%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT317^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 0.96s 0.39s
% Output : Refutation 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT317^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 18:32:36 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.96/0.39 % (1640445)Will run a generic schedule for satisfiability detection.
% 0.96/0.39 % (1640452)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2404523020:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.96/0.39 % (1640451)% WARNING: option uhcvi not known.
% 0.96/0.39 % (1640451)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1193574416:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.96/0.39 % (1640453)dis+10_1_sil=32000:sp=arity:random_seed=2229080013:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.96/0.39 % (1640450)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=350300888_2999 on theBenchmark for (2999ds/0Mi)
% 0.96/0.39 % (1640451)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.96/0.39 % (1640454)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1809745378:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.96/0.39 % (1640451)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.96/0.39 % (1640454)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.96/0.39 % Exception at run slice level
% 0.96/0.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.96/0.39 % (1640455)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1542978262:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.96/0.39 % (1640456)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2879075522:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.96/0.39 % (1640462)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=980659304:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.96/0.39 % Exception at run slice level
% 0.96/0.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.96/0.39 % (1640466)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3376700201:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.96/0.39 % (1640453)Instruction limit reached!
% 0.96/0.39 % (1640453)------------------------------
% 0.96/0.39 % (1640453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (1640453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (1640453)CaDiCaL version: 2.1.3
% 0.96/0.39 % (1640453)Termination reason: Instruction limit
% 0.96/0.39 % (1640453)Termination phase: Saturation
% 0.96/0.39 % (1640453)Time elapsed: 0.055 s
% 0.96/0.39 % (1640453)Peak memory usage: 12 MB
% 0.96/0.39 % (1640453)Instructions burned: 103 (million)
% 0.96/0.39 % (1640454)Instruction limit reached!
% 0.96/0.39 % (1640454)------------------------------
% 0.96/0.39 % (1640454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (1640454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (1640454)CaDiCaL version: 2.1.3
% 0.96/0.39 % (1640454)Termination reason: Instruction limit
% 0.96/0.39 % (1640454)Termination phase: Saturation
% 0.96/0.39 % (1640454)Time elapsed: 0.060 s
% 0.96/0.39 % (1640454)Peak memory usage: 12 MB
% 0.96/0.39 % (1640454)Instructions burned: 117 (million)
% 0.96/0.39 % (1640468)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=2141850932:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.96/0.39 % (1640468)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.96/0.39 % (1640468)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.96/0.39 % (1640469)ott-21_1_sil=16000:fs=off:random_seed=543158105:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.96/0.39 % (1640455)Instruction limit reached!
% 0.96/0.39 % (1640455)------------------------------
% 0.96/0.39 % (1640455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (1640455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (1640455)CaDiCaL version: 2.1.3
% 0.96/0.39 % (1640455)Termination reason: Instruction limit
% 0.96/0.39 % (1640455)Termination phase: Saturation
% 0.96/0.39 % (1640455)Time elapsed: 0.068 s
% 0.96/0.39 % (1640455)Peak memory usage: 12 MB
% 0.96/0.39 % (1640455)Instructions burned: 132 (million)
% 0.96/0.39 % (1640472)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3474600583:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.96/0.39 % (1640456)Instruction limit reached!
% 0.96/0.39 % (1640456)------------------------------
% 0.96/0.39 % (1640456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (1640456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (1640456)CaDiCaL version: 2.1.3
% 0.96/0.39 % (1640456)Termination reason: Instruction limit
% 0.96/0.39 % (1640456)Termination phase: Saturation
% 0.96/0.39 % (1640456)Time elapsed: 0.101 s
% 0.96/0.39 % (1640456)Peak memory usage: 12 MB
% 0.96/0.39 % (1640456)Instructions burned: 159 (million)
% 0.96/0.39 % (1640466) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1640445-1640466"...
% 0.96/0.39 % (1640466)...printing done.
% 0.96/0.39 % (1640466)Refutation found. Thanks to Tanya!
% 0.96/0.39 % SZS status Theorem for theBenchmark
% 0.96/0.39 % SZS output start Proof for theBenchmark
% 0.96/0.39 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.96/0.39 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.96/0.39 thf(type_def_7, type, sK2: $tType).
% 0.96/0.39 thf(func_def_0, type, 'const/lists/TL': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.96/0.39 thf(func_def_1, type, 'const/lists/HD': !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0))).
% 0.96/0.39 thf(func_def_2, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.96/0.39 thf(func_def_3, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.96/0.39 thf(func_def_7, type, sK0: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.96/0.39 thf(func_def_8, type, sK1: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.96/0.39 thf(func_def_9, type, sK3: 'type/ind_types/list' @ sK2).
% 0.96/0.39 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.96/0.39 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.96/0.39 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.96/0.39 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.96/0.39 thf(func_def_15, type, db1: !>[X0: $tType]:(X0)).
% 0.96/0.39 thf(f1,axiom,(
% 0.96/0.39 ! [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))),
% 0.96/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.96/0.39 thf(f2,axiom,(
% 0.96/0.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X2)),
% 0.96/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/TL_')).
% 0.96/0.39 thf(f3,axiom,(
% 0.96/0.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : ((('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) = X2)),
% 0.96/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/HD_')).
% 0.96/0.39 thf(f5,conjecture,(
% 0.96/0.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) => (X1 = (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)))))),
% 0.96/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/CONS_HD_TL_')).
% 0.96/0.39 thf(f6,negated_conjecture,(
% 0.96/0.39 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((X1 != 'const/ind_types/NIL' @ X0) => (X1 = (('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1)))))),
% 0.96/0.39 inference(negated_conjecture,[status(cth)],[f5])).
% 0.96/0.39 thf(f7,plain,(
% 0.96/0.39 ! [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))),
% 0.96/0.39 inference(rectify,[],[f1])).
% 0.96/0.39 thf(f8,plain,(
% 0.96/0.39 ! [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))),
% 0.96/0.39 inference(fool_elimination,[],[f7])).
% 0.96/0.39 thf(f9,plain,(
% 0.96/0.39 ! [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)))),
% 0.96/0.39 inference(ennf_transformation,[],[f8])).
% 0.96/0.39 thf(f10,plain,(
% 0.96/0.39 ! [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))),
% 0.96/0.39 inference(flattening,[],[f9])).
% 0.96/0.39 thf(f11,plain,(
% 0.96/0.39 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1))) != X1) & (X1 != 'const/ind_types/NIL' @ X0))),
% 0.96/0.39 inference(ennf_transformation,[],[f6])).
% 0.96/0.39 thf(f12,plain,(
% 0.96/0.39 ! [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))),
% 0.96/0.39 inference(rectify,[],[f10])).
% 0.96/0.39 thf(f13,plain,(
% 0.96/0.39 ! [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))),
% 0.96/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK1 @ X0 @ X1),skolemize(X4,sK1 @ X0 @ X1)],[f12])).
% 0.96/0.39 thf(f14,plain,(
% 0.96/0.39 (sK3 != (('const/ind_types/CONS' @ sK2 @ ('const/lists/HD' @ sK2 @ sK3) @ ('const/lists/TL' @ sK2 @ sK3)))) & (sK3 != 'const/ind_types/NIL' @ sK2)),
% 0.96/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11])).
% 0.96/0.39 thf(f16,plain,(
% 0.96/0.39 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : ('type/ind_types/list' @ X0 > $o)] : ((((X1 @ 'const/ind_types/NIL' @ X0)) != $true) | ($true != ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))))) | (((X1 @ X2)) = $true)) )),
% 0.96/0.39 inference(cnf_transformation,[],[f13])).
% 0.96/0.39 thf(f17,plain,(
% 0.96/0.39 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = X2)) )),
% 0.96/0.39 inference(cnf_transformation,[],[f2])).
% 0.96/0.39 thf(f18,plain,(
% 0.96/0.39 ( ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1))) = X2)) )),
% 0.96/0.39 inference(cnf_transformation,[],[f3])).
% 0.96/0.39 thf(f20,plain,(
% 0.96/0.39 (sK3 != 'const/ind_types/NIL' @ sK2)),
% 0.96/0.39 inference(cnf_transformation,[],[f14])).
% 0.96/0.39 thf(f21,plain,(
% 0.96/0.39 (sK3 != (('const/ind_types/CONS' @ sK2 @ ('const/lists/HD' @ sK2 @ sK3) @ ('const/lists/TL' @ sK2 @ sK3))))),
% 0.96/0.39 inference(cnf_transformation,[],[f14])).
% 0.96/0.39 thf(f85,plain,(
% 0.96/0.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ($true != (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1))) @ ('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))))))))) )),
% 0.96/0.39 inference(leibniz_equality_elimination,[],[f16])).
% 0.96/0.39 thf(f107,plain,(
% 0.96/0.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ($true != ((~ (('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))))) )),
% 0.96/0.39 inference(beta-eta_normalization,[],[f85])).
% 0.96/0.39 thf(f108,plain,(
% 0.96/0.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/ind_types/NIL' @ X0 = X1) | ($true = ((('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)))) )),
% 0.96/0.39 inference(not_proxy_clausification,[],[f107])).
% 0.96/0.39 thf(f109,plain,(
% 0.96/0.39 ( ! [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)) )),
% 0.96/0.39 inference(equality_proxy_clausification,[],[f108])).
% 0.96/0.39 thf(f849,plain,(
% 0.96/0.39 ( ! [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)) )),
% 0.96/0.39 inference(constrained_superposition,[],[f17,f109])).
% 0.96/0.39 thf(f850,plain,(
% 0.96/0.39 ( ! [X1 : $tType,X0 : 'type/ind_types/list' @ X1] : ((((sK0 @ X1 @ (^[Y0 : 'type/ind_types/list' @ X1]: (~ (Y0 = X0))))) = (('const/lists/HD' @ X1 @ X0))) | ('const/ind_types/NIL' @ X1 = X0)) )),
% 0.96/0.39 inference(constrained_superposition,[],[f18,f109])).
% 0.96/0.39 thf(f866,plain,(
% 0.96/0.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (Y0 = X1)))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.96/0.39 inference(backward_subsumption_demodulation,[],[f109,f850])).
% 0.96/0.39 thf(f874,plain,(
% 0.96/0.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ ('const/lists/HD' @ X0 @ X1) @ ('const/lists/TL' @ X0 @ X1))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 0.96/0.39 inference(forward_subsumption_demodulation,[],[f866,f849])).
% 0.96/0.39 thf(f904,plain,(
% 0.96/0.39 (sK3 != sK3) | (sK3 = 'const/ind_types/NIL' @ sK2)),
% 0.96/0.39 inference(constrained_superposition,[],[f21,f874])).
% 0.96/0.39 thf(f906,plain,(
% 0.96/0.39 (sK3 = 'const/ind_types/NIL' @ sK2)),
% 0.96/0.39 inference(trivial_inequality_removal,[],[f904])).
% 0.96/0.39 thf(f913,plain,(
% 0.96/0.39 $false),
% 0.96/0.39 inference(forward_subsumption_resolution,[],[f906,f20])).
% 0.96/0.39 % SZS output end Proof for theBenchmark
% 0.96/0.39 % (1640466)------------------------------
% 0.96/0.39 % (1640466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.39 % (1640466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.39 % (1640466)CaDiCaL version: 2.1.3
% 0.96/0.39 % (1640466)Termination reason: Refutation
% 0.96/0.39 % (1640466)Time elapsed: 0.088 s
% 0.96/0.39 % (1640466)Peak memory usage: 13 MB
% 0.96/0.39 % (1640466)Instructions burned: 131 (million)
% 0.96/0.39 % (1640445)Success in time 0.169 s
% 0.96/0.39 % Vampire exiting
%------------------------------------------------------------------------------