%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT314^1 : 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 : n004.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 07:49:10 AM UTC 2026
% Result : Theorem 2.34s 0.66s
% Output : Refutation 2.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : DAT314^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.26 % Computer : n004.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 18:25:22 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 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
% 2.34/0.66 % (1657467)Will run a generic schedule for satisfiability detection.
% 2.34/0.66 % (1657473)% WARNING: option uhcvi not known.
% 2.34/0.66 % (1657473)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2481612866:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.34/0.66 % (1657473)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.34/0.66 % (1657473)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.34/0.66 % (1657475)dis+10_1_sil=32000:sp=arity:random_seed=3912313027:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.34/0.66 % (1657472)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3955547952_2999 on theBenchmark for (2999ds/0Mi)
% 2.34/0.66 % (1657476)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2069393962:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.34/0.66 % (1657477)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2275799871:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.34/0.66 % (1657478)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2497542990:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.34/0.66 % (1657474)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3793776599:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.34/0.66 % (1657476)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.34/0.66 % Exception at run slice level
% 2.34/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.34/0.66 % (1657487)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4096309316:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.34/0.66 % Exception at run slice level
% 2.34/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.34/0.66 % (1657490)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1424811776:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.34/0.66 % (1657475)Instruction limit reached!
% 2.34/0.66 % (1657475)------------------------------
% 2.34/0.66 % (1657475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.66 % (1657475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.66 % (1657475)CaDiCaL version: 2.1.3
% 2.34/0.66 % (1657475)Termination reason: Instruction limit
% 2.34/0.66 % (1657475)Termination phase: Saturation
% 2.34/0.66 % (1657475)Time elapsed: 0.095 s
% 2.34/0.66 % (1657475)Peak memory usage: 12 MB
% 2.34/0.66 % (1657475)Instructions burned: 104 (million)
% 2.34/0.66 % (1657476)Instruction limit reached!
% 2.34/0.66 % (1657476)------------------------------
% 2.34/0.66 % (1657476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.66 % (1657476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.66 % (1657476)CaDiCaL version: 2.1.3
% 2.34/0.66 % (1657476)Termination reason: Instruction limit
% 2.34/0.66 % (1657476)Termination phase: Saturation
% 2.34/0.66 % (1657476)Time elapsed: 0.100 s
% 2.34/0.66 % (1657476)Peak memory usage: 12 MB
% 2.34/0.66 % (1657476)Instructions burned: 116 (million)
% 2.34/0.66 % (1657477)Instruction limit reached!
% 2.34/0.66 % (1657477)------------------------------
% 2.34/0.66 % (1657477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.66 % (1657477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.66 % (1657477)CaDiCaL version: 2.1.3
% 2.34/0.66 % (1657477)Termination reason: Instruction limit
% 2.34/0.66 % (1657477)Termination phase: Saturation
% 2.34/0.66 % (1657477)Time elapsed: 0.115 s
% 2.34/0.66 % (1657477)Peak memory usage: 12 MB
% 2.34/0.66 % (1657477)Instructions burned: 131 (million)
% 2.34/0.66 % (1657492)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2461357283:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.34/0.66 % (1657492)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.34/0.66 % (1657492)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.34/0.66 % (1657493)ott-21_1_sil=16000:fs=off:random_seed=244696292:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.34/0.66 % (1657478)Instruction limit reached!
% 2.34/0.66 % (1657478)------------------------------
% 2.34/0.66 % (1657478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.66 % (1657478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.66 % (1657478)CaDiCaL version: 2.1.3
% 2.34/0.66 % (1657478)Termination reason: Instruction limit
% 2.34/0.66 % (1657478)Termination phase: Saturation
% 2.34/0.66 % (1657478)Time elapsed: 0.138 s
% 2.34/0.66 % (1657478)Peak memory usage: 12 MB
% 2.34/0.66 % (1657478)Instructions burned: 159 (million)
% 2.34/0.66 % (1657494)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3837681112:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.34/0.66 % (1657497)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3444363152:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.34/0.66 % Exception at run slice level
% 2.34/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.34/0.66 % (1657490)Instruction limit reached!
% 2.34/0.66 % (1657490)------------------------------
% 2.34/0.66 % (1657490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.66 % (1657490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.66 % (1657490)CaDiCaL version: 2.1.3
% 2.34/0.66 % (1657490)Termination reason: Instruction limit
% 2.34/0.66 % (1657490)Termination phase: Saturation
% 2.34/0.66 % (1657490)Time elapsed: 0.120 s
% 2.34/0.66 % (1657490)Peak memory usage: 13 MB
% 2.34/0.66 % (1657490)Instructions burned: 131 (million)
% 2.34/0.66 % (1657500)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4166580115:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.34/0.66 % (1657501)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1409297831:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.34/0.66 % Exception at run slice level
% 2.34/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.34/0.66 % (1657504)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1013863773:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.34/0.66 % (1657504)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.34/0.66 % (1657493)Instruction limit reached!
% 2.34/0.66 % (1657493)------------------------------
% 2.34/0.66 % (1657493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.66 % (1657493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.66 % (1657493)CaDiCaL version: 2.1.3
% 2.34/0.66 % (1657493)Termination reason: Instruction limit
% 2.34/0.66 % (1657493)Termination phase: Saturation
% 2.34/0.66 % (1657493)Time elapsed: 0.155 s
% 2.34/0.66 % (1657493)Peak memory usage: 12 MB
% 2.34/0.66 % (1657493)Instructions burned: 180 (million)
% 2.34/0.66 % (1657504) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1657467-1657504"...
% 2.34/0.66 % (1657504)...printing done.
% 2.34/0.66 % (1657504)Refutation found. Thanks to Tanya!
% 2.34/0.66 % SZS status Theorem for theBenchmark
% 2.34/0.66 % SZS output start Proof for theBenchmark
% 2.34/0.66 thf(type_def_5, type, 'type/nums/num': $tType).
% 2.34/0.66 thf(type_def_6, type, 'type/ind_types/list': $tType > $tType).
% 2.34/0.66 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 2.34/0.66 thf(type_def_8, type, sK2: $tType).
% 2.34/0.66 thf(func_def_0, type, 'const/nums/SUC': ('type/nums/num' > 'type/nums/num')).
% 2.34/0.66 thf(func_def_1, type, 'const/nums/NUMERAL': ('type/nums/num' > 'type/nums/num')).
% 2.34/0.66 thf(func_def_2, type, 'const/nums/BIT1': ('type/nums/num' > 'type/nums/num')).
% 2.34/0.66 thf(func_def_3, type, 'const/nums/_0': 'type/nums/num').
% 2.34/0.66 thf(func_def_4, type, 'const/lists/TL': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 2.34/0.66 thf(func_def_5, type, 'const/lists/LENGTH': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/nums/num'))).
% 2.34/0.66 thf(func_def_6, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 2.34/0.66 thf(func_def_7, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 2.34/0.66 thf(func_def_8, type, 'const/arith/-': ('type/nums/num' > 'type/nums/num' > 'type/nums/num')).
% 2.34/0.66 thf(func_def_12, type, sK0: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 2.34/0.66 thf(func_def_13, type, sK1: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 2.34/0.66 thf(func_def_14, type, sK3: 'type/ind_types/list' @ sK2).
% 2.34/0.66 thf(func_def_15, type, vNOT: ($o > $o)).
% 2.34/0.66 thf(func_def_16, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.34/0.66 thf(func_def_17, type, db0: !>[X0: $tType]:(X0)).
% 2.34/0.66 thf(func_def_18, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.34/0.66 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 2.34/0.66 thf(func_def_21, type, sK5: !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 2.34/0.66 thf(func_def_22, type, sK6: !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0))).
% 2.34/0.66 thf(f1,axiom,(
% 2.34/0.66 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 2.34/0.66 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 2.34/0.66 thf(f2,axiom,(
% 2.34/0.66 ! [X0 : 'type/nums/num'] : ((('const/arith/-' @ ('const/nums/SUC' @ X0) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = X0)),
% 2.34/0.66 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/arith/SUC_SUB1_')).
% 2.34/0.66 thf(f3,axiom,(
% 2.34/0.66 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2))))),
% 2.34/0.66 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/LENGTH_1')).
% 2.34/0.66 thf(f4,axiom,(
% 2.34/0.66 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X2)),
% 2.34/0.66 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/TL_')).
% 2.34/0.66 thf(f8,conjecture,(
% 2.34/0.66 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) => ((('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) = (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),
% 2.34/0.66 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/LENGTH_TL_')).
% 2.34/0.66 thf(f9,negated_conjecture,(
% 2.34/0.66 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) => ((('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) = (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))))),
% 2.34/0.66 inference(negated_conjecture,[status(cth)],[f8])).
% 2.34/0.66 thf(f10,plain,(
% 2.34/0.66 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 2.34/0.66 inference(rectify,[],[f1])).
% 2.34/0.66 thf(f11,plain,(
% 2.34/0.66 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ X3)) = $true) => (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) = $true)) & (((X1 @ 'const/ind_types/NIL' @ X0)) = $true)) => ! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true))),
% 2.34/0.66 inference(fool_elimination,[],[f10])).
% 2.34/0.66 thf(f12,plain,(
% 2.34/0.66 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true) & (((X1 @ X3)) = $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)))),
% 2.34/0.66 inference(ennf_transformation,[],[f11])).
% 2.34/0.66 thf(f13,plain,(
% 2.34/0.66 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4)) = $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) != $true) & (((X1 @ X3)) = $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 2.34/0.66 inference(flattening,[],[f12])).
% 2.34/0.66 thf(f14,plain,(
% 2.34/0.66 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) != (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) & (X1 != 'const/ind_types/NIL' @ X0))),
% 2.34/0.67 inference(ennf_transformation,[],[f9])).
% 2.34/0.67 thf(f15,plain,(
% 2.34/0.67 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | ? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)))) & (((X1 @ X4)) = $true)) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 2.34/0.67 inference(rectify,[],[f13])).
% 2.34/0.67 thf(f16,plain,(
% 2.34/0.67 ! [X0 : $tType,X1 : ('type/ind_types/list' @ X0 > $o)] : (! [X2 : 'type/ind_types/list' @ X0] : (((X1 @ X2)) = $true) | (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))))) & ($true = ((X1 @ (sK1 @ X0 @ X1))))) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true))),
% 2.34/0.67 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK1 @ X0 @ X1),skolemize(X4,sK1 @ X0 @ X1)],[f15])).
% 2.34/0.67 thf(f17,plain,(
% 2.34/0.67 ((('const/lists/LENGTH' @ sK2 @ ('const/lists/TL' @ sK2 @ sK3))) != (('const/arith/-' @ ('const/lists/LENGTH' @ sK2 @ sK3) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) & (sK3 != 'const/ind_types/NIL' @ sK2)),
% 2.34/0.67 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f14])).
% 2.34/0.67 thf(f19,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : ('type/ind_types/list' @ X0 > $o)] : (($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))))) | (((X1 @ X2)) = $true) | (((X1 @ 'const/ind_types/NIL' @ X0)) != $true)) )),
% 2.34/0.67 inference(cnf_transformation,[],[f16])).
% 2.34/0.67 thf(f20,plain,(
% 2.34/0.67 ( ! [X0 : 'type/nums/num'] : (((('const/arith/-' @ ('const/nums/SUC' @ X0) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))) = X0)) )),
% 2.34/0.67 inference(cnf_transformation,[],[f2])).
% 2.34/0.67 thf(f21,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/LENGTH' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X0 @ X2))))) )),
% 2.34/0.67 inference(cnf_transformation,[],[f3])).
% 2.34/0.67 thf(f22,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X2)) )),
% 2.34/0.67 inference(cnf_transformation,[],[f4])).
% 2.34/0.67 thf(f26,plain,(
% 2.34/0.67 (sK3 != 'const/ind_types/NIL' @ sK2)),
% 2.34/0.67 inference(cnf_transformation,[],[f17])).
% 2.34/0.67 thf(f27,plain,(
% 2.34/0.67 ((('const/lists/LENGTH' @ sK2 @ ('const/lists/TL' @ sK2 @ sK3))) != (('const/arith/-' @ ('const/lists/LENGTH' @ sK2 @ sK3) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0')))))),
% 2.34/0.67 inference(cnf_transformation,[],[f17])).
% 2.34/0.67 thf(f187,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0)))) )),
% 2.34/0.67 inference(leibniz_equality_elimination,[],[f19])).
% 2.34/0.67 thf(f225,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true != ((~ ('const/ind_types/NIL' @ X0 = X1))))) )),
% 2.34/0.67 inference(beta-eta_normalization,[],[f187])).
% 2.34/0.67 thf(f226,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ($true = (('const/ind_types/NIL' @ X0 = X1)))) )),
% 2.34/0.67 inference(not_proxy_clausification,[],[f225])).
% 2.34/0.67 thf(f227,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(equality_proxy_clausification,[],[f226])).
% 2.34/0.67 thf(f361,plain,(
% 2.34/0.67 ( ! [X1 : $tType,X0 : 'type/ind_types/list' @ X1] : ((((sK1 @ X1 @ (^[Y0 : 'type/ind_types/list' @ X1]: (~ (Y0 = X0))))) = (('const/lists/TL' @ X1 @ X0))) | ('const/ind_types/NIL' @ X1 = X0)) )),
% 2.34/0.67 inference(constrained_superposition,[],[f22,f227])).
% 2.34/0.67 thf(f375,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))))) | ($true = (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ X2))) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ 'const/ind_types/NIL' @ X0))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(constrained_superposition,[],[f19,f361])).
% 2.34/0.67 thf(f405,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (($true != ((~ (('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)) = X1)))) | ($true = ((~ (X2 = X1)))) | ($true != ((~ ('const/ind_types/NIL' @ X0 = X1)))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(beta-eta_normalization,[],[f375])).
% 2.34/0.67 thf(f406,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (($true = ((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1)) = X1))) | ($true = ((~ (X2 = X1)))) | ($true != ((~ ('const/ind_types/NIL' @ X0 = X1)))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(not_proxy_clausification,[],[f405])).
% 2.34/0.67 thf(f407,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))) = X1) | ($true = ((~ (X2 = X1)))) | ($true != ((~ ('const/ind_types/NIL' @ X0 = X1)))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(equality_proxy_clausification,[],[f406])).
% 2.34/0.67 thf(f408,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))) = X1) | ($false = ((X2 = X1))) | ($true != ((~ ('const/ind_types/NIL' @ X0 = X1)))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(not_proxy_clausification,[],[f407])).
% 2.34/0.67 thf(f409,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))) = X1) | (X1 != X2) | ($true != ((~ ('const/ind_types/NIL' @ X0 = X1)))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(equality_proxy_clausification,[],[f408])).
% 2.34/0.67 thf(f410,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))) = X1) | (X1 != X2) | ($true = (('const/ind_types/NIL' @ X0 = X1))) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(not_proxy_clausification,[],[f409])).
% 2.34/0.67 thf(f411,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))) = X1) | (X1 != X2) | ('const/ind_types/NIL' @ X0 = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 2.34/0.67 inference(equality_proxy_clausification,[],[f410])).
% 2.34/0.67 thf(f412,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))) @ ('const/lists/TL' @ X0 @ X1))) = X1) | ('const/ind_types/NIL' @ X0 = X1) | (X1 != X2)) )),
% 2.34/0.67 inference(duplicate_literal_removal,[],[f411])).
% 2.34/0.67 thf(f445,plain,(
% 2.34/0.67 ( ! [X1 : $tType,X2 : 'type/ind_types/list' @ X1,X0 : 'type/ind_types/list' @ X1] : (((('const/lists/LENGTH' @ X1 @ X0)) = (('const/nums/SUC' @ ('const/lists/LENGTH' @ X1 @ ('const/lists/TL' @ X1 @ X0))))) | ('const/ind_types/NIL' @ X1 = X0) | (X0 != X2)) )),
% 2.34/0.67 inference(constrained_superposition,[],[f21,f412])).
% 2.34/0.67 thf(f455,plain,(
% 2.34/0.67 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/LENGTH' @ X0 @ ('const/lists/TL' @ X0 @ X1))) = (('const/arith/-' @ ('const/lists/LENGTH' @ X0 @ X1) @ ('const/nums/NUMERAL' @ ('const/nums/BIT1' @ 'const/nums/_0'))))) | ('const/ind_types/NIL' @ X0 = X1) | (X1 != X2)) )),
% 2.34/0.67 inference(constrained_superposition,[],[f20,f445])).
% 2.34/0.67 thf(f460,plain,(
% 2.34/0.67 ( ! [X0 : 'type/ind_types/list' @ sK2] : (((('const/lists/LENGTH' @ sK2 @ ('const/lists/TL' @ sK2 @ sK3))) != (('const/lists/LENGTH' @ sK2 @ ('const/lists/TL' @ sK2 @ sK3)))) | (sK3 = 'const/ind_types/NIL' @ sK2) | (sK3 != X0)) )),
% 2.34/0.67 inference(constrained_superposition,[],[f27,f455])).
% 2.34/0.67 thf(f461,plain,(
% 2.34/0.67 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((sK3 = 'const/ind_types/NIL' @ sK2) | (sK3 != X0)) )),
% 2.34/0.67 inference(trivial_inequality_removal,[],[f460])).
% 2.34/0.67 thf(f463,plain,(
% 2.34/0.67 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((sK3 != X0)) )),
% 2.34/0.67 inference(forward_subsumption_resolution,[],[f461,f26])).
% 2.34/0.67 thf(f466,plain,(
% 2.34/0.67 $false),
% 2.34/0.67 inference(equality_resolution,[],[f463])).
% 2.34/0.67 % SZS output end Proof for theBenchmark
% 2.34/0.67 % (1657504)------------------------------
% 2.34/0.67 % (1657504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.34/0.67 % (1657504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.67 % (1657504)CaDiCaL version: 2.1.3
% 2.34/0.67 % (1657504)Termination reason: Refutation
% 2.34/0.67 % (1657504)Time elapsed: 0.043 s
% 2.34/0.67 % (1657504)Peak memory usage: 13 MB
% 2.34/0.67 % (1657504)Instructions burned: 42 (million)
% 2.34/0.67 % (1657467)Success in time 0.337 s
% 2.34/0.67 % Vampire exiting
%------------------------------------------------------------------------------