399)) % 0.82/1.11 (step @p402 :rule cong :premises (@p401 @p381) :args ((= @t182 @t178))) % 0.82/1.11 (step @p403 :rule symm :premises (@p402)) % 0.82/1.11 (step @p404 :rule eq_resolve :premises (@p384 @p403)) % 0.82/1.11 (step @p405 :rule refl :args ((_ @t176 @t146))) % 0.82/1.11 (step @p406 :rule ho_cong :premises (@p376 @p387)) % 0.82/1.11 (step @p407 :rule trans :premises (@p406 @p405)) % 0.82/1.11 (step @p408 :rule cong :premises (@p407 @p390) :args ((= @t183 @t179))) % 0.82/1.11 (step @p409 :rule symm :premises (@p408)) % 0.82/1.11 (step @p410 :rule eq_resolve :premises (@p393 @p409)) % 0.82/1.11 (step @p411 :rule cong :premises (@p410) :args (@t184)) % 0.82/1.11 (step @p412 :rule nary_cong :premises (@p411 @p404) :args (@t185)) % 0.82/1.11 (step @p413 :rule cong :premises (@p397 @p412) :args ((=> @t33 @t185))) % 0.82/1.11 (assume-push @p434 @t33) % 0.82/1.11 (step @p415 :rule instantiate :premises (@p55) :args ((@list @t116 @t146))) % 0.82/1.11 (step-pop @p435 :rule scope :premises (@p415)) % 0.82/1.11 (step @p416 :rule process_scope :premises (@p435) :args (@t185)) % 0.82/1.11 (step @p418 :rule eq_resolve :premises (@p416 @p413)) % 0.82/1.11 (step @p419 :rule eq_resolve :premises (@p418 @p398)) % 0.82/1.11 (step @p420 :rule implies_elim :premises (@p419)) % 0.82/1.11 (step @p421 false :rule chain_m_resolution :premises (@p420 @p371 @p55) :args (false @t142 (@list @t173 @t33))) % 0.82/1.11 ) % 0.82/1.11 % SZS output end Proof % 0.82/1.11 % cvc5 exiting %------------------------------------------------------------------------------