%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI636_1 : TPTP v9.2.1. Released v6.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n027.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 08:08:02 AM UTC 2026 % Result : Theorem 45.38s 45.61s % Output : Proof 45.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI636_1 : TPTP v9.2.1. Released v6.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n027.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 02:30:36 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.49 %----Proving TF0_ARI % 45.38/45.61 --- Run --finite-model-find --decision=internal at 45... % 45.38/45.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 45.38/45.61 % SZS status Theorem % 45.38/45.61 % SZS output start Proof % 45.38/45.61 ( % 45.38/45.61 (declare-const tptp.x Real) % 45.38/45.61 (declare-const tptp.y Real) % 45.38/45.61 (declare-const tptp.u Real) % 45.38/45.61 (declare-const tptp.v Real) % 45.38/45.61 (declare-const tptp.f (-> Real Real)) % 45.38/45.61 (define @t1 () (@var "Y" Real)) % 45.38/45.61 (define @t2 () (tptp.f @t1)) % 45.38/45.61 (define @t3 () (@var "X" Real)) % 45.38/45.61 (define @t4 () (tptp.f @t3)) % 45.38/45.61 (define @t5 () (>= @t4 @t2)) % 45.38/45.61 (define @t6 () (>= @t3 @t1)) % 45.38/45.61 (define @t7 () (=> @t6 @t5)) % 45.38/45.61 (define @t8 () (@list @t3 @t1)) % 45.38/45.61 (define @t9 () (forall @t8 @t7)) % 45.38/45.61 (define @t10 () (> tptp.v 1/1)) % 45.38/45.61 (define @t11 () (tptp.f tptp.y)) % 45.38/45.61 (define @t12 () (* tptp.v tptp.v)) % 45.38/45.61 (define @t13 () (+ @t12 @t11)) % 45.38/45.61 (define @t14 () (tptp.f tptp.x)) % 45.38/45.61 (define @t15 () (+ @t14 tptp.u)) % 45.38/45.61 (define @t16 () (not (< @t15 @t13))) % 45.38/45.61 (define @t17 () (* -1/1 tptp.v)) % 45.38/45.61 (define @t18 () (+ tptp.u @t17)) % 45.38/45.61 (define @t19 () (>= @t18 0/1)) % 45.38/45.61 (define @t20 () (>= tptp.u tptp.v)) % 45.38/45.61 (define @t21 () (* tptp.v tptp.v)) % 45.38/45.61 (define @t22 () (* -1/1 @t21)) % 45.38/45.61 (define @t23 () (* -1/1 @t11)) % 45.38/45.61 (define @t24 () (+ tptp.u @t14 @t23 @t22)) % 45.38/45.61 (define @t25 () (>= @t24 0/1)) % 45.38/45.61 (define @t26 () (+ @t11 @t21)) % 45.38/45.61 (define @t27 () (+ tptp.u @t14)) % 45.38/45.61 (define @t28 () (>= @t15 @t13)) % 45.38/45.61 (define @t29 () (>= @t17 -1/1)) % 45.38/45.61 (define @t30 () (>= 1/1 tptp.v)) % 45.38/45.61 (define @t31 () (>= tptp.v 0/1)) % 45.38/45.61 (define @t32 () (not @t31)) % 45.38/45.61 (define @t33 () (not @t29)) % 45.38/45.61 (define @t34 () (not @t33)) % 45.38/45.61 (define @t35 () (< tptp.v 0/1)) % 45.38/45.61 (define @t36 () (not true)) % 45.38/45.61 (define @t37 () (>= 0/1 -1/1)) % 45.38/45.61 (define @t38 () (+ 0/1 -1/1)) % 45.38/45.61 (define @t39 () (* -1/1 1/1)) % 45.38/45.61 (define @t40 () (+ 0/1 @t39)) % 45.38/45.61 (define @t41 () (+ tptp.v @t17)) % 45.38/45.61 (define @t42 () (= @t41 0/1)) % 45.38/45.61 (define @t43 () (>= @t41 @t40)) % 45.38/45.61 (define @t44 () (not @t43)) % 45.38/45.61 (define @t45 () (< -1/1 0/1)) % 45.38/45.61 (define @t46 () (and @t32 @t33)) % 45.38/45.61 (define @t47 () (@list true)) % 45.38/45.61 (define @t48 () (@list @t29)) % 45.38/45.61 (define @t49 () (>= tptp.v -1/1)) % 45.38/45.61 (define @t50 () (not @t49)) % 45.38/45.61 (define @t51 () (ite @t31 @t33 @t50)) % 45.38/45.61 (define @t52 () (@list true false)) % 45.38/45.61 (define @t53 () (= tptp.v 0/1)) % 45.38/45.61 (define @t54 () (not @t53)) % 45.38/45.61 (define @t55 () (and @t53 @t33)) % 45.38/45.61 (define @t56 () (not @t51)) % 45.38/45.61 (define @t57 () (and @t51 @t54)) % 45.38/45.61 (define @t58 () (not @t54)) % 45.38/45.61 (define @t59 () (+ @t17 @t21)) % 45.38/45.61 (define @t60 () (* -1/1 (- @t59 0/1))) % 45.38/45.61 (define @t61 () (>= @t59 0/1)) % 45.38/45.61 (define @t62 () (- tptp.v)) % 45.38/45.61 (define @t63 () (- @t21)) % 45.38/45.61 (define @t64 () (<= @t63 @t62)) % 45.38/45.61 (define @t65 () (+ tptp.v @t21)) % 45.38/45.61 (define @t66 () (>= @t65 0/1)) % 45.38/45.61 (define @t67 () (<= @t63 tptp.v)) % 45.38/45.61 (define @t68 () (ite @t31 (> @t63 tptp.v) (> @t63 @t62))) % 45.38/45.61 (define @t69 () (+ @t17 @t22)) % 45.38/45.61 (define @t70 () (>= @t69 0/1)) % 45.38/45.61 (define @t71 () (<= @t21 @t62)) % 45.38/45.61 (define @t72 () (+ tptp.v @t22)) % 45.38/45.61 (define @t73 () (>= @t72 0/1)) % 45.38/45.61 (define @t74 () (>= tptp.v @t21)) % 45.38/45.61 (define @t75 () (ite @t31 (> @t21 tptp.v) (> @t21 @t62))) % 45.38/45.61 (define @t76 () (>= @t21 0/1)) % 45.38/45.61 (define @t77 () (ite @t76 @t75 @t68)) % 45.38/45.61 (define @t78 () (>= tptp.v 1/1)) % 45.38/45.61 (define @t79 () (- 1/1)) % 45.38/45.61 (define @t80 () (<= @t62 @t79)) % 45.38/45.61 (define @t81 () (<= @t62 1/1)) % 45.38/45.61 (define @t82 () (>= 1/1 0/1)) % 45.38/45.61 (define @t83 () (ite @t82 (> @t62 1/1) (> @t62 @t79))) % 45.38/45.61 (define @t84 () (>= @t17 1/1)) % 45.38/45.61 (define @t85 () (<= tptp.v @t79)) % 45.38/45.61 (define @t86 () (ite @t82 @t10 (> tptp.v @t79))) % 45.38/45.61 (define @t87 () (ite @t31 @t86 @t83)) % 45.38/45.61 (define @t88 () (and @t87 @t54)) % 45.38/45.61 (define @t89 () (abs @t21)) % 45.38/45.61 (define @t90 () (abs tptp.v)) % 45.38/45.61 (define @t91 () (+ @t90 (* -1/1 @t89))) % 45.38/45.61 (define @t92 () (>= @t90 @t89)) % 45.38/45.61 (define @t93 () (* 1/1 tptp.v)) % 45.38/45.61 (define @t94 () (abs @t93)) % 45.38/45.61 (define @t95 () (<= @t89 @t94)) % 45.38/45.61 (define @t96 () (not @t61)) % 45.38/45.61 (define @t97 () (not @t73)) % 45.38/45.61 (define @t98 () (ite @t31 @t97 (not @t70))) % 45.38/45.61 (define @t99 () (ite @t76 @t98 (ite @t31 (not @t66) @t96))) % 45.38/45.61 (define @t100 () (@list false)) % 45.38/45.61 (define @t101 () (>= @t22 0/1)) % 45.38/45.61 (define @t102 () (not @t101)) % 45.38/45.61 (define @t103 () (>= 0/1 @t21)) % 45.38/45.61 (define @t104 () (> @t21 0/1)) % 45.38/45.61 (define @t105 () (< @t21 0/1)) % 45.38/45.61 (define @t106 () (>= 0/1 0/1)) % 45.38/45.61 (define @t107 () (+ 0/1 0/1)) % 45.38/45.61 (define @t108 () (* -1/1 0/1)) % 45.38/45.61 (define @t109 () (+ 0/1 @t108)) % 45.38/45.61 (define @t110 () (+ @t21 @t22)) % 45.38/45.61 (define @t111 () (>= @t110 @t109)) % 45.38/45.61 (define @t112 () (@list false false)) % 45.38/45.61 (define @t113 () (= (* -1/1 (- 0/1 @t72)) @t60)) % 45.38/45.61 (define @t114 () (>= 0/1 @t72)) % 45.38/45.61 (define @t115 () (= @t114 @t61)) % 45.38/45.61 (define @t116 () (> @t72 0/1)) % 45.38/45.61 (define @t117 () (+ @t108 0/1)) % 45.38/45.61 (define @t118 () (* 0/1 tptp.v)) % 45.38/45.61 (define @t119 () (* 0/1 @t21)) % 45.38/45.61 (define @t120 () (= @t119 0/1)) % 45.38/45.61 (define @t121 () (+ @t119 @t118)) % 45.38/45.61 (define @t122 () (+ (* -1/1 @t72) @t72)) % 45.38/45.61 (define @t123 () (>= @t122 @t117)) % 45.38/45.61 (define @t124 () (+ @t3 (* -1/1 @t1))) % 45.38/45.61 (define @t125 () (>= @t124 0/1)) % 45.38/45.61 (define @t126 () (+ @t4 (* -1/1 @t2))) % 45.38/45.61 (define @t127 () (>= @t126 0/1)) % 45.38/45.61 (define @t128 () (* -1/1 @t14)) % 45.38/45.61 (define @t129 () (+ @t128 @t11)) % 45.38/45.61 (define @t130 () (+ @t11 @t128)) % 45.38/45.61 (define @t131 () (>= @t130 0/1)) % 45.38/45.61 (define @t132 () (* -1/1 tptp.x)) % 45.38/45.61 (define @t133 () (+ @t132 tptp.y)) % 45.38/45.61 (define @t134 () (+ tptp.y @t132)) % 45.38/45.61 (define @t135 () (>= @t134 0/1)) % 45.38/45.61 (define @t136 () (not @t135)) % 45.38/45.61 (define @t137 () (or @t136 @t131)) % 45.38/45.61 (define @t138 () (forall @t8 (or (not @t125) @t127))) % 45.38/45.61 (define @t139 () (>= @t129 0/1)) % 45.38/45.61 (define @t140 () (>= @t133 0/1)) % 45.38/45.61 (define @t141 () (not @t140)) % 45.38/45.61 (define @t142 () (or @t141 @t139)) % 45.38/45.61 (define @t143 () (@list @t140 @t142)) % 45.38/45.61 (define @t144 () (not @t139)) % 45.38/45.61 (define @t145 () (not @t25)) % 45.38/45.61 (define @t146 () (not @t19)) % 45.38/45.61 (define @t147 () (+ @t14 @t23)) % 45.38/45.61 (define @t148 () (>= 0/1 @t147)) % 45.38/45.61 (define @t149 () (<= @t147 0/1)) % 45.38/45.61 (define @t150 () (+ 0/1 @t108 0/1 0/1)) % 45.38/45.61 (define @t151 () (* 0/1 tptp.u)) % 45.38/45.61 (define @t152 () (* 0/1 @t14)) % 45.38/45.61 (define @t153 () (* 0/1 @t11)) % 45.38/45.61 (define @t154 () (+ @t119 @t153 @t17 @t152 tptp.v @t151)) % 45.38/45.61 (define @t155 () (+ @t147 (* -1/1 @t24) @t18 @t72)) % 45.38/45.61 (define @t156 () (>= @t155 @t150)) % 45.38/45.61 (define @t157 () (and @t61 @t146 @t25 @t139)) % 45.38/45.61 (assume @p1 @t9) % 45.38/45.61 (assume @p2 (< tptp.u tptp.v)) % 45.38/45.61 (assume @p3 @t10) % 45.38/45.61 (assume @p4 (<= tptp.x tptp.y)) % 45.38/45.61 (assume @p5 @t16) % 45.38/45.61 (assume @p6 true) % 45.38/45.61 (step @p7 :rule arith_poly_norm :args ((= (* 1/1 (- tptp.u tptp.v)) (* 1/1 (- @t18 0/1))))) % 45.38/45.61 (step @p8 :rule arith_poly_norm_rel :premises (@p7) :args ((= @t20 @t19))) % 45.38/45.61 (step @p9 :rule cong :premises (@p8) :args ((not @t20))) % 45.38/45.61 (step @p10 :rule arith-elim-lt :args (tptp.u tptp.v)) % 45.38/45.61 (step @p11 :rule trans :premises (@p10 @p9)) % 45.38/45.61 (step @p12 :rule eq_resolve :premises (@p2 @p11)) % 45.38/45.61 (step @p13 :rule bool-double-not-elim :args (@t25)) % 45.38/45.61 (step @p14 :rule arith_poly_norm :args ((= (* 1/1 (- @t27 @t26)) (* 1/1 (- @t24 0/1))))) % 45.38/45.61 (step @p15 :rule arith_poly_norm_rel :premises (@p14) :args ((= (>= @t27 @t26) @t25))) % 45.38/45.61 (step @p16 :rule arith_poly_norm :args ((= (+ @t21 @t11) @t26))) % 45.38/45.61 (step @p17 :rule refl :args (@t11)) % 45.38/45.61 (step @p18 :rule arith_poly_norm :args ((= @t12 @t21))) % 45.38/45.61 (step @p19 :rule nary_cong :premises (@p18 @p17) :args (@t13)) % 45.38/45.61 (step @p20 :rule trans :premises (@p19 @p16)) % 45.38/45.61 (step @p21 :rule arith_poly_norm :args ((= @t15 @t27))) % 45.38/45.61 (step @p22 :rule cong :premises (@p21 @p20) :args (@t28)) % 45.38/45.61 (step @p23 :rule trans :premises (@p22 @p15)) % 45.38/45.61 (step @p24 :rule cong :premises (@p23) :args ((not @t28))) % 45.38/45.61 (step @p25 :rule arith-elim-lt :args (@t15 @t13)) % 45.38/45.61 (step @p26 :rule trans :premises (@p25 @p24)) % 45.38/45.61 (step @p27 :rule cong :premises (@p26) :args (@t16)) % 45.38/45.61 (step @p28 :rule trans :premises (@p27 @p13)) % 45.38/45.61 (step @p29 :rule eq_resolve :premises (@p5 @p28)) % 45.38/45.61 (step @p30 :rule arith_poly_norm :args ((= (* 1/1 (- 1/1 tptp.v)) (* 1/1 (- @t17 -1/1))))) % 45.38/45.61 (step @p31 :rule arith_poly_norm_rel :premises (@p30) :args ((= @t30 @t29))) % 45.38/45.61 (step @p32 :rule arith-elim-leq :args (tptp.v 1/1)) % 45.38/45.61 (step @p33 :rule trans :premises (@p32 @p31)) % 45.38/45.61 (step @p34 :rule cong :premises (@p33) :args ((not (<= tptp.v 1/1)))) % 45.38/45.61 (step @p35 :rule symm :premises (@p32)) % 45.38/45.61 (step @p36 :rule cong :premises (@p35) :args ((not @t30))) % 45.38/45.61 (step @p37 :rule arith-elim-gt :args (tptp.v 1/1)) % 45.38/45.61 (step @p38 :rule trans :premises (@p37 @p36)) % 45.38/45.61 (step @p39 :rule trans :premises (@p38 @p34)) % 45.38/45.61 (step @p40 :rule eq_resolve :premises (@p3 @p39)) % 45.38/45.61 (step @p41 :rule bool-double-not-elim :args (@t31)) % 45.38/45.61 (step @p42 :rule bool-double-not-elim :args (@t29)) % 45.38/45.61 (step @p43 :rule nary_cong :premises (@p42 @p41) :args ((or @t34 (not @t32)))) % 45.38/45.61 (assume-push @p513 @t32) % 45.38/45.61 (assume-push @p514 @t33) % 45.38/45.61 (step @p46 :rule arith-elim-lt :args (tptp.v 0/1)) % 45.38/45.61 (step @p47 :rule symm :premises (@p46)) % 45.38/45.61 (step @p48 :rule eq_resolve :premises (@p513 @p47)) % 45.38/45.61 (step @p49 :rule eq_resolve :premises (@p48 @p46)) % 45.38/45.61 (step @p50 :rule cong :premises (@p46) :args ((not @t35))) % 45.38/45.61 (step @p51 :rule trans :premises (@p50 @p41)) % 45.38/45.61 (assume-push @p515 @t35) % 45.38/45.61 (step @p53 :rule evaluate :args (@t36)) % 45.38/45.61 (step @p54 :rule evaluate :args (@t37)) % 45.38/45.61 (step @p55 :rule evaluate :args (@t38)) % 45.38/45.61 (step @p56 :rule evaluate :args (@t39)) % 45.38/45.61 (step @p57 :rule refl :args (0/1)) % 45.38/45.61 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t40)) % 45.38/45.61 (step @p59 :rule trans :premises (@p58 @p55)) % 45.38/45.61 (step @p60 :rule arith_poly_norm :args (@t42)) % 45.38/45.61 (step @p61 :rule cong :premises (@p60 @p59) :args (@t43)) % 45.38/45.61 (step @p62 :rule trans :premises (@p61 @p54)) % 45.38/45.61 (step @p63 :rule cong :premises (@p62) :args (@t44)) % 45.38/45.61 (step @p64 :rule trans :premises (@p63 @p53)) % 45.38/45.61 (step @p65 :rule arith-elim-lt :args (@t41 @t40)) % 45.38/45.61 (step @p66 :rule trans :premises (@p65 @p64)) % 45.38/45.61 (step @p67 :rule arith_mult_neg :args (-1/1 @t10)) % 45.38/45.61 (step @p68 :rule evaluate :args (@t45)) % 45.38/45.61 (step @p69 :rule true_elim :premises (@p68)) % 45.38/45.61 (step @p70 :rule and_intro :premises (@p69 @p3)) % 45.38/45.61 (step @p71 :rule modus_ponens :premises (@p70 @p67)) % 45.38/45.61 (step @p72 :rule arith_sum_ub :premises (@p515 @p71)) % 45.38/45.61 (step @p73 false :rule eq_resolve :premises (@p72 @p66)) % 45.38/45.61 (step-pop @p516 :rule scope :premises (@p73)) % 45.38/45.61 (step @p74 :rule process_scope :premises (@p516) :args (false)) % 45.38/45.61 (step @p76 :rule eq_resolve :premises (@p74 @p51)) % 45.38/45.61 (step @p77 false :rule contra :premises (@p76 @p49)) % 45.38/45.61 (step-pop @p517 :rule scope :premises (@p77)) % 45.38/45.61 (step-pop @p518 :rule scope :premises (@p517)) % 45.38/45.61 (step @p78 :rule process_scope :premises (@p518) :args (false)) % 45.38/45.61 (assume-push @p519 @t33) % 45.38/45.61 (assume-push @p520 @t32) % 45.38/45.61 (step @p83 :rule and_intro :premises (@p520 @p40)) % 45.38/45.61 (step-pop @p521 :rule scope :premises (@p83)) % 45.38/45.61 (step-pop @p522 :rule scope :premises (@p521)) % 45.38/45.61 (step @p84 :rule process_scope :premises (@p522) :args (@t46)) % 45.38/45.61 (step @p87 :rule implies_elim :premises (@p84)) % 45.38/45.61 (step @p88 :rule resolution :premises (@p87 @p78) :args (true @t46)) % 45.38/45.61 (step @p89 :rule not_and :premises (@p88)) % 45.38/45.61 (step @p90 :rule eq_resolve :premises (@p89 @p43)) % 45.38/45.61 (step @p91 :rule chain_m_resolution :premises (@p90 @p40) :args (@t31 @t47 @t48)) % 45.38/45.61 (step @p92 :rule refl :args (@t32)) % 45.38/45.61 (step @p93 :rule refl :args (@t51)) % 45.38/45.61 (step @p94 :rule nary_cong :premises (@p93 @p92 @p42) :args ((or @t51 @t32 @t34))) % 45.38/45.61 (step @p95 :rule cnf_ite_neg1 :args (@t51)) % 45.38/45.61 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 45.38/45.61 (step @p97 :rule reordering :premises (@p96) :args ((or @t29 @t51 @t32))) % 45.38/45.61 (step @p98 :rule chain_m_resolution :premises (@p97 @p40 @p91) :args (@t51 @t52 (@list @t29 @t31))) % 45.38/45.61 (step @p99 :rule refl :args (@t54)) % 45.38/45.61 (step @p100 :rule nary_cong :premises (@p42 @p99) :args ((or @t34 @t54))) % 45.38/45.61 (assume-push @p523 @t53) % 45.38/45.61 (assume-push @p524 @t33) % 45.38/45.61 (assume-push @p525 @t53) % 45.38/45.61 (step @p53 :rule evaluate :args (@t36)) % 45.38/45.61 (step @p54 :rule evaluate :args (@t37)) % 45.38/45.61 (step @p55 :rule evaluate :args (@t38)) % 45.38/45.61 (step @p56 :rule evaluate :args (@t39)) % 45.38/45.61 (step @p57 :rule refl :args (0/1)) % 45.38/45.61 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t40)) % 45.38/45.61 (step @p59 :rule trans :premises (@p58 @p55)) % 45.38/45.61 (step @p60 :rule arith_poly_norm :args (@t42)) % 45.38/45.61 (step @p61 :rule cong :premises (@p60 @p59) :args (@t43)) % 45.38/45.61 (step @p62 :rule trans :premises (@p61 @p54)) % 45.38/45.61 (step @p63 :rule cong :premises (@p62) :args (@t44)) % 45.38/45.61 (step @p64 :rule trans :premises (@p63 @p53)) % 45.38/45.61 (step @p65 :rule arith-elim-lt :args (@t41 @t40)) % 45.38/45.61 (step @p66 :rule trans :premises (@p65 @p64)) % 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(step @p338 :rule chain_m_resolution :premises (@p337 @p298) :args (@t76 @t47 (@list @t101))) % 45.38/45.61 (step @p339 :rule cnf_ite_pos1 :args (@t99)) % 45.38/45.61 (step @p340 :rule reordering :premises (@p339) :args ((or (not @t76) @t98 (not @t99)))) % 45.38/45.61 (step @p341 :rule chain_m_resolution :premises (@p340 @p338 @p280) :args (@t98 @t112 (@list @t76 @t99))) % 45.38/45.61 (step @p342 :rule cnf_ite_pos1 :args (@t98)) % 45.38/45.61 (step @p343 :rule reordering :premises (@p342) :args ((or @t32 @t97 (not @t98)))) % 45.38/45.61 (step @p344 :rule chain_m_resolution :premises (@p343 @p91 @p341) :args (@t97 @t112 (@list @t31 @t98))) % 45.38/45.61 (step @p345 :rule refl :args (@t61)) % 45.38/45.61 (step @p346 :rule bool-double-not-elim :args (@t73)) % 45.38/45.61 (step @p347 :rule nary_cong :premises (@p346 @p345) :args ((or (not @t97) @t61))) % 45.38/45.61 (assume-push @p543 @t97) % 45.38/45.61 (assume-push @p544 @t97) % 45.38/45.61 (step @p350 :rule arith_poly_norm :args (@t113)) % 45.38/45.61 (step @p351 :rule arith_poly_norm_rel :premises (@p350) :args (@t115)) % 45.38/45.61 (step @p352 :rule arith-elim-leq :args (@t72 0/1)) % 45.38/45.61 (step @p353 :rule trans :premises (@p352 @p351)) % 45.38/45.61 (step @p354 :rule symm :premises (@p353)) % 45.38/45.61 (step @p355 :rule bool-double-not-elim :args (@t61)) % 45.38/45.61 (step @p356 :rule cong :premises (@p353) :args ((not (<= @t72 0/1)))) % 45.38/45.61 (step @p357 :rule symm :premises (@p352)) % 45.38/45.61 (step @p358 :rule cong :premises (@p357) :args ((not @t114))) % 45.38/45.61 (step @p359 :rule arith-elim-gt :args (@t72 0/1)) % 45.38/45.61 (step @p360 :rule trans :premises (@p359 @p358)) % 45.38/45.61 (step @p361 :rule trans :premises (@p360 @p356)) % 45.38/45.61 (step @p362 :rule cong :premises (@p361) :args ((not @t116))) % 45.38/45.61 (step @p363 :rule trans :premises (@p362 @p355)) % 45.38/45.61 (step @p364 :rule trans :premises (@p363 @p354)) % 45.38/45.61 (assume-push @p545 @t116) % 45.38/45.61 (step @p53 :rule evaluate :args (@t36)) % 45.38/45.61 (step @p309 :rule evaluate :args (@t106)) % 45.38/45.61 (step @p310 :rule evaluate :args (@t107)) % 45.38/45.61 (step @p57 :rule refl :args (0/1)) % 45.38/45.61 (step @p311 :rule evaluate :args (@t108)) % 45.38/45.61 (step @p366 :rule nary_cong :premises (@p311 @p57) :args (@t117)) % 45.38/45.61 (step @p367 :rule trans :premises (@p366 @p310)) % 45.38/45.61 (step @p368 :rule arith_poly_norm :args ((= @t118 0/1))) % 45.38/45.61 (step @p369 :rule arith_poly_norm :args (@t120)) % 45.38/45.61 (step @p370 :rule nary_cong :premises (@p369 @p368) :args (@t121)) % 45.38/45.61 (step @p371 :rule trans :premises (@p370 @p310)) % 45.38/45.61 (step @p372 :rule arith_poly_norm :args ((= @t122 @t121))) % 45.38/45.61 (step @p373 :rule trans :premises (@p372 @p371)) % 45.38/45.61 (step @p374 :rule cong :premises (@p373 @p367) :args (@t123)) % 45.38/45.61 (step @p375 :rule trans :premises (@p374 @p309)) % 45.38/45.61 (step @p376 :rule 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(@p546) :args (false)) % 45.38/45.61 (step @p390 :rule eq_resolve :premises (@p388 @p364)) % 45.38/45.61 (step @p391 :rule eq_resolve :premises (@p390 @p353)) % 45.38/45.61 (step-pop @p547 :rule scope :premises (@p391)) % 45.38/45.61 (step @p392 :rule process_scope :premises (@p547) :args (@t61)) % 45.38/45.61 (step @p394 :rule modus_ponens :premises (@p543 @p392)) % 45.38/45.61 (step-pop @p548 :rule scope :premises (@p394)) % 45.38/45.61 (step @p395 :rule process_scope :premises (@p548) :args (@t61)) % 45.38/45.61 (step @p397 :rule implies_elim :premises (@p395)) % 45.38/45.61 (step @p398 :rule eq_resolve :premises (@p397 @p347)) % 45.38/45.61 (step @p399 :rule chain_m_resolution :premises (@p398 @p344) :args (@t61 @t47 (@list @t73))) % 45.38/45.61 (step @p400 :rule bool-impl-elim :args (@t125 @t127)) % 45.38/45.61 (step @p401 :rule cong :premises (@p400) :args ((forall @t8 (=> @t125 @t127)))) % 45.38/45.61 (step @p402 :rule arith_poly_norm :args ((= (* 1/1 (- @t4 @t2)) (* 1/1 (- @t126 0/1))))) % 45.38/45.61 (step @p403 :rule arith_poly_norm_rel :premises (@p402) :args ((= @t5 @t127))) % 45.38/45.61 (step @p404 :rule arith_poly_norm :args ((= (* 1/1 (- @t3 @t1)) (* 1/1 (- @t124 0/1))))) % 45.38/45.61 (step @p405 :rule arith_poly_norm_rel :premises (@p404) :args ((= @t6 @t125))) % 45.38/45.61 (step @p406 :rule cong :premises (@p405 @p403) :args (@t7)) % 45.38/45.61 (step @p407 :rule cong :premises (@p406) :args (@t9)) % 45.38/45.61 (step @p408 :rule trans :premises (@p407 @p401)) % 45.38/45.61 (step @p409 :rule eq_resolve :premises (@p1 @p408)) % 45.38/45.61 (step @p410 :rule refl :args (0/1)) % 45.38/45.61 (step @p411 :rule arith_poly_norm :args ((= @t130 @t129))) % 45.38/45.61 (step @p412 :rule cong :premises (@p411 @p410) :args (@t131)) % 45.38/45.61 (step @p413 :rule refl :args (0/1)) % 45.38/45.61 (step @p414 :rule arith_poly_norm :args ((= @t134 @t133))) % 45.38/45.61 (step @p415 :rule cong :premises (@p414 @p413) :args (@t135)) % 45.38/45.61 (step @p416 :rule cong :premises (@p415) :args (@t136)) % 45.38/45.61 (step @p417 :rule nary_cong :premises (@p416 @p412) :args (@t137)) % 45.38/45.61 (step @p418 :rule refl :args (@t138)) % 45.38/45.61 (step @p419 :rule cong :premises (@p418 @p417) :args ((=> @t138 @t137))) % 45.38/45.61 (assume-push @p549 @t138) % 45.38/45.61 (step @p421 :rule instantiate :premises (@p409) :args ((@list tptp.y tptp.x))) % 45.38/45.61 (step-pop @p550 :rule scope :premises (@p421)) % 45.38/45.61 (step @p422 :rule process_scope :premises (@p550) :args (@t137)) % 45.38/45.61 (step @p424 :rule eq_resolve :premises (@p422 @p419)) % 45.38/45.61 (step @p425 :rule implies_elim :premises (@p424)) % 45.38/45.61 (step @p426 :rule chain_m_resolution :premises (@p425 @p409) :args (@t142 @t100 (@list @t138))) % 45.38/45.61 (step @p427 :rule arith_poly_norm :args ((= (* -1/1 (- tptp.y tptp.x)) (* -1/1 (- @t133 0/1))))) % 45.38/45.61 (step @p428 :rule arith_poly_norm_rel :premises (@p427) :args ((= (>= tptp.y tptp.x) @t140))) % 45.38/45.61 (step @p429 :rule arith-elim-leq :args (tptp.x tptp.y)) % 45.38/45.61 (step @p430 :rule trans :premises (@p429 @p428)) % 45.38/45.61 (step @p431 :rule eq_resolve :premises (@p4 @p430)) % 45.38/45.61 (step @p432 :rule cnf_or_pos :args (@t142)) % 45.38/45.61 (step @p433 :rule reordering :premises (@p432) :args ((or @t141 @t139 (not @t142)))) % 45.38/45.61 (step @p434 :rule chain_m_resolution :premises (@p433 @p431 @p426) :args (@t139 @t112 @t143)) % 45.38/45.61 (step @p435 :rule refl :args (@t144)) % 45.38/45.61 (step @p436 :rule refl :args (@t96)) % 45.38/45.61 (step @p437 :rule refl :args (@t145)) % 45.38/45.61 (step @p438 :rule bool-double-not-elim :args (@t19)) % 45.38/45.61 (step @p439 :rule nary_cong :premises (@p438 @p437 @p436 @p435) :args ((or (not @t146) @t145 @t96 @t144))) % 45.38/45.61 (assume-push @p551 @t61) % 45.38/45.61 (assume-push @p552 @t146) % 45.38/45.61 (assume-push @p553 @t25) % 45.38/45.61 (assume-push @p554 @t139) % 45.38/45.61 (step @p444 :rule arith-elim-leq :args (@t147 0/1)) % 45.38/45.61 (step @p445 :rule symm :premises (@p444)) % 45.38/45.61 (step @p446 :rule cong :premises (@p445) :args ((not @t148))) % 45.38/45.61 (step @p447 :rule arith-elim-gt :args (@t147 0/1)) % 45.38/45.61 (step @p448 :rule trans :premises (@p447 @p446)) % 45.38/45.61 (step @p449 :rule arith_poly_norm :args ((= (* -1/1 (- 0/1 @t147)) (* -1/1 (- @t129 0/1))))) % 45.38/45.61 (step @p450 :rule arith_poly_norm_rel :premises (@p449) :args ((= @t148 @t139))) % 45.38/45.61 (step @p451 :rule trans :premises (@p444 @p450)) % 45.38/45.61 (step @p452 :rule cong :premises (@p451) :args ((not @t149))) % 45.38/45.61 (step @p453 :rule trans :premises (@p448 @p452)) % 45.38/45.61 (step @p454 :rule symm :premises (@p453)) % 45.38/45.61 (step @p455 :rule trans :premises (@p452 @p454)) % 45.38/45.61 (assume-push @p555 @t149) % 45.38/45.61 (step @p53 :rule evaluate :args (@t36)) % 45.38/45.61 (step @p309 :rule evaluate :args (@t106)) % 45.38/45.61 (step @p457 :rule evaluate :args ((+ 0/1 0/1 0/1 0/1))) % 45.38/45.61 (step @p57 :rule refl :args (0/1)) % 45.38/45.61 (step @p311 :rule evaluate :args (@t108)) % 45.38/45.61 (step @p458 :rule nary_cong :premises (@p57 @p311 @p57 @p57) :args (@t150)) % 45.38/45.61 (step @p459 :rule trans :premises (@p458 @p457)) % 45.38/45.61 (step @p460 :rule arith_poly_norm :args ((= (+ 0/1 0/1 @t17 0/1 tptp.v 0/1) 0/1))) % 45.38/45.61 (step @p461 :rule arith_poly_norm :args ((= @t151 0/1))) % 45.38/45.61 (step @p462 :rule arith_poly_norm :args ((= @t152 0/1))) % 45.38/45.61 (step @p463 :rule refl :args (@t17)) % 45.38/45.61 (step @p464 :rule arith_poly_norm :args ((= @t153 0/1))) % 45.38/45.61 (step @p369 :rule arith_poly_norm :args (@t120)) % 45.38/45.61 (step @p465 :rule nary_cong :premises (@p369 @p464 @p463 @p462 @p150 @p461) :args (@t154)) % 45.38/45.61 (step @p466 :rule trans :premises (@p465 @p460)) % 45.38/45.61 (step @p467 :rule arith_poly_norm :args ((= @t155 @t154))) % 45.38/45.61 (step @p468 :rule trans :premises (@p467 @p466)) % 45.38/45.61 (step @p469 :rule cong :premises (@p468 @p459) :args (@t156)) % 45.38/45.61 (step @p470 :rule trans :premises (@p469 @p309)) % 45.38/45.61 (step @p471 :rule cong :premises (@p470) :args ((not @t156))) % 45.38/45.61 (step @p472 :rule trans :premises (@p471 @p53)) % 45.38/45.61 (step @p473 :rule arith-elim-lt :args (@t155 @t150)) % 45.38/45.61 (step @p474 :rule trans :premises (@p473 @p472)) % 45.38/45.61 (step @p350 :rule arith_poly_norm :args (@t113)) % 45.38/45.61 (step @p351 :rule arith_poly_norm_rel :premises (@p350) :args (@t115)) % 45.38/45.61 (step @p352 :rule arith-elim-leq :args (@t72 0/1)) % 45.38/45.61 (step @p353 :rule trans :premises (@p352 @p351)) % 45.38/45.61 (step @p354 :rule symm :premises (@p353)) % 45.38/45.61 (step @p475 :rule eq_resolve :premises (@p551 @p354)) % 45.38/45.61 (step @p476 :rule arith-elim-lt :args (@t18 0/1)) % 45.38/45.61 (step @p477 :rule symm :premises (@p476)) % 45.38/45.61 (step @p478 :rule eq_resolve :premises (@p12 @p477)) % 45.38/45.61 (step @p479 :rule arith_mult_neg :args (-1/1 @t25)) % 45.38/45.61 (step @p68 :rule evaluate :args (@t45)) % 45.38/45.61 (step @p69 :rule true_elim :premises (@p68)) % 45.38/45.61 (step @p480 :rule and_intro :premises (@p69 @p29)) % 45.38/45.61 (step @p481 :rule modus_ponens :premises (@p480 @p479)) % 45.38/45.61 (step @p482 :rule symm :premises (@p451)) % 45.38/45.61 (step @p483 :rule chain_m_resolution :premises (@p433 @p431 @p426) :args (@t139 @t112 @t143)) % 45.38/45.61 (step @p484 :rule eq_resolve :premises (@p483 @p482)) % 45.38/45.61 (step @p485 :rule arith_sum_ub :premises (@p484 @p481 @p478 @p475)) % 45.38/45.61 (step @p486 false :rule eq_resolve :premises (@p485 @p474)) % 45.38/45.61 (step-pop @p556 :rule scope :premises (@p486)) % 45.38/45.61 (step @p487 :rule process_scope :premises (@p556) :args (false)) % 45.38/45.61 (step @p489 :rule eq_resolve :premises (@p487 @p455)) % 45.38/45.61 (step @p490 :rule eq_resolve :premises (@p489 @p448)) % 45.38/45.61 (step @p482 :rule symm :premises (@p451)) % 45.38/45.61 (step @p491 :rule eq_resolve :premises (@p434 @p482)) % 45.38/45.61 (step @p492 false :rule contra :premises (@p491 @p490)) % 45.38/45.61 (step-pop @p557 :rule scope :premises (@p492)) % 45.38/45.61 (step-pop @p558 :rule scope :premises (@p557)) % 45.38/45.61 (step-pop @p559 :rule scope :premises (@p558)) % 45.38/45.61 (step-pop @p560 :rule scope :premises (@p559)) % 45.38/45.61 (step @p493 :rule process_scope :premises (@p560) :args (false)) % 45.38/45.61 (assume-push @p561 @t146) % 45.38/45.61 (assume-push @p562 @t25) % 45.38/45.61 (assume-push @p563 @t61) % 45.38/45.61 (assume-push @p564 @t139) % 45.38/45.61 (step @p502 :rule and_intro :premises (@p563 @p12 @p29 @p434)) % 45.38/45.61 (step-pop @p565 :rule scope :premises (@p502)) % 45.38/45.61 (step-pop @p566 :rule scope :premises (@p565)) % 45.38/45.61 (step-pop @p567 :rule scope :premises (@p566)) % 45.38/45.61 (step-pop @p568 :rule scope :premises (@p567)) % 45.38/45.61 (step @p503 :rule process_scope :premises (@p568) :args (@t157)) % 45.38/45.61 (step @p508 :rule implies_elim :premises (@p503)) % 45.38/45.61 (step @p509 :rule resolution :premises (@p508 @p493) :args (true @t157)) % 45.38/45.61 (step @p510 :rule not_and :premises (@p509)) % 45.38/45.61 (step @p511 :rule eq_resolve :premises (@p510 @p439)) % 45.38/45.61 (step @p512 false :rule chain_m_resolution :premises (@p511 @p434 @p399 @p29 @p12) :args (false (@list false false false true) (@list @t139 @t61 @t25 @t19))) % 45.38/45.61 ) % 45.38/45.61 % SZS output end Proof % 45.38/45.61 % cvc5 exiting %------------------------------------------------------------------------------