%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV260^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:39:14 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV260^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:30:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.26 % (225296)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (225304)dis+10_1_sil=32000:sp=arity:random_seed=3344205436:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.26 % (225304) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-225296-225304"...
% 0.18/0.26 % (225302)% WARNING: option uhcvi not known.
% 0.18/0.26 % (225304)...printing done.
% 0.18/0.26 % (225304)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% 0.18/0.26 thf(type_def_5, type, a: $tType).
% 0.18/0.26 thf(type_def_6, type, b: $tType).
% 0.18/0.26 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.26 thf(func_def_3, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.18/0.26 thf(func_def_4, type, vNOT: ($o > $o)).
% 0.18/0.26 thf(func_def_5, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.18/0.26 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.18/0.26 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.18/0.26 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.18/0.26 thf(func_def_9, type, sK0: ((a > $o) > $o)).
% 0.18/0.26 thf(func_def_10, type, sK1: ((b > $o) > $o)).
% 0.18/0.26 thf(func_def_11, type, sK2: (a > b)).
% 0.18/0.26 thf(func_def_12, type, sK3: (b > $o)).
% 0.18/0.26 thf(func_def_13, type, sK4: (a > $o)).
% 0.18/0.26 thf(func_def_14, type, sK5: (a > $o)).
% 0.18/0.26 thf(func_def_15, type, sK6: (((b > $o) > $o) > b > $o)).
% 0.18/0.26 thf(func_def_16, type, sK7: (((a > $o) > $o) > a > $o)).
% 0.18/0.26 thf(f1,conjecture,(
% 0.18/0.26 ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X9 : (b > $o)] : ((X1 @ X9) => ! [X7 : (a > $o)] : ((X7 = (^[X10 : a] : ((X9 @ (X2 @ X10))))) => (X0 @ X7))) & ! [X7 : (b > $o),X8 : (b > $o),X6 : (b > $o)] : (((X6 = (^[X4 : b] : ((X8 @ X4) & (X7 @ X4)))) & (X1 @ X8) & (X1 @ X7)) => (X1 @ X6)) & ! [X5 : ((b > $o) > $o),X3 : (b > $o)] : (((X3 = (^[X4 : b] : (? [X6 : (b > $o)] : ((X6 @ X4) & (X5 @ X6))))) & ! [X4 : (b > $o)] : ((X5 @ X4) => (X1 @ X4))) => (X1 @ X3)) & ! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : (~$false))) => (X1 @ X3)) & ! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : ($false))) => (X1 @ X3)) & ! [X7 : (a > $o),X8 : (a > $o),X6 : (a > $o)] : (((X6 = (^[X4 : a] : ((X8 @ X4) & (X7 @ X4)))) & (X0 @ X8) & (X0 @ X7)) => (X0 @ X6)) & ! [X5 : ((a > $o) > $o),X3 : (a > $o)] : (((X3 = (^[X4 : a] : (? [X6 : (a > $o)] : ((X6 @ X4) & (X5 @ X6))))) & ! [X4 : (a > $o)] : ((X5 @ X4) => (X0 @ X4))) => (X0 @ X3)) & ! [X3 : (a > $o)] : ((X3 = (^[X4 : a] : (~$false))) => (X0 @ X3)) & ! [X3 : (a > $o)] : ((X3 = (^[X4 : a] : ($false))) => (X0 @ X3))) => ! [X9 : (b > $o)] : (! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : (~(X9 @ X4)))) => (X1 @ X3)) => ! [X7 : (a > $o)] : ((X7 = (^[X10 : a] : ((X9 @ (X2 @ X10))))) => ! [X3 : (a > $o)] : ((X3 = (^[X4 : a] : (~(X7 @ X4)))) => (X0 @ X3)))))),
% 0.18/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCLOSED_THM1_pme)).
% 0.18/0.26 thf(f2,negated_conjecture,(
% 0.18/0.26 ~ ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X9 : (b > $o)] : ((X1 @ X9) => ! [X7 : (a > $o)] : ((X7 = (^[X10 : a] : ((X9 @ (X2 @ X10))))) => (X0 @ X7))) & ! [X7 : (b > $o),X8 : (b > $o),X6 : (b > $o)] : (((X6 = (^[X4 : b] : ((X8 @ X4) & (X7 @ X4)))) & (X1 @ X8) & (X1 @ X7)) => (X1 @ X6)) & ! [X5 : ((b > $o) > $o),X3 : (b > $o)] : (((X3 = (^[X4 : b] : (? [X6 : (b > $o)] : ((X6 @ X4) & (X5 @ X6))))) & ! [X4 : (b > $o)] : ((X5 @ X4) => (X1 @ X4))) => (X1 @ X3)) & ! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : (~$false))) => (X1 @ X3)) & ! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : ($false))) => (X1 @ X3)) & ! [X7 : (a > $o),X8 : (a > $o),X6 : (a > $o)] : (((X6 = (^[X4 : a] : ((X8 @ X4) & (X7 @ X4)))) & (X0 @ X8) & (X0 @ X7)) => (X0 @ X6)) & ! [X5 : ((a > $o) > $o),X3 : (a > $o)] : (((X3 = (^[X4 : a] : (? [X6 : (a > $o)] : ((X6 @ X4) & (X5 @ X6))))) & ! [X4 : (a > $o)] : ((X5 @ X4) => (X0 @ X4))) => (X0 @ X3)) & ! [X3 : (a > $o)] : ((X3 = (^[X4 : a] : (~$false))) => (X0 @ X3)) & ! [X3 : (a > $o)] : ((X3 = (^[X4 : a] : ($false))) => (X0 @ X3))) => ! [X9 : (b > $o)] : (! [X3 : (b > $o)] : ((X3 = (^[X4 : b] : (~(X9 @ X4)))) => (X1 @ X3)) => ! [X7 : (a > $o)] : ((X7 = (^[X10 : a] : ((X9 @ (X2 @ X10))))) => ! [X3 : (a > $o)] : ((X3 = (^[X4 : a] : (~(X7 @ X4)))) => (X0 @ X3)))))),
% 0.18/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.18/0.26 thf(f3,plain,(
% 0.18/0.26 ~ ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X3 : (b > $o)] : ((X1 @ X3) => ! [X4 : (a > $o)] : ((X4 = (^[X5 : a] : ((X3 @ (X2 @ X5))))) => (X0 @ X4))) & ! [X6 : (b > $o),X7 : (b > $o),X8 : (b > $o)] : (((X8 = (^[X9 : b] : ((X7 @ X9) & (X6 @ X9)))) & (X1 @ X7) & (X1 @ X6)) => (X1 @ X8)) & ! [X10 : ((b > $o) > $o),X11 : (b > $o)] : (((X11 = (^[X12 : b] : (? [X13 : (b > $o)] : ((X13 @ X12) & (X10 @ X13))))) & ! [X14 : (b > $o)] : ((X10 @ X14) => (X1 @ X14))) => (X1 @ X11)) & ! [X15 : (b > $o)] : ((X15 = (^[X16 : b] : (~$false))) => (X1 @ X15)) & ! [X17 : (b > $o)] : ((X17 = (^[X18 : b] : ($false))) => (X1 @ X17)) & ! [X19 : (a > $o),X20 : (a > $o),X21 : (a > $o)] : (((X21 = (^[X22 : a] : ((X20 @ X22) & (X19 @ X22)))) & (X0 @ X20) & (X0 @ X19)) => (X0 @ X21)) & ! [X23 : ((a > $o) > $o),X24 : (a > $o)] : (((X24 = (^[X25 : a] : (? [X26 : (a > $o)] : ((X26 @ X25) & (X23 @ X26))))) & ! [X27 : (a > $o)] : ((X23 @ X27) => (X0 @ X27))) => (X0 @ X24)) & ! [X28 : (a > $o)] : ((X28 = (^[X29 : a] : (~$false))) => (X0 @ X28)) & ! [X30 : (a > $o)] : ((X30 = (^[X31 : a] : ($false))) => (X0 @ X30))) => ! [X32 : (b > $o)] : (! [X33 : (b > $o)] : ((X33 = (^[X34 : b] : (~(X32 @ X34)))) => (X1 @ X33)) => ! [X35 : (a > $o)] : ((X35 = (^[X36 : a] : ((X32 @ (X2 @ X36))))) => ! [X37 : (a > $o)] : ((X37 = (^[X38 : a] : (~(X35 @ X38)))) => (X0 @ X37)))))),
% 0.18/0.26 inference(rectify,[],[f2])).
% 0.18/0.26 thf(f4,plain,(
% 0.18/0.26 ~ ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X3 : (b > $o)] : ((((X1 @ X3)) = $true) => ! [X4 : (a > $o)] : (((^[Y0 : a]: (X3 @ (X2 @ Y0))) = X4) => (((X0 @ X4)) = $true))) & ! [X6 : (b > $o),X7 : (b > $o),X8 : (b > $o)] : ((((^[Y0 : b]: ((X6 @ Y0) & (X7 @ Y0))) = X8) & (((X1 @ X7)) = $true) & (((X1 @ X6)) = $true)) => (((X1 @ X8)) = $true)) & ! [X10 : ((b > $o) > $o),X11 : (b > $o)] : ((((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X10 @ Y1) & (Y1 @ Y0))))) = X11) & ! [X14 : (b > $o)] : ((((X10 @ X14)) = $true) => (((X1 @ X14)) = $true))) => (((X1 @ X11)) = $true)) & ! [X15 : (b > $o)] : (((^[Y0 : b]: (~ $false)) = X15) => (((X1 @ X15)) = $true)) & ! [X17 : (b > $o)] : (((^[Y0 : b]: ($false)) = X17) => (((X1 @ X17)) = $true)) & ! [X19 : (a > $o),X20 : (a > $o),X21 : (a > $o)] : ((((^[Y0 : a]: ((X19 @ Y0) & (X20 @ Y0))) = X21) & (((X0 @ X20)) = $true) & (((X0 @ X19)) = $true)) => (((X0 @ X21)) = $true)) & ! [X23 : ((a > $o) > $o),X24 : (a > $o)] : ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X23 @ Y1) & (Y1 @ Y0))))) = X24) & ! [X27 : (a > $o)] : ((((X23 @ X27)) = $true) => (((X0 @ X27)) = $true))) => (((X0 @ X24)) = $true)) & ! [X28 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X28) => (((X0 @ X28)) = $true)) & ! [X30 : (a > $o)] : (((^[Y0 : a]: ($false)) = X30) => (((X0 @ X30)) = $true))) => ! [X32 : (b > $o)] : (! [X33 : (b > $o)] : (((^[Y0 : b]: (~ (X32 @ Y0))) = X33) => (((X1 @ X33)) = $true)) => ! [X35 : (a > $o)] : (((^[Y0 : a]: (X32 @ (X2 @ Y0))) = X35) => ! [X37 : (a > $o)] : (((^[Y0 : a]: (~ (X35 @ Y0))) = X37) => (((X0 @ X37)) = $true)))))),
% 0.18/0.26 inference(fool_elimination,[],[f3])).
% 0.18/0.26 thf(f5,plain,(
% 0.18/0.26 ~ ! [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : ((! [X3 : (b > $o)] : ((((X1 @ X3)) = $true) => ! [X4 : (a > $o)] : (((^[Y0 : a]: (X3 @ (X2 @ Y0))) = X4) => (((X0 @ X4)) = $true))) & ! [X5 : (b > $o),X6 : (b > $o),X7 : (b > $o)] : ((((^[Y0 : b]: ((X5 @ Y0) & (X6 @ Y0))) = X7) & (((X1 @ X6)) = $true) & ($true = ((X1 @ X5)))) => (((X1 @ X7)) = $true)) & ! [X8 : ((b > $o) > $o),X9 : (b > $o)] : ((((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X8 @ Y1) & (Y1 @ Y0))))) = X9) & ! [X10 : (b > $o)] : (($true = ((X8 @ X10))) => ($true = ((X1 @ X10))))) => (((X1 @ X9)) = $true)) & ! [X11 : (b > $o)] : (((^[Y0 : b]: (~ $false)) = X11) => (((X1 @ X11)) = $true)) & ! [X12 : (b > $o)] : (((^[Y0 : b]: ($false)) = X12) => ($true = ((X1 @ X12)))) & ! [X13 : (a > $o),X14 : (a > $o),X15 : (a > $o)] : ((((^[Y0 : a]: ((X13 @ Y0) & (X14 @ Y0))) = X15) & ($true = ((X0 @ X14))) & ($true = ((X0 @ X13)))) => ($true = ((X0 @ X15)))) & ! [X16 : ((a > $o) > $o),X17 : (a > $o)] : ((((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X16 @ Y1) & (Y1 @ Y0))))) = X17) & ! [X18 : (a > $o)] : (($true = ((X16 @ X18))) => ($true = ((X0 @ X18))))) => ($true = ((X0 @ X17)))) & ! [X19 : (a > $o)] : (((^[Y0 : a]: (~ $false)) = X19) => (((X0 @ X19)) = $true)) & ! [X20 : (a > $o)] : (((^[Y0 : a]: ($false)) = X20) => (((X0 @ X20)) = $true))) => ! [X21 : (b > $o)] : (! [X22 : (b > $o)] : (((^[Y0 : b]: (~ (X21 @ Y0))) = X22) => ($true = ((X1 @ X22)))) => ! [X23 : (a > $o)] : (((^[Y0 : a]: (X21 @ (X2 @ Y0))) = X23) => ! [X24 : (a > $o)] : (((^[Y0 : a]: (~ (X23 @ Y0))) = X24) => (((X0 @ X24)) = $true)))))),
% 0.18/0.27 inference(rectify,[],[f4])).
% 0.18/0.27 thf(f6,plain,(
% 0.18/0.27 ? [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : (? [X21 : (b > $o)] : (? [X23 : (a > $o)] : (? [X24 : (a > $o)] : ((((X0 @ X24)) != $true) & ((^[Y0 : a]: (~ (X23 @ Y0))) = X24)) & ((^[Y0 : a]: (X21 @ (X2 @ Y0))) = X23)) & ! [X22 : (b > $o)] : (($true = ((X1 @ X22))) | ((^[Y0 : b]: (~ (X21 @ Y0))) != X22))) & (! [X3 : (b > $o)] : (! [X4 : (a > $o)] : ((((X0 @ X4)) = $true) | ((^[Y0 : a]: (X3 @ (X2 @ Y0))) != X4)) | (((X1 @ X3)) != $true)) & ! [X5 : (b > $o),X6 : (b > $o),X7 : (b > $o)] : ((((X1 @ X7)) = $true) | (((^[Y0 : b]: ((X5 @ Y0) & (X6 @ Y0))) != X7) | (((X1 @ X6)) != $true) | ($true != ((X1 @ X5))))) & ! [X8 : ((b > $o) > $o),X9 : (b > $o)] : ((((X1 @ X9)) = $true) | (((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X8 @ Y1) & (Y1 @ Y0))))) != X9) | ? [X10 : (b > $o)] : (($true != ((X1 @ X10))) & ($true = ((X8 @ X10)))))) & ! [X11 : (b > $o)] : ((((X1 @ X11)) = $true) | ((^[Y0 : b]: (~ $false)) != X11)) & ! [X12 : (b > $o)] : (($true = ((X1 @ X12))) | ((^[Y0 : b]: ($false)) != X12)) & ! [X13 : (a > $o),X14 : (a > $o),X15 : (a > $o)] : (($true = ((X0 @ X15))) | (((^[Y0 : a]: ((X13 @ Y0) & (X14 @ Y0))) != X15) | ($true != ((X0 @ X14))) | ($true != ((X0 @ X13))))) & ! [X16 : ((a > $o) > $o),X17 : (a > $o)] : (($true = ((X0 @ X17))) | (((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X16 @ Y1) & (Y1 @ Y0))))) != X17) | ? [X18 : (a > $o)] : (($true != ((X0 @ X18))) & ($true = ((X16 @ X18)))))) & ! [X19 : (a > $o)] : ((((X0 @ X19)) = $true) | ((^[Y0 : a]: (~ $false)) != X19)) & ! [X20 : (a > $o)] : ((((X0 @ X20)) = $true) | ((^[Y0 : a]: ($false)) != X20))))),
% 0.18/0.27 inference(ennf_transformation,[],[f5])).
% 0.18/0.27 thf(f7,plain,(
% 0.18/0.27 ? [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : (? [X21 : (b > $o)] : (? [X23 : (a > $o)] : (? [X24 : (a > $o)] : ((((X0 @ X24)) != $true) & ((^[Y0 : a]: (~ (X23 @ Y0))) = X24)) & ((^[Y0 : a]: (X21 @ (X2 @ Y0))) = X23)) & ! [X22 : (b > $o)] : (($true = ((X1 @ X22))) | ((^[Y0 : b]: (~ (X21 @ Y0))) != X22))) & ! [X3 : (b > $o)] : (! [X4 : (a > $o)] : ((((X0 @ X4)) = $true) | ((^[Y0 : a]: (X3 @ (X2 @ Y0))) != X4)) | (((X1 @ X3)) != $true)) & ! [X5 : (b > $o),X6 : (b > $o),X7 : (b > $o)] : ((((X1 @ X7)) = $true) | ((^[Y0 : b]: ((X5 @ Y0) & (X6 @ Y0))) != X7) | (((X1 @ X6)) != $true) | ($true != ((X1 @ X5)))) & ! [X8 : ((b > $o) > $o),X9 : (b > $o)] : ((((X1 @ X9)) = $true) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X8 @ Y1) & (Y1 @ Y0))))) != X9) | ? [X10 : (b > $o)] : (($true != ((X1 @ X10))) & ($true = ((X8 @ X10))))) & ! [X11 : (b > $o)] : ((((X1 @ X11)) = $true) | ((^[Y0 : b]: (~ $false)) != X11)) & ! [X12 : (b > $o)] : (($true = ((X1 @ X12))) | ((^[Y0 : b]: ($false)) != X12)) & ! [X13 : (a > $o),X14 : (a > $o),X15 : (a > $o)] : (($true = ((X0 @ X15))) | ((^[Y0 : a]: ((X13 @ Y0) & (X14 @ Y0))) != X15) | ($true != ((X0 @ X14))) | ($true != ((X0 @ X13)))) & ! [X16 : ((a > $o) > $o),X17 : (a > $o)] : (($true = ((X0 @ X17))) | ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X16 @ Y1) & (Y1 @ Y0))))) != X17) | ? [X18 : (a > $o)] : (($true != ((X0 @ X18))) & ($true = ((X16 @ X18))))) & ! [X19 : (a > $o)] : ((((X0 @ X19)) = $true) | ((^[Y0 : a]: (~ $false)) != X19)) & ! [X20 : (a > $o)] : ((((X0 @ X20)) = $true) | ((^[Y0 : a]: ($false)) != X20)))),
% 0.18/0.27 inference(flattening,[],[f6])).
% 0.18/0.27 thf(f8,plain,(
% 0.18/0.27 ? [X0 : ((a > $o) > $o),X1 : ((b > $o) > $o),X2 : (a > b)] : (? [X3 : (b > $o)] : (? [X4 : (a > $o)] : (? [X5 : (a > $o)] : (($true != ((X0 @ X5))) & ((^[Y0 : a]: (~ (X4 @ Y0))) = X5)) & ((^[Y0 : a]: (X3 @ (X2 @ Y0))) = X4)) & ! [X6 : (b > $o)] : ((((X1 @ X6)) = $true) | ((^[Y0 : b]: (~ (X3 @ Y0))) != X6))) & ! [X7 : (b > $o)] : (! [X8 : (a > $o)] : ((((X0 @ X8)) = $true) | ((^[Y0 : a]: (X7 @ (X2 @ Y0))) != X8)) | (((X1 @ X7)) != $true)) & ! [X9 : (b > $o),X10 : (b > $o),X11 : (b > $o)] : ((((X1 @ X11)) = $true) | ((^[Y0 : b]: ((X9 @ Y0) & (X10 @ Y0))) != X11) | ($true != ((X1 @ X10))) | (((X1 @ X9)) != $true)) & ! [X12 : ((b > $o) > $o),X13 : (b > $o)] : (($true = ((X1 @ X13))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X12 @ Y1) & (Y1 @ Y0))))) != X13) | ? [X14 : (b > $o)] : ((((X1 @ X14)) != $true) & ($true = ((X12 @ X14))))) & ! [X15 : (b > $o)] : ((((X1 @ X15)) = $true) | ((^[Y0 : b]: (~ $false)) != X15)) & ! [X16 : (b > $o)] : (($true = ((X1 @ X16))) | ((^[Y0 : b]: ($false)) != X16)) & ! [X17 : (a > $o),X18 : (a > $o),X19 : (a > $o)] : ((((X0 @ X19)) = $true) | ((^[Y0 : a]: ((X17 @ Y0) & (X18 @ Y0))) != X19) | ($true != ((X0 @ X18))) | ($true != ((X0 @ X17)))) & ! [X20 : ((a > $o) > $o),X21 : (a > $o)] : ((((X0 @ X21)) = $true) | ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X20 @ Y1) & (Y1 @ Y0))))) != X21) | ? [X22 : (a > $o)] : (($true != ((X0 @ X22))) & ($true = ((X20 @ X22))))) & ! [X23 : (a > $o)] : (($true = ((X0 @ X23))) | ((^[Y0 : a]: (~ $false)) != X23)) & ! [X24 : (a > $o)] : ((((X0 @ X24)) = $true) | ((^[Y0 : a]: ($false)) != X24)))),
% 0.18/0.27 inference(rectify,[],[f7])).
% 0.18/0.27 thf(f9,plain,(
% 0.18/0.27 (((($true != ((sK0 @ sK5))) & (sK5 = (^[Y0 : a]: (~ (sK4 @ Y0))))) & (sK4 = (^[Y0 : a]: (sK3 @ (sK2 @ Y0))))) & ! [X6 : (b > $o)] : (($true = ((sK1 @ X6))) | ((^[Y0 : b]: (~ (sK3 @ Y0))) != X6))) & ! [X7 : (b > $o)] : (! [X8 : (a > $o)] : (($true = ((sK0 @ X8))) | ((^[Y0 : a]: (X7 @ (sK2 @ Y0))) != X8)) | ($true != ((sK1 @ X7)))) & ! [X9 : (b > $o),X10 : (b > $o),X11 : (b > $o)] : (($true = ((sK1 @ X11))) | ((^[Y0 : b]: ((X9 @ Y0) & (X10 @ Y0))) != X11) | ($true != ((sK1 @ X10))) | ($true != ((sK1 @ X9)))) & ! [X12 : ((b > $o) > $o),X13 : (b > $o)] : (($true = ((sK1 @ X13))) | ((^[Y0 : b]: (?? @ (b > $o) @ (^[Y1 : b > $o]: ((X12 @ Y1) & (Y1 @ Y0))))) != X13) | (($true != ((sK1 @ (sK6 @ X12)))) & ($true = ((X12 @ (sK6 @ X12)))))) & ! [X15 : (b > $o)] : (($true = ((sK1 @ X15))) | ((^[Y0 : b]: (~ $false)) != X15)) & ! [X16 : (b > $o)] : (($true = ((sK1 @ X16))) | ((^[Y0 : b]: ($false)) != X16)) & ! [X17 : (a > $o),X18 : (a > $o),X19 : (a > $o)] : (($true = ((sK0 @ X19))) | ((^[Y0 : a]: ((X17 @ Y0) & (X18 @ Y0))) != X19) | ($true != ((sK0 @ X18))) | ($true != ((sK0 @ X17)))) & ! [X20 : ((a > $o) > $o),X21 : (a > $o)] : (($true = ((sK0 @ X21))) | ((^[Y0 : a]: (?? @ (a > $o) @ (^[Y1 : a > $o]: ((X20 @ Y1) & (Y1 @ Y0))))) != X21) | (($true != ((sK0 @ (sK7 @ X20)))) & ($true = ((X20 @ (sK7 @ X20)))))) & ! [X23 : (a > $o)] : (($true = ((sK0 @ X23))) | ((^[Y0 : a]: (~ $false)) != X23)) & ! [X24 : (a > $o)] : (($true = ((sK0 @ X24))) | ((^[Y0 : a]: ($false)) != X24))),
% 0.18/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X22,sK7 @ X20),skolemize(X22,sK7 @ X20)],[f8])).
% 0.18/0.27 thf(f20,plain,(
% 0.18/0.27 ( ! [X8 : (a > $o),X7 : (b > $o)] : (($true = ((sK0 @ X8))) | ((^[Y0 : a]: (X7 @ (sK2 @ Y0))) != X8) | ($true != ((sK1 @ X7)))) )),
% 0.18/0.27 inference(cnf_transformation,[],[f9])).
% 0.18/0.27 thf(f21,plain,(
% 0.18/0.27 ( ! [X6 : (b > $o)] : (($true = ((sK1 @ X6))) | ((^[Y0 : b]: (~ (sK3 @ Y0))) != X6)) )),
% 0.18/0.27 inference(cnf_transformation,[],[f9])).
% 0.18/0.27 thf(f22,plain,(
% 0.18/0.27 (sK4 = (^[Y0 : a]: (sK3 @ (sK2 @ Y0))))),
% 0.18/0.27 inference(cnf_transformation,[],[f9])).
% 0.18/0.27 thf(f23,plain,(
% 0.18/0.27 (sK5 = (^[Y0 : a]: (~ (sK4 @ Y0))))),
% 0.18/0.27 inference(cnf_transformation,[],[f9])).
% 0.18/0.27 thf(f24,plain,(
% 0.18/0.27 ($true != ((sK0 @ sK5)))),
% 0.18/0.27 inference(cnf_transformation,[],[f9])).
% 0.18/0.27 thf(f27,plain,(
% 0.18/0.27 (sK5 = (^[Y0 : a]: (~ ((^[Y1 : a]: (sK3 @ (sK2 @ Y1))) @ Y0))))),
% 0.18/0.27 inference(definition_unfolding,[],[f23,f22])).
% 0.18/0.27 thf(f28,plain,(
% 0.18/0.27 ($true != ((sK0 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK3 @ (sK2 @ Y1))) @ Y0))))))),
% 0.18/0.27 inference(definition_unfolding,[],[f24,f27])).
% 0.18/0.27 thf(f29,plain,(
% 0.18/0.27 ($true = ((sK1 @ (^[Y0 : b]: (~ (sK3 @ Y0))))))),
% 0.18/0.27 inference(equality_resolution,[],[f21])).
% 0.18/0.27 thf(f30,plain,(
% 0.18/0.27 ( ! [X7 : (b > $o)] : (($true != ((sK1 @ X7))) | ($true = ((sK0 @ (^[Y0 : a]: (X7 @ (sK2 @ Y0))))))) )),
% 0.18/0.27 inference(equality_resolution,[],[f20])).
% 0.18/0.27 thf(f43,plain,(
% 0.18/0.27 ($true != ((sK0 @ (^[Y0 : a]: (~ (sK3 @ (sK2 @ Y0)))))))),
% 0.18/0.27 inference(beta-eta_normalization,[],[f28])).
% 0.18/0.27 thf(f46,plain,(
% 0.18/0.27 ($true != $true) | ($true = ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (~ (sK3 @ Y1))) @ (sK2 @ Y0))))))),
% 0.18/0.27 inference(constrained_superposition,[],[f30,f29])).
% 0.18/0.27 thf(f47,plain,(
% 0.18/0.27 ($true = ((sK0 @ (^[Y0 : a]: ((^[Y1 : b]: (~ (sK3 @ Y1))) @ (sK2 @ Y0))))))),
% 0.18/0.27 inference(trivial_inequality_removal,[],[f46])).
% 0.18/0.27 thf(f48,plain,(
% 0.18/0.27 ($true = ((sK0 @ (^[Y0 : a]: (~ (sK3 @ (sK2 @ Y0)))))))),
% 0.18/0.27 inference(beta-eta_normalization,[],[f47])).
% 0.18/0.27 thf(f53,plain,(
% 0.18/0.27 $false),
% 0.18/0.27 inference(forward_subsumption_resolution,[],[f48,f43])).
% 0.18/0.27 % SZS output end Proof for theBenchmark
% 0.18/0.27 % (225304)------------------------------
% 0.18/0.27 % (225304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (225304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (225304)CaDiCaL version: 2.1.3
% 0.18/0.27 % (225304)Termination reason: Refutation
% 0.18/0.27 % (225304)Time elapsed: 0.003 s
% 0.18/0.27 % (225304)Peak memory usage: 12 MB
% 0.18/0.27 % (225304)Instructions burned: 9 (million)
% 0.18/0.27 % (225296)Success in time 0.033 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------