%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG201+1 : TPTP v9.2.1. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.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 08:05:29 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : ALG201+1 : TPTP v9.2.1. Released v2.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n001.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 01:41:50 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.57 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.57 (define @t3 () (@list @t1)) % 0.37/0.57 (define @t4 () (tptp.sorti1 @t2)) % 0.37/0.57 (define @t5 () (@list @t2)) % 0.37/0.57 (define @t6 () (tptp.sorti2 @t1)) % 0.37/0.57 (define @t7 () (tptp.sorti2 @t2)) % 0.37/0.57 (define @t8 () (tptp.op1 @t2 @t2)) % 0.37/0.57 (define @t9 () (not (= @t8 @t2))) % 0.37/0.57 (define @t10 () (=> @t4 @t9)) % 0.37/0.57 (define @t11 () (forall @t5 @t10)) % 0.37/0.57 (define @t12 () (tptp.op2 @t2 @t2)) % 0.37/0.57 (define @t13 () (not (= @t12 @t2))) % 0.37/0.57 (define @t14 () (=> @t7 @t13)) % 0.37/0.57 (define @t15 () (forall @t5 @t14)) % 0.37/0.57 (define @t16 () (not @t15)) % 0.37/0.57 (define @t17 () (@var "X2" $$unsorted)) % 0.37/0.57 (define @t18 () (tptp.j (tptp.h @t17))) % 0.37/0.57 (define @t19 () (tptp.sorti1 @t17)) % 0.37/0.57 (define @t20 () (=> @t19 (= @t18 @t17))) % 0.37/0.57 (define @t21 () (@list @t17)) % 0.37/0.57 (define @t22 () (forall @t21 @t20)) % 0.37/0.57 (define @t23 () (@var "X1" $$unsorted)) % 0.37/0.57 (define @t24 () (tptp.h (tptp.j @t23))) % 0.37/0.57 (define @t25 () (tptp.sorti2 @t23)) % 0.37/0.57 (define @t26 () (=> @t25 (= @t24 @t23))) % 0.37/0.57 (define @t27 () (@list @t23)) % 0.37/0.57 (define @t28 () (forall @t27 @t26)) % 0.37/0.57 (define @t29 () (@var "Z" $$unsorted)) % 0.37/0.57 (define @t30 () (@var "Y" $$unsorted)) % 0.37/0.57 (define @t31 () (tptp.j @t30)) % 0.37/0.57 (define @t32 () (= (tptp.j (tptp.op2 @t30 @t29)) (tptp.op1 @t31 (tptp.j @t29)))) % 0.37/0.57 (define @t33 () (tptp.sorti2 @t29)) % 0.37/0.57 (define @t34 () (@list @t29)) % 0.37/0.57 (define @t35 () (forall @t34 (=> @t33 @t32))) % 0.37/0.57 (define @t36 () (tptp.sorti2 @t30)) % 0.37/0.57 (define @t37 () (=> @t36 @t35)) % 0.37/0.57 (define @t38 () (@list @t30)) % 0.37/0.57 (define @t39 () (forall @t38 @t37)) % 0.37/0.57 (define @t40 () (@var "X" $$unsorted)) % 0.37/0.57 (define @t41 () (@var "W" $$unsorted)) % 0.37/0.57 (define @t42 () (tptp.h @t41)) % 0.37/0.57 (define @t43 () (= (tptp.h (tptp.op1 @t41 @t40)) (tptp.op2 @t42 (tptp.h @t40)))) % 0.37/0.57 (define @t44 () (tptp.sorti1 @t40)) % 0.37/0.57 (define @t45 () (@list @t40)) % 0.37/0.57 (define @t46 () (forall @t45 (=> @t44 @t43))) % 0.37/0.57 (define @t47 () (tptp.sorti1 @t41)) % 0.37/0.57 (define @t48 () (=> @t47 @t46)) % 0.37/0.57 (define @t49 () (@list @t41)) % 0.37/0.57 (define @t50 () (forall @t49 @t48)) % 0.37/0.57 (define @t51 () (and @t50 @t39 @t28 @t22)) % 0.37/0.57 (define @t52 () (not @t51)) % 0.37/0.57 (define @t53 () (tptp.sorti1 (tptp.j @t1))) % 0.37/0.57 (define @t54 () (forall @t3 (=> @t6 @t53))) % 0.37/0.57 (define @t55 () (tptp.sorti2 (tptp.h @t2))) % 0.37/0.57 (define @t56 () (forall @t5 (=> @t4 @t55))) % 0.37/0.57 (define @t57 () (and @t56 @t54)) % 0.37/0.57 (define @t58 () (=> @t57 @t52)) % 0.37/0.57 (define @t59 () (not @t58)) % 0.37/0.57 (define @t60 () (not (= @t2 @t8))) % 0.37/0.57 (define @t61 () (= @t17 @t18)) % 0.37/0.57 (define @t62 () (= @t23 @t24)) % 0.37/0.57 (define @t63 () (@var "BOUND_VARIABLE_7601" $$unsorted)) % 0.37/0.57 (define @t64 () (= (tptp.j (tptp.op2 @t30 @t63)) (tptp.op1 @t31 (tptp.j @t63)))) % 0.37/0.57 (define @t65 () (not (tptp.sorti2 @t63))) % 0.37/0.57 (define @t66 () (not @t36)) % 0.37/0.57 (define @t67 () (or @t65 @t64)) % 0.37/0.57 (define @t68 () (or @t66 @t67)) % 0.37/0.57 (define @t69 () (forall (@list @t30 @t63) @t68)) % 0.37/0.57 (define @t70 () (@list @t63)) % 0.37/0.57 (define @t71 () (forall @t70 @t68)) % 0.37/0.57 (define @t72 () (forall @t70 @t67)) % 0.37/0.57 (define @t73 () (or @t66 @t72)) % 0.37/0.57 (define @t74 () (forall @t34 (or (not @t33) @t32))) % 0.37/0.57 (define @t75 () (@var "BOUND_VARIABLE_7578" $$unsorted)) % 0.37/0.57 (define @t76 () (= (tptp.h (tptp.op1 @t41 @t75)) (tptp.op2 @t42 (tptp.h @t75)))) % 0.37/0.57 (define @t77 () (not (tptp.sorti1 @t75))) % 0.37/0.57 (define @t78 () (not @t47)) % 0.37/0.57 (define @t79 () (or @t77 @t76)) % 0.37/0.57 (define @t80 () (or @t78 @t79)) % 0.37/0.57 (define @t81 () (forall (@list @t41 @t75) @t80)) % 0.37/0.57 (define @t82 () (@list @t75)) % 0.37/0.57 (define @t83 () (forall @t82 @t80)) % 0.37/0.57 (define @t84 () (forall @t82 @t79)) % 0.37/0.57 (define @t85 () (or @t78 @t84)) % 0.37/0.57 (define @t86 () (forall @t45 (or (not @t44) @t43))) % 0.37/0.57 (define @t87 () (not (= @t2 @t12))) % 0.37/0.57 (define @t88 () (@quantifiers_skolemize (forall @t5 (or (not @t7) @t87)) 0)) % 0.37/0.57 (define @t89 () (tptp.sorti2 @t88)) % 0.37/0.57 (define @t90 () (tptp.op2 @t88 @t88)) % 0.37/0.57 (define @t91 () (= @t88 @t90)) % 0.37/0.57 (define @t92 () (not @t91)) % 0.37/0.57 (define @t93 () (not @t89)) % 0.37/0.57 (define @t94 () (or @t93 @t92)) % 0.37/0.57 (define @t95 () (@list true)) % 0.37/0.57 (define @t96 () (@list @t94)) % 0.37/0.57 (define @t97 () (tptp.j @t88)) % 0.37/0.57 (define @t98 () (tptp.op1 @t97 @t97)) % 0.37/0.57 (define @t99 () (= (tptp.j @t90) @t98)) % 0.37/0.57 (define @t100 () (or @t93 @t93 @t99)) % 0.37/0.57 (define @t101 () (@list false false)) % 0.37/0.57 (define @t102 () (tptp.sorti1 @t97)) % 0.37/0.57 (define @t103 () (or @t93 @t102)) % 0.37/0.57 (define @t104 () (= @t97 @t98)) % 0.37/0.57 (define @t105 () (not @t104)) % 0.37/0.57 (define @t106 () (not @t102)) % 0.37/0.57 (define @t107 () (or @t106 @t105)) % 0.37/0.57 (define @t108 () (not @t107)) % 0.37/0.57 (define @t109 () (forall @t5 (or (not @t4) @t60))) % 0.37/0.57 (assume @p1 (forall @t5 (=> @t4 (forall @t3 (=> (tptp.sorti1 @t1) (tptp.sorti1 (tptp.op1 @t2 @t1))))))) % 0.37/0.57 (assume @p2 (forall @t5 (=> @t7 (forall @t3 (=> @t6 (tptp.sorti2 (tptp.op2 @t2 @t1))))))) % 0.37/0.57 (assume @p3 @t11) % 0.37/0.57 (assume @p4 @t16) % 0.37/0.57 (assume @p5 @t59) % 0.37/0.57 (assume @p6 true) % 0.37/0.57 (step @p7 :rule bool-impl-elim :args (@t4 @t60)) % 0.37/0.57 (step @p8 :rule cong :premises (@p7) :args ((forall @t5 (=> @t4 @t60)))) % 0.37/0.57 (step @p9 :rule eq-symm :args (@t8 @t2)) % 0.37/0.57 (step @p10 :rule cong :premises (@p9) :args (@t9)) % 0.37/0.57 (step @p11 :rule refl :args (@t4)) % 0.37/0.57 (step @p12 :rule cong :premises (@p11 @p10) :args (@t10)) % 0.37/0.57 (step @p13 :rule cong :premises (@p12) :args (@t11)) % 0.37/0.57 (step @p14 :rule trans :premises (@p13 @p8)) % 0.37/0.57 (step @p15 :rule eq_resolve :premises (@p3 @p14)) % 0.37/0.57 (step @p16 :rule bool-impl-elim :args (@t19 @t61)) % 0.37/0.57 (step @p17 :rule cong :premises (@p16) :args ((forall @t21 (=> @t19 @t61)))) % 0.37/0.57 (step @p18 :rule eq-symm :args (@t18 @t17)) % 0.37/0.57 (step @p19 :rule refl :args (@t19)) % 0.37/0.57 (step @p20 :rule cong :premises (@p19 @p18) :args (@t20)) % 0.37/0.57 (step @p21 :rule cong :premises (@p20) :args (@t22)) % 0.37/0.57 (step @p22 :rule trans :premises (@p21 @p17)) % 0.37/0.57 (step @p23 :rule bool-impl-elim :args (@t25 @t62)) % 0.37/0.57 (step @p24 :rule cong :premises (@p23) :args ((forall @t27 (=> @t25 @t62)))) % 0.37/0.57 (step @p25 :rule eq-symm :args (@t24 @t23)) % 0.37/0.57 (step @p26 :rule refl :args (@t25)) % 0.37/0.57 (step @p27 :rule cong :premises (@p26 @p25) :args (@t26)) % 0.37/0.57 (step @p28 :rule cong :premises (@p27) :args (@t28)) % 0.37/0.57 (step @p29 :rule trans :premises (@p28 @p24)) % 0.37/0.57 (step @p30 :rule aci_norm :args ((= @t68 (or @t66 @t65 @t64)))) % 0.37/0.57 (step @p31 :rule cong :premises (@p30) :args (@t69)) % 0.37/0.57 (step @p32 :rule quant-merge-prenex :args ((= (forall @t38 @t71) @t69))) % 0.37/0.57 (step @p33 :rule alpha_equiv :args (@t72 (@list @t63) (@list @t29))) % 0.37/0.57 (step @p34 :rule refl :args (@t66)) % 0.37/0.57 (step @p35 :rule nary_cong :premises (@p34 @p33) :args (@t73)) % 0.37/0.57 (step @p36 :rule quant-miniscope-or :args ((= @t71 @t73))) % 0.37/0.57 (step @p37 :rule trans :premises (@p36 @p35)) % 0.37/0.57 (step @p38 :rule symm :premises (@p37)) % 0.37/0.57 (step @p39 :rule cong :premises (@p38) :args ((forall @t38 (or @t66 @t74)))) % 0.37/0.57 (step @p40 :rule trans :premises (@p39 @p32)) % 0.37/0.57 (step @p41 :rule trans :premises (@p40 @p31)) % 0.37/0.57 (step @p42 :rule bool-impl-elim :args (@t36 @t74)) % 0.37/0.57 (step @p43 :rule cong :premises (@p42) :args ((forall @t38 (=> @t36 @t74)))) % 0.37/0.57 (step @p44 :rule trans :premises (@p43 @p41)) % 0.37/0.57 (step @p45 :rule bool-impl-elim :args (@t33 @t32)) % 0.37/0.57 (step @p46 :rule cong :premises (@p45) :args (@t35)) % 0.37/0.57 (step @p47 :rule refl :args (@t36)) % 0.37/0.57 (step @p48 :rule cong :premises (@p47 @p46) :args (@t37)) % 0.37/0.57 (step @p49 :rule cong :premises (@p48) :args (@t39)) % 0.37/0.57 (step @p50 :rule trans :premises (@p49 @p44)) % 0.37/0.57 (step @p51 :rule aci_norm :args ((= @t80 (or @t78 @t77 @t76)))) % 0.37/0.57 (step @p52 :rule cong :premises (@p51) :args (@t81)) % 0.37/0.57 (step @p53 :rule quant-merge-prenex :args ((= (forall @t49 @t83) @t81))) % 0.37/0.57 (step @p54 :rule alpha_equiv :args (@t84 (@list @t75) (@list @t40))) % 0.37/0.57 (step @p55 :rule refl :args (@t78)) % 0.37/0.57 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t85)) % 0.37/0.57 (step @p57 :rule quant-miniscope-or :args ((= @t83 @t85))) % 0.37/0.57 (step @p58 :rule trans :premises (@p57 @p56)) % 0.37/0.57 (step @p59 :rule symm :premises (@p58)) % 0.37/0.57 (step @p60 :rule cong :premises (@p59) :args ((forall @t49 (or @t78 @t86)))) % 0.37/0.57 (step @p61 :rule trans :premises (@p60 @p53)) % 0.37/0.57 (step @p62 :rule trans :premises (@p61 @p52)) % 0.37/0.57 (step @p63 :rule bool-impl-elim :args (@t47 @t86)) % 0.37/0.57 (step @p64 :rule cong :premises (@p63) :args ((forall @t49 (=> @t47 @t86)))) % 0.37/0.57 (step @p65 :rule trans :premises (@p64 @p62)) % 0.37/0.57 (step @p66 :rule bool-impl-elim :args (@t44 @t43)) % 0.37/0.57 (step @p67 :rule cong :premises (@p66) :args (@t46)) % 0.37/0.57 (step @p68 :rule refl :args (@t47)) % 0.37/0.57 (step @p69 :rule cong :premises (@p68 @p67) :args (@t48)) % 0.37/0.57 (step @p70 :rule cong :premises (@p69) :args (@t50)) % 0.37/0.57 (step @p71 :rule trans :premises (@p70 @p65)) % 0.37/0.57 (step @p72 :rule nary_cong :premises (@p71 @p50 @p29 @p22) :args (@t51)) % 0.37/0.57 (step @p73 :rule cong :premises (@p72) :args (@t52)) % 0.37/0.57 (step @p74 :rule bool-impl-elim :args (@t6 @t53)) % 0.37/0.57 (step @p75 :rule cong :premises (@p74) :args (@t54)) % 0.37/0.57 (step @p76 :rule bool-impl-elim :args (@t4 @t55)) % 0.37/0.57 (step @p77 :rule cong :premises (@p76) :args (@t56)) % 0.37/0.57 (step @p78 :rule nary_cong :premises (@p77 @p75) :args (@t57)) % 0.37/0.57 (step @p79 :rule cong :premises (@p78 @p73) :args (@t58)) % 0.37/0.57 (step @p80 :rule cong :premises (@p79) :args (@t59)) % 0.37/0.57 (step @p81 :rule eq_resolve :premises (@p5 @p80)) % 0.37/0.57 (step @p82 :rule not_implies_elim2 :premises (@p81)) % 0.37/0.57 (step @p83 :rule not_not_elim :premises (@p82)) % 0.37/0.57 (step @p84 :rule and_elim :premises (@p83) :args (1)) % 0.37/0.57 (step @p85 :rule instantiate :premises (@p84) :args ((@list @t88 @t88))) % 0.37/0.57 (step @p86 :rule bool-impl-elim :args (@t7 @t87)) % 0.37/0.57 (step @p87 :rule cong :premises (@p86) :args ((forall @t5 (=> @t7 @t87)))) % 0.37/0.57 (step @p88 :rule eq-symm :args (@t12 @t2)) % 0.37/0.57 (step @p89 :rule cong :premises (@p88) :args (@t13)) % 0.37/0.57 (step @p90 :rule refl :args (@t7)) % 0.37/0.57 (step @p91 :rule cong :premises (@p90 @p89) :args (@t14)) % 0.37/0.57 (step @p92 :rule cong :premises (@p91) :args (@t15)) % 0.37/0.57 (step @p93 :rule trans :premises (@p92 @p87)) % 0.37/0.57 (step @p94 :rule cong :premises (@p93) :args (@t16)) % 0.37/0.57 (step @p95 :rule eq_resolve :premises (@p4 @p94)) % 0.37/0.57 (step @p96 :rule skolemize :premises (@p95)) % 0.37/0.57 (step @p97 :rule bool-double-not-elim :args (@t89)) % 0.37/0.57 (step @p98 :rule refl :args (@t94)) % 0.37/0.57 (step @p99 :rule nary_cong :premises (@p98 @p97) :args ((or @t94 (not @t93)))) % 0.37/0.57 (step @p100 :rule cnf_or_neg :args (@t94 0)) % 0.37/0.57 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.37/0.57 (step @p102 :rule reordering :premises (@p101) :args ((or @t89 @t94))) % 0.37/0.57 (step @p103 :rule chain_m_resolution :premises (@p102 @p96) :args (@t89 @t95 @t96)) % 0.37/0.57 (step @p104 :rule cnf_or_pos :args (@t100)) % 0.37/0.57 (step @p105 :rule factoring :premises (@p104)) % 0.37/0.57 (step @p106 :rule reordering :premises (@p105) :args ((or @t93 @t99 (not @t100)))) % 0.37/0.57 (step @p107 :rule chain_m_resolution :premises (@p106 @p103 @p85) :args (@t99 @t101 (@list @t89 @t100))) % 0.37/0.57 (step @p108 :rule bool-double-not-elim :args (@t91)) % 0.37/0.57 (step @p109 :rule nary_cong :premises (@p98 @p108) :args ((or @t94 (not @t92)))) % 0.37/0.57 (step @p110 :rule cnf_or_neg :args (@t94 1)) % 0.37/0.57 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 0.37/0.57 (step @p112 :rule reordering :premises (@p111) :args ((or @t91 @t94))) % 0.37/0.57 (step @p113 :rule chain_m_resolution :premises (@p112 @p96) :args (@t91 @t95 @t96)) % 0.37/0.57 (step @p114 :rule cong :premises (@p113) :args (@t97)) % 0.37/0.57 (step @p115 :rule trans :premises (@p114 @p107)) % 0.37/0.57 (step @p116 :rule not_implies_elim1 :premises (@p81)) % 0.37/0.57 (step @p117 :rule and_elim :premises (@p116) :args (1)) % 0.37/0.57 (step @p118 :rule instantiate :premises (@p117) :args ((@list @t88))) % 0.37/0.57 (step @p119 :rule cnf_or_pos :args (@t103)) % 0.37/0.57 (step @p120 :rule reordering :premises (@p119) :args ((or @t93 @t102 (not @t103)))) % 0.37/0.57 (step @p121 :rule chain_m_resolution :premises (@p120 @p103 @p118) :args (@t102 @t101 (@list @t89 @t103))) % 0.37/0.57 (step @p122 :rule cnf_or_pos :args (@t107)) % 0.37/0.57 (step @p123 :rule reordering :premises (@p122) :args ((or @t106 @t105 @t108))) % 0.37/0.57 (step @p124 :rule chain_m_resolution :premises (@p123 @p121 @p115) :args (@t108 @t101 (@list @t102 @t104))) % 0.37/0.57 (assume-push @p131 @t109) % 0.37/0.57 (step @p126 :rule instantiate :premises (@p15) :args ((@list @t97))) % 0.37/0.57 (step-pop @p132 :rule scope :premises (@p126)) % 0.37/0.57 (step @p127 :rule process_scope :premises (@p132) :args (@t107)) % 0.37/0.57 (step @p129 :rule implies_elim :premises (@p127)) % 0.37/0.57 (step @p130 false :rule chain_m_resolution :premises (@p129 @p124 @p15) :args (false (@list true false) (@list @t107 @t109))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------