%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ARI734_1 : TPTP v9.2.1. Released v6.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n026.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 0.37s 0.55s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ARI734_1 : TPTP v9.2.1. Released v6.4.0. % 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 : n026.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 02:32:55 EDT 2026 % 0.18/0.34 % CPUTime : % 0.26/0.49 %----Proving TF0_ARI % 0.37/0.55 --- Run --finite-model-find --decision=internal at 45... % 0.37/0.55 % SZS status Theorem % 0.37/0.55 % SZS output start Proof % 0.37/0.55 ( % 0.37/0.55 (define @t1 () (@var "I" Int)) % 0.37/0.55 (define @t2 () (* 2 @t1)) % 0.37/0.55 (define @t3 () (@var "Res_1" Int)) % 0.37/0.55 (define @t4 () (= @t3 @t2)) % 0.37/0.55 (define @t5 () (@var "Res1_2" Int)) % 0.37/0.55 (define @t6 () (+ @t5 2)) % 0.37/0.55 (define @t7 () (= @t3 @t6)) % 0.37/0.55 (define @t8 () (= @t1 0)) % 0.37/0.55 (define @t9 () (not @t8)) % 0.37/0.55 (define @t10 () (=> @t9 @t7)) % 0.37/0.55 (define @t11 () (= @t3 0)) % 0.37/0.55 (define @t12 () (=> @t8 @t11)) % 0.37/0.55 (define @t13 () (@var "I_3" Int)) % 0.37/0.55 (define @t14 () (= @t5 (* 2 @t13))) % 0.37/0.55 (define @t15 () (- @t1 1)) % 0.37/0.55 (define @t16 () (= @t13 @t15)) % 0.37/0.55 (define @t17 () (and @t16 @t14)) % 0.37/0.55 (define @t18 () (@list @t13)) % 0.37/0.55 (define @t19 () (exists @t18 @t17)) % 0.37/0.55 (define @t20 () (and @t19 @t12 @t10)) % 0.37/0.55 (define @t21 () (@list @t5)) % 0.37/0.55 (define @t22 () (exists @t21 @t20)) % 0.37/0.55 (define @t23 () (and @t22 @t4)) % 0.37/0.55 (define @t24 () (@list @t3)) % 0.37/0.55 (define @t25 () (exists @t24 @t23)) % 0.37/0.55 (define @t26 () (>= @t1 0)) % 0.37/0.55 (define @t27 () (=> @t26 @t25)) % 0.37/0.55 (define @t28 () (@list @t1)) % 0.37/0.55 (define @t29 () (forall @t28 @t27)) % 0.37/0.55 (define @t30 () (not @t29)) % 0.37/0.55 (define @t31 () (not @t26)) % 0.37/0.55 (define @t32 () (or @t31 true)) % 0.37/0.55 (define @t33 () (and @t8 @t9)) % 0.37/0.55 (define @t34 () (not @t33)) % 0.37/0.55 (define @t35 () (not (= @t2 @t2))) % 0.37/0.55 (define @t36 () (and @t9 @t35)) % 0.37/0.55 (define @t37 () (= @t2 0)) % 0.37/0.55 (define @t38 () (not @t37)) % 0.37/0.55 (define @t39 () (and @t8 @t38)) % 0.37/0.55 (define @t40 () (or @t39 @t36 @t35)) % 0.37/0.55 (define @t41 () (not @t4)) % 0.37/0.55 (define @t42 () (and @t9 @t41)) % 0.37/0.55 (define @t43 () (and @t8 (not @t11))) % 0.37/0.55 (define @t44 () (or @t41 @t43 @t42 @t41)) % 0.37/0.55 (define @t45 () (or @t43 @t42 @t41)) % 0.37/0.55 (define @t46 () (or @t43 @t42)) % 0.37/0.55 (define @t47 () (not @t46)) % 0.37/0.55 (define @t48 () (and @t47 @t4)) % 0.37/0.55 (define @t49 () (forall @t24 (not @t48))) % 0.37/0.55 (define @t50 () (not @t49)) % 0.37/0.55 (define @t51 () (+ -2 @t2)) % 0.37/0.55 (define @t52 () (+ 2 @t51)) % 0.37/0.55 (define @t53 () (= @t3 @t52)) % 0.37/0.55 (define @t54 () (not @t53)) % 0.37/0.55 (define @t55 () (and @t9 @t54)) % 0.37/0.55 (define @t56 () (not (= @t51 @t51))) % 0.37/0.55 (define @t57 () (or @t56 @t55)) % 0.37/0.55 (define @t58 () (+ 2 @t5)) % 0.37/0.55 (define @t59 () (= @t3 @t58)) % 0.37/0.55 (define @t60 () (and @t9 (not @t59))) % 0.37/0.55 (define @t61 () (= @t5 @t51)) % 0.37/0.55 (define @t62 () (not @t61)) % 0.37/0.55 (define @t63 () (or @t62 @t62 @t60)) % 0.37/0.55 (define @t64 () (or @t62 @t60)) % 0.37/0.55 (define @t65 () (forall @t21 @t64)) % 0.37/0.55 (define @t66 () (or @t43 @t65)) % 0.37/0.55 (define @t67 () (or @t43 @t64)) % 0.37/0.55 (define @t68 () (or @t62 @t43 @t60)) % 0.37/0.55 (define @t69 () (=> @t9 @t59)) % 0.37/0.55 (define @t70 () (not @t69)) % 0.37/0.55 (define @t71 () (not @t12)) % 0.37/0.55 (define @t72 () (or @t62 @t71 @t70)) % 0.37/0.55 (define @t73 () (and @t61 @t12 @t69)) % 0.37/0.55 (define @t74 () (forall @t21 (not @t73))) % 0.37/0.55 (define @t75 () (not @t74)) % 0.37/0.55 (define @t76 () (+ -1 @t1)) % 0.37/0.55 (define @t77 () (* 2 @t76)) % 0.37/0.55 (define @t78 () (= @t5 @t77)) % 0.37/0.55 (define @t79 () (not @t78)) % 0.37/0.55 (define @t80 () (+ 1 @t76)) % 0.37/0.55 (define @t81 () (= @t1 @t80)) % 0.37/0.55 (define @t82 () (not @t81)) % 0.37/0.55 (define @t83 () (or @t82 @t79)) % 0.37/0.55 (define @t84 () (not @t14)) % 0.37/0.55 (define @t85 () (+ 1 @t13)) % 0.37/0.55 (define @t86 () (= @t1 @t85)) % 0.37/0.55 (define @t87 () (not @t86)) % 0.37/0.55 (define @t88 () (= @t13 @t76)) % 0.37/0.55 (define @t89 () (* -1 (- @t13 @t76))) % 0.37/0.55 (define @t90 () (* 1 (- @t1 @t85))) % 0.37/0.55 (define @t91 () (or @t87 @t87 @t84)) % 0.37/0.55 (define @t92 () (or @t87 @t84)) % 0.37/0.55 (define @t93 () (and @t86 @t14)) % 0.37/0.55 (define @t94 () (forall @t18 (not @t93))) % 0.37/0.55 (define @t95 () (not @t94)) % 0.37/0.55 (define @t96 () (* -1 1)) % 0.37/0.55 (define @t97 () (+ @t1 @t96)) % 0.37/0.55 (assume @p1 @t30) % 0.37/0.55 (assume @p2 true) % 0.37/0.55 (step @p3 :rule evaluate :args ((not true))) % 0.37/0.55 (step @p4 :rule quant-unused-vars :args ((= (forall @t28 true) true))) % 0.37/0.55 (step @p5 :rule absorb :args ((= @t32 true))) % 0.37/0.55 (step @p6 :rule cong :premises (@p5) :args ((forall @t28 @t32))) % 0.37/0.55 (step @p7 :rule trans :premises (@p6 @p4)) % 0.37/0.55 (step @p8 :rule bool-or-taut2 :args (false @t8 false false)) % 0.37/0.55 (step @p9 :rule bool-double-not-elim :args (@t8)) % 0.37/0.55 (step @p10 :rule refl :args (@t9)) % 0.37/0.55 (step @p11 :rule nary_cong :premises (@p10 @p9) :args ((or @t9 (not @t9)))) % 0.37/0.55 (step @p12 :rule bool-and-de-morgan :args (@t8 @t9 true)) % 0.37/0.55 (step @p13 :rule trans :premises (@p12 @p11)) % 0.37/0.55 (step @p14 :rule trans :premises (@p13 @p8)) % 0.37/0.55 (step @p15 :rule refl :args (@t31)) % 0.37/0.55 (step @p16 :rule nary_cong :premises (@p15 @p14) :args ((or @t31 @t34))) % 0.37/0.55 (step @p17 :rule bool-impl-elim :args (@t26 @t34)) % 0.37/0.55 (step @p18 :rule trans :premises (@p17 @p16)) % 0.37/0.55 (step @p19 :rule cong :premises (@p18) :args ((forall @t28 (=> @t26 @t34)))) % 0.37/0.55 (step @p20 :rule trans :premises (@p19 @p7)) % 0.37/0.55 (step @p21 :rule aci_norm :args ((= (or @t33 false false) @t33))) % 0.37/0.55 (step @p22 :rule eq-refl :args (@t2)) % 0.37/0.55 (step @p23 :rule cong :premises (@p22) :args (@t35)) % 0.37/0.55 (step @p24 :rule trans :premises (@p23 @p3)) % 0.37/0.55 (step @p25 :rule absorb :args ((= (and @t9 false) false))) % 0.37/0.55 (step @p26 :rule refl :args (@t9)) % 0.37/0.55 (step @p27 :rule nary_cong :premises (@p26 @p24) :args (@t36)) % 0.37/0.55 (step @p28 :rule trans :premises (@p27 @p25)) % 0.37/0.55 (step @p29 :rule arith_poly_norm :args ((= (* 1 (- @t2 0)) (* 2 (- @t1 0))))) % 0.37/0.55 (step @p30 :rule arith_poly_norm_rel :premises (@p29) :args ((= @t37 @t8))) % 0.37/0.55 (step @p31 :rule cong :premises (@p30) :args (@t38)) % 0.37/0.55 (step @p32 :rule refl :args (@t8)) % 0.37/0.55 (step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t39)) % 0.37/0.55 (step @p34 :rule nary_cong :premises (@p33 @p28 @p24) :args (@t40)) % 0.37/0.55 (step @p35 :rule trans :premises (@p34 @p21)) % 0.37/0.55 (step @p36 :rule quant-var-elim-eq :args ((= (forall @t24 @t44) @t40))) % 0.37/0.55 (step @p37 :rule aci_norm :args ((= @t45 @t44))) % 0.37/0.55 (step @p38 :rule cong :premises (@p37) :args ((forall @t24 @t45))) % 0.37/0.55 (step @p39 :rule trans :premises (@p38 @p36)) % 0.37/0.55 (step @p40 :rule trans :premises (@p39 @p35)) % 0.37/0.55 (step @p41 :rule aci_norm :args ((= (or @t46 @t41) @t45))) % 0.37/0.55 (step @p42 :rule refl :args (@t41)) % 0.37/0.55 (step @p43 :rule bool-double-not-elim :args (@t46)) % 0.37/0.55 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or (not @t47) @t41))) % 0.37/0.55 (step @p45 :rule bool-and-de-morgan :args (@t47 @t4 true)) % 0.37/0.55 (step @p46 :rule trans :premises (@p45 @p44)) % 0.37/0.55 (step @p47 :rule trans :premises (@p46 @p41)) % 0.37/0.55 (step @p48 :rule cong :premises (@p47) :args (@t49)) % 0.37/0.55 (step @p49 :rule trans :premises (@p48 @p40)) % 0.37/0.55 (step @p50 :rule cong :premises (@p49) :args (@t50)) % 0.37/0.55 (step @p51 :rule exists-elim :args ((= (exists @t24 @t48) @t50))) % 0.37/0.55 (step @p52 :rule trans :premises (@p51 @p50)) % 0.37/0.55 (step @p53 :rule refl :args (@t4)) % 0.37/0.55 (step @p54 :rule aci_norm :args ((= (or false @t42) @t42))) % 0.37/0.55 (step @p55 :rule arith_poly_norm :args ((= @t52 @t2))) % 0.37/0.55 (step @p56 :rule refl :args (@t3)) % 0.37/0.55 (step @p57 :rule cong :premises (@p56 @p55) :args (@t53)) % 0.37/0.55 (step @p58 :rule cong :premises (@p57) :args (@t54)) % 0.37/0.55 (step @p59 :rule nary_cong :premises (@p26 @p58) :args (@t55)) % 0.37/0.55 (step @p60 :rule eq-refl :args (@t51)) % 0.37/0.55 (step @p61 :rule cong :premises (@p60) :args (@t56)) % 0.37/0.55 (step @p62 :rule trans :premises (@p61 @p3)) % 0.37/0.55 (step @p63 :rule nary_cong :premises (@p62 @p59) :args (@t57)) % 0.37/0.55 (step @p64 :rule trans :premises (@p63 @p54)) % 0.37/0.55 (step @p65 :rule quant-var-elim-eq :args ((= (forall @t21 @t63) @t57))) % 0.37/0.55 (step @p66 :rule aci_norm :args ((= @t64 @t63))) % 0.37/0.55 (step @p67 :rule cong :premises (@p66) :args (@t65)) % 0.37/0.55 (step @p68 :rule trans :premises (@p67 @p65)) % 0.37/0.55 (step @p69 :rule trans :premises (@p68 @p64)) % 0.37/0.55 (step @p70 :rule refl :args (@t43)) % 0.37/0.55 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t66)) % 0.37/0.55 (step @p72 :rule quant-miniscope-or :args ((= (forall @t21 @t67) @t66))) % 0.37/0.55 (step @p73 :rule aci_norm :args ((= @t68 @t67))) % 0.37/0.55 (step @p74 :rule cong :premises (@p73) :args ((forall @t21 @t68))) % 0.37/0.55 (step @p75 :rule trans :premises (@p74 @p72)) % 0.37/0.55 (step @p76 :rule trans :premises (@p75 @p71)) % 0.37/0.55 (step @p77 :rule bool-implies-de-morgan :args (@t9 @t59)) % 0.37/0.55 (step @p78 :rule bool-implies-de-morgan :args (@t8 @t11)) % 0.37/0.55 (step @p79 :rule refl :args (@t62)) % 0.37/0.55 (step @p80 :rule nary_cong :premises (@p79 @p78 @p77) :args (@t72)) % 0.37/0.55 (step @p81 :rule aci_norm :args ((= (or @t62 (or @t71 @t70)) @t72))) % 0.37/0.55 (step @p82 :rule bool-and-de-morgan :args (@t12 @t69 true)) % 0.37/0.55 (step @p83 :rule nary_cong :premises (@p79 @p82) :args ((or @t62 (not (and @t12 @t69))))) % 0.37/0.55 (step @p84 :rule bool-and-de-morgan :args (@t61 @t12 (and @t69))) % 0.37/0.55 (step @p85 :rule trans :premises (@p84 @p83)) % 0.37/0.55 (step @p86 :rule trans :premises (@p85 @p81)) % 0.37/0.55 (step @p87 :rule trans :premises (@p86 @p80)) % 0.37/0.55 (step @p88 :rule cong :premises (@p87) :args (@t74)) % 0.37/0.55 (step @p89 :rule trans :premises (@p88 @p76)) % 0.37/0.55 (step @p90 :rule cong :premises (@p89) :args (@t75)) % 0.37/0.55 (step @p91 :rule exists-elim :args ((= (exists @t21 @t73) @t75))) % 0.37/0.55 (step @p92 :rule trans :premises (@p91 @p90)) % 0.37/0.55 (step @p93 :rule arith_poly_norm :args ((= @t6 @t58))) % 0.37/0.55 (step @p94 :rule cong :premises (@p56 @p93) :args (@t7)) % 0.37/0.55 (step @p95 :rule cong :premises (@p26 @p94) :args (@t10)) % 0.37/0.56 (step @p96 :rule refl :args (@t12)) % 0.37/0.56 (step @p97 :rule bool-double-not-elim :args (@t61)) % 0.37/0.56 (step @p98 :rule aci_norm :args ((= (or false @t62) @t62))) % 0.37/0.56 (step @p99 :rule arith_poly_norm :args ((= @t77 @t51))) % 0.37/0.56 (step @p100 :rule refl :args (@t5)) % 0.37/0.56 (step @p101 :rule cong :premises (@p100 @p99) :args (@t78)) % 0.37/0.56 (step @p102 :rule cong :premises (@p101) :args (@t79)) % 0.37/0.56 (step @p103 :rule eq-refl :args (@t1)) % 0.37/0.56 (step @p104 :rule arith_poly_norm :args ((= @t80 @t1))) % 0.37/0.56 (step @p105 :rule refl :args (@t1)) % 0.37/0.56 (step @p106 :rule cong :premises (@p105 @p104) :args (@t81)) % 0.37/0.56 (step @p107 :rule trans :premises (@p106 @p103)) % 0.37/0.56 (step @p108 :rule cong :premises (@p107) :args (@t82)) % 0.37/0.56 (step @p109 :rule trans :premises (@p108 @p3)) % 0.37/0.56 (step @p110 :rule nary_cong :premises (@p109 @p102) :args (@t83)) % 0.37/0.56 (step @p111 :rule trans :premises (@p110 @p98)) % 0.37/0.56 (step @p112 :rule quant-var-elim-eq :args ((= (forall @t18 (or (not @t88) @t87 @t84)) @t83))) % 0.37/0.56 (step @p113 :rule refl :args (@t84)) % 0.37/0.56 (step @p114 :rule refl :args (@t87)) % 0.37/0.56 (step @p115 :rule arith_poly_norm :args ((= @t90 @t89))) % 0.37/0.56 (step @p116 :rule arith_poly_norm_rel :premises (@p115) :args ((= @t86 @t88))) % 0.37/0.56 (step @p117 :rule cong :premises (@p116) :args (@t87)) % 0.37/0.56 (step @p118 :rule nary_cong :premises (@p117 @p114 @p113) :args (@t91)) % 0.37/0.56 (step @p119 :rule aci_norm :args ((= @t92 @t91))) % 0.37/0.56 (step @p120 :rule trans :premises (@p119 @p118)) % 0.37/0.56 (step @p121 :rule cong :premises (@p120) :args ((forall @t18 @t92))) % 0.37/0.56 (step @p122 :rule trans :premises (@p121 @p112)) % 0.37/0.56 (step @p123 :rule trans :premises (@p122 @p111)) % 0.37/0.56 (step @p124 :rule bool-and-de-morgan :args (@t86 @t14 true)) % 0.37/0.56 (step @p125 :rule cong :premises (@p124) :args (@t94)) % 0.37/0.56 (step @p126 :rule trans :premises (@p125 @p123)) % 0.37/0.56 (step @p127 :rule cong :premises (@p126) :args (@t95)) % 0.37/0.56 (step @p128 :rule trans :premises (@p127 @p97)) % 0.37/0.56 (step @p129 :rule exists-elim :args ((= (exists @t18 @t93) @t95))) % 0.37/0.56 (step @p130 :rule trans :premises (@p129 @p128)) % 0.37/0.56 (step @p131 :rule refl :args (@t14)) % 0.37/0.56 (step @p132 :rule arith_poly_norm :args ((= @t89 @t90))) % 0.37/0.56 (step @p133 :rule arith_poly_norm_rel :premises (@p132) :args ((= @t88 @t86))) % 0.37/0.56 (step @p134 :rule arith_poly_norm :args ((= (+ @t1 -1) @t76))) % 0.37/0.56 (step @p135 :rule evaluate :args (@t96)) % 0.37/0.56 (step @p136 :rule nary_cong :premises (@p105 @p135) :args (@t97)) % 0.37/0.56 (step @p137 :rule trans :premises (@p136 @p134)) % 0.37/0.56 (step @p138 :rule arith_poly_norm :args ((= @t15 @t97))) % 0.37/0.56 (step @p139 :rule trans :premises (@p138 @p137)) % 0.37/0.56 (step @p140 :rule refl :args (@t13)) % 0.37/0.56 (step @p141 :rule cong :premises (@p140 @p139) :args (@t16)) % 0.37/0.56 (step @p142 :rule trans :premises (@p141 @p133)) % 0.37/0.56 (step @p143 :rule nary_cong :premises (@p142 @p131) :args (@t17)) % 0.37/0.56 (step @p144 :rule cong :premises (@p143) :args (@t19)) % 0.37/0.56 (step @p145 :rule trans :premises (@p144 @p130)) % 0.37/0.56 (step @p146 :rule nary_cong :premises (@p145 @p96 @p95) :args (@t20)) % 0.37/0.56 (step @p147 :rule cong :premises (@p146) :args (@t22)) % 0.37/0.56 (step @p148 :rule trans :premises (@p147 @p92)) % 0.37/0.56 (step @p149 :rule nary_cong :premises (@p148 @p53) :args (@t23)) % 0.37/0.56 (step @p150 :rule cong :premises (@p149) :args (@t25)) % 0.37/0.56 (step @p151 :rule trans :premises (@p150 @p52)) % 0.37/0.56 (step @p152 :rule refl :args (@t26)) % 0.37/0.56 (step @p153 :rule cong :premises (@p152 @p151) :args (@t27)) % 0.37/0.56 (step @p154 :rule cong :premises (@p153) :args (@t29)) % 0.37/0.56 (step @p155 :rule trans :premises (@p154 @p20)) % 0.37/0.56 (step @p156 :rule cong :premises (@p155) :args (@t30)) % 0.37/0.56 (step @p157 :rule trans :premises (@p156 @p3)) % 0.37/0.56 (step @p158 false :rule eq_resolve :premises (@p1 @p157)) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------