%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI740_1 : TPTP v9.2.1. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:08:13 AM UTC 2026 % Result : Theorem 0.43s 0.65s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI740_1 : TPTP v9.2.1. Released v7.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n014.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 : Wed Jun 3 02:32:58 EDT 2026 % 0.18/0.35 % CPUTime : % 0.31/0.51 %----Proving TF0_ARI % 0.43/0.65 --- Run --finite-model-find --decision=internal at 45... % 0.43/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 0.43/0.65 % SZS status Theorem % 0.43/0.65 % SZS output start Proof % 0.43/0.65 ( % 0.43/0.65 (declare-const tptp.power (-> Real Int Real)) % 0.43/0.65 (define @t1 () (@var "X" Real)) % 0.43/0.65 (define @t2 () (@list @t1)) % 0.43/0.65 (define @t3 () (@var "N" Int)) % 0.43/0.65 (define @t4 () (tptp.power @t1 @t3)) % 0.43/0.65 (define @t5 () (* @t1 @t4)) % 0.43/0.65 (define @t6 () (+ @t3 1)) % 0.43/0.65 (define @t7 () (tptp.power @t1 @t6)) % 0.43/0.65 (define @t8 () (= @t7 @t5)) % 0.43/0.65 (define @t9 () (<= 0 @t3)) % 0.43/0.65 (define @t10 () (=> @t9 @t8)) % 0.43/0.65 (define @t11 () (@list @t1 @t3)) % 0.43/0.65 (define @t12 () (forall @t11 @t10)) % 0.43/0.65 (define @t13 () (tptp.power @t1 1)) % 0.43/0.65 (define @t14 () (= @t13 @t1)) % 0.43/0.65 (define @t15 () (forall @t2 @t14)) % 0.43/0.65 (define @t16 () (@var "M" Int)) % 0.43/0.65 (define @t17 () (tptp.power @t1 @t16)) % 0.43/0.65 (define @t18 () (* @t4 @t17)) % 0.43/0.65 (define @t19 () (tptp.power @t1 (+ @t3 @t16))) % 0.43/0.65 (define @t20 () (= @t19 @t18)) % 0.43/0.65 (define @t21 () (<= 0 @t16)) % 0.43/0.65 (define @t22 () (=> @t21 @t20)) % 0.43/0.65 (define @t23 () (=> @t9 @t22)) % 0.43/0.65 (define @t24 () (@list @t1 @t3 @t16)) % 0.43/0.65 (define @t25 () (forall @t24 @t23)) % 0.43/0.65 (define @t26 () (@var "Y" Real)) % 0.43/0.65 (define @t27 () (tptp.power @t26 @t3)) % 0.43/0.65 (define @t28 () (* @t4 @t27)) % 0.43/0.65 (define @t29 () (* @t1 @t26)) % 0.43/0.65 (define @t30 () (tptp.power @t29 @t3)) % 0.43/0.65 (define @t31 () (= @t30 @t28)) % 0.43/0.65 (define @t32 () (=> @t9 @t31)) % 0.43/0.65 (define @t33 () (@list @t1 @t26 @t3)) % 0.43/0.65 (define @t34 () (forall @t33 @t32)) % 0.43/0.65 (define @t35 () (tptp.power 2/1 2)) % 0.43/0.65 (define @t36 () (>= @t3 0)) % 0.43/0.65 (define @t37 () (* @t4 @t27)) % 0.43/0.65 (define @t38 () (* @t1 @t26)) % 0.43/0.65 (define @t39 () (= (tptp.power @t38 @t3) @t37)) % 0.43/0.65 (define @t40 () (tptp.power 2/1 1)) % 0.43/0.65 (define @t41 () (* @t40 @t40)) % 0.43/0.65 (define @t42 () (= (tptp.power 4/1 1) @t41)) % 0.43/0.65 (define @t43 () (* 2/1 2/1)) % 0.43/0.65 (define @t44 () (tptp.power @t43 1)) % 0.43/0.65 (define @t45 () (= @t44 @t41)) % 0.43/0.65 (define @t46 () (>= 1 0)) % 0.43/0.65 (define @t47 () (not @t46)) % 0.43/0.65 (define @t48 () (or @t47 @t45)) % 0.43/0.65 (define @t49 () (not @t36)) % 0.43/0.65 (define @t50 () (forall @t33 (or @t49 @t39))) % 0.43/0.65 (define @t51 () (@list false)) % 0.43/0.65 (define @t52 () (* @t1 @t4)) % 0.43/0.65 (define @t53 () (+ 1 @t3)) % 0.43/0.65 (define @t54 () (= (tptp.power @t1 @t53) @t52)) % 0.43/0.65 (define @t55 () (tptp.power 2/1 3)) % 0.43/0.65 (define @t56 () (* 1/2 @t55)) % 0.43/0.65 (define @t57 () (= @t35 @t56)) % 0.43/0.65 (define @t58 () (* 2/1 @t35)) % 0.43/0.65 (define @t59 () (* 2/1 @t35)) % 0.43/0.65 (define @t60 () (+ 1 2)) % 0.43/0.65 (define @t61 () (tptp.power 2/1 @t60)) % 0.43/0.65 (define @t62 () (= @t61 @t59)) % 0.43/0.65 (define @t63 () (>= 2 0)) % 0.43/0.65 (define @t64 () (not @t63)) % 0.43/0.65 (define @t65 () (or @t64 @t62)) % 0.43/0.65 (define @t66 () (forall @t11 (or @t49 @t54))) % 0.43/0.65 (define @t67 () (* @t4 @t17)) % 0.43/0.65 (define @t68 () (= @t19 @t67)) % 0.43/0.65 (define @t69 () (>= @t16 0)) % 0.43/0.65 (define @t70 () (not @t69)) % 0.43/0.65 (define @t71 () (or @t49 @t70 @t68)) % 0.43/0.65 (define @t72 () (=> @t69 @t68)) % 0.43/0.65 (define @t73 () (= @t35 @t41)) % 0.43/0.65 (define @t74 () (+ 1 1)) % 0.43/0.65 (define @t75 () (tptp.power 2/1 @t74)) % 0.43/0.65 (define @t76 () (= @t75 @t41)) % 0.43/0.65 (define @t77 () (or @t47 @t47 @t76)) % 0.43/0.65 (define @t78 () (forall @t24 @t71)) % 0.43/0.65 (assume @p1 (forall @t2 (= (tptp.power @t1 0) 1/1))) % 0.43/0.65 (assume @p2 @t12) % 0.43/0.65 (assume @p3 (forall @t11 (=> (< 0 @t3) (= @t4 (* @t1 (tptp.power @t1 (- @t3 1))))))) % 0.43/0.65 (assume @p4 @t15) % 0.43/0.65 (assume @p5 @t25) % 0.43/0.65 (assume @p6 (forall @t24 (=> @t9 (=> @t21 (= (tptp.power @t1 (* @t3 @t16)) (tptp.power @t4 @t16)))))) % 0.43/0.65 (assume @p7 @t34) % 0.43/0.65 (assume @p8 (forall @t11 (=> (and @t9 (<= 1/1 @t1)) (<= 1/1 @t4)))) % 0.43/0.65 (assume @p9 (not (= @t35 4/1))) % 0.43/0.65 (assume @p10 true) % 0.43/0.65 (step @p11 :rule evaluate :args ((= false true))) % 0.43/0.65 (step @p12 :rule bool-impl-elim :args (@t36 @t39)) % 0.43/0.65 (step @p13 :rule cong :premises (@p12) :args ((forall @t33 (=> @t36 @t39)))) % 0.43/0.65 (step @p14 :rule arith_poly_norm :args ((= @t28 @t37))) % 0.43/0.65 (step @p15 :rule refl :args (@t3)) % 0.43/0.65 (step @p16 :rule arith_poly_norm :args ((= @t29 @t38))) % 0.43/0.65 (step @p17 :rule cong :premises (@p16 @p15) :args (@t30)) % 0.43/0.65 (step @p18 :rule cong :premises (@p17 @p14) :args (@t31)) % 0.43/0.65 (step @p19 :rule arith-elim-leq :args (0 @t3)) % 0.43/0.65 (step @p20 :rule cong :premises (@p19 @p18) :args (@t32)) % 0.43/0.65 (step @p21 :rule cong :premises (@p20) :args (@t34)) % 0.43/0.65 (step @p22 :rule trans :premises (@p21 @p13)) % 0.43/0.65 (step @p23 :rule eq_resolve :premises (@p7 @p22)) % 0.43/0.65 (step @p24 :rule aci_norm :args ((= (or false @t42) @t42))) % 0.43/0.65 (step @p25 :rule refl :args (@t41)) % 0.43/0.65 (step @p26 :rule refl :args (1)) % 0.43/0.65 (step @p27 :rule evaluate :args (@t43)) % 0.43/0.65 (step @p28 :rule cong :premises (@p27 @p26) :args (@t44)) % 0.43/0.65 (step @p29 :rule cong :premises (@p28 @p25) :args (@t45)) % 0.43/0.65 (step @p30 :rule evaluate :args ((not true))) % 0.43/0.65 (step @p31 :rule evaluate :args (@t46)) % 0.43/0.65 (step @p32 :rule cong :premises (@p31) :args (@t47)) % 0.43/0.65 (step @p33 :rule trans :premises (@p32 @p30)) % 0.43/0.65 (step @p34 :rule nary_cong :premises (@p33 @p29) :args (@t48)) % 0.43/0.65 (step @p35 :rule trans :premises (@p34 @p24)) % 0.43/0.65 (step @p36 :rule refl :args (@t50)) % 0.43/0.65 (step @p37 :rule cong :premises (@p36 @p35) :args ((=> @t50 @t48))) % 0.43/0.65 (assume-push @p127 @t50) % 0.43/0.65 (step @p39 :rule instantiate :premises (@p23) :args ((@list 2/1 2/1 1))) % 0.43/0.65 (step-pop @p128 :rule scope :premises (@p39)) % 0.43/0.65 (step @p40 :rule process_scope :premises (@p128) :args (@t48)) % 0.43/0.65 (step @p42 :rule eq_resolve :premises (@p40 @p37)) % 0.43/0.65 (step @p43 :rule implies_elim :premises (@p42)) % 0.43/0.65 (step @p44 :rule chain_m_resolution :premises (@p43 @p23) :args (@t42 @t51 (@list @t50))) % 0.43/0.65 (step @p45 :rule arith_poly_norm :args ((= (* 1/1 (- @t13 @t1)) (* -1/1 (- @t1 @t13))))) % 0.43/0.65 (step @p46 :rule arith_poly_norm_rel :premises (@p45) :args ((= @t14 (= @t1 @t13)))) % 0.43/0.65 (step @p47 :rule cong :premises (@p46) :args (@t15)) % 0.43/0.65 (step @p48 :rule eq_resolve :premises (@p4 @p47)) % 0.43/0.65 (step @p49 :rule instantiate :premises (@p48) :args ((@list 4/1))) % 0.43/0.65 (step @p50 :rule trans :premises (@p49 @p44)) % 0.43/0.65 (step @p51 :rule symm :premises (@p50)) % 0.43/0.65 (step @p52 :rule bool-impl-elim :args (@t36 @t54)) % 0.43/0.65 (step @p53 :rule cong :premises (@p52) :args ((forall @t11 (=> @t36 @t54)))) % 0.43/0.65 (step @p54 :rule arith_poly_norm :args ((= @t5 @t52))) % 0.43/0.65 (step @p55 :rule arith_poly_norm :args ((= @t6 @t53))) % 0.43/0.65 (step @p56 :rule refl :args (@t1)) % 0.43/0.65 (step @p57 :rule cong :premises (@p56 @p55) :args (@t7)) % 0.43/0.65 (step @p58 :rule cong :premises (@p57 @p54) :args (@t8)) % 0.43/0.65 (step @p59 :rule cong :premises (@p19 @p58) :args (@t10)) % 0.43/0.65 (step @p60 :rule cong :premises (@p59) :args (@t12)) % 0.43/0.65 (step @p61 :rule trans :premises (@p60 @p53)) % 0.43/0.65 (step @p62 :rule eq_resolve :premises (@p2 @p61)) % 0.43/0.65 (step @p63 :rule aci_norm :args ((= (or false @t57) @t57))) % 0.43/0.65 (step @p64 :rule arith_poly_norm :args ((= (* 1/1 (- @t55 @t58)) (* -2/1 (- @t35 @t56))))) % 0.43/0.65 (step @p65 :rule arith_poly_norm_rel :premises (@p64) :args ((= (= @t55 @t58) @t57))) % 0.43/0.65 (step @p66 :rule arith_poly_norm :args ((= @t59 @t58))) % 0.43/0.65 (step @p67 :rule evaluate :args (@t60)) % 0.43/0.65 (step @p68 :rule refl :args (2/1)) % 0.43/0.65 (step @p69 :rule cong :premises (@p68 @p67) :args (@t61)) % 0.43/0.65 (step @p70 :rule cong :premises (@p69 @p66) :args (@t62)) % 0.43/0.65 (step @p71 :rule trans :premises (@p70 @p65)) % 0.43/0.65 (step @p72 :rule evaluate :args (@t63)) % 0.43/0.65 (step @p73 :rule cong :premises (@p72) :args (@t64)) % 0.43/0.65 (step @p74 :rule trans :premises (@p73 @p30)) % 0.43/0.65 (step @p75 :rule nary_cong :premises (@p74 @p71) :args (@t65)) % 0.43/0.65 (step @p76 :rule trans :premises (@p75 @p63)) % 0.43/0.65 (step @p77 :rule refl :args (@t66)) % 0.43/0.65 (step @p78 :rule cong :premises (@p77 @p76) :args ((=> @t66 @t65))) % 0.43/0.65 (assume-push @p129 @t66) % 0.43/0.65 (step @p80 :rule instantiate :premises (@p62) :args ((@list 2/1 2))) % 0.43/0.65 (step-pop @p130 :rule scope :premises (@p80)) % 0.43/0.65 (step @p81 :rule process_scope :premises (@p130) :args (@t65)) % 0.43/0.65 (step @p83 :rule eq_resolve :premises (@p81 @p78)) % 0.43/0.65 (step @p84 :rule implies_elim :premises (@p83)) % 0.43/0.65 (step @p85 :rule chain_m_resolution :premises (@p84 @p62) :args (@t57 @t51 (@list @t66))) % 0.43/0.65 (step @p86 :rule aci_norm :args ((= (or @t49 (or @t70 @t68)) @t71))) % 0.43/0.65 (step @p87 :rule bool-impl-elim :args (@t69 @t68)) % 0.43/0.65 (step @p88 :rule refl :args (@t49)) % 0.43/0.65 (step @p89 :rule nary_cong :premises (@p88 @p87) :args ((or @t49 @t72))) % 0.43/0.65 (step @p90 :rule trans :premises (@p89 @p86)) % 0.43/0.65 (step @p91 :rule bool-impl-elim :args (@t36 @t72)) % 0.43/0.65 (step @p92 :rule trans :premises (@p91 @p90)) % 0.43/0.65 (step @p93 :rule cong :premises (@p92) :args ((forall @t24 (=> @t36 @t72)))) % 0.43/0.65 (step @p94 :rule arith_poly_norm :args ((= @t18 @t67))) % 0.43/0.65 (step @p95 :rule refl :args (@t19)) % 0.43/0.65 (step @p96 :rule cong :premises (@p95 @p94) :args (@t20)) % 0.43/0.65 (step @p97 :rule arith-elim-leq :args (0 @t16)) % 0.43/0.65 (step @p98 :rule cong :premises (@p97 @p96) :args (@t22)) % 0.43/0.65 (step @p99 :rule cong :premises (@p19 @p98) :args (@t23)) % 0.43/0.65 (step @p100 :rule cong :premises (@p99) :args (@t25)) % 0.43/0.65 (step @p101 :rule trans :premises (@p100 @p93)) % 0.43/0.65 (step @p102 :rule eq_resolve :premises (@p5 @p101)) % 0.43/0.65 (step @p103 :rule aci_norm :args ((= (or false false @t73) @t73))) % 0.43/0.65 (step @p104 :rule evaluate :args (@t74)) % 0.43/0.65 (step @p105 :rule cong :premises (@p68 @p104) :args (@t75)) % 0.43/0.65 (step @p106 :rule cong :premises (@p105 @p25) :args (@t76)) % 0.43/0.65 (step @p107 :rule nary_cong :premises (@p33 @p33 @p106) :args (@t77)) % 0.43/0.65 (step @p108 :rule trans :premises (@p107 @p103)) % 0.43/0.65 (step @p109 :rule refl :args (@t78)) % 0.43/0.65 (step @p110 :rule cong :premises (@p109 @p108) :args ((=> @t78 @t77))) % 0.43/0.65 (assume-push @p131 @t78) % 0.43/0.65 (step @p112 :rule instantiate :premises (@p102) :args ((@list 2/1 1 1))) % 0.43/0.65 (step-pop @p132 :rule scope :premises (@p112)) % 0.43/0.65 (step @p113 :rule process_scope :premises (@p132) :args (@t77)) % 0.43/0.65 (step @p115 :rule eq_resolve :premises (@p113 @p110)) % 0.43/0.65 (step @p116 :rule implies_elim :premises (@p115)) % 0.43/0.65 (step @p117 :rule chain_m_resolution :premises (@p116 @p102) :args (@t73 @t51 (@list @t78))) % 0.43/0.65 (step @p118 :rule symm :premises (@p117)) % 0.43/0.65 (step @p119 :rule trans :premises (@p118 @p85)) % 0.43/0.65 (step @p120 :rule symm :premises (@p119)) % 0.43/0.65 (step @p121 :rule trans :premises (@p85 @p120 @p51)) % 0.43/0.65 (step @p122 :rule true_intro :premises (@p121)) % 0.43/0.65 (step @p123 :rule false_intro :premises (@p9)) % 0.43/0.65 (step @p124 :rule symm :premises (@p123)) % 0.43/0.65 (step @p125 :rule trans :premises (@p124 @p122)) % 0.43/0.65 (step @p126 false :rule eq_resolve :premises (@p125 @p11)) % 0.43/0.65 ) % 0.43/0.65 % SZS output end Proof % 0.43/0.65 % cvc5 exiting %------------------------------------------------------------------------------