%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX102_1 : TPTP v9.2.1. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:07:08 AM UTC 2026 % Result : Theorem 0.38s 0.62s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX102_1 : TPTP v9.2.1. Released v9.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n011.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 22:56:05 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.51 %----Proving TF0_ARI % 0.38/0.62 --- Run --finite-model-find --decision=internal at 45... % 0.38/0.62 % SZS status Theorem % 0.38/0.62 % SZS output start Proof % 0.38/0.62 ( % 0.38/0.62 (declare-sort tptp.symbol 0) % 0.38/0.62 (declare-sort tptp.general 0) % 0.38/0.62 (declare-const tptp.composite_p (-> tptp.general Bool)) % 0.38/0.62 (declare-const tptp.f__integer__ (-> Int tptp.general)) % 0.38/0.62 (declare-const tptp.f__symbolic__ (-> tptp.symbol tptp.general)) % 0.38/0.62 (declare-const tptp.sqrtb (-> tptp.general Bool)) % 0.38/0.62 (declare-const tptp.p__is_symbolic__ (-> tptp.general Bool)) % 0.38/0.62 (declare-const tptp.c__supremum__ tptp.general) % 0.38/0.62 (declare-const tptp.c__infimum__ tptp.general) % 0.38/0.62 (declare-const tptp.p__is_integer__ (-> tptp.general Bool)) % 0.38/0.62 (declare-const tptp.composite (-> tptp.general Bool)) % 0.38/0.62 (declare-const tptp.prime (-> tptp.general Bool)) % 0.38/0.62 (declare-const tptp.p__less_equal__ (-> tptp.general tptp.general Bool)) % 0.38/0.62 (declare-const tptp.sqrt (-> tptp.general tptp.general Bool)) % 0.38/0.62 (declare-const tptp.p__less__ (-> tptp.general tptp.general Bool)) % 0.38/0.62 (declare-const tptp.b_i Int) % 0.38/0.62 (declare-const tptp.p__greater__ (-> tptp.general tptp.general Bool)) % 0.38/0.62 (declare-const tptp.p__greater_equal__ (-> tptp.general tptp.general Bool)) % 0.38/0.62 (declare-const tptp.a_i Int) % 0.38/0.62 (define @t1 () (@var "N" Int)) % 0.38/0.62 (define @t2 () (tptp.f__integer__ @t1)) % 0.38/0.62 (define @t3 () (@var "X" tptp.general)) % 0.38/0.62 (define @t4 () (@list @t1)) % 0.38/0.62 (define @t5 () (tptp.p__is_integer__ @t3)) % 0.38/0.62 (define @t6 () (@list @t3)) % 0.38/0.62 (define @t7 () (@var "X2" tptp.symbol)) % 0.38/0.62 (define @t8 () (@var "X1" tptp.general)) % 0.38/0.62 (define @t9 () (@var "N2" Int)) % 0.38/0.62 (define @t10 () (@var "N1" Int)) % 0.38/0.62 (define @t11 () (tptp.f__integer__ @t9)) % 0.38/0.62 (define @t12 () (tptp.f__integer__ @t10)) % 0.38/0.62 (define @t13 () (@list @t10 @t9)) % 0.38/0.62 (define @t14 () (@var "S2" tptp.symbol)) % 0.38/0.62 (define @t15 () (@var "S1" tptp.symbol)) % 0.38/0.62 (define @t16 () (@var "X2" tptp.general)) % 0.38/0.62 (define @t17 () (= @t8 @t16)) % 0.38/0.62 (define @t18 () (tptp.p__less_equal__ @t16 @t8)) % 0.38/0.62 (define @t19 () (tptp.p__less_equal__ @t8 @t16)) % 0.38/0.62 (define @t20 () (@list @t8 @t16)) % 0.38/0.62 (define @t21 () (@var "X3" tptp.general)) % 0.38/0.62 (define @t22 () (not @t17)) % 0.38/0.62 (define @t23 () (@var "S" tptp.symbol)) % 0.38/0.62 (define @t24 () (tptp.f__symbolic__ @t23)) % 0.38/0.62 (define @t25 () (@var "Z1_g" tptp.general)) % 0.38/0.62 (define @t26 () (@var "Z_g" tptp.general)) % 0.38/0.62 (define @t27 () (= @t26 @t25)) % 0.38/0.62 (define @t28 () (@var "J_i" Int)) % 0.38/0.62 (define @t29 () (@var "K_i" Int)) % 0.38/0.62 (define @t30 () (<= @t29 @t28)) % 0.38/0.62 (define @t31 () (@var "I_i" Int)) % 0.38/0.62 (define @t32 () (<= @t31 @t29)) % 0.38/0.62 (define @t33 () (= @t25 (tptp.f__integer__ @t29))) % 0.38/0.62 (define @t34 () (= @t28 tptp.b_i)) % 0.38/0.62 (define @t35 () (= @t31 2)) % 0.38/0.62 (define @t36 () (@list @t31 @t28 @t29)) % 0.38/0.62 (define @t37 () (exists @t36 (and @t35 @t34 @t33 @t32 @t30))) % 0.38/0.62 (define @t38 () (@var "J_g" tptp.general)) % 0.38/0.62 (define @t39 () (@list @t26 @t25)) % 0.38/0.62 (define @t40 () (exists @t39 (and (= @t26 @t38) @t37 @t27))) % 0.38/0.62 (define @t41 () (@var "I_g" tptp.general)) % 0.38/0.62 (define @t42 () (= @t26 @t41)) % 0.38/0.62 (define @t43 () (@var "J1_i" Int)) % 0.38/0.62 (define @t44 () (@var "I1_i" Int)) % 0.38/0.62 (define @t45 () (tptp.f__integer__ @t44)) % 0.38/0.62 (define @t46 () (@var "V1_g" tptp.general)) % 0.38/0.62 (define @t47 () (exists (@list @t44 @t43) (and (= @t46 (tptp.f__integer__ (* @t44 @t43))) (= @t45 @t41) (= (tptp.f__integer__ @t43) @t38)))) % 0.38/0.62 (define @t48 () (@list @t46)) % 0.38/0.62 (define @t49 () (= @t25 (tptp.f__integer__ tptp.b_i))) % 0.38/0.62 (define @t50 () (@var "M_g" tptp.general)) % 0.38/0.62 (define @t51 () (tptp.f__integer__ @t31)) % 0.38/0.62 (define @t52 () (= @t51 @t50)) % 0.38/0.62 (define @t53 () (= @t26 (tptp.f__integer__ (* @t31 @t28)))) % 0.38/0.62 (define @t54 () (@list @t31 @t28)) % 0.38/0.62 (define @t55 () (= (tptp.f__integer__ @t28) @t50)) % 0.38/0.62 (define @t56 () (= @t26 @t50)) % 0.38/0.62 (define @t57 () (@list @t26)) % 0.38/0.62 (define @t58 () (+ @t31 1)) % 0.38/0.62 (define @t59 () (* @t58 @t58)) % 0.38/0.62 (define @t60 () (@var "N_i" Int)) % 0.38/0.62 (define @t61 () (* @t31 @t31)) % 0.38/0.62 (define @t62 () (<= @t61 @t60)) % 0.38/0.62 (define @t63 () (>= @t31 0)) % 0.38/0.62 (define @t64 () (and @t63 @t62 (< @t60 @t59))) % 0.38/0.62 (define @t65 () (tptp.sqrt @t51 (tptp.f__integer__ @t60))) % 0.38/0.62 (define @t66 () (= @t65 @t64)) % 0.38/0.62 (define @t67 () (@list @t31 @t60)) % 0.38/0.62 (define @t68 () (forall @t67 @t66)) % 0.38/0.62 (define @t69 () (+ @t60 1)) % 0.38/0.62 (define @t70 () (tptp.f__integer__ 0)) % 0.38/0.62 (define @t71 () (tptp.sqrt @t51 @t70)) % 0.38/0.62 (define @t72 () (@list @t31)) % 0.38/0.62 (define @t73 () (exists @t72 @t71)) % 0.38/0.62 (define @t74 () (not @t73)) % 0.38/0.62 (define @t75 () (forall @t72 (not @t71))) % 0.38/0.62 (define @t76 () (* @t31 @t31)) % 0.38/0.62 (define @t77 () (* 2 @t31)) % 0.38/0.62 (define @t78 () (+ @t77 (* -1 @t60) @t76)) % 0.38/0.62 (define @t79 () (>= @t78 0)) % 0.38/0.62 (define @t80 () (+ 1 @t77 @t76)) % 0.38/0.62 (define @t81 () (+ @t78 1)) % 0.38/0.62 (define @t82 () (+ 1 @t31)) % 0.38/0.62 (define @t83 () (>= @t60 @t59)) % 0.38/0.62 (define @t84 () (+ @t60 (* -1 @t76))) % 0.38/0.62 (define @t85 () (>= @t84 0)) % 0.38/0.62 (define @t86 () (tptp.sqrt @t70 @t70)) % 0.38/0.62 (define @t87 () (>= 0 0)) % 0.38/0.62 (define @t88 () (* 0 0)) % 0.38/0.62 (define @t89 () (* -1 0)) % 0.38/0.62 (define @t90 () (* 2 0)) % 0.38/0.62 (define @t91 () (+ @t90 @t89 @t88)) % 0.38/0.62 (define @t92 () (>= @t91 0)) % 0.38/0.62 (define @t93 () (* -1 @t88)) % 0.38/0.62 (define @t94 () (+ 0 @t93)) % 0.38/0.62 (define @t95 () (>= @t94 0)) % 0.38/0.62 (define @t96 () (and @t87 @t95 @t92)) % 0.38/0.62 (define @t97 () (= @t86 @t96)) % 0.38/0.62 (define @t98 () (forall @t67 (= @t65 (and @t63 @t85 @t79)))) % 0.38/0.62 (assume @p1 (forall @t6 (= @t5 (exists @t4 (= @t3 @t2))))) % 0.38/0.62 (assume @p2 (forall (@list @t8) (= (tptp.p__is_symbolic__ @t8) (exists (@list @t7) (= @t8 (tptp.f__symbolic__ @t7)))))) % 0.38/0.62 (assume @p3 (forall @t6 (or (= @t3 tptp.c__infimum__) @t5 (tptp.p__is_symbolic__ @t3) (= @t3 tptp.c__supremum__)))) % 0.38/0.62 (assume @p4 (forall @t13 (= (= @t12 @t11) (= @t10 @t9)))) % 0.38/0.62 (assume @p5 (forall (@list @t15 @t14) (= (= (tptp.f__symbolic__ @t15) (tptp.f__symbolic__ @t14)) (= @t15 @t14)))) % 0.38/0.62 (assume @p6 (forall @t13 (= (tptp.p__less_equal__ @t12 @t11) (<= @t10 @t9)))) % 0.38/0.62 (assume @p7 (forall @t20 (=> (and @t19 @t18) @t17))) % 0.38/0.62 (assume @p8 (forall (@list @t8 @t16 @t21) (=> (and @t19 (tptp.p__less_equal__ @t16 @t21)) (tptp.p__less_equal__ @t8 @t21)))) % 0.38/0.62 (assume @p9 (forall @t20 (or @t19 @t18))) % 0.38/0.62 (assume @p10 (forall @t20 (= (tptp.p__less__ @t8 @t16) (and @t19 @t22)))) % 0.38/0.62 (assume @p11 (forall @t20 (= (tptp.p__greater_equal__ @t8 @t16) @t18))) % 0.38/0.62 (assume @p12 (forall @t20 (= (tptp.p__greater__ @t8 @t16) (and @t18 @t22)))) % 0.38/0.62 (assume @p13 (forall @t4 (tptp.p__less__ tptp.c__infimum__ @t2))) % 0.38/0.62 (assume @p14 (forall (@list @t1 @t23) (tptp.p__less__ @t2 @t24))) % 0.38/0.62 (assume @p15 (forall (@list @t23) (tptp.p__less__ @t24 tptp.c__supremum__))) % 0.38/0.62 (assume @p16 (> tptp.a_i 1)) % 0.38/0.62 (assume @p17 (forall @t48 (= (tptp.composite @t46) (exists (@list @t41 @t38) (and @t47 (exists @t39 (and @t42 @t37 @t27)) @t40))))) % 0.38/0.62 (assume @p18 (forall @t48 (= (tptp.sqrtb @t46) (exists (@list @t50) (and (= @t46 @t50) (exists @t39 (and @t56 (exists @t36 (and (= @t31 1) @t34 @t33 @t32 @t30)) @t27)) (exists @t39 (and (exists @t54 (and @t53 @t52 @t55)) @t49 (tptp.p__less_equal__ @t26 @t25))) (exists @t39 (and (exists @t54 (and @t53 (exists (@list @t44 @t28) (and (= @t31 (+ @t44 @t28)) (= @t45 @t50) (= @t28 1))) (exists (@list @t31 @t43) (and (= @t28 (+ @t31 @t43)) @t52 (= @t43 1))))) @t49 (tptp.p__greater__ @t26 @t25)))))))) % 0.38/0.62 (assume @p19 (forall @t48 (= (tptp.composite_p @t46) (exists (@list @t41 @t38 @t50) (and @t47 (exists @t57 (and @t56 (tptp.sqrtb @t26))) (exists @t39 (and @t42 (exists @t36 (and @t35 @t55 @t33 @t32 @t30)) @t27)) @t40))))) % 0.38/0.62 (assume @p20 (forall @t48 (= (tptp.prime @t46) (exists (@list @t41) (and (= @t46 @t41) (exists @t39 (and @t42 (exists @t36 (and (= @t31 tptp.a_i) @t34 @t33 @t32 @t30)) @t27)) (exists @t57 (and @t42 (not (tptp.composite_p @t26))))))))) % 0.38/0.62 (assume @p21 @t68) % 0.38/0.62 (assume @p22 (forall @t67 (=> (and @t65 (<= @t59 @t69)) (tptp.sqrt (tptp.f__integer__ @t58) (tptp.f__integer__ @t69))))) % 0.38/0.62 (assume @p23 @t74) % 0.38/0.62 (assume @p24 true) % 0.38/0.62 (step @p25 :rule bool-double-not-elim :args (@t75)) % 0.38/0.62 (step @p26 :rule exists-elim :args ((= @t73 (not @t75)))) % 0.38/0.62 (step @p27 :rule cong :premises (@p26) :args (@t74)) % 0.38/0.62 (step @p28 :rule trans :premises (@p27 @p25)) % 0.38/0.62 (step @p29 :rule eq_resolve :premises (@p23 @p28)) % 0.38/0.62 (step @p30 :rule bool-double-not-elim :args (@t79)) % 0.38/0.62 (step @p31 :rule arith_poly_norm :args ((= (* -1 (- 0 @t81)) (* -1 (- @t60 @t80))))) % 0.38/0.62 (step @p32 :rule arith_poly_norm_rel :premises (@p31) :args ((= (>= 0 @t81) (>= @t60 @t80)))) % 0.38/0.62 (step @p33 :rule arith-geq-tighten :args (@t78 0)) % 0.38/0.62 (step @p34 :rule trans :premises (@p33 @p32)) % 0.38/0.62 (step @p35 :rule symm :premises (@p34)) % 0.38/0.62 (step @p36 :rule arith_poly_norm :args ((= (* @t82 @t82) @t80))) % 0.38/0.62 (step @p37 :rule arith_poly_norm :args ((= @t58 @t82))) % 0.38/0.62 (step @p38 :rule nary_cong :premises (@p37 @p37) :args (@t59)) % 0.38/0.62 (step @p39 :rule trans :premises (@p38 @p36)) % 0.38/0.62 (step @p40 :rule refl :args (@t60)) % 0.38/0.62 (step @p41 :rule cong :premises (@p40 @p39) :args (@t83)) % 0.38/0.62 (step @p42 :rule trans :premises (@p41 @p35)) % 0.38/0.62 (step @p43 :rule cong :premises (@p42) :args ((not @t83))) % 0.38/0.62 (step @p44 :rule trans :premises (@p43 @p30)) % 0.38/0.62 (step @p45 :rule arith-elim-lt :args (@t60 @t59)) % 0.38/0.62 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.62 (step @p47 :rule arith_poly_norm :args ((= (* 1 (- @t60 @t76)) (* 1 (- @t84 0))))) % 0.38/0.62 (step @p48 :rule arith_poly_norm_rel :premises (@p47) :args ((= (>= @t60 @t76) @t85))) % 0.38/0.62 (step @p49 :rule arith-elim-leq :args (@t76 @t60)) % 0.38/0.62 (step @p50 :rule trans :premises (@p49 @p48)) % 0.38/0.62 (step @p51 :rule arith_poly_norm :args ((= @t61 @t76))) % 0.38/0.62 (step @p52 :rule cong :premises (@p51 @p40) :args (@t62)) % 0.38/0.62 (step @p53 :rule trans :premises (@p52 @p50)) % 0.38/0.62 (step @p54 :rule refl :args (@t63)) % 0.38/0.62 (step @p55 :rule nary_cong :premises (@p54 @p53 @p46) :args (@t64)) % 0.38/0.62 (step @p56 :rule refl :args (@t65)) % 0.38/0.62 (step @p57 :rule cong :premises (@p56 @p55) :args (@t66)) % 0.38/0.62 (step @p58 :rule cong :premises (@p57) :args (@t68)) % 0.38/0.62 (step @p59 :rule eq_resolve :premises (@p21 @p58)) % 0.38/0.62 (step @p60 :rule bool-eq-true :args (@t86)) % 0.38/0.62 (step @p61 :rule evaluate :args ((and true true true))) % 0.38/0.62 (step @p62 :rule evaluate :args (@t87)) % 0.38/0.62 (step @p63 :rule refl :args (0)) % 0.38/0.62 (step @p64 :rule evaluate :args ((+ 0 0 0))) % 0.38/0.62 (step @p65 :rule evaluate :args (@t88)) % 0.38/0.62 (step @p66 :rule evaluate :args (@t89)) % 0.38/0.62 (step @p67 :rule evaluate :args (@t90)) % 0.38/0.62 (step @p68 :rule nary_cong :premises (@p67 @p66 @p65) :args (@t91)) % 0.38/0.62 (step @p69 :rule trans :premises (@p68 @p64)) % 0.38/0.62 (step @p70 :rule cong :premises (@p69 @p63) :args (@t92)) % 0.38/0.62 (step @p71 :rule trans :premises (@p70 @p62)) % 0.38/0.62 (step @p72 :rule evaluate :args ((+ 0 0))) % 0.38/0.62 (step @p73 :rule refl :args (-1)) % 0.38/0.62 (step @p74 :rule nary_cong :premises (@p73 @p65) :args (@t93)) % 0.38/0.62 (step @p75 :rule trans :premises (@p74 @p66)) % 0.38/0.62 (step @p76 :rule nary_cong :premises (@p63 @p75) :args (@t94)) % 0.38/0.62 (step @p77 :rule trans :premises (@p76 @p72)) % 0.38/0.62 (step @p78 :rule cong :premises (@p77 @p63) :args (@t95)) % 0.38/0.62 (step @p79 :rule trans :premises (@p78 @p62)) % 0.38/0.62 (step @p80 :rule nary_cong :premises (@p62 @p79 @p71) :args (@t96)) % 0.38/0.62 (step @p81 :rule trans :premises (@p80 @p61)) % 0.38/0.62 (step @p82 :rule refl :args (@t86)) % 0.38/0.62 (step @p83 :rule cong :premises (@p82 @p81) :args (@t97)) % 0.38/0.62 (step @p84 :rule trans :premises (@p83 @p60)) % 0.38/0.62 (step @p85 :rule refl :args (@t98)) % 0.38/0.62 (step @p86 :rule cong :premises (@p85 @p84) :args ((=> @t98 @t97))) % 0.38/0.62 (assume-push @p100 @t98) % 0.38/0.62 (step @p88 :rule instantiate :premises (@p59) :args ((@list 0 0))) % 0.38/0.62 (step-pop @p101 :rule scope :premises (@p88)) % 0.38/0.62 (step @p89 :rule process_scope :premises (@p101) :args (@t97)) % 0.38/0.62 (step @p91 :rule eq_resolve :premises (@p89 @p86)) % 0.38/0.62 (step @p92 :rule implies_elim :premises (@p91)) % 0.38/0.62 (step @p93 :rule chain_m_resolution :premises (@p92 @p59) :args (@t86 (@list false) (@list @t98))) % 0.38/0.62 (assume-push @p102 @t75) % 0.38/0.62 (step @p95 :rule instantiate :premises (@p29) :args ((@list 0))) % 0.38/0.62 (step-pop @p103 :rule scope :premises (@p95)) % 0.38/0.62 (step @p96 :rule process_scope :premises (@p103) :args ((not @t86))) % 0.38/0.62 (step @p98 :rule implies_elim :premises (@p96)) % 0.38/0.62 (step @p99 false :rule chain_m_resolution :premises (@p98 @p93 @p29) :args (false (@list false false) (@list @t86 @t75))) % 0.38/0.62 ) % 0.38/0.62 % SZS output end Proof % 0.38/0.62 % cvc5 exiting %------------------------------------------------------------------------------