%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT327^1 : 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 : n014.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 07:49:11 AM UTC 2026
% Result : Theorem 0.19s 0.37s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT327^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 % Computer : n014.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 18:27:45 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.19/0.37 % (3030832)Will run a generic schedule for satisfiability detection.
% 0.19/0.37 % (3030843)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2542188727:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.37 % (3030837)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1926993668_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.37 % (3030840)dis+10_1_sil=32000:sp=arity:random_seed=2364073778:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.37 % (3030841)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3070870479:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.37 % (3030839)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2239318822:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.37 % (3030841)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.37 % Exception at run slice level
% 0.19/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.37 % (3030838)% WARNING: option uhcvi not known.
% 0.19/0.37 % (3030838)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3867649353:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.37 % (3030838)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.37 % (3030842)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=369040297:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.37 % (3030838)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.37 % (3030849)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2934638532:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.37 % Exception at run slice level
% 0.19/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.37 % (3030843)Instruction limit reached!
% 0.19/0.37 % (3030843)------------------------------
% 0.19/0.37 % (3030843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.37 % (3030843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.37 % (3030843)CaDiCaL version: 2.1.3
% 0.19/0.37 % (3030843)Termination reason: Instruction limit
% 0.19/0.37 % (3030843)Termination phase: Saturation
% 0.19/0.37 % (3030843)Time elapsed: 0.045 s
% 0.19/0.37 % (3030843)Peak memory usage: 13 MB
% 0.19/0.37 % (3030843)Instructions burned: 162 (million)
% 0.19/0.37 % (3030853)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3274410547:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.37 % (3030855)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=3870229846:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.19/0.37 % (3030855)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.37 % (3030855)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.37 % (3030840)Instruction limit reached!
% 0.19/0.37 % (3030840)------------------------------
% 0.19/0.37 % (3030840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.37 % (3030840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.37 % (3030840)CaDiCaL version: 2.1.3
% 0.19/0.37 % (3030840)Termination reason: Instruction limit
% 0.19/0.37 % (3030840)Termination phase: Saturation
% 0.19/0.37 % (3030840)Time elapsed: 0.054 s
% 0.19/0.37 % (3030840)Peak memory usage: 12 MB
% 0.19/0.37 % (3030840)Instructions burned: 103 (million)
% 0.19/0.37 % (3030857)ott-21_1_sil=16000:fs=off:random_seed=332028486:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/0.37 % (3030841)Instruction limit reached!
% 0.19/0.37 % (3030841)------------------------------
% 0.19/0.37 % (3030841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.37 % (3030841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.37 % (3030841)CaDiCaL version: 2.1.3
% 0.19/0.37 % (3030841)Termination reason: Instruction limit
% 0.19/0.37 % (3030841)Termination phase: Saturation
% 0.19/0.37 % (3030841)Time elapsed: 0.074 s
% 0.19/0.37 % (3030841)Peak memory usage: 12 MB
% 0.19/0.37 % (3030841)Instructions burned: 116 (million)
% 0.19/0.37 % (3030842)Instruction limit reached!
% 0.19/0.37 % (3030842)------------------------------
% 0.19/0.37 % (3030842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.37 % (3030842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.37 % (3030842)CaDiCaL version: 2.1.3
% 0.19/0.37 % (3030842)Termination reason: Instruction limit
% 0.19/0.37 % (3030842)Termination phase: Saturation
% 0.19/0.37 % (3030842)Time elapsed: 0.067 s
% 0.19/0.37 % (3030842)Peak memory usage: 12 MB
% 0.19/0.37 % (3030842)Instructions burned: 132 (million)
% 0.19/0.37 % (3030838) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3030832-3030838"...
% 0.19/0.37 % (3030838)...printing done.
% 0.19/0.37 % (3030859)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2241268726:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.19/0.37 % (3030838)Refutation found. Thanks to Tanya!
% 0.19/0.37 % SZS status Theorem for theBenchmark
% 0.19/0.37 % SZS output start Proof for theBenchmark
% 0.19/0.37 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.19/0.37 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.37 thf(type_def_7, type, sK2: $tType).
% 0.19/0.37 thf(func_def_0, type, 'const/sets/set_of_list': !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0 > $o))).
% 0.19/0.37 thf(func_def_1, type, 'const/sets/INSERT': !>[X0: $tType]:((X0 > (X0 > $o) > X0 > $o))).
% 0.19/0.37 thf(func_def_2, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.19/0.37 thf(func_def_3, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.19/0.37 thf(func_def_4, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.19/0.37 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.37 thf(func_def_9, type, sK0: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.19/0.37 thf(func_def_10, type, sK1: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.19/0.37 thf(func_def_11, type, sK3: 'type/ind_types/list' @ sK2).
% 0.19/0.37 thf(func_def_12, type, vNOT: ($o > $o)).
% 0.19/0.37 thf(func_def_14, type, sK5: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.19/0.37 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.37 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.37 thf(func_def_17, type, sK6: !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > X0))).
% 0.19/0.37 thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.37 thf(func_def_19, type, sK7: !>[X0: $tType]:(('type/ind_types/list' @ X0 > X0))).
% 0.19/0.37 thf(func_def_20, type, sK8: ('type/ind_types/list' @ sK2 > sK2)).
% 0.19/0.37 thf(f1,axiom,(
% 0.19/0.37 ! [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))),
% 0.19/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.19/0.37 thf(f3,axiom,(
% 0.19/0.37 ! [X0 : $tType,X1 : X0,X2 : (X0 > $o)] : ((('const/sets/INSERT' @ X0 @ X1 @ X2)) != 'const/sets/EMPTY' @ X0)),
% 0.19/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/NOT_INSERT_EMPTY_')).
% 0.19/0.37 thf(f4,axiom,(
% 0.19/0.37 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/set_of_list' @ X0 @ X2))))),
% 0.19/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/set_of_list_1')).
% 0.19/0.37 thf(f5,axiom,(
% 0.19/0.37 ! [X0 : $tType] : ((('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0)) = 'const/sets/EMPTY' @ X0)),
% 0.19/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/set_of_list_0')).
% 0.19/0.37 thf(f6,conjecture,(
% 0.19/0.37 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/sets/set_of_list' @ X0 @ X1)) = 'const/sets/EMPTY' @ X0) = (X1 = 'const/ind_types/NIL' @ X0))),
% 0.19/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SET_OF_LIST_EQ_EMPTY_')).
% 0.19/0.37 thf(f7,negated_conjecture,(
% 0.19/0.37 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/sets/set_of_list' @ X0 @ X1)) = 'const/sets/EMPTY' @ X0) = (X1 = 'const/ind_types/NIL' @ X0))),
% 0.19/0.37 inference(negated_conjecture,[status(cth)],[f6])).
% 0.19/0.37 thf(f8,plain,(
% 0.19/0.37 ! [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))),
% 0.19/0.37 inference(rectify,[],[f1])).
% 0.19/0.37 thf(f9,plain,(
% 0.19/0.37 ! [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))),
% 0.19/0.37 inference(fool_elimination,[],[f8])).
% 0.19/0.37 thf(f10,plain,(
% 0.19/0.37 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ X1))) = (('const/ind_types/NIL' @ X0 = X1)))),
% 0.19/0.37 inference(fool_elimination,[],[f7])).
% 0.19/0.37 thf(f11,plain,(
% 0.19/0.37 ! [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)))),
% 0.19/0.37 inference(ennf_transformation,[],[f9])).
% 0.19/0.37 thf(f12,plain,(
% 0.19/0.37 ! [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))),
% 0.19/0.37 inference(flattening,[],[f11])).
% 0.19/0.37 thf(f13,plain,(
% 0.19/0.37 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ X1))) != (('const/ind_types/NIL' @ X0 = X1)))),
% 0.19/0.37 inference(ennf_transformation,[],[f10])).
% 0.19/0.37 thf(f14,plain,(
% 0.19/0.37 ! [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))),
% 0.19/0.37 inference(rectify,[],[f12])).
% 0.19/0.37 thf(f15,plain,(
% 0.19/0.37 ! [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))),
% 0.19/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK1 @ X0 @ X1),skolemize(X4,sK1 @ X0 @ X1)],[f14])).
% 0.19/0.37 thf(f16,plain,(
% 0.19/0.37 ((('const/sets/EMPTY' @ sK2 = ('const/sets/set_of_list' @ sK2 @ sK3))) != (('const/ind_types/NIL' @ sK2 = sK3)))),
% 0.19/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13])).
% 0.19/0.37 thf(f18,plain,(
% 0.19/0.37 ( ! [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)) )),
% 0.19/0.37 inference(cnf_transformation,[],[f15])).
% 0.19/0.37 thf(f20,plain,(
% 0.19/0.37 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (((('const/sets/INSERT' @ X0 @ X1 @ X2)) != 'const/sets/EMPTY' @ X0)) )),
% 0.19/0.37 inference(cnf_transformation,[],[f3])).
% 0.19/0.37 thf(f21,plain,(
% 0.19/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) = (('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/set_of_list' @ X0 @ X2))))) )),
% 0.19/0.37 inference(cnf_transformation,[],[f4])).
% 0.19/0.37 thf(f22,plain,(
% 0.19/0.37 ( ! [X0 : $tType] : (('const/sets/EMPTY' @ X0 = (('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0)))) )),
% 0.19/0.37 inference(cnf_transformation,[],[f5])).
% 0.19/0.37 thf(f23,plain,(
% 0.19/0.37 ((('const/sets/EMPTY' @ sK2 = ('const/sets/set_of_list' @ sK2 @ sK3))) != (('const/ind_types/NIL' @ sK2 = sK3)))),
% 0.19/0.37 inference(cnf_transformation,[],[f16])).
% 0.19/0.37 thf(f26,plain,(
% 0.19/0.37 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : X0] : (((('const/sets/INSERT' @ X0 @ X1 @ X2)) != (('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0)))) )),
% 0.19/0.37 inference(definition_unfolding,[],[f20,f22])).
% 0.19/0.37 thf(f27,plain,(
% 0.19/0.37 ((('const/ind_types/NIL' @ sK2 = sK3)) != ((('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))))),
% 0.19/0.37 inference(definition_unfolding,[],[f23,f22])).
% 0.19/0.37 thf(f28,plain,(
% 0.19/0.37 ($true = (('const/ind_types/NIL' @ sK2 = sK3))) | ($true = ((('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))))),
% 0.19/0.37 inference(xor_proxy_clausification,[],[f27])).
% 0.19/0.37 thf(f29,plain,(
% 0.19/0.37 ((('const/ind_types/NIL' @ sK2 = sK3)) = $false) | ($false = ((('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))))),
% 0.19/0.37 inference(xor_proxy_clausification,[],[f27])).
% 0.19/0.37 thf(f30,plain,(
% 0.19/0.37 (sK3 != 'const/ind_types/NIL' @ sK2) | ($false = ((('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))))),
% 0.19/0.37 inference(equality_proxy_clausification,[],[f29])).
% 0.19/0.37 thf(f31,plain,(
% 0.19/0.37 (sK3 != 'const/ind_types/NIL' @ sK2) | ((('const/sets/set_of_list' @ sK2 @ sK3)) != (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2)))),
% 0.19/0.37 inference(equality_proxy_clausification,[],[f30])).
% 0.19/0.37 thf(f32,plain,(
% 0.19/0.37 (sK3 = 'const/ind_types/NIL' @ sK2) | ($true = ((('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))))),
% 0.19/0.37 inference(equality_proxy_clausification,[],[f28])).
% 0.19/0.37 thf(f33,plain,(
% 0.19/0.37 (sK3 = 'const/ind_types/NIL' @ sK2) | ((('const/sets/set_of_list' @ sK2 @ sK3)) = (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2)))),
% 0.19/0.37 inference(equality_proxy_clausification,[],[f32])).
% 0.19/0.37 thf(f35,definition,(
% 0.19/0.37 spl4_1 <=> ((('const/sets/set_of_list' @ sK2 @ sK3)) = (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2)))),
% 0.19/0.37 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.19/0.37 thf(f36,plain,(
% 0.19/0.37 ((('const/sets/set_of_list' @ sK2 @ sK3)) = (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2))) | ~spl4_1),
% 0.19/0.37 inference(avatar_component_clause,[],[f35])).
% 0.19/0.37 thf(f37,plain,(
% 0.19/0.37 ((('const/sets/set_of_list' @ sK2 @ sK3)) != (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2))) | spl4_1),
% 0.19/0.37 inference(avatar_component_clause,[],[f35])).
% 0.19/0.37 thf(f39,definition,(
% 0.19/0.37 spl4_2 <=> (sK3 = 'const/ind_types/NIL' @ sK2)),
% 0.19/0.37 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.19/0.37 thf(f40,plain,(
% 0.19/0.37 (sK3 = 'const/ind_types/NIL' @ sK2) | ~spl4_2),
% 0.19/0.37 inference(avatar_component_clause,[],[f39])).
% 0.19/0.37 thf(f41,plain,(
% 0.19/0.37 (sK3 != 'const/ind_types/NIL' @ sK2) | spl4_2),
% 0.19/0.37 inference(avatar_component_clause,[],[f39])).
% 0.19/0.37 thf(f42,plain,(
% 0.19/0.37 ~spl4_1 | ~spl4_2),
% 0.19/0.37 inference(avatar_split_clause,[],[f31,f39,f35])).
% 0.19/0.37 thf(f43,plain,(
% 0.19/0.37 spl4_1 | spl4_2),
% 0.19/0.37 inference(avatar_split_clause,[],[f33,f39,f35])).
% 0.19/0.37 thf(f77,plain,(
% 0.19/0.37 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) != (('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0)))) )),
% 0.19/0.37 inference(constrained_superposition,[],[f26,f21])).
% 0.19/0.37 thf(f80,plain,(
% 0.19/0.37 ( ! [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)))) )),
% 0.19/0.37 inference(leibniz_equality_elimination,[],[f18])).
% 0.19/0.37 thf(f99,plain,(
% 0.19/0.37 ( ! [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))))) )),
% 0.19/0.37 inference(beta-eta_normalization,[],[f80])).
% 0.19/0.37 thf(f100,plain,(
% 0.19/0.37 ( ! [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)))) )),
% 0.19/0.37 inference(not_proxy_clausification,[],[f99])).
% 0.19/0.37 thf(f101,plain,(
% 0.19/0.37 ( ! [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)) )),
% 0.19/0.37 inference(equality_proxy_clausification,[],[f100])).
% 0.19/0.37 thf(f102,plain,(
% 0.19/0.37 ((('const/sets/set_of_list' @ sK2 @ sK3)) != (('const/sets/set_of_list' @ sK2 @ sK3))) | (spl4_1 | ~spl4_2)),
% 0.19/0.37 inference(forward_demodulation,[],[f37,f40])).
% 0.19/0.37 thf(f103,plain,(
% 0.19/0.37 $false | (spl4_1 | ~spl4_2)),
% 0.19/0.37 inference(trivial_inequality_removal,[],[f102])).
% 0.19/0.37 thf(f104,plain,(
% 0.19/0.37 spl4_1 | ~spl4_2),
% 0.19/0.37 inference(avatar_contradiction_clause,[],[f103])).
% 0.19/0.37 thf(f832,plain,(
% 0.19/0.37 ( ! [X1 : $tType,X0 : 'type/ind_types/list' @ X1] : (((('const/sets/set_of_list' @ X1 @ 'const/ind_types/NIL' @ X1)) != (('const/sets/set_of_list' @ X1 @ X0))) | ('const/ind_types/NIL' @ X1 = X0)) )),
% 0.19/0.37 inference(constrained_superposition,[],[f77,f101])).
% 0.19/0.37 thf(f946,plain,(
% 0.19/0.37 ( ! [X0 : 'type/ind_types/list' @ sK2] : (((('const/sets/set_of_list' @ sK2 @ sK3)) != (('const/sets/set_of_list' @ sK2 @ X0))) | ('const/ind_types/NIL' @ sK2 = X0)) ) | ~spl4_1),
% 0.19/0.37 inference(constrained_superposition,[],[f832,f36])).
% 0.19/0.37 thf(f1133,plain,(
% 0.19/0.37 (sK3 = 'const/ind_types/NIL' @ sK2) | ~spl4_1),
% 0.19/0.37 inference(equality_resolution,[],[f946])).
% 0.19/0.37 thf(f1136,plain,(
% 0.19/0.37 $false | (~spl4_1 | spl4_2)),
% 0.19/0.37 inference(forward_subsumption_resolution,[],[f1133,f41])).
% 0.19/0.37 thf(f1137,plain,(
% 0.19/0.37 ~spl4_1 | spl4_2),
% 0.19/0.37 inference(avatar_contradiction_clause,[],[f1136])).
% 0.19/0.37 cnf(s1, plain, ~spl4_1 | ~spl4_2, inference(sat_conversion,[],[f42])).
% 0.19/0.37 cnf(s2, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f43])).
% 0.19/0.37 cnf(s3, plain, spl4_1 | ~spl4_2, inference(sat_conversion,[],[f104])).
% 0.19/0.37 cnf(s20, plain, ~spl4_1 | spl4_2, inference(sat_conversion,[],[f1137])).
% 0.19/0.37 cnf(s23, plain, spl4_1, inference(rat,[],[s2,s3])).
% 0.19/0.37 cnf(s24, plain, spl4_2, inference(rat,[],[s20,s23])).
% 0.19/0.37 cnf(s26, plain, $false, inference(rat,[],[s1,s24,s23])).
% 0.19/0.37 thf(f1140,plain,(
% 0.19/0.37 $false),
% 0.19/0.37 inference(avatar_sat_refutation,[],[s26])).
% 0.19/0.37 % SZS output end Proof for theBenchmark
% 0.19/0.37 % (3030838)------------------------------
% 0.19/0.37 % (3030838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.37 % (3030838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.37 % (3030838)CaDiCaL version: 2.1.3
% 0.19/0.37 % (3030838)Termination reason: Refutation
% 0.19/0.37 % (3030838)Time elapsed: 0.080 s
% 0.19/0.37 % (3030838)Peak memory usage: 13 MB
% 0.19/0.37 % (3030838)Instructions burned: 123 (million)
% 0.19/0.37 % (3030832)Success in time 0.133 s
% 0.19/0.37 % Vampire exiting
%------------------------------------------------------------------------------