%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PLA050_1 : TPTP v9.2.1. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:43:29 AM UTC 2026 % Result : Theorem 153.39s 153.61s % Output : Proof 153.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PLA050_1 : TPTP v9.2.1. Released v7.3.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n002.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 13:04:48 EDT 2026 % 0.18/0.34 % CPUTime : % 0.32/0.49 %----Proving TF0_ARI % 153.39/153.61 --- Run --finite-model-find --decision=internal at 45... % 153.39/153.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 153.39/153.61 --- Run --no-e-matching --full-saturate-quant at 45... % 153.39/153.61 --- Run --cegqi-all --purify-triggers --full-saturate-quant at 45... % 153.39/153.61 % SZS status Theorem % 153.39/153.61 % SZS output start Proof % 153.39/153.61 ( % 153.39/153.61 (declare-const tptp.mylk (-> Int Int)) % 153.39/153.61 (declare-const tptp.mysumr (-> Real Int Int Int Real)) % 153.39/153.61 (declare-const tptp.mysump (-> Real Int Int Int Real)) % 153.39/153.61 (declare-const tptp.imp (-> Real Int Int Real)) % 153.39/153.61 (declare-const tptp.dc (-> Real Int Int Real)) % 153.39/153.61 (declare-const tptp.ns (-> Int Int)) % 153.39/153.61 (declare-const tptp.lk (-> Int Int)) % 153.39/153.61 (declare-const tptp.problen Int) % 153.39/153.61 (declare-const tptp.recexp (-> Real Int Int Real)) % 153.39/153.61 (declare-const tptp.probsize Int) % 153.39/153.61 (define @t1 () (@var "S" Real)) % 153.39/153.61 (define @t2 () (@var "C" Int)) % 153.39/153.61 (define @t3 () (@var "Probsize" Int)) % 153.39/153.61 (define @t4 () (@var "Problen" Int)) % 153.39/153.61 (define @t5 () (tptp.lk 0)) % 153.39/153.61 (define @t6 () (@var "K" Int)) % 153.39/153.61 (define @t7 () (tptp.lk @t6)) % 153.39/153.61 (define @t8 () (- @t6 1)) % 153.39/153.61 (define @t9 () (tptp.lk @t8)) % 153.39/153.61 (define @t10 () (<= 1 @t6)) % 153.39/153.61 (define @t11 () (and @t10 (<= @t6 tptp.problen))) % 153.39/153.61 (define @t12 () (@list @t6)) % 153.39/153.61 (define @t13 () (- tptp.problen 1)) % 153.39/153.61 (define @t14 () (tptp.ns @t2)) % 153.39/153.61 (define @t15 () (@var "D" Real)) % 153.39/153.61 (define @t16 () (@var "T" Int)) % 153.39/153.61 (define @t17 () (to_real @t16)) % 153.39/153.61 (define @t18 () (tptp.dc @t15 @t16 @t2)) % 153.39/153.61 (define @t19 () (@list @t15 @t16 @t2)) % 153.39/153.61 (define @t20 () (@list @t15 @t16)) % 153.39/153.61 (define @t21 () (- @t2 2)) % 153.39/153.61 (define @t22 () (tptp.mysump @t15 @t16 @t2 @t21)) % 153.39/153.61 (define @t23 () (- @t2 1)) % 153.39/153.61 (define @t24 () (tptp.lk @t23)) % 153.39/153.61 (define @t25 () (to_real @t24)) % 153.39/153.61 (define @t26 () (* @t15 @t25)) % 153.39/153.61 (define @t27 () (+ @t26 @t22)) % 153.39/153.61 (define @t28 () (tptp.imp @t15 @t16 @t2)) % 153.39/153.61 (define @t29 () (* @t17 @t28)) % 153.39/153.61 (define @t30 () (= @t29 @t27)) % 153.39/153.61 (define @t31 () (<= 1 @t2)) % 153.39/153.61 (define @t32 () (=> @t31 @t30)) % 153.39/153.61 (define @t33 () (forall @t19 @t32)) % 153.39/153.61 (define @t34 () (to_real @t7)) % 153.39/153.61 (define @t35 () (@list @t15 @t16 @t2 @t6)) % 153.39/153.61 (define @t36 () (tptp.mysumr @t15 @t16 @t2 @t21)) % 153.39/153.61 (define @t37 () (tptp.recexp @t15 @t16 @t23)) % 153.39/153.61 (define @t38 () (* @t15 @t37)) % 153.39/153.61 (define @t39 () (* @t38 @t25)) % 153.39/153.61 (define @t40 () (+ (+ @t17 @t39) @t36)) % 153.39/153.61 (define @t41 () (tptp.recexp @t15 @t16 @t2)) % 153.39/153.61 (define @t42 () (* @t17 @t41)) % 153.39/153.61 (define @t43 () (* @t28 @t42)) % 153.39/153.61 (define @t44 () (= @t43 @t40)) % 153.39/153.61 (define @t45 () (=> @t31 @t44)) % 153.39/153.61 (define @t46 () (forall @t19 @t45)) % 153.39/153.61 (define @t47 () (>= @t2 1)) % 153.39/153.61 (define @t48 () (+ -1 @t2)) % 153.39/153.61 (define @t49 () (to_real (tptp.lk @t48))) % 153.39/153.61 (define @t50 () (tptp.recexp @t15 @t16 @t48)) % 153.39/153.61 (define @t51 () (* @t15 @t50 @t49)) % 153.39/153.61 (define @t52 () (+ -2 @t2)) % 153.39/153.61 (define @t53 () (* @t28 @t41 @t17)) % 153.39/153.61 (define @t54 () (= @t53 (+ (tptp.mysumr @t15 @t16 @t2 @t52) @t51 @t17))) % 153.39/153.61 (define @t55 () (* @t15 @t50)) % 153.39/153.61 (define @t56 () (* -1 1)) % 153.39/153.61 (define @t57 () (+ @t2 @t56)) % 153.39/153.61 (define @t58 () (* -1 2)) % 153.39/153.61 (define @t59 () (+ @t2 @t58)) % 153.39/153.61 (define @t60 () (+ @t36 @t39 @t17)) % 153.39/153.61 (define @t61 () (* @t41 @t17)) % 153.39/153.61 (define @t62 () (tptp.mysumr 0/1 -1 2 0)) % 153.39/153.61 (define @t63 () (* -1/1 @t62)) % 153.39/153.61 (define @t64 () (+ 1/1 @t63)) % 153.39/153.61 (define @t65 () (tptp.recexp 0/1 -1 2)) % 153.39/153.61 (define @t66 () (tptp.imp 0/1 -1 2)) % 153.39/153.61 (define @t67 () (* @t66 @t65)) % 153.39/153.62 (define @t68 () (= @t67 @t64)) % 153.39/153.62 (define @t69 () (- @t67 @t64)) % 153.39/153.62 (define @t70 () (+ -1/1 @t62)) % 153.39/153.62 (define @t71 () (* -1/1 @t67)) % 153.39/153.62 (define @t72 () (+ -1 2)) % 153.39/153.62 (define @t73 () (to_real (tptp.lk @t72))) % 153.39/153.62 (define @t74 () (* 0/1 (tptp.recexp 0/1 -1 @t72) @t73)) % 153.39/153.62 (define @t75 () (+ -2 2)) % 153.39/153.62 (define @t76 () (tptp.mysumr 0/1 -1 2 @t75)) % 153.39/153.62 (define @t77 () (+ @t76 @t74 -1/1)) % 153.39/153.62 (define @t78 () (* @t66 @t65 -1/1)) % 153.39/153.62 (define @t79 () (= @t78 @t77)) % 153.39/153.62 (define @t80 () (>= 2 1)) % 153.39/153.62 (define @t81 () (not @t80)) % 153.39/153.62 (define @t82 () (or @t81 @t79)) % 153.39/153.62 (define @t83 () (not @t47)) % 153.39/153.62 (define @t84 () (forall @t19 (or @t83 @t54))) % 153.39/153.62 (define @t85 () (to_real -1)) % 153.39/153.62 (define @t86 () (+ @t76 @t74 @t85)) % 153.39/153.62 (define @t87 () (* @t66 @t65 @t85)) % 153.39/153.62 (define @t88 () (= @t87 @t86)) % 153.39/153.62 (define @t89 () (@list 0/1 -1 2)) % 153.39/153.62 (define @t90 () (@list false)) % 153.39/153.62 (define @t91 () (* @t15 @t49)) % 153.39/153.62 (define @t92 () (* @t28 @t17)) % 153.39/153.62 (define @t93 () (= @t92 (+ @t91 (tptp.mysump @t15 @t16 @t2 @t52)))) % 153.39/153.62 (define @t94 () (tptp.mysump 0/1 -1 2 0)) % 153.39/153.62 (define @t95 () (* -1/1 @t94)) % 153.39/153.62 (define @t96 () (= @t66 @t95)) % 153.39/153.62 (define @t97 () (- @t66 @t95)) % 153.39/153.62 (define @t98 () (* -1/1 @t66)) % 153.39/153.62 (define @t99 () (tptp.mysump 0/1 -1 2 @t75)) % 153.39/153.62 (define @t100 () (* 0/1 @t73)) % 153.39/153.62 (define @t101 () (+ @t100 @t99)) % 153.39/153.62 (define @t102 () (* @t66 -1/1)) % 153.39/153.62 (define @t103 () (= @t102 @t101)) % 153.39/153.62 (define @t104 () (or @t81 @t103)) % 153.39/153.62 (define @t105 () (forall @t19 (or @t83 @t93))) % 153.39/153.62 (define @t106 () (* @t66 @t85)) % 153.39/153.62 (define @t107 () (= @t106 @t101)) % 153.39/153.62 (define @t108 () (@list @t105)) % 153.39/153.62 (define @t109 () (>= @t98 0/1)) % 153.39/153.62 (define @t110 () (= @t94 0/1)) % 153.39/153.62 (define @t111 () (not @t110)) % 153.39/153.62 (define @t112 () (not @t96)) % 153.39/153.62 (define @t113 () (not @t109)) % 153.39/153.62 (define @t114 () (+ @t66 @t94)) % 153.39/153.62 (define @t115 () (= @t114 0/1)) % 153.39/153.62 (define @t116 () (>= 0/1 0/1)) % 153.39/153.62 (define @t117 () (+ 0/1 0/1 0/1)) % 153.39/153.62 (define @t118 () (* -1/1 0/1)) % 153.39/153.62 (define @t119 () (+ 0/1 @t118 @t118)) % 153.39/153.62 (define @t120 () (+ @t95 @t98 @t94 @t66)) % 153.39/153.62 (define @t121 () (+ @t114 @t95 @t98)) % 153.39/153.62 (define @t122 () (>= @t121 @t119)) % 153.39/153.62 (define @t123 () (= (* -1/1 (- 0/1 @t66)) (* -1/1 (- @t98 0/1)))) % 153.39/153.62 (define @t124 () (>= 0/1 @t66)) % 153.39/153.62 (define @t125 () (= @t124 @t109)) % 153.39/153.62 (define @t126 () (< -1/1 0/1)) % 153.39/153.62 (define @t127 () (= (* 1/1 (- @t114 0/1)) (* 1/1 @t97))) % 153.39/153.62 (define @t128 () (= @t115 @t96)) % 153.39/153.62 (define @t129 () (and @t113 @t110 @t96)) % 153.39/153.62 (define @t130 () (= @t66 0/1)) % 153.39/153.62 (define @t131 () (not @t130)) % 153.39/153.62 (define @t132 () (+ @t118 0/1 0/1)) % 153.39/153.62 (define @t133 () (+ @t98 @t95)) % 153.39/153.62 (define @t134 () (* -1/1 @t114)) % 153.39/153.62 (define @t135 () (+ @t134 @t94 @t66)) % 153.39/153.62 (define @t136 () (>= @t135 @t132)) % 153.39/153.62 (define @t137 () (and @t131 @t109 @t110 @t96)) % 153.39/153.62 (define @t138 () (@list false false false)) % 153.39/153.62 (define @t139 () (= (* 0/1 @t65) 0/1)) % 153.39/153.62 (define @t140 () (= @t67 0/1)) % 153.39/153.62 (define @t141 () (= @t62 0/1)) % 153.39/153.62 (define @t142 () (* -1/1 1/1)) % 153.39/153.62 (define @t143 () (+ 0/1 0/1 @t142)) % 153.39/153.62 (define @t144 () (+ @t71 @t63)) % 153.39/153.62 (define @t145 () (+ @t67 @t62)) % 153.39/153.62 (define @t146 () (* -1/1 @t145)) % 153.39/153.62 (define @t147 () (+ @t67 @t62 @t146)) % 153.39/153.62 (define @t148 () (= @t145 1/1)) % 153.39/153.62 (define @t149 () (and @t68 @t141 @t140)) % 153.39/153.62 (assume @p1 (not (forall (@list @t1 @t2 @t4 @t3) (=> (and (<= 2 @t4) (= tptp.problen @t4) (<= (* @t4 @t4) @t3) (= tptp.probsize @t3) (<= (* @t2 2) tptp.problen) (<= (to_real tptp.probsize) (tptp.recexp @t1 tptp.probsize @t2)) (<= (/ 9 10) @t1) (<= @t1 10/1)) (<= @t1 1/1))))) % 153.39/153.62 (assume @p2 (= @t5 1)) % 153.39/153.62 (assume @p3 (forall @t12 (=> @t11 (<= @t9 @t7)))) % 153.39/153.62 (assume @p4 (= (tptp.ns 0) (+ @t5 (tptp.lk 1)))) % 153.39/153.62 (assume @p5 (= (tptp.ns tptp.problen) (+ (tptp.lk @t13) (tptp.lk tptp.problen)))) % 153.39/153.62 (assume @p6 (forall @t12 (=> (and @t10 (<= @t6 @t13)) (= (tptp.ns @t6) (+ (+ @t9 @t7) (tptp.lk (+ @t6 1))))))) % 153.39/153.62 (assume @p7 (forall @t19 (= (* @t18 (to_real (- @t16 @t14))) (- @t17 (* @t15 (to_real @t14)))))) % 153.39/153.62 (assume @p8 (forall @t20 (= (tptp.imp @t15 @t16 0) 0/1))) % 153.39/153.62 (assume @p9 @t33) % 153.39/153.62 (assume @p10 (forall @t19 (= (tptp.mysump @t15 @t16 @t2 0) 0/1))) % 153.39/153.62 (assume @p11 (forall @t35 (=> @t10 (= (tptp.mysump @t15 @t16 @t2 @t6) (+ (* @t18 @t34) (tptp.mysump @t15 @t16 @t2 @t8)))))) % 153.39/153.62 (assume @p12 (forall @t20 (= (tptp.recexp @t15 @t16 0) 0/1))) % 153.39/153.62 (assume @p13 @t46) % 153.39/153.62 (assume @p14 (= (tptp.mylk 0) 1)) % 153.39/153.62 (assume @p15 (forall @t12 (=> @t11 (= (tptp.mylk @t6) (+ @t7 (tptp.mylk @t8)))))) % 153.39/153.62 (assume @p16 (<= (tptp.mylk tptp.problen) tptp.probsize)) % 153.39/153.62 (assume @p17 (forall @t19 (= (tptp.mysumr @t15 @t16 @t2 0) 0/1))) % 153.39/153.62 (assume @p18 (forall @t35 (=> @t10 (= (tptp.mysumr @t15 @t16 @t2 @t6) (+ (* @t18 (* (tptp.recexp @t15 @t16 @t6) @t34)) (tptp.mysumr @t15 @t16 @t2 @t8)))))) % 153.39/153.62 (assume @p19 true) % 153.39/153.62 (step @p20 :rule bool-impl-elim :args (@t47 @t54)) % 153.39/153.62 (step @p21 :rule cong :premises (@p20) :args ((forall @t19 (=> @t47 @t54)))) % 153.39/153.62 (step @p22 :rule refl :args (@t17)) % 153.39/153.62 (step @p23 :rule arith_poly_norm :args ((= (* @t55 @t49) @t51))) % 153.39/153.62 (step @p24 :rule arith_poly_norm :args ((= (+ @t2 -1) @t48))) % 153.39/153.62 (step @p25 :rule evaluate :args (@t56)) % 153.39/153.62 (step @p26 :rule refl :args (@t2)) % 153.39/153.62 (step @p27 :rule nary_cong :premises (@p26 @p25) :args (@t57)) % 153.39/153.62 (step @p28 :rule trans :premises (@p27 @p24)) % 153.39/153.62 (step @p29 :rule arith_poly_norm :args ((= @t23 @t57))) % 153.39/153.62 (step @p30 :rule trans :premises (@p29 @p28)) % 153.39/153.62 (step @p31 :rule cong :premises (@p30) :args (@t24)) % 153.39/153.62 (step @p32 :rule cong :premises (@p31) :args (@t25)) % 153.39/153.62 (step @p33 :rule arith_poly_norm :args ((= (* @t15 @t50) @t55))) % 153.39/153.62 (step @p34 :rule refl :args (@t16)) % 153.39/153.62 (step @p35 :rule refl :args (@t15)) % 153.39/153.62 (step @p36 :rule cong :premises (@p35 @p34 @p30) :args (@t37)) % 153.39/153.62 (step @p37 :rule nary_cong :premises (@p35 @p36) :args (@t38)) % 153.39/153.62 (step @p38 :rule trans :premises (@p37 @p33)) % 153.39/153.62 (step @p39 :rule nary_cong :premises (@p38 @p32) :args (@t39)) % 153.39/153.62 (step @p40 :rule trans :premises (@p39 @p23)) % 153.39/153.62 (step @p41 :rule arith_poly_norm :args ((= (+ @t2 -2) @t52))) % 153.39/153.62 (step @p42 :rule evaluate :args (@t58)) % 153.39/153.62 (step @p43 :rule nary_cong :premises (@p26 @p42) :args (@t59)) % 153.39/153.62 (step @p44 :rule trans :premises (@p43 @p41)) % 153.39/153.62 (step @p45 :rule arith_poly_norm :args ((= @t21 @t59))) % 153.39/153.62 (step @p46 :rule trans :premises (@p45 @p44)) % 153.39/153.62 (step @p47 :rule cong :premises (@p35 @p34 @p26 @p46) :args (@t36)) % 153.39/153.62 (step @p48 :rule nary_cong :premises (@p47 @p40 @p22) :args (@t60)) % 153.39/153.62 (step @p49 :rule arith_poly_norm :args ((= @t40 @t60))) % 153.39/153.62 (step @p50 :rule trans :premises (@p49 @p48)) % 153.39/153.62 (step @p51 :rule arith_poly_norm :args ((= (* @t28 @t61) @t53))) % 153.39/153.62 (step @p52 :rule arith_poly_norm :args ((= @t42 @t61))) % 153.39/153.62 (step @p53 :rule refl :args (@t28)) % 153.39/153.62 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t43)) % 153.39/153.62 (step @p55 :rule trans :premises (@p54 @p51)) % 153.39/153.62 (step @p56 :rule cong :premises (@p55 @p50) :args (@t44)) % 153.39/153.62 (step @p57 :rule arith-elim-leq :args (1 @t2)) % 153.39/153.62 (step @p58 :rule cong :premises (@p57 @p56) :args (@t45)) % 153.39/153.62 (step @p59 :rule cong :premises (@p58) :args (@t46)) % 153.39/153.62 (step @p60 :rule trans :premises (@p59 @p21)) % 153.39/153.62 (step @p61 :rule eq_resolve :premises (@p13 @p60)) % 153.39/153.62 (step @p62 :rule aci_norm :args ((= (or false @t68) @t68))) % 153.39/153.62 (step @p63 :rule arith_poly_norm :args ((= (* -1/1 (- @t71 @t70)) (* 1/1 @t69)))) % 153.39/153.62 (step @p64 :rule arith_poly_norm_rel :premises (@p63) :args ((= (= @t71 @t70) @t68))) % 153.39/153.62 (step @p65 :rule arith_poly_norm :args ((= (+ @t62 0/1 -1/1) @t70))) % 153.39/153.62 (step @p66 :rule refl :args (-1/1)) % 153.39/153.62 (step @p67 :rule arith_poly_norm :args ((= @t74 0/1))) % 153.39/153.62 (step @p68 :rule evaluate :args (@t75)) % 153.39/153.62 (step @p69 :rule refl :args (2)) % 153.39/153.62 (step @p70 :rule refl :args (-1)) % 153.39/153.62 (step @p71 :rule refl :args (0/1)) % 153.39/153.62 (step @p72 :rule cong :premises (@p71 @p70 @p69 @p68) :args (@t76)) % 153.39/153.62 (step @p73 :rule nary_cong :premises (@p72 @p67 @p66) :args (@t77)) % 153.39/153.62 (step @p74 :rule trans :premises (@p73 @p65)) % 153.39/153.62 (step @p75 :rule arith_poly_norm :args ((= @t78 @t71))) % 153.39/153.62 (step @p76 :rule cong :premises (@p75 @p74) :args (@t79)) % 153.39/153.62 (step @p77 :rule trans :premises (@p76 @p64)) % 153.39/153.62 (step @p78 :rule evaluate :args ((not true))) % 153.39/153.62 (step @p79 :rule evaluate :args (@t80)) % 153.39/153.62 (step @p80 :rule cong :premises (@p79) :args (@t81)) % 153.39/153.62 (step @p81 :rule trans :premises (@p80 @p78)) % 153.39/153.62 (step @p82 :rule nary_cong :premises (@p81 @p77) :args (@t82)) % 153.39/153.62 (step @p83 :rule trans :premises (@p82 @p62)) % 153.39/153.62 (step @p84 :rule refl :args (@t84)) % 153.39/153.62 (step @p85 :rule cong :premises (@p84 @p83) :args ((=> @t84 @t82))) % 153.39/153.62 (assume-push @p334 @t84) % 153.39/153.62 (step @p87 :rule evaluate :args (@t85)) % 153.39/153.62 (step @p88 :rule refl :args (@t74)) % 153.39/153.62 (step @p89 :rule refl :args (@t76)) % 153.39/153.62 (step @p90 :rule nary_cong :premises (@p89 @p88 @p87) :args (@t86)) % 153.39/153.62 (step @p91 :rule refl :args (@t65)) % 153.39/153.62 (step @p92 :rule refl :args (@t66)) % 153.39/153.62 (step @p93 :rule nary_cong :premises (@p92 @p91 @p87) :args (@t87)) % 153.39/153.62 (step @p94 :rule cong :premises (@p93 @p90) :args (@t88)) % 153.39/153.62 (step @p95 :rule refl :args (@t81)) % 153.39/153.62 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((or @t81 @t88))) % 153.39/153.62 (step @p97 :rule instantiate :premises (@p61) :args (@t89)) % 153.39/153.62 (step @p98 :rule eq_resolve :premises (@p97 @p96)) % 153.39/153.62 (step-pop @p335 :rule scope :premises (@p98)) % 153.39/153.62 (step @p99 :rule process_scope :premises (@p335) :args (@t82)) % 153.39/153.62 (step @p101 :rule eq_resolve :premises (@p99 @p85)) % 153.39/153.62 (step @p102 :rule implies_elim :premises (@p101)) % 153.39/153.62 (step @p103 :rule chain_m_resolution :premises (@p102 @p61) :args (@t68 @t90 (@list @t84))) % 153.39/153.62 (step @p104 :rule instantiate :premises (@p17) :args (@t89)) % 153.39/153.62 (step @p105 :rule instantiate :premises (@p10) :args (@t89)) % 153.39/153.62 (step @p106 :rule bool-impl-elim :args (@t47 @t93)) % 153.39/153.62 (step @p107 :rule cong :premises (@p106) :args ((forall @t19 (=> @t47 @t93)))) % 153.39/153.62 (step @p108 :rule cong :premises (@p35 @p34 @p26 @p46) :args (@t22)) % 153.39/153.62 (step @p109 :rule arith_poly_norm :args ((= (* @t15 @t49) @t91))) % 153.39/153.62 (step @p110 :rule nary_cong :premises (@p35 @p32) :args (@t26)) % 153.39/153.62 (step @p111 :rule trans :premises (@p110 @p109)) % 153.39/153.62 (step @p112 :rule nary_cong :premises (@p111 @p108) :args (@t27)) % 153.39/153.62 (step @p113 :rule arith_poly_norm :args ((= @t29 @t92))) % 153.39/153.62 (step @p114 :rule cong :premises (@p113 @p112) :args (@t30)) % 153.39/153.62 (step @p115 :rule cong :premises (@p57 @p114) :args (@t32)) % 153.39/153.62 (step @p116 :rule cong :premises (@p115) :args (@t33)) % 153.39/153.62 (step @p117 :rule trans :premises (@p116 @p107)) % 153.39/153.62 (step @p118 :rule eq_resolve :premises (@p9 @p117)) % 153.39/153.62 (step @p119 :rule aci_norm :args ((= (or false @t96) @t96))) % 153.39/153.62 (step @p120 :rule arith_poly_norm :args ((= (* 1/1 (- @t98 @t94)) (* -1/1 @t97)))) % 153.39/153.62 (step @p121 :rule arith_poly_norm_rel :premises (@p120) :args ((= (= @t98 @t94) @t96))) % 153.39/153.62 (step @p122 :rule arith_poly_norm :args ((= (+ 0/1 @t94) @t94))) % 153.39/153.62 (step @p123 :rule cong :premises (@p71 @p70 @p69 @p68) :args (@t99)) % 153.39/153.62 (step @p124 :rule arith_poly_norm :args ((= @t100 0/1))) % 153.39/153.62 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t101)) % 153.39/153.62 (step @p126 :rule trans :premises (@p125 @p122)) % 153.39/153.62 (step @p127 :rule arith_poly_norm :args ((= @t102 @t98))) % 153.39/153.62 (step @p128 :rule cong :premises (@p127 @p126) :args (@t103)) % 153.39/153.62 (step @p129 :rule trans :premises (@p128 @p121)) % 153.39/153.62 (step @p130 :rule nary_cong :premises (@p81 @p129) :args (@t104)) % 153.39/153.62 (step @p131 :rule trans :premises (@p130 @p119)) % 153.39/153.62 (step @p132 :rule refl :args (@t105)) % 153.39/153.62 (step @p133 :rule cong :premises (@p132 @p131) :args ((=> @t105 @t104))) % 153.39/153.62 (assume-push @p336 @t105) % 153.39/153.62 (step @p135 :rule refl :args (@t101)) % 153.39/153.62 (step @p136 :rule evaluate :args (@t85)) % 153.39/153.62 (step @p137 :rule refl :args (@t66)) % 153.39/153.62 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t106)) % 153.39/153.62 (step @p139 :rule cong :premises (@p138 @p135) :args (@t107)) % 153.39/153.62 (step @p140 :rule refl :args (@t81)) % 153.39/153.62 (step @p141 :rule nary_cong :premises (@p140 @p139) :args ((or @t81 @t107))) % 153.39/153.62 (step @p142 :rule instantiate :premises (@p118) :args (@t89)) % 153.39/153.62 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 153.39/153.62 (step-pop @p337 :rule scope :premises (@p143)) % 153.39/153.62 (step @p144 :rule process_scope :premises (@p337) :args (@t104)) % 153.39/153.62 (step @p146 :rule eq_resolve :premises (@p144 @p133)) % 153.39/153.62 (step @p147 :rule implies_elim :premises (@p146)) % 153.39/153.62 (step @p148 :rule chain_m_resolution :premises (@p147 @p118) :args (@t96 @t90 @t108)) % 153.39/153.62 (step @p149 :rule bool-double-not-elim :args (@t109)) % 153.39/153.62 (step @p150 :rule refl :args (@t111)) % 153.39/153.62 (step @p151 :rule refl :args (@t112)) % 153.39/153.62 (step @p152 :rule nary_cong :premises (@p151 @p150 @p149) :args ((or @t112 @t111 (not @t113)))) % 153.39/153.62 (assume-push @p338 @t113) % 153.39/153.62 (assume-push @p339 @t110) % 153.39/153.62 (assume-push @p340 @t96) % 153.39/153.62 (assume-push @p341 @t115) % 153.39/153.62 (step @p157 :rule evaluate :args (@t116)) % 153.39/153.62 (step @p158 :rule evaluate :args (@t117)) % 153.39/153.62 (step @p159 :rule evaluate :args (@t118)) % 153.39/153.62 (step @p160 :rule nary_cong :premises (@p71 @p159 @p159) :args (@t119)) % 153.39/153.62 (step @p161 :rule trans :premises (@p160 @p158)) % 153.39/153.62 (step @p162 :rule arith_poly_norm :args ((= @t120 0/1))) % 153.39/153.62 (step @p163 :rule arith_poly_norm :args ((= @t121 @t120))) % 153.39/153.62 (step @p164 :rule trans :premises (@p163 @p162)) % 153.39/153.62 (step @p165 :rule cong :premises (@p164 @p161) :args (@t122)) % 153.39/153.62 (step @p166 :rule trans :premises (@p165 @p157)) % 153.39/153.62 (step @p167 :rule cong :premises (@p166) :args ((not @t122))) % 153.39/153.62 (step @p168 :rule trans :premises (@p167 @p78)) % 153.39/153.62 (step @p169 :rule arith-elim-lt :args (@t121 @t119)) % 153.39/153.62 (step @p170 :rule trans :premises (@p169 @p168)) % 153.39/153.62 (step @p171 :rule arith_mult_neg :args (-1/1 (> @t66 0/1))) % 153.39/153.62 (step @p172 :rule arith_poly_norm :args (@t123)) % 153.39/153.62 (step @p173 :rule arith_poly_norm_rel :premises (@p172) :args (@t125)) % 153.39/153.62 (step @p174 :rule arith-elim-leq :args (@t66 0/1)) % 153.39/153.62 (step @p175 :rule trans :premises (@p174 @p173)) % 153.39/153.62 (step @p176 :rule cong :premises (@p175) :args ((not (<= @t66 0/1)))) % 153.39/153.62 (step @p177 :rule symm :premises (@p174)) % 153.39/153.62 (step @p178 :rule cong :premises (@p177) :args ((not @t124))) % 153.39/153.62 (step @p179 :rule arith-elim-gt :args (@t66 0/1)) % 153.39/153.62 (step @p180 :rule trans :premises (@p179 @p178)) % 153.39/153.62 (step @p181 :rule trans :premises (@p180 @p176)) % 153.39/153.62 (step @p182 :rule symm :premises (@p181)) % 153.39/153.62 (step @p183 :rule eq_resolve :premises (@p338 @p182)) % 153.39/153.62 (step @p184 :rule evaluate :args (@t126)) % 153.39/153.62 (step @p185 :rule true_elim :premises (@p184)) % 153.39/153.62 (step @p186 :rule and_intro :premises (@p185 @p183)) % 153.39/153.62 (step @p187 :rule modus_ponens :premises (@p186 @p171)) % 153.39/153.62 (step @p188 :rule arith_mult_neg :args (-1/1 @t110)) % 153.39/153.62 (step @p189 :rule and_intro :premises (@p185 @p105)) % 153.39/153.62 (step @p190 :rule modus_ponens :premises (@p189 @p188)) % 153.39/153.62 (step @p191 :rule arith_poly_norm :args (@t127)) % 153.39/153.62 (step @p192 :rule arith_poly_norm_rel :premises (@p191) :args (@t128)) % 153.39/153.62 (step @p193 :rule symm :premises (@p192)) % 153.39/153.62 (step @p194 :rule chain_m_resolution :premises (@p147 @p118) :args (@t96 @t90 @t108)) % 153.39/153.62 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 153.39/153.62 (step @p196 :rule arith_sum_ub :premises (@p195 @p190 @p187)) % 153.39/153.62 (step @p197 false :rule eq_resolve :premises (@p196 @p170)) % 153.39/153.62 (step-pop @p342 :rule scope :premises (@p197)) % 153.39/153.62 (step @p198 :rule process_scope :premises (@p342) :args (false)) % 153.39/153.62 (step @p191 :rule arith_poly_norm :args (@t127)) % 153.39/153.62 (step @p192 :rule arith_poly_norm_rel :premises (@p191) :args (@t128)) % 153.39/153.62 (step @p193 :rule symm :premises (@p192)) % 153.39/153.62 (step @p200 :rule eq_resolve :premises (@p148 @p193)) % 153.39/153.62 (step @p201 false :rule contra :premises (@p200 @p198)) % 153.39/153.62 (step-pop @p343 :rule scope :premises (@p201)) % 153.39/153.62 (step-pop @p344 :rule scope :premises (@p343)) % 153.39/153.62 (step-pop @p345 :rule scope :premises (@p344)) % 153.39/153.62 (step @p202 :rule process_scope :premises (@p345) :args (false)) % 153.39/153.62 (assume-push @p346 @t96) % 153.39/153.62 (assume-push @p347 @t110) % 153.39/153.62 (assume-push @p348 @t113) % 153.39/153.62 (step @p209 :rule and_intro :premises (@p348 @p105 @p148)) % 153.39/153.62 (step-pop @p349 :rule scope :premises (@p209)) % 153.39/153.62 (step-pop @p350 :rule scope :premises (@p349)) % 153.39/153.62 (step-pop @p351 :rule scope :premises (@p350)) % 153.39/153.62 (step @p210 :rule process_scope :premises (@p351) :args (@t129)) % 153.39/153.62 (step @p214 :rule implies_elim :premises (@p210)) % 153.39/153.62 (step @p215 :rule resolution :premises (@p214 @p202) :args (true @t129)) % 153.39/153.62 (step @p216 :rule not_and :premises (@p215)) % 153.39/153.62 (step @p217 :rule eq_resolve :premises (@p216 @p152)) % 153.39/153.62 (step @p218 :rule chain_m_resolution :premises (@p217 @p148 @p105) :args (@t109 (@list false false) (@list @t96 @t110))) % 153.39/153.62 (step @p219 :rule refl :args (@t113)) % 153.39/153.62 (step @p220 :rule bool-double-not-elim :args (@t130)) % 153.39/153.62 (step @p221 :rule nary_cong :premises (@p151 @p150 @p220 @p219) :args ((or @t112 @t111 (not @t131) @t113))) % 153.39/153.62 (assume-push @p352 @t131) % 153.39/153.62 (assume-push @p353 @t109) % 153.39/153.62 (assume-push @p354 @t110) % 153.39/153.62 (assume-push @p355 @t96) % 153.39/153.62 (assume-push @p356 @t115) % 153.39/153.62 (step @p157 :rule evaluate :args (@t116)) % 153.39/153.62 (step @p158 :rule evaluate :args (@t117)) % 153.39/153.62 (step @p159 :rule evaluate :args (@t118)) % 153.39/153.62 (step @p227 :rule nary_cong :premises (@p159 @p71 @p71) :args (@t132)) % 153.39/153.62 (step @p228 :rule trans :premises (@p227 @p158)) % 153.39/153.62 (step @p229 :rule arith_poly_norm :args ((= (+ @t133 @t94 @t66) 0/1))) % 153.39/153.62 (step @p230 :rule refl :args (@t66)) % 153.39/153.62 (step @p231 :rule refl :args (@t94)) % 153.39/153.62 (step @p232 :rule arith_poly_norm :args ((= @t134 @t133))) % 153.39/153.62 (step @p233 :rule nary_cong :premises (@p232 @p231 @p230) :args (@t135)) % 153.39/153.62 (step @p234 :rule trans :premises (@p233 @p229)) % 153.39/153.62 (step @p235 :rule cong :premises (@p234 @p228) :args (@t136)) % 153.39/153.62 (step @p236 :rule trans :premises (@p235 @p157)) % 153.39/153.62 (step @p237 :rule cong :premises (@p236) :args ((not @t136))) % 153.39/153.62 (step @p238 :rule trans :premises (@p237 @p78)) % 153.39/153.62 (step @p239 :rule arith-elim-lt :args (@t135 @t132)) % 153.39/153.62 (step @p240 :rule trans :premises (@p239 @p238)) % 153.39/153.62 (step @p172 :rule arith_poly_norm :args (@t123)) % 153.39/153.62 (step @p173 :rule arith_poly_norm_rel :premises (@p172) :args (@t125)) % 153.39/153.62 (step @p174 :rule arith-elim-leq :args (@t66 0/1)) % 153.39/153.62 (step @p175 :rule trans :premises (@p174 @p173)) % 153.39/153.62 (step @p241 :rule symm :premises (@p175)) % 153.39/153.62 (step @p242 :rule eq_resolve :premises (@p353 @p241)) % 153.39/153.62 (step @p243 :rule arith_trichotomy :premises (@p352 @p242)) % 153.39/153.62 (step @p244 :rule arith_mult_neg :args (-1/1 @t115)) % 153.39/153.62 (step @p191 :rule arith_poly_norm :args (@t127)) % 153.39/153.62 (step @p192 :rule arith_poly_norm_rel :premises (@p191) :args (@t128)) % 153.39/153.62 (step @p193 :rule symm :premises (@p192)) % 153.39/153.62 (step @p200 :rule eq_resolve :premises (@p148 @p193)) % 153.39/153.62 (step @p184 :rule evaluate :args (@t126)) % 153.39/153.62 (step @p185 :rule true_elim :premises (@p184)) % 153.39/153.62 (step @p245 :rule and_intro :premises (@p185 @p200)) % 153.39/153.62 (step @p246 :rule modus_ponens :premises (@p245 @p244)) % 153.39/153.62 (step @p247 :rule arith_sum_ub :premises (@p246 @p105 @p243)) % 153.39/153.62 (step @p248 false :rule eq_resolve :premises (@p247 @p240)) % 153.39/153.62 (step-pop @p357 :rule scope :premises (@p248)) % 153.39/153.62 (step @p249 :rule process_scope :premises (@p357) :args (false)) % 153.39/153.62 (step @p191 :rule arith_poly_norm :args (@t127)) % 153.39/153.62 (step @p192 :rule arith_poly_norm_rel :premises (@p191) :args (@t128)) % 153.39/153.62 (step @p193 :rule symm :premises (@p192)) % 153.39/153.62 (step @p200 :rule eq_resolve :premises (@p148 @p193)) % 153.39/153.62 (step @p251 false :rule contra :premises (@p200 @p249)) % 153.39/153.62 (step-pop @p358 :rule scope :premises (@p251)) % 153.39/153.62 (step-pop @p359 :rule scope :premises (@p358)) % 153.39/153.62 (step-pop @p360 :rule scope :premises (@p359)) % 153.39/153.62 (step-pop @p361 :rule scope :premises (@p360)) % 153.39/153.62 (step @p252 :rule process_scope :premises (@p361) :args (false)) % 153.39/153.62 (assume-push @p362 @t96) % 153.39/153.62 (assume-push @p363 @t110) % 153.39/153.62 (assume-push @p364 @t131) % 153.39/153.62 (assume-push @p365 @t109) % 153.39/153.62 (step @p261 :rule and_intro :premises (@p364 @p365 @p105 @p148)) % 153.39/153.62 (step-pop @p366 :rule scope :premises (@p261)) % 153.39/153.62 (step-pop @p367 :rule scope :premises (@p366)) % 153.39/153.62 (step-pop @p368 :rule scope :premises (@p367)) % 153.39/153.62 (step-pop @p369 :rule scope :premises (@p368)) % 153.39/153.62 (step @p262 :rule process_scope :premises (@p369) :args (@t137)) % 153.39/153.62 (step @p267 :rule implies_elim :premises (@p262)) % 153.39/153.62 (step @p268 :rule resolution :premises (@p267 @p252) :args (true @t137)) % 153.39/153.62 (step @p269 :rule not_and :premises (@p268)) % 153.39/153.62 (step @p270 :rule eq_resolve :premises (@p269 @p221)) % 153.39/153.62 (step @p271 :rule reordering :premises (@p270) :args ((or @t130 @t112 @t111 @t113))) % 153.39/153.62 (step @p272 :rule chain_m_resolution :premises (@p271 @p148 @p105 @p218) :args (@t130 @t138 (@list @t96 @t110 @t109))) % 153.39/153.62 (assume-push @p370 @t130) % 153.39/153.62 (step @p274 :rule evaluate :args ((= 0/1 0/1))) % 153.39/153.62 (step @p275 :rule arith_poly_norm :args (@t139)) % 153.39/153.62 (step @p276 :rule cong :premises (@p275 @p71) :args (@t139)) % 153.39/153.62 (step @p277 :rule trans :premises (@p276 @p274)) % 153.39/153.62 (step @p278 :rule refl :args (@t65)) % 153.39/153.62 (step @p279 :rule nary_cong :premises (@p370 @p278) :args (@t67)) % 153.39/153.62 (step @p280 :rule cong :premises (@p279 @p71) :args (@t140)) % 153.39/153.62 (step @p281 :rule trans :premises (@p280 @p277)) % 153.39/153.62 (step @p282 :rule true_elim :premises (@p281)) % 153.39/153.62 (step-pop @p371 :rule scope :premises (@p282)) % 153.39/153.62 (step @p283 :rule process_scope :premises (@p371) :args (@t140)) % 153.39/153.62 (step @p285 :rule implies_elim :premises (@p283)) % 153.39/153.62 (step @p286 :rule reordering :premises (@p285) :args ((or @t140 @t131))) % 153.39/153.62 (step @p287 :rule chain_m_resolution :premises (@p286 @p272) :args (@t140 @t90 (@list @t130))) % 153.39/153.62 (assume-push @p372 @t68) % 153.39/153.62 (assume-push @p373 @t141) % 153.39/153.62 (assume-push @p374 @t140) % 153.39/153.62 (assume-push @p375 @t140) % 153.39/153.62 (step @p292 :rule evaluate :args ((<= 0/1 -1/1))) % 153.39/153.62 (step @p293 :rule evaluate :args ((+ 0/1 0/1 -1/1))) % 153.39/153.62 (step @p294 :rule evaluate :args (@t142)) % 153.39/153.62 (step @p295 :rule nary_cong :premises (@p71 @p71 @p294) :args (@t143)) % 153.39/153.62 (step @p296 :rule trans :premises (@p295 @p293)) % 153.39/153.62 (step @p297 :rule arith_poly_norm :args ((= (+ @t67 @t62 @t144) 0/1))) % 153.39/153.62 (step @p298 :rule arith_poly_norm :args ((= @t146 @t144))) % 153.39/153.62 (step @p299 :rule refl :args (@t62)) % 153.39/153.62 (step @p300 :rule refl :args (@t67)) % 153.39/153.62 (step @p301 :rule nary_cong :premises (@p300 @p299 @p298) :args (@t147)) % 153.39/153.62 (step @p302 :rule trans :premises (@p301 @p297)) % 153.39/153.62 (step @p303 :rule cong :premises (@p302 @p296) :args ((<= @t147 @t143))) % 153.39/153.62 (step @p304 :rule trans :premises (@p303 @p292)) % 153.39/153.62 (step @p305 :rule arith_mult_neg :args (-1/1 @t148)) % 153.39/153.62 (step @p306 :rule arith_poly_norm :args ((= (* -1/1 (- @t145 1/1)) (* -1/1 @t69)))) % 153.39/153.62 (step @p307 :rule arith_poly_norm_rel :premises (@p306) :args ((= @t148 @t68))) % 153.39/153.62 (step @p308 :rule symm :premises (@p307)) % 153.39/153.62 (step @p309 :rule eq_resolve :premises (@p103 @p308)) % 153.39/153.62 (step @p184 :rule evaluate :args (@t126)) % 153.39/153.62 (step @p185 :rule true_elim :premises (@p184)) % 153.39/153.62 (step @p310 :rule and_intro :premises (@p185 @p309)) % 153.39/153.62 (step @p311 :rule modus_ponens :premises (@p310 @p305)) % 153.39/153.62 (step @p312 :rule arith_sum_ub :premises (@p374 @p104 @p311)) % 153.39/153.62 (step @p313 false :rule eq_resolve :premises (@p312 @p304)) % 153.39/153.62 (step-pop @p376 :rule scope :premises (@p313)) % 153.39/153.62 (step @p314 :rule process_scope :premises (@p376) :args (false)) % 153.39/153.62 (step @p316 false :rule contra :premises (@p374 @p314)) % 153.39/153.62 (step-pop @p377 :rule scope :premises (@p316)) % 153.39/153.62 (step-pop @p378 :rule scope :premises (@p377)) % 153.39/153.62 (step-pop @p379 :rule scope :premises (@p378)) % 153.39/153.62 (step @p317 :rule process_scope :premises (@p379) :args (false)) % 153.39/153.62 (assume-push @p380 @t68) % 153.39/153.62 (assume-push @p381 @t140) % 153.39/153.62 (assume-push @p382 @t141) % 153.39/153.62 (step @p324 :rule and_intro :premises (@p103 @p104 @p381)) % 153.39/153.62 (step-pop @p383 :rule scope :premises (@p324)) % 153.39/153.62 (step-pop @p384 :rule scope :premises (@p383)) % 153.39/153.62 (step-pop @p385 :rule scope :premises (@p384)) % 153.39/153.62 (step @p325 :rule process_scope :premises (@p385) :args (@t149)) % 153.39/153.62 (step @p329 :rule implies_elim :premises (@p325)) % 153.39/153.62 (step @p330 :rule resolution :premises (@p329 @p317) :args (true @t149)) % 153.39/153.62 (step @p331 :rule not_and :premises (@p330)) % 153.39/153.62 (step @p332 :rule reordering :premises (@p331) :args ((or (not @t68) (not @t141) (not @t140)))) % 153.39/153.62 (step @p333 false :rule chain_m_resolution :premises (@p332 @p287 @p104 @p103) :args (false @t138 (@list @t140 @t141 @t68))) % 153.39/153.62 ) % 153.39/153.62 % SZS output end Proof % 153.39/153.62 % cvc5 exiting %------------------------------------------------------------------------------