%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM505+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 : n010.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 08:39:38 AM UTC 2026 % Result : Theorem 16.84s 17.06s % Output : Proof 16.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : NUM505+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n010.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 11:25:10 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.52 %----Proving TF0_NAR, FOF, or CNF % 16.84/17.06 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 16.84/17.06 --- Run --no-e-matching --full-saturate-quant at 6... % 16.84/17.06 % SZS status Theorem % 16.84/17.06 % SZS output start Proof % 16.84/17.06 ( % 16.84/17.06 (declare-sort $$unsorted 0) % 16.84/17.06 (declare-const tptp.xr $$unsorted) % 16.84/17.06 (declare-const tptp.xk $$unsorted) % 16.84/17.06 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 16.84/17.06 (declare-const tptp.xm $$unsorted) % 16.84/17.06 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.84/17.06 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 16.84/17.06 (declare-const tptp.xn $$unsorted) % 16.84/17.06 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 16.84/17.06 (declare-const tptp.sz00 $$unsorted) % 16.84/17.06 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.84/17.06 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.84/17.06 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.84/17.06 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 16.84/17.06 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 16.84/17.06 (declare-const tptp.sz10 $$unsorted) % 16.84/17.06 (declare-const tptp.xp $$unsorted) % 16.84/17.06 (define @t1 () (@var "W0" $$unsorted)) % 16.84/17.06 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 16.84/17.06 (define @t3 () (@list @t1)) % 16.84/17.06 (define @t4 () (@var "W1" $$unsorted)) % 16.84/17.06 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 16.84/17.06 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 16.84/17.06 (define @t7 () (and @t2 @t6)) % 16.84/17.06 (define @t8 () (@list @t1 @t4)) % 16.84/17.06 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 16.84/17.06 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 16.84/17.06 (define @t11 () (forall @t8 (=> @t7 @t10))) % 16.84/17.06 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 16.84/17.06 (define @t13 () (@var "W2" $$unsorted)) % 16.84/17.06 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 16.84/17.06 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 16.84/17.06 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 16.84/17.06 (define @t17 () (and @t2 @t6 @t16)) % 16.84/17.06 (define @t18 () (@list @t1 @t4 @t13)) % 16.84/17.06 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 16.84/17.06 (define @t20 () (tptp.sdtasdt0 @t13 @t1)) % 16.84/17.06 (define @t21 () (tptp.sdtasdt0 @t1 @t13)) % 16.84/17.06 (define @t22 () (= @t4 @t13)) % 16.84/17.06 (define @t23 () (tptp.sdtpldt0 @t13 @t1)) % 16.84/17.06 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 16.84/17.06 (define @t25 () (= @t19 @t20)) % 16.84/17.06 (define @t26 () (= @t9 @t21)) % 16.84/17.06 (define @t27 () (= @t1 tptp.sz00)) % 16.84/17.06 (define @t28 () (not @t27)) % 16.84/17.06 (define @t29 () (= @t4 tptp.sz00)) % 16.84/17.06 (define @t30 () (and @t16 (= @t24 @t4))) % 16.84/17.06 (define @t31 () (@list @t13)) % 16.84/17.06 (define @t32 () (tptp.sdtlseqdt0 @t1 @t4)) % 16.84/17.06 (define @t33 () (tptp.sdtlseqdt0 @t1 @t1)) % 16.84/17.06 (define @t34 () (forall @t3 (=> @t2 @t33))) % 16.84/17.06 (define @t35 () (= @t1 @t4)) % 16.84/17.06 (define @t36 () (tptp.sdtlseqdt0 @t4 @t1)) % 16.84/17.06 (define @t37 () (tptp.sdtlseqdt0 @t4 @t13)) % 16.84/17.06 (define @t38 () (= @t4 @t1)) % 16.84/17.06 (define @t39 () (not @t38)) % 16.84/17.06 (define @t40 () (and @t39 @t36)) % 16.84/17.06 (define @t41 () (or @t32 @t40)) % 16.84/17.06 (define @t42 () (=> @t7 @t41)) % 16.84/17.06 (define @t43 () (forall @t8 @t42)) % 16.84/17.06 (define @t44 () (tptp.sdtpldt0 @t13 @t4)) % 16.84/17.06 (define @t45 () (not @t35)) % 16.84/17.06 (define @t46 () (and @t45 @t32)) % 16.84/17.06 (define @t47 () (= @t1 tptp.sz10)) % 16.84/17.06 (define @t48 () (tptp.iLess0 @t1 @t4)) % 16.84/17.06 (define @t49 () (and @t16 (= @t4 @t21))) % 16.84/17.06 (define @t50 () (tptp.doDivides0 @t1 @t4)) % 16.84/17.06 (define @t51 () (tptp.sdtsldt0 @t4 @t1)) % 16.84/17.06 (define @t52 () (= @t13 @t51)) % 16.84/17.06 (define @t53 () (forall @t31 (= @t52 @t49))) % 16.84/17.06 (define @t54 () (and @t28 @t50)) % 16.84/17.06 (define @t55 () (=> @t54 @t53)) % 16.84/17.06 (define @t56 () (=> @t7 @t55)) % 16.84/17.06 (define @t57 () (forall @t8 @t56)) % 16.84/17.06 (define @t58 () (tptp.doDivides0 @t1 @t13)) % 16.84/17.06 (define @t59 () (tptp.doDivides0 @t1 @t14)) % 16.84/17.06 (define @t60 () (or (= @t4 tptp.sz10) @t38)) % 16.84/17.06 (define @t61 () (tptp.doDivides0 @t4 @t1)) % 16.84/17.06 (define @t62 () (and @t6 @t61)) % 16.84/17.06 (define @t63 () (=> @t62 @t60)) % 16.84/17.06 (define @t64 () (@list @t4)) % 16.84/17.06 (define @t65 () (forall @t64 @t63)) % 16.84/17.06 (define @t66 () (not @t47)) % 16.84/17.06 (define @t67 () (and @t28 @t66 @t65)) % 16.84/17.06 (define @t68 () (tptp.isPrime0 @t1)) % 16.84/17.06 (define @t69 () (= @t68 @t67)) % 16.84/17.06 (define @t70 () (=> @t2 @t69)) % 16.84/17.06 (define @t71 () (forall @t3 @t70)) % 16.84/17.06 (define @t72 () (tptp.aNaturalNumber0 tptp.xp)) % 16.84/17.06 (define @t73 () (tptp.aNaturalNumber0 tptp.xm)) % 16.84/17.06 (define @t74 () (tptp.aNaturalNumber0 tptp.xn)) % 16.84/17.06 (define @t75 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 16.84/17.06 (define @t76 () (tptp.doDivides0 tptp.xp @t75)) % 16.84/17.06 (define @t77 () (tptp.isPrime0 tptp.xp)) % 16.84/17.06 (define @t78 () (tptp.sdtsldt0 @t75 tptp.xp)) % 16.84/17.06 (define @t79 () (= tptp.xk tptp.sz10)) % 16.84/17.06 (define @t80 () (= tptp.xk tptp.sz00)) % 16.84/17.06 (define @t81 () (tptp.sdtlseqdt0 tptp.xk tptp.xp)) % 16.84/17.06 (define @t82 () (not (= tptp.xk tptp.xp))) % 16.84/17.06 (define @t83 () (and @t82 @t81)) % 16.84/17.06 (define @t84 () (tptp.sdtlseqdt0 tptp.xp tptp.xk)) % 16.84/17.06 (define @t85 () (not @t84)) % 16.84/17.06 (define @t86 () (=> @t85 @t83)) % 16.84/17.06 (define @t87 () (not @t86)) % 16.84/17.06 (define @t88 () (@list tptp.xp)) % 16.84/17.06 (define @t89 () (tptp.sdtlseqdt0 tptp.xp tptp.xp)) % 16.84/17.06 (define @t90 () (not @t72)) % 16.84/17.06 (define @t91 () (or @t90 @t89)) % 16.84/17.06 (define @t92 () (@list false false)) % 16.84/17.06 (define @t93 () (= tptp.xp tptp.xk)) % 16.84/17.06 (define @t94 () (not @t93)) % 16.84/17.06 (define @t95 () (and @t94 @t81)) % 16.84/17.06 (define @t96 () (=> @t85 @t95)) % 16.84/17.06 (define @t97 () (not @t89)) % 16.84/17.06 (define @t98 () (= tptp.xp @t78)) % 16.84/17.06 (define @t99 () (not @t98)) % 16.84/17.06 (define @t100 () (tptp.sdtlseqdt0 tptp.xp @t78)) % 16.84/17.06 (define @t101 () (not @t100)) % 16.84/17.06 (define @t102 () (and @t89 @t98 @t101)) % 16.84/17.06 (define @t103 () (tptp.sdtlseqdt0 @t78 tptp.xp)) % 16.84/17.06 (define @t104 () (not @t103)) % 16.84/17.06 (define @t105 () (@list true)) % 16.84/17.06 (define @t106 () (@var "BOUND_VARIABLE_8019" $$unsorted)) % 16.84/17.06 (define @t107 () (and (tptp.aNaturalNumber0 @t106) (= @t4 (tptp.sdtasdt0 @t1 @t106)))) % 16.84/17.06 (define @t108 () (= @t107 (= @t106 @t51))) % 16.84/17.06 (define @t109 () (not @t50)) % 16.84/17.06 (define @t110 () (not @t6)) % 16.84/17.06 (define @t111 () (not @t2)) % 16.84/17.06 (define @t112 () (or @t111 @t110 @t27 @t109 @t108)) % 16.84/17.06 (define @t113 () (@list @t1 @t4 @t106)) % 16.84/17.06 (define @t114 () (forall @t113 @t112)) % 16.84/17.06 (define @t115 () (@list @t106)) % 16.84/17.06 (define @t116 () (forall @t115 @t112)) % 16.84/17.06 (define @t117 () (forall @t115 @t108)) % 16.84/17.06 (define @t118 () (or @t111 @t110 @t27 @t109 @t117)) % 16.84/17.06 (define @t119 () (forall @t31 (= @t49 @t52))) % 16.84/17.06 (define @t120 () (or @t111 @t110 @t27 @t109 @t119)) % 16.84/17.06 (define @t121 () (or @t27 @t109 @t119)) % 16.84/17.06 (define @t122 () (or @t111 @t110)) % 16.84/17.06 (define @t123 () (=> @t54 @t119)) % 16.84/17.06 (define @t124 () (not @t7)) % 16.84/17.06 (define @t125 () (tptp.aNaturalNumber0 @t78)) % 16.84/17.06 (define @t126 () (and @t125 (= @t75 (tptp.sdtasdt0 tptp.xp @t78)))) % 16.84/17.06 (define @t127 () (= @t78 @t78)) % 16.84/17.06 (define @t128 () (not @t76)) % 16.84/17.06 (define @t129 () (tptp.aNaturalNumber0 @t75)) % 16.84/17.06 (define @t130 () (not @t129)) % 16.84/17.06 (define @t131 () (= tptp.xp tptp.sz00)) % 16.84/17.06 (define @t132 () (or @t90 @t130 @t131 @t128 (= @t126 @t127))) % 16.84/17.06 (define @t133 () (forall @t113 (or @t111 @t110 @t27 @t109 (= @t107 (= @t51 @t106))))) % 16.84/17.06 (define @t134 () (= tptp.sz00 tptp.xp)) % 16.84/17.06 (define @t135 () (or @t90 @t130 @t134 @t128 @t126)) % 16.84/17.06 (define @t136 () (@list false)) % 16.84/17.06 (define @t137 () (not @t73)) % 16.84/17.06 (define @t138 () (not @t74)) % 16.84/17.06 (define @t139 () (or @t138 @t137 @t129)) % 16.84/17.06 (define @t140 () (= tptp.sz10 @t4)) % 16.84/17.06 (define @t141 () (not @t61)) % 16.84/17.06 (define @t142 () (or @t110 @t141 @t140 @t35)) % 16.84/17.06 (define @t143 () (= @t68 (and @t28 @t66 (forall @t64 @t142)))) % 16.84/17.06 (define @t144 () (or @t140 @t35)) % 16.84/17.06 (define @t145 () (not (tptp.doDivides0 @t4 tptp.xp))) % 16.84/17.06 (define @t146 () (or @t110 @t145 @t140 (= tptp.xp @t4))) % 16.84/17.06 (define @t147 () (forall @t64 @t146)) % 16.84/17.06 (define @t148 () (not (= tptp.xp tptp.sz10))) % 16.84/17.06 (define @t149 () (not @t131)) % 16.84/17.06 (define @t150 () (and @t149 @t148 @t147)) % 16.84/17.06 (define @t151 () (= @t77 @t150)) % 16.84/17.06 (define @t152 () (or @t90 @t151)) % 16.84/17.06 (define @t153 () (forall @t3 (or @t111 @t143))) % 16.84/17.06 (define @t154 () (not @t134)) % 16.84/17.06 (define @t155 () (and @t154 (not (= tptp.sz10 tptp.xp)) (forall @t64 (or @t110 @t145 @t140 (= @t4 tptp.xp))))) % 16.84/17.06 (define @t156 () (= @t77 @t155)) % 16.84/17.06 (define @t157 () (or @t90 @t156)) % 16.84/17.06 (define @t158 () (and @t99 @t100)) % 16.84/17.06 (define @t159 () (not @t158)) % 16.84/17.06 (define @t160 () (and @t45 @t36)) % 16.84/17.06 (define @t161 () (or @t111 @t110 @t32 @t160)) % 16.84/17.06 (define @t162 () (or @t32 @t160)) % 16.84/17.06 (define @t163 () (not (= @t78 tptp.xp))) % 16.84/17.06 (define @t164 () (and @t163 @t100)) % 16.84/17.06 (define @t165 () (not @t125)) % 16.84/17.06 (define @t166 () (or @t165 @t90 @t103 @t164)) % 16.84/17.06 (define @t167 () (forall @t8 @t161)) % 16.84/17.06 (define @t168 () (or @t165 @t90 @t103 @t158)) % 16.84/17.06 (assume @p1 (forall @t3 (=> @t2 true))) % 16.84/17.06 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 16.84/17.06 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 16.84/17.06 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 16.84/17.06 (assume @p5 @t11) % 16.84/17.06 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 16.84/17.06 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 16.84/17.06 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 16.84/17.06 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t19)))) % 16.84/17.06 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 16.84/17.06 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 16.84/17.06 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 16.84/17.06 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t21)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t20)))))) % 16.84/17.06 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t24) (= @t12 @t23)) @t22)))) % 16.84/17.06 (assume @p15 (forall @t3 (=> @t2 (=> @t28 (forall (@list @t4 @t13) (=> (and @t6 @t16) (=> (or @t26 @t25) @t22))))))) % 16.84/17.06 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t27 @t29))))) % 16.84/17.06 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t27 @t29))))) % 16.84/17.06 (assume @p18 (forall @t8 (=> @t7 (= @t32 (exists @t31 @t30))))) % 16.84/17.06 (assume @p19 (forall @t8 (=> @t7 (=> @t32 (forall @t31 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t30)))))) % 16.84/17.06 (assume @p20 @t34) % 16.84/17.06 (assume @p21 (forall @t8 (=> @t7 (=> (and @t32 @t36) @t35)))) % 16.84/17.06 (assume @p22 (forall @t18 (=> @t17 (=> (and @t32 @t37) (tptp.sdtlseqdt0 @t1 @t13))))) % 16.84/17.06 (assume @p23 @t43) % 16.84/17.06 (assume @p24 (forall @t8 (=> @t7 (=> @t46 (forall @t31 (=> @t16 (and (not (= @t23 @t44)) (tptp.sdtlseqdt0 @t23 @t44) (not (= @t24 @t14)) (tptp.sdtlseqdt0 @t24 @t14)))))))) % 16.84/17.06 (assume @p25 (forall @t18 (=> @t17 (=> (and @t28 (not @t22) @t37) (and (not @t26) (tptp.sdtlseqdt0 @t9 @t21) (not @t25) (tptp.sdtlseqdt0 @t19 @t20)))))) % 16.84/17.06 (assume @p26 (forall @t3 (=> @t2 (or @t27 @t47 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 16.84/17.06 (assume @p27 (forall @t8 (=> @t7 (=> @t28 (tptp.sdtlseqdt0 @t4 @t19))))) % 16.84/17.06 (assume @p28 (forall @t8 (=> @t7 (=> @t48 true)))) % 16.84/17.06 (assume @p29 (forall @t8 (=> @t7 (=> @t46 @t48)))) % 16.84/17.06 (assume @p30 (forall @t8 (=> @t7 (= @t50 (exists @t31 @t49))))) % 16.84/17.06 (assume @p31 @t57) % 16.84/17.06 (assume @p32 (forall @t18 (=> @t17 (=> (and @t50 (tptp.doDivides0 @t4 @t13)) @t58)))) % 16.84/17.06 (assume @p33 (forall @t18 (=> @t17 (=> (and @t50 @t58) @t59)))) % 16.84/17.06 (assume @p34 (forall @t18 (=> @t17 (=> (and @t50 @t59) @t58)))) % 16.84/17.06 (assume @p35 (forall @t8 (=> @t7 (=> (and @t50 (not @t29)) @t32)))) % 16.84/17.06 (assume @p36 (forall @t8 (=> @t7 (=> @t54 (forall @t31 (=> @t16 (= (tptp.sdtasdt0 @t13 @t51) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 16.84/17.06 (assume @p37 @t71) % 16.84/17.06 (assume @p38 (forall @t3 (=> (and @t2 @t28 @t66) (exists @t64 (and @t6 @t61 (tptp.isPrime0 @t4)))))) % 16.84/17.06 (assume @p39 (and @t74 @t73 @t72)) % 16.84/17.06 (assume @p40 (forall @t18 (=> @t17 (=> (and (tptp.isPrime0 @t13) (tptp.doDivides0 @t13 @t9)) (=> (tptp.iLess0 @t15 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 @t13 @t1) (tptp.doDivides0 @t13 @t4))))))) % 16.84/17.06 (assume @p41 (and @t77 @t76)) % 16.84/17.06 (assume @p42 (not (tptp.sdtlseqdt0 tptp.xp tptp.xn))) % 16.84/17.06 (assume @p43 (not (tptp.sdtlseqdt0 tptp.xp tptp.xm))) % 16.84/17.06 (assume @p44 (and (not (= tptp.xn tptp.xp)) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (tptp.sdtlseqdt0 tptp.xm tptp.xp))) % 16.84/17.06 (assume @p45 (= tptp.xk @t78)) % 16.84/17.06 (assume @p46 (not (or @t80 @t79))) % 16.84/17.06 (assume @p47 (and (not @t80) (not @t79))) % 16.84/17.06 (assume @p48 (and (tptp.aNaturalNumber0 tptp.xr) (tptp.doDivides0 tptp.xr tptp.xk) (tptp.isPrime0 tptp.xr))) % 16.84/17.06 (assume @p49 (and (tptp.sdtlseqdt0 tptp.xr tptp.xk) (tptp.doDivides0 tptp.xr @t75))) % 16.84/17.06 (assume @p50 @t87) % 16.84/17.06 (assume @p51 true) % 16.84/17.06 (step @p52 :rule and_elim :premises (@p39) :args (2)) % 16.84/17.06 (step @p53 :rule bool-impl-elim :args (@t2 @t33)) % 16.84/17.06 (step @p54 :rule cong :premises (@p53) :args (@t34)) % 16.84/17.06 (step @p55 :rule eq_resolve :premises (@p20 @p54)) % 16.84/17.06 (step @p56 :rule instantiate :premises (@p55) :args (@t88)) % 16.84/17.06 (step @p57 :rule cnf_or_pos :args (@t91)) % 16.84/17.06 (step @p58 :rule reordering :premises (@p57) :args ((or @t90 @t89 (not @t91)))) % 16.84/17.06 (step @p59 :rule chain_m_resolution :premises (@p58 @p52 @p56) :args (@t89 @t92 (@list @t72 @t91))) % 16.84/17.06 (step @p60 :rule refl :args (tptp.xp)) % 16.84/17.06 (step @p61 :rule cong :premises (@p45 @p60) :args (@t81)) % 16.84/17.06 (step @p62 :rule cong :premises (@p60 @p45) :args (@t93)) % 16.84/17.06 (step @p63 :rule cong :premises (@p62) :args (@t94)) % 16.84/17.06 (step @p64 :rule nary_cong :premises (@p63 @p61) :args (@t95)) % 16.84/17.06 (step @p65 :rule cong :premises (@p60 @p45) :args (@t84)) % 16.84/17.06 (step @p66 :rule cong :premises (@p65) :args (@t85)) % 16.84/17.06 (step @p67 :rule cong :premises (@p66 @p64) :args (@t96)) % 16.84/17.06 (step @p68 :rule cong :premises (@p67) :args ((not @t96))) % 16.84/17.06 (step @p69 :rule refl :args (@t81)) % 16.84/17.06 (step @p70 :rule eq-symm :args (tptp.xk tptp.xp)) % 16.84/17.06 (step @p71 :rule cong :premises (@p70) :args (@t82)) % 16.84/17.06 (step @p72 :rule nary_cong :premises (@p71 @p69) :args (@t83)) % 16.84/17.06 (step @p73 :rule refl :args (@t85)) % 16.84/17.06 (step @p74 :rule cong :premises (@p73 @p72) :args (@t86)) % 16.84/17.06 (step @p75 :rule cong :premises (@p74) :args (@t87)) % 16.84/17.06 (step @p76 :rule trans :premises (@p75 @p68)) % 16.84/17.06 (step @p77 :rule eq_resolve :premises (@p50 @p76)) % 16.84/17.06 (step @p78 :rule not_implies_elim1 :premises (@p77)) % 16.84/17.06 (step @p79 :rule refl :args (@t97)) % 16.84/17.06 (step @p80 :rule refl :args (@t99)) % 16.84/17.06 (step @p81 :rule bool-double-not-elim :args (@t100)) % 16.84/17.06 (step @p82 :rule nary_cong :premises (@p81 @p80 @p79) :args ((or (not @t101) @t99 @t97))) % 16.84/17.06 (assume-push @p307 @t89) % 16.84/17.06 (assume-push @p308 @t98) % 16.84/17.06 (assume-push @p309 @t101) % 16.84/17.06 (step @p86 :rule evaluate :args ((= false true))) % 16.84/17.06 (step @p87 :rule true_intro :premises (@p59)) % 16.84/17.06 (step @p88 :rule symm :premises (@p308)) % 16.84/17.06 (step @p89 :rule cong :premises (@p60 @p88) :args (@t100)) % 16.84/17.06 (step @p90 :rule false_intro :premises (@p78)) % 16.84/17.06 (step @p91 :rule symm :premises (@p90)) % 16.84/17.06 (step @p92 :rule trans :premises (@p91 @p89 @p87)) % 16.84/17.06 (step @p93 false :rule eq_resolve :premises (@p92 @p86)) % 16.84/17.06 (step-pop @p310 :rule scope :premises (@p93)) % 16.84/17.06 (step-pop @p311 :rule scope :premises (@p310)) % 16.84/17.06 (step-pop @p312 :rule scope :premises (@p311)) % 16.84/17.06 (step @p94 :rule process_scope :premises (@p312) :args (false)) % 16.84/17.06 (assume-push @p313 @t101) % 16.84/17.06 (assume-push @p314 @t98) % 16.84/17.06 (assume-push @p315 @t89) % 16.84/17.06 (step @p101 :rule and_intro :premises (@p59 @p314 @p78)) % 16.84/17.06 (step-pop @p316 :rule scope :premises (@p101)) % 16.84/17.06 (step-pop @p317 :rule scope :premises (@p316)) % 16.84/17.06 (step-pop @p318 :rule scope :premises (@p317)) % 16.84/17.06 (step @p102 :rule process_scope :premises (@p318) :args (@t102)) % 16.84/17.06 (step @p106 :rule implies_elim :premises (@p102)) % 16.84/17.06 (step @p107 :rule resolution :premises (@p106 @p94) :args (true @t102)) % 16.84/17.06 (step @p108 :rule not_and :premises (@p107)) % 16.84/17.06 (step @p109 :rule eq_resolve :premises (@p108 @p82)) % 16.84/17.06 (step @p110 :rule chain_m_resolution :premises (@p109 @p78 @p59) :args (@t99 (@list true false) (@list @t100 @t89))) % 16.84/17.06 (step @p111 :rule refl :args (@t104)) % 16.84/17.06 (step @p112 :rule bool-double-not-elim :args (@t98)) % 16.84/17.06 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or (not @t99) @t104))) % 16.84/17.06 (step @p114 :rule not_implies_elim2 :premises (@p77)) % 16.84/17.06 (step @p115 :rule not_and :premises (@p114)) % 16.84/17.06 (step @p116 :rule eq_resolve :premises (@p115 @p113)) % 16.84/17.06 (step @p117 :rule chain_m_resolution :premises (@p116 @p110) :args (@t104 @t105 (@list @t98))) % 16.84/17.06 (step @p118 :rule eq-symm :args (@t106 @t51)) % 16.84/17.06 (step @p119 :rule refl :args (@t107)) % 16.84/17.06 (step @p120 :rule cong :premises (@p119 @p118) :args (@t108)) % 16.84/17.06 (step @p121 :rule refl :args (@t109)) % 16.84/17.06 (step @p122 :rule refl :args (@t27)) % 16.84/17.06 (step @p123 :rule refl :args (@t110)) % 16.84/17.06 (step @p124 :rule refl :args (@t111)) % 16.84/17.06 (step @p125 :rule nary_cong :premises (@p124 @p123 @p122 @p121 @p120) :args (@t112)) % 16.84/17.06 (step @p126 :rule cong :premises (@p125) :args (@t114)) % 16.84/17.06 (step @p127 :rule quant-merge-prenex :args ((= (forall @t8 @t116) @t114))) % 16.84/17.06 (step @p128 :rule alpha_equiv :args (@t117 (@list @t106) (@list @t13))) % 16.84/17.06 (step @p129 :rule refl :args (@t109)) % 16.84/17.06 (step @p130 :rule refl :args (@t27)) % 16.84/17.06 (step @p131 :rule refl :args (@t110)) % 16.84/17.06 (step @p132 :rule refl :args (@t111)) % 16.84/17.06 (step @p133 :rule nary_cong :premises (@p132 @p131 @p130 @p129 @p128) :args (@t118)) % 16.84/17.06 (step @p134 :rule quant-miniscope-or :args ((= @t116 @t118))) % 16.84/17.06 (step @p135 :rule trans :premises (@p134 @p133)) % 16.84/17.06 (step @p136 :rule symm :premises (@p135)) % 16.84/17.06 (step @p137 :rule cong :premises (@p136) :args ((forall @t8 @t120))) % 16.84/17.06 (step @p138 :rule trans :premises (@p137 @p127)) % 16.84/17.06 (step @p139 :rule trans :premises (@p138 @p126)) % 16.84/17.06 (step @p140 :rule aci_norm :args ((= (or @t122 @t121) @t120))) % 16.84/17.06 (step @p141 :rule aci_norm :args ((= (or (or @t27 @t109) @t119) @t121))) % 16.84/17.06 (step @p142 :rule refl :args (@t119)) % 16.84/17.06 (step @p143 :rule bool-double-not-elim :args (@t27)) % 16.84/17.06 (step @p144 :rule nary_cong :premises (@p143 @p129) :args ((or (not @t28) @t109))) % 16.84/17.06 (step @p145 :rule bool-and-de-morgan :args (@t28 @t50 true)) % 16.84/17.06 (step @p146 :rule trans :premises (@p145 @p144)) % 16.84/17.06 (step @p147 :rule nary_cong :premises (@p146 @p142) :args ((or (not @t54) @t119))) % 16.84/17.06 (step @p148 :rule trans :premises (@p147 @p141)) % 16.84/17.06 (step @p149 :rule bool-impl-elim :args (@t54 @t119)) % 16.84/17.06 (step @p150 :rule trans :premises (@p149 @p148)) % 16.84/17.06 (step @p151 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 16.84/17.06 (step @p152 :rule nary_cong :premises (@p151 @p150) :args ((or @t124 @t123))) % 16.84/17.06 (step @p153 :rule trans :premises (@p152 @p140)) % 16.84/17.06 (step @p154 :rule bool-impl-elim :args (@t7 @t123)) % 16.84/17.06 (step @p155 :rule trans :premises (@p154 @p153)) % 16.84/17.06 (step @p156 :rule cong :premises (@p155) :args ((forall @t8 (=> @t7 @t123)))) % 16.84/17.06 (step @p157 :rule trans :premises (@p156 @p139)) % 16.84/17.06 (step @p158 :rule eq-symm :args (@t52 @t49)) % 16.84/17.06 (step @p159 :rule cong :premises (@p158) :args (@t53)) % 16.84/17.06 (step @p160 :rule refl :args (@t54)) % 16.84/17.06 (step @p161 :rule cong :premises (@p160 @p159) :args (@t55)) % 16.84/17.06 (step @p162 :rule refl :args (@t7)) % 16.84/17.06 (step @p163 :rule cong :premises (@p162 @p161) :args (@t56)) % 16.84/17.06 (step @p164 :rule cong :premises (@p163) :args (@t57)) % 16.84/17.06 (step @p165 :rule trans :premises (@p164 @p157)) % 16.84/17.06 (step @p166 :rule eq_resolve :premises (@p31 @p165)) % 16.84/17.06 (step @p167 :rule bool-eq-true :args (@t126)) % 16.84/17.06 (step @p168 :rule eq-symm :args (true @t126)) % 16.84/17.06 (step @p169 :rule trans :premises (@p168 @p167)) % 16.84/17.06 (step @p170 :rule refl :args (@t126)) % 16.84/17.06 (step @p171 :rule eq-refl :args (@t78)) % 16.84/17.06 (step @p172 :rule cong :premises (@p171 @p170) :args ((= @t127 @t126))) % 16.84/17.06 (step @p173 :rule trans :premises (@p172 @p169)) % 16.84/17.06 (step @p174 :rule eq-symm :args (@t126 @t127)) % 16.84/17.06 (step @p175 :rule trans :premises (@p174 @p173)) % 16.84/17.06 (step @p176 :rule refl :args (@t128)) % 16.84/17.06 (step @p177 :rule eq-symm :args (tptp.xp tptp.sz00)) % 16.84/17.06 (step @p178 :rule refl :args (@t130)) % 16.84/17.06 (step @p179 :rule refl :args (@t90)) % 16.84/17.06 (step @p180 :rule nary_cong :premises (@p179 @p178 @p177 @p176 @p175) :args (@t132)) % 16.84/17.06 (step @p181 :rule refl :args (@t133)) % 16.84/17.06 (step @p182 :rule cong :premises (@p181 @p180) :args ((=> @t133 @t132))) % 16.84/17.06 (assume-push @p319 @t133) % 16.84/17.06 (step @p184 :rule instantiate :premises (@p166) :args ((@list tptp.xp @t75 @t78))) % 16.84/17.06 (step-pop @p320 :rule scope :premises (@p184)) % 16.84/17.06 (step @p185 :rule process_scope :premises (@p320) :args (@t132)) % 16.84/17.06 (step @p187 :rule eq_resolve :premises (@p185 @p182)) % 16.84/17.06 (step @p188 :rule implies_elim :premises (@p187)) % 16.84/17.06 (step @p189 :rule chain_m_resolution :premises (@p188 @p166) :args (@t135 @t136 (@list @t133))) % 16.84/17.06 (step @p190 :rule aci_norm :args ((= (or @t122 @t10) (or @t111 @t110 @t10)))) % 16.84/17.06 (step @p191 :rule refl :args (@t10)) % 16.84/17.06 (step @p192 :rule nary_cong :premises (@p151 @p191) :args ((or @t124 @t10))) % 16.84/17.06 (step @p193 :rule trans :premises (@p192 @p190)) % 16.84/17.06 (step @p194 :rule bool-impl-elim :args (@t7 @t10)) % 16.84/17.06 (step @p195 :rule trans :premises (@p194 @p193)) % 16.84/17.06 (step @p196 :rule cong :premises (@p195) :args (@t11)) % 16.84/17.06 (step @p197 :rule eq_resolve :premises (@p5 @p196)) % 16.84/17.06 (step @p198 :rule instantiate :premises (@p197) :args ((@list tptp.xn tptp.xm))) % 16.84/17.06 (step @p199 :rule and_elim :premises (@p39) :args (1)) % 16.84/17.06 (step @p200 :rule and_elim :premises (@p39) :args (0)) % 16.84/17.06 (step @p201 :rule cnf_or_pos :args (@t139)) % 16.84/17.06 (step @p202 :rule reordering :premises (@p201) :args ((or @t138 @t137 @t129 (not @t139)))) % 16.84/17.06 (step @p203 :rule chain_m_resolution :premises (@p202 @p200 @p199 @p198) :args (@t129 (@list false false false) (@list @t74 @t73 @t139))) % 16.84/17.06 (step @p204 :rule bool-impl-elim :args (@t2 @t143)) % 16.84/17.06 (step @p205 :rule cong :premises (@p204) :args ((forall @t3 (=> @t2 @t143)))) % 16.84/17.06 (step @p206 :rule aci_norm :args ((= (or (or @t110 @t141) @t144) @t142))) % 16.84/17.06 (step @p207 :rule refl :args (@t144)) % 16.84/17.06 (step @p208 :rule bool-and-de-morgan :args (@t6 @t61 true)) % 16.84/17.06 (step @p209 :rule nary_cong :premises (@p208 @p207) :args ((or (not @t62) @t144))) % 16.84/17.06 (step @p210 :rule trans :premises (@p209 @p206)) % 16.84/17.06 (step @p211 :rule bool-impl-elim :args (@t62 @t144)) % 16.84/17.06 (step @p212 :rule trans :premises (@p211 @p210)) % 16.84/17.06 (step @p213 :rule cong :premises (@p212) :args ((forall @t64 (=> @t62 @t144)))) % 16.84/17.06 (step @p214 :rule eq-symm :args (@t4 @t1)) % 16.84/17.06 (step @p215 :rule eq-symm :args (@t4 tptp.sz10)) % 16.84/17.06 (step @p216 :rule nary_cong :premises (@p215 @p214) :args (@t60)) % 16.84/17.06 (step @p217 :rule refl :args (@t62)) % 16.84/17.06 (step @p218 :rule cong :premises (@p217 @p216) :args (@t63)) % 16.84/17.06 (step @p219 :rule cong :premises (@p218) :args (@t65)) % 16.84/17.06 (step @p220 :rule trans :premises (@p219 @p213)) % 16.84/17.06 (step @p221 :rule refl :args (@t66)) % 16.84/17.06 (step @p222 :rule refl :args (@t28)) % 16.84/17.06 (step @p223 :rule nary_cong :premises (@p222 @p221 @p220) :args (@t67)) % 16.84/17.06 (step @p224 :rule refl :args (@t68)) % 16.84/17.06 (step @p225 :rule cong :premises (@p224 @p223) :args (@t69)) % 16.84/17.06 (step @p226 :rule refl :args (@t2)) % 16.84/17.06 (step @p227 :rule cong :premises (@p226 @p225) :args (@t70)) % 16.84/17.06 (step @p228 :rule cong :premises (@p227) :args (@t71)) % 16.84/17.06 (step @p229 :rule trans :premises (@p228 @p205)) % 16.84/17.06 (step @p230 :rule eq_resolve :premises (@p37 @p229)) % 16.84/17.06 (step @p231 :rule eq-symm :args (tptp.xp @t4)) % 16.84/17.06 (step @p232 :rule refl :args (@t140)) % 16.84/17.06 (step @p233 :rule refl :args (@t145)) % 16.84/17.06 (step @p234 :rule nary_cong :premises (@p123 @p233 @p232 @p231) :args (@t146)) % 16.84/17.06 (step @p235 :rule cong :premises (@p234) :args (@t147)) % 16.84/17.06 (step @p236 :rule eq-symm :args (tptp.xp tptp.sz10)) % 16.84/17.06 (step @p237 :rule cong :premises (@p236) :args (@t148)) % 16.84/17.06 (step @p238 :rule cong :premises (@p177) :args (@t149)) % 16.84/17.06 (step @p239 :rule nary_cong :premises (@p238 @p237 @p235) :args (@t150)) % 16.84/17.06 (step @p240 :rule refl :args (@t77)) % 16.84/17.06 (step @p241 :rule cong :premises (@p240 @p239) :args (@t151)) % 16.84/17.06 (step @p242 :rule nary_cong :premises (@p179 @p241) :args (@t152)) % 16.84/17.06 (step @p243 :rule refl :args (@t153)) % 16.84/17.06 (step @p244 :rule cong :premises (@p243 @p242) :args ((=> @t153 @t152))) % 16.84/17.06 (assume-push @p321 @t153) % 16.84/17.06 (step @p246 :rule instantiate :premises (@p230) :args (@t88)) % 16.84/17.06 (step-pop @p322 :rule scope :premises (@p246)) % 16.84/17.06 (step @p247 :rule process_scope :premises (@p322) :args (@t152)) % 16.84/17.06 (step @p249 :rule eq_resolve :premises (@p247 @p244)) % 16.84/17.06 (step @p250 :rule implies_elim :premises (@p249)) % 16.84/17.06 (step @p251 :rule chain_m_resolution :premises (@p250 @p230) :args (@t157 @t136 (@list @t153))) % 16.84/17.06 (step @p252 :rule cnf_or_pos :args (@t157)) % 16.84/17.06 (step @p253 :rule reordering :premises (@p252) :args ((or @t90 @t156 (not @t157)))) % 16.84/17.07 (step @p254 :rule chain_m_resolution :premises (@p253 @p52 @p251) :args (@t156 @t92 (@list @t72 @t157))) % 16.84/17.07 (step @p255 :rule and_elim :premises (@p41) :args (0)) % 16.84/17.07 (step @p256 :rule cnf_equiv_pos1 :args (@t156)) % 16.84/17.07 (step @p257 :rule reordering :premises (@p256) :args ((or (not @t77) @t155 (not @t156)))) % 16.84/17.07 (step @p258 :rule chain_m_resolution :premises (@p257 @p255 @p254) :args (@t155 @t92 (@list @t77 @t156))) % 16.84/17.07 (step @p259 :rule cnf_and_pos :args (@t155 0)) % 16.84/17.07 (step @p260 :rule reordering :premises (@p259) :args ((or @t154 (not @t155)))) % 16.84/17.07 (step @p261 :rule chain_m_resolution :premises (@p260 @p258) :args (@t154 @t136 (@list @t155))) % 16.84/17.07 (step @p262 :rule and_elim :premises (@p41) :args (1)) % 16.84/17.07 (step @p263 :rule cnf_or_pos :args (@t135)) % 16.84/17.07 (step @p264 :rule reordering :premises (@p263) :args ((or @t90 @t128 @t134 @t130 @t126 (not @t135)))) % 16.84/17.07 (step @p265 :rule chain_m_resolution :premises (@p264 @p52 @p262 @p261 @p203 @p189) :args (@t126 (@list false false true false false) (@list @t72 @t76 @t134 @t129 @t135))) % 16.84/17.07 (step @p266 :rule cnf_and_pos :args (@t126 0)) % 16.84/17.07 (step @p267 :rule reordering :premises (@p266) :args ((or @t125 (not @t126)))) % 16.84/17.07 (step @p268 :rule chain_m_resolution :premises (@p267 @p265) :args (@t125 @t136 (@list @t126))) % 16.84/17.07 (step @p269 :rule cnf_and_pos :args (@t158 1)) % 16.84/17.07 (step @p270 :rule reordering :premises (@p269) :args ((or @t100 @t159))) % 16.84/17.07 (step @p271 :rule chain_m_resolution :premises (@p270 @p78) :args (@t159 @t105 (@list @t100))) % 16.84/17.07 (step @p272 :rule aci_norm :args ((= (or @t122 @t162) @t161))) % 16.84/17.07 (step @p273 :rule refl :args (@t162)) % 16.84/17.07 (step @p274 :rule nary_cong :premises (@p151 @p273) :args ((or @t124 @t162))) % 16.84/17.07 (step @p275 :rule trans :premises (@p274 @p272)) % 16.84/17.07 (step @p276 :rule bool-impl-elim :args (@t7 @t162)) % 16.84/17.07 (step @p277 :rule trans :premises (@p276 @p275)) % 16.84/17.07 (step @p278 :rule cong :premises (@p277) :args ((forall @t8 (=> @t7 @t162)))) % 16.84/17.07 (step @p279 :rule refl :args (@t36)) % 16.84/17.07 (step @p280 :rule cong :premises (@p214) :args (@t39)) % 16.84/17.07 (step @p281 :rule nary_cong :premises (@p280 @p279) :args (@t40)) % 16.84/17.07 (step @p282 :rule refl :args (@t32)) % 16.84/17.07 (step @p283 :rule nary_cong :premises (@p282 @p281) :args (@t41)) % 16.84/17.07 (step @p284 :rule cong :premises (@p162 @p283) :args (@t42)) % 16.84/17.07 (step @p285 :rule cong :premises (@p284) :args (@t43)) % 16.84/17.07 (step @p286 :rule trans :premises (@p285 @p278)) % 16.84/17.07 (step @p287 :rule eq_resolve :premises (@p23 @p286)) % 16.84/17.07 (step @p288 :rule refl :args (@t100)) % 16.84/17.07 (step @p289 :rule eq-symm :args (@t78 tptp.xp)) % 16.84/17.07 (step @p290 :rule cong :premises (@p289) :args (@t163)) % 16.84/17.07 (step @p291 :rule nary_cong :premises (@p290 @p288) :args (@t164)) % 16.84/17.07 (step @p292 :rule refl :args (@t103)) % 16.84/17.07 (step @p293 :rule refl :args (@t165)) % 16.84/17.07 (step @p294 :rule nary_cong :premises (@p293 @p179 @p292 @p291) :args (@t166)) % 16.84/17.07 (step @p295 :rule refl :args (@t167)) % 16.84/17.07 (step @p296 :rule cong :premises (@p295 @p294) :args ((=> @t167 @t166))) % 16.84/17.07 (assume-push @p323 @t167) % 16.84/17.07 (step @p298 :rule instantiate :premises (@p287) :args ((@list @t78 tptp.xp))) % 16.84/17.07 (step-pop @p324 :rule scope :premises (@p298)) % 16.84/17.07 (step @p299 :rule process_scope :premises (@p324) :args (@t166)) % 16.84/17.07 (step @p301 :rule eq_resolve :premises (@p299 @p296)) % 16.84/17.07 (step @p302 :rule implies_elim :premises (@p301)) % 16.84/17.07 (step @p303 :rule chain_m_resolution :premises (@p302 @p287) :args (@t168 @t136 (@list @t167))) % 16.84/17.07 (step @p304 :rule cnf_or_pos :args (@t168)) % 16.84/17.07 (step @p305 :rule reordering :premises (@p304) :args ((or @t103 @t90 @t165 @t158 (not @t168)))) % 16.84/17.07 (step @p306 false :rule chain_m_resolution :premises (@p305 @p303 @p271 @p268 @p117 @p52) :args (false (@list false true false true false) (@list @t168 @t158 @t125 @t103 @t72))) % 16.84/17.07 ) % 16.84/17.07 % SZS output end Proof % 16.84/17.07 % cvc5 exiting %------------------------------------------------------------------------------