%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT288^1 : 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 : n008.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 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT288^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 18:24:34 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.19/0.30 % (3540654)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (3540663)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1441341773:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (3540663)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % (3540660)% WARNING: option uhcvi not known.
% 0.19/0.30 % (3540659)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3973503434_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (3540660)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=251099420:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (3540661)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=42990294:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (3540662)dis+10_1_sil=32000:sp=arity:random_seed=3005532418:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (3540664)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3541316284:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % (3540660)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % (3540665)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2614309602:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % (3540660)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.30 % (3540673)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1615487225:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (3540663)Instruction limit reached!
% 0.19/0.30 % (3540663)------------------------------
% 0.19/0.30 % (3540663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (3540663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (3540663)CaDiCaL version: 2.1.3
% 0.19/0.30 % (3540663)Termination reason: Instruction limit
% 0.19/0.30 % (3540663)Termination phase: Saturation
% 0.19/0.30 % (3540663)Time elapsed: 0.032 s
% 0.19/0.30 % (3540663)Peak memory usage: 12 MB
% 0.19/0.30 % (3540663)Instructions burned: 118 (million)
% 0.19/0.30 % (3540660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3540654-3540660"...
% 0.19/0.30 % (3540660)...printing done.
% 0.19/0.30 % (3540662) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3540654-3540662"...
% 0.19/0.30 % (3540660)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% 0.19/0.30 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.19/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.30 thf(type_def_7, type, sK2: $tType).
% 0.19/0.30 thf(func_def_0, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.19/0.30 thf(func_def_1, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.19/0.30 thf(func_def_5, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.30 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.19/0.30 thf(func_def_7, type, sK0: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > X0))).
% 0.19/0.30 thf(func_def_8, type, sK1: !>[X0: $tType]:((('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0))).
% 0.19/0.30 thf(func_def_9, type, sK3: 'type/ind_types/list' @ sK2).
% 0.19/0.30 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.19/0.30 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.30 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.30 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.30 thf(f1,axiom,(
% 0.19/0.30 ! [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))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_')).
% 0.19/0.30 thf(f4,conjecture,(
% 0.19/0.30 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (X1 = (('const/ind_types/CONS' @ X0 @ X2 @ X3))) | (X1 = 'const/ind_types/NIL' @ X0))),
% 0.19/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/list_CASES_')).
% 0.19/0.30 thf(f5,negated_conjecture,(
% 0.19/0.30 ~ ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (X1 = (('const/ind_types/CONS' @ X0 @ X2 @ X3))) | (X1 = 'const/ind_types/NIL' @ X0))),
% 0.19/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.19/0.30 thf(f6,plain,(
% 0.19/0.30 ! [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))),
% 0.19/0.30 inference(rectify,[],[f1])).
% 0.19/0.30 thf(f7,plain,(
% 0.19/0.30 ! [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))),
% 0.19/0.30 inference(fool_elimination,[],[f6])).
% 0.19/0.30 thf(f9,plain,(
% 0.19/0.30 ! [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)))),
% 0.19/0.30 inference(ennf_transformation,[],[f7])).
% 0.19/0.30 thf(f10,plain,(
% 0.19/0.30 ! [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))),
% 0.19/0.30 inference(flattening,[],[f9])).
% 0.19/0.30 thf(f11,plain,(
% 0.19/0.30 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X2 @ X3)) != X1) & ('const/ind_types/NIL' @ X0 != X1))),
% 0.19/0.30 inference(ennf_transformation,[],[f5])).
% 0.19/0.30 thf(f12,plain,(
% 0.19/0.30 ! [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))),
% 0.19/0.30 inference(rectify,[],[f10])).
% 0.19/0.30 thf(f13,plain,(
% 0.19/0.30 ! [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))),
% 0.19/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X4,sK1 @ X0 @ X1),skolemize(X4,sK1 @ X0 @ X1)],[f12])).
% 0.19/0.30 thf(f14,plain,(
% 0.19/0.30 ! [X2 : sK2,X3 : 'type/ind_types/list' @ sK2] : (sK3 != (('const/ind_types/CONS' @ sK2 @ X2 @ X3))) & (sK3 != 'const/ind_types/NIL' @ sK2)),
% 0.19/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f11])).
% 0.19/0.30 thf(f16,plain,(
% 0.19/0.30 ( ! [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)) )),
% 0.19/0.30 inference(cnf_transformation,[],[f13])).
% 0.19/0.30 thf(f19,plain,(
% 0.19/0.30 (sK3 != 'const/ind_types/NIL' @ sK2)),
% 0.19/0.30 inference(cnf_transformation,[],[f14])).
% 0.19/0.30 thf(f20,plain,(
% 0.19/0.30 ( ! [X2 : sK2,X3 : 'type/ind_types/list' @ sK2] : ((sK3 != (('const/ind_types/CONS' @ sK2 @ X2 @ X3)))) )),
% 0.19/0.30 inference(cnf_transformation,[],[f14])).
% 0.19/0.30 thf(f62,plain,(
% 0.19/0.30 ( ! [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)))) )),
% 0.19/0.30 inference(leibniz_equality_elimination,[],[f16])).
% 0.19/0.30 thf(f81,plain,(
% 0.19/0.30 ( ! [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))))) )),
% 0.19/0.30 inference(beta-eta_normalization,[],[f62])).
% 0.19/0.30 thf(f82,plain,(
% 0.19/0.30 ( ! [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)))) )),
% 0.19/0.30 inference(not_proxy_clausification,[],[f81])).
% 0.19/0.30 thf(f83,plain,(
% 0.19/0.30 ( ! [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)) )),
% 0.19/0.30 inference(equality_proxy_clausification,[],[f82])).
% 0.19/0.30 thf(f650,plain,(
% 0.19/0.30 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((sK3 != X0) | ('const/ind_types/NIL' @ sK2 = X0)) )),
% 0.19/0.30 inference(constrained_superposition,[],[f20,f83])).
% 0.19/0.30 thf(f676,plain,(
% 0.19/0.30 (sK3 = 'const/ind_types/NIL' @ sK2)),
% 0.19/0.30 inference(equality_resolution,[],[f650])).
% 0.19/0.30 thf(f677,plain,(
% 0.19/0.30 $false),
% 0.19/0.30 inference(forward_subsumption_resolution,[],[f676,f19])).
% 0.19/0.30 % SZS output end Proof for theBenchmark
% 0.19/0.30 % (3540660)------------------------------
% 0.19/0.30 % (3540660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (3540660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (3540660)CaDiCaL version: 2.1.3
% 0.19/0.30 % (3540660)Termination reason: Refutation
% 0.19/0.30 % (3540660)Time elapsed: 0.027 s
% 0.19/0.30 % (3540660)Peak memory usage: 12 MB
% 0.19/0.30 % (3540660)Instructions burned: 48 (million)
% 0.19/0.30 % (3540654)Success in time 0.067 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------