%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT284^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 07:49:08 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT284^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n026.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 18:22:57 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.20/0.29 % (976821)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (976827)% WARNING: option uhcvi not known.
% 0.20/0.29 % (976827)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=317505455:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (976827)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (976827)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (976828)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=683929899:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (976826)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=279528199_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (976829)dis+10_1_sil=32000:sp=arity:random_seed=1624058502:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (976830)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3291768144:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (976830)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (976832)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=423071061:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (976831)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1560284056:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (976838)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2511527071:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (976827) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-976821-976827"...
% 0.20/0.29 % (976827)...printing done.
% 0.20/0.29 % (976827)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, 'type/nums/num': $tType).
% 0.20/0.29 thf(type_def_6, type, 'type/ind_types/list': $tType > $tType).
% 0.20/0.29 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(type_def_8, type, sK1: $tType).
% 0.20/0.29 thf(func_def_0, type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_1, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_2, type, 'const/nums/BIT1': ('type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 0.20/0.29 thf(func_def_4, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.20/0.29 thf(func_def_5, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.29 thf(func_def_6, type, 'const/arith/+': ('type/nums/num' > 'type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_7, type, 'const/arith/<=': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.20/0.29 thf(func_def_8, type, 'const/arith/<': ('type/nums/num' > 'type/nums/num' > $o)).
% 0.20/0.29 thf(func_def_10, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_14, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_15, type, vAND: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_16, type, sK0: !>[X0: $tType, X1: $tType]:(((X1 > 'type/ind_types/list' @ X1 > X0 > X0) > X0 > 'type/ind_types/list' @ X1 > X0))).
% 0.20/0.29 thf(func_def_17, type, sK2: sK1).
% 0.20/0.29 thf(func_def_18, type, sK3: 'type/ind_types/list' @ sK1).
% 0.20/0.29 thf(func_def_21, type, sK4: ('type/nums/num' > 'type/nums/num' > 'type/nums/num')).
% 0.20/0.29 thf(func_def_22, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_23, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_24, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_25, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_27, type, db5: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_28, type, db7: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_29, type, db6: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : (X0 > 'type/ind_types/list' @ X0 > X1 > X1)] : ? [X4 : ('type/ind_types/list' @ X0 > X1)] : (! [X5 : X0,X6 : 'type/ind_types/list' @ X0] : (((X4 @ ('const/ind_types/CONS' @ X0 @ X5 @ X6))) = ((X3 @ X5 @ X6 @ (X4 @ X6)))) & (((X4 @ 'const/ind_types/NIL' @ X0)) = X2))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/ind_types/list_RECURSION_')).
% 0.20/0.29 thf(f11,conjecture,(
% 0.20/0.29 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X1 @ X2)) != 'const/ind_types/NIL' @ X0)),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/NOT_CONS_NIL_')).
% 0.20/0.29 thf(f12,negated_conjecture,(
% 0.20/0.29 ~ ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X1 @ X2)) != 'const/ind_types/NIL' @ X0)),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f11])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X1 > 'type/ind_types/list' @ X1 > X0 > X0)] : ? [X4 : ('type/ind_types/list' @ X1 > X0)] : (! [X5 : X1,X6 : 'type/ind_types/list' @ X1] : (((X4 @ ('const/ind_types/CONS' @ X1 @ X5 @ X6))) = ((X3 @ X5 @ X6 @ (X4 @ X6)))) & (((X4 @ 'const/ind_types/NIL' @ X1)) = X2))),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ('const/ind_types/NIL' @ X0 = (('const/ind_types/CONS' @ X0 @ X1 @ X2)))),
% 0.20/0.29 inference(ennf_transformation,[],[f12])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X1 > 'type/ind_types/list' @ X1 > X0 > X0)] : (! [X5 : X1,X6 : 'type/ind_types/list' @ X1] : (((sK0 @ X0 @ X1 @ X3 @ X2 @ ('const/ind_types/CONS' @ X1 @ X5 @ X6))) = ((X3 @ X5 @ X6 @ (sK0 @ X0 @ X1 @ X3 @ X2 @ X6)))) & (((sK0 @ X0 @ X1 @ X3 @ X2 @ 'const/ind_types/NIL' @ X1)) = X2))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X0 @ X1 @ X3 @ X2)],[f18])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 ('const/ind_types/NIL' @ sK1 = (('const/ind_types/CONS' @ sK1 @ sK2 @ sK3)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f19])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X1 > 'type/ind_types/list' @ X1 > X0 > X0)] : ((((sK0 @ X0 @ X1 @ X3 @ X2 @ 'const/ind_types/NIL' @ X1)) = X2)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f20])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X1 > 'type/ind_types/list' @ X1 > X0 > X0),X6 : 'type/ind_types/list' @ X1,X5 : X1] : ((((sK0 @ X0 @ X1 @ X3 @ X2 @ ('const/ind_types/CONS' @ X1 @ X5 @ X6))) = ((X3 @ X5 @ X6 @ (sK0 @ X0 @ X1 @ X3 @ X2 @ X6))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f20])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 ('const/ind_types/NIL' @ sK1 = (('const/ind_types/CONS' @ sK1 @ sK2 @ sK3)))),
% 0.20/0.29 inference(cnf_transformation,[],[f21])).
% 0.20/0.29 thf(f34,definition,(
% 0.20/0.29 ($true != $false)),
% 0.20/0.29 introduced(theory,[fool_distinctness_axiom])).
% 0.20/0.29 thf(f96,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ sK1,X3 : X0,X1 : (X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ sK1 > sK1),X4 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ sK1 = ((sK0 @ 'type/ind_types/list' @ sK1 @ X0 @ (^[Y0 : X0]: ((^[Y1 : 'type/ind_types/list' @ X0]: ((^[Y2 : 'type/ind_types/list' @ sK1]: ('const/ind_types/CONS' @ sK1 @ (X1 @ Y0 @ Y1 @ Y2) @ ((^[Y3 : X0]: ((^[Y4 : 'type/ind_types/list' @ X0]: ((^[Y5 : 'type/ind_types/list' @ sK1]: (sK3)))))) @ Y0 @ Y1 @ Y2))))))) @ X2 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)))) | (sK2 != ((X1 @ X3 @ X4 @ (sK0 @ 'type/ind_types/list' @ sK1 @ X0 @ (^[Y0 : X0]: ((^[Y1 : 'type/ind_types/list' @ X0]: ((^[Y2 : 'type/ind_types/list' @ sK1]: ('const/ind_types/CONS' @ sK1 @ (X1 @ Y0 @ Y1 @ Y2) @ sK3)))))) @ X2 @ X4))))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f23,f33])).
% 0.20/0.29 thf(f114,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ sK1,X3 : X0,X1 : (X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ sK1 > sK1),X4 : 'type/ind_types/list' @ X0] : ((sK2 != ((X1 @ X3 @ X4 @ (sK0 @ 'type/ind_types/list' @ sK1 @ X0 @ (^[Y0 : X0]: ((^[Y1 : 'type/ind_types/list' @ X0]: ((^[Y2 : 'type/ind_types/list' @ sK1]: ('const/ind_types/CONS' @ sK1 @ (X1 @ Y0 @ Y1 @ Y2) @ sK3)))))) @ X2 @ X4)))) | ('const/ind_types/NIL' @ sK1 = ((sK0 @ 'type/ind_types/list' @ sK1 @ X0 @ (^[Y0 : X0]: ((^[Y1 : 'type/ind_types/list' @ X0]: ((^[Y2 : 'type/ind_types/list' @ sK1]: ('const/ind_types/CONS' @ sK1 @ (X1 @ Y0 @ Y1 @ Y2) @ sK3)))))) @ X2 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4))))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f96])).
% 0.20/0.29 thf(f137,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ sK1] : (('const/ind_types/NIL' @ sK1 = ((sK0 @ 'type/ind_types/list' @ sK1 @ X0 @ (^[Y0 : X0]: ((^[Y1 : 'type/ind_types/list' @ X0]: ((^[Y2 : 'type/ind_types/list' @ sK1]: ('const/ind_types/CONS' @ sK1 @ ((^[Y3 : X0]: ((^[Y4 : 'type/ind_types/list' @ X0]: ((^[Y5 : 'type/ind_types/list' @ sK1]: (sK2)))))) @ Y0 @ Y1 @ Y2) @ sK3)))))) @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))))) )),
% 0.20/0.29 inference(equality_resolution,[],[f114])).
% 0.20/0.29 thf(f138,plain,(
% 0.20/0.29 ( ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ sK1] : (('const/ind_types/NIL' @ sK1 = ((sK0 @ 'type/ind_types/list' @ sK1 @ X0 @ (^[Y0 : X0]: ((^[Y1 : 'type/ind_types/list' @ X0]: ((^[Y2 : 'type/ind_types/list' @ sK1]: ('const/ind_types/CONS' @ sK1 @ sK2 @ sK3)))))) @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))))) )),
% 0.20/0.29 inference(beta-eta_normalization,[],[f137])).
% 0.20/0.29 thf(f199,plain,(
% 0.20/0.29 ( ! [X0 : 'type/ind_types/list' @ sK1] : (('const/ind_types/NIL' @ sK1 = ((sK0 @ 'type/ind_types/list' @ sK1 @ sK1 @ (^[Y0 : sK1]: ((^[Y1 : 'type/ind_types/list' @ sK1]: ((^[Y2 : 'type/ind_types/list' @ sK1]: ('const/ind_types/NIL' @ sK1)))))) @ X0 @ 'const/ind_types/NIL' @ sK1)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f138,f33])).
% 0.20/0.29 thf(f231,plain,(
% 0.20/0.29 ( ! [X0 : 'type/ind_types/list' @ sK1] : (('const/ind_types/NIL' @ sK1 = X0)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f199,f22])).
% 0.20/0.29 thf(f262,plain,(
% 0.20/0.29 ( ! [X1 : $tType,X2 : (sK1 > 'type/ind_types/list' @ sK1 > X1 > X1),X3 : X1,X0 : 'type/ind_types/list' @ sK1] : ((((sK0 @ X1 @ sK1 @ X2 @ X3 @ X0)) = X3)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f22,f231])).
% 0.20/0.29 thf(f306,plain,(
% 0.20/0.29 ( ! [X1 : $tType,X2 : (sK1 > 'type/ind_types/list' @ sK1 > X1 > X1),X3 : sK1,X0 : X1,X4 : 'type/ind_types/list' @ sK1] : ((((sK0 @ X1 @ sK1 @ X2 @ X0 @ ('const/ind_types/CONS' @ sK1 @ X3 @ X4))) = ((X2 @ X3 @ X4 @ X0)))) )),
% 0.20/0.29 inference(constrained_superposition,[],[f23,f262])).
% 0.20/0.29 thf(f312,plain,(
% 0.20/0.29 ( ! [X1 : $tType,X2 : (sK1 > 'type/ind_types/list' @ sK1 > X1 > X1),X3 : sK1,X0 : X1,X4 : 'type/ind_types/list' @ sK1] : ((((X2 @ X3 @ X4 @ X0)) = X0)) )),
% 0.20/0.29 inference(forward_demodulation,[],[f306,f262])).
% 0.20/0.29 thf(f492,plain,(
% 0.20/0.29 ( ! [X0 : $o] : (($false != X0)) )),
% 0.20/0.29 inference(constrained_superposition,[],[f34,f312])).
% 0.20/0.29 thf(f569,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(equality_resolution,[],[f492])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (976827)------------------------------
% 0.20/0.29 % (976827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (976827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (976827)CaDiCaL version: 2.1.3
% 0.20/0.30 % (976827)Termination reason: Refutation
% 0.20/0.30 % (976827)Time elapsed: 0.042 s
% 0.20/0.30 % (976827)Peak memory usage: 13 MB
% 0.20/0.30 % (976827)Instructions burned: 145 (million)
% 0.20/0.30 % (976821)Success in time 0.071 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------