%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT297^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 07:48:43 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT297^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 18:24:00 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.28 % (171562)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (171573)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.28 % (171573)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.28 % (171571)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2079069415:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.28 % (171569)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2939162913:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.28 % (171568)lrs+10_16_si=on:nwc=1.5:random_seed=1803524154:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.28 % (171567)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=354119401:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.28 % (171570)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3611157684:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.28 % (171573)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2090312086:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.28 % (171572)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3512856942:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.28 % (171569)Instruction limit reached!
% 0.22/0.28 % (171569)------------------------------
% 0.22/0.28 % (171569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (171569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (171569)CaDiCaL version: 2.1.3
% 0.22/0.28 % (171569)Termination reason: Instruction limit
% 0.22/0.28 % (171569)Termination phase: Saturation
% 0.22/0.28 % (171569)Time elapsed: 0.003 s
% 0.22/0.28 % (171569)Peak memory usage: 12 MB
% 0.22/0.28 % (171569)Instructions burned: 4 (million)
% 0.22/0.28 % (171572) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-171562-171572"...
% 0.22/0.28 % (171572)...printing done.
% 0.22/0.28 % (171572)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.22/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(type_def_7, type, sK0: $tType).
% 0.22/0.28 thf(type_def_8, type, sK1: $tType).
% 0.22/0.28 thf(func_def_0, type, 'const/lists/ITLIST': !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > 'type/ind_types/list' @ X0 > X1 > X1))).
% 0.22/0.28 thf(func_def_1, type, 'const/lists/APPEND': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.22/0.28 thf(func_def_2, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 0.22/0.28 thf(func_def_3, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.22/0.28 thf(func_def_5, type, sK2: sK0).
% 0.22/0.28 thf(func_def_6, type, sK3: (sK1 > sK0 > sK0)).
% 0.22/0.28 thf(func_def_7, type, sK4: 'type/ind_types/list' @ sK1).
% 0.22/0.28 thf(func_def_8, type, sK5: sK1).
% 0.22/0.28 thf(f1,axiom,(
% 0.22/0.28 ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1 > X1),X3 : X1] : ((('const/lists/ITLIST' @ X0 @ X1 @ X2 @ 'const/ind_types/NIL' @ X0 @ X3)) = X3)),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST_0')).
% 0.22/0.28 thf(f2,axiom,(
% 0.22/0.28 ! [X1 : $tType,X0 : $tType,X2 : X0,X4 : 'type/ind_types/list' @ X0,X3 : (X0 > X1 > X1),X5 : X1] : ((('const/lists/ITLIST' @ X0 @ X1 @ X3 @ ('const/ind_types/CONS' @ X0 @ X2 @ X4) @ X5)) = ((X3 @ X2 @ ('const/lists/ITLIST' @ X0 @ X1 @ X3 @ X4 @ X5))))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST_1')).
% 0.22/0.28 thf(f3,axiom,(
% 0.22/0.28 ! [X0 : $tType,X1 : $tType,X3 : X1,X2 : (X0 > X1 > X1),X5 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/ITLIST' @ X0 @ X1 @ X2 @ ('const/lists/APPEND' @ X0 @ X4 @ X5) @ X3)) = (('const/lists/ITLIST' @ X0 @ X1 @ X2 @ X4 @ ('const/lists/ITLIST' @ X0 @ X1 @ X2 @ X5 @ X3))))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST_APPEND_')).
% 0.22/0.28 thf(f4,conjecture,(
% 0.22/0.28 ! [X1 : $tType,X0 : $tType,X3 : X0,X5 : 'type/ind_types/list' @ X0,X4 : X1,X2 : (X0 > X1 > X1)] : ((('const/lists/ITLIST' @ X0 @ X1 @ X2 @ ('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X3 @ 'const/ind_types/NIL' @ X0)) @ X4)) = (('const/lists/ITLIST' @ X0 @ X1 @ X2 @ X5 @ (X2 @ X3 @ X4))))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/lists/ITLIST_EXTRA_')).
% 0.22/0.28 thf(f5,negated_conjecture,(
% 0.22/0.28 ~ ! [X1 : $tType,X0 : $tType,X3 : X0,X5 : 'type/ind_types/list' @ X0,X4 : X1,X2 : (X0 > X1 > X1)] : ((('const/lists/ITLIST' @ X0 @ X1 @ X2 @ ('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X3 @ 'const/ind_types/NIL' @ X0)) @ X4)) = (('const/lists/ITLIST' @ X0 @ X1 @ X2 @ X5 @ (X2 @ X3 @ X4))))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 ! [X0 : $tType,X1 : $tType,X3 : X0,X2 : (X1 > X0 > X0)] : ((('const/lists/ITLIST' @ X1 @ X0 @ X2 @ 'const/ind_types/NIL' @ X1 @ X3)) = X3)),
% 0.22/0.28 inference(rectify,[],[f1])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ! [X0 : $tType,X1 : $tType,X5 : 'type/ind_types/list' @ X0,X3 : (X0 > X1 > X1),X4 : 'type/ind_types/list' @ X0,X2 : X1] : ((('const/lists/ITLIST' @ X0 @ X1 @ X3 @ X5 @ ('const/lists/ITLIST' @ X0 @ X1 @ X3 @ X4 @ X2))) = (('const/lists/ITLIST' @ X0 @ X1 @ X3 @ ('const/lists/APPEND' @ X0 @ X5 @ X4) @ X2)))),
% 0.22/0.28 inference(rectify,[],[f3])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ~ ! [X1 : $tType,X0 : $tType,X4 : X0,X2 : X1,X5 : (X1 > X0 > X0),X3 : 'type/ind_types/list' @ X1] : ((('const/lists/ITLIST' @ X1 @ X0 @ X5 @ ('const/lists/APPEND' @ X1 @ X3 @ ('const/ind_types/CONS' @ X1 @ X2 @ 'const/ind_types/NIL' @ X1)) @ X4)) = (('const/lists/ITLIST' @ X1 @ X0 @ X5 @ X3 @ (X5 @ X2 @ X4))))),
% 0.22/0.28 inference(rectify,[],[f5])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ! [X1 : $tType,X0 : $tType,X2 : X1,X5 : X0,X4 : (X1 > X0 > X0),X3 : 'type/ind_types/list' @ X1] : ((('const/lists/ITLIST' @ X1 @ X0 @ X4 @ ('const/ind_types/CONS' @ X1 @ X2 @ X3) @ X5)) = ((X4 @ X2 @ ('const/lists/ITLIST' @ X1 @ X0 @ X4 @ X3 @ X5))))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ? [X0 : $tType,X1 : $tType,X4 : X0,X5 : (X1 > X0 > X0),X3 : 'type/ind_types/list' @ X1,X2 : X1] : ((('const/lists/ITLIST' @ X1 @ X0 @ X5 @ ('const/lists/APPEND' @ X1 @ X3 @ ('const/ind_types/CONS' @ X1 @ X2 @ 'const/ind_types/NIL' @ X1)) @ X4)) != (('const/lists/ITLIST' @ X1 @ X0 @ X5 @ X3 @ (X5 @ X2 @ X4))))),
% 0.22/0.28 inference(ennf_transformation,[],[f8])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ? [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X1 > X0 > X0),X4 : 'type/ind_types/list' @ X1,X5 : X1] : ((('const/lists/ITLIST' @ X1 @ X0 @ X3 @ ('const/lists/APPEND' @ X1 @ X4 @ ('const/ind_types/CONS' @ X1 @ X5 @ 'const/ind_types/NIL' @ X1)) @ X2)) != (('const/lists/ITLIST' @ X1 @ X0 @ X3 @ X4 @ (X3 @ X5 @ X2))))),
% 0.22/0.28 inference(rectify,[],[f10])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ((('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ ('const/lists/APPEND' @ sK1 @ sK4 @ ('const/ind_types/CONS' @ sK1 @ sK5 @ 'const/ind_types/NIL' @ sK1)) @ sK2)) != (('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ sK4 @ (sK3 @ sK5 @ sK2))))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f11])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X1 > X0 > X0)] : ((('const/lists/ITLIST' @ X1 @ X0 @ X3 @ 'const/ind_types/NIL' @ X1 @ X2)) = X2)),
% 0.22/0.28 inference(rectify,[],[f6])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 ! [X0 : $tType,X1 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : (X0 > X1 > X1),X4 : 'type/ind_types/list' @ X0,X5 : X1] : ((('const/lists/ITLIST' @ X0 @ X1 @ X3 @ X2 @ ('const/lists/ITLIST' @ X0 @ X1 @ X3 @ X4 @ X5))) = (('const/lists/ITLIST' @ X0 @ X1 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X4) @ X5)))),
% 0.22/0.28 inference(rectify,[],[f7])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1,X4 : (X0 > X1 > X1),X5 : 'type/ind_types/list' @ X0] : ((('const/lists/ITLIST' @ X0 @ X1 @ X4 @ ('const/ind_types/CONS' @ X0 @ X2 @ X5) @ X3)) = ((X4 @ X2 @ ('const/lists/ITLIST' @ X0 @ X1 @ X4 @ X5 @ X3))))),
% 0.22/0.28 inference(rectify,[],[f9])).
% 0.22/0.28 thf(f16,plain,(
% 0.22/0.28 ((('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ ('const/lists/APPEND' @ sK1 @ sK4 @ ('const/ind_types/CONS' @ sK1 @ sK5 @ 'const/ind_types/NIL' @ sK1)) @ sK2)) != (('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ sK4 @ (sK3 @ sK5 @ sK2))))),
% 0.22/0.28 inference(cnf_transformation,[],[f12])).
% 0.22/0.28 thf(f17,plain,(
% 0.22/0.28 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X1 > X0 > X0)] : (((('const/lists/ITLIST' @ X1 @ X0 @ X3 @ 'const/ind_types/NIL' @ X1 @ X2)) = X2)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f13])).
% 0.22/0.28 thf(f18,plain,(
% 0.22/0.28 ( ! [X1 : $tType,X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : (X0 > X1 > X1),X4 : 'type/ind_types/list' @ X0,X5 : X1] : (((('const/lists/ITLIST' @ X0 @ X1 @ X3 @ X2 @ ('const/lists/ITLIST' @ X0 @ X1 @ X3 @ X4 @ X5))) = (('const/lists/ITLIST' @ X0 @ X1 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X4) @ X5)))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f14])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : (X0 > X1 > X1),X5 : 'type/ind_types/list' @ X0] : (((('const/lists/ITLIST' @ X0 @ X1 @ X4 @ ('const/ind_types/CONS' @ X0 @ X2 @ X5) @ X3)) = ((X4 @ X2 @ ('const/lists/ITLIST' @ X0 @ X1 @ X4 @ X5 @ X3))))) )),
% 0.22/0.28 inference(cnf_transformation,[],[f15])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 ((('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ sK4 @ ('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ ('const/ind_types/CONS' @ sK1 @ sK5 @ 'const/ind_types/NIL' @ sK1) @ sK2))) != (('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ sK4 @ (sK3 @ sK5 @ sK2))))),
% 0.22/0.28 inference(backward_demodulation,[],[f16,f18])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ((('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ sK4 @ (sK3 @ sK5 @ ('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ 'const/ind_types/NIL' @ sK1 @ sK2)))) != (('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ sK4 @ (sK3 @ sK5 @ sK2))))),
% 0.22/0.28 inference(forward_demodulation,[],[f20,f19])).
% 0.22/0.28 thf(f22,plain,(
% 0.22/0.28 ((('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ sK4 @ (sK3 @ sK5 @ sK2))) != (('const/lists/ITLIST' @ sK1 @ sK0 @ sK3 @ sK4 @ (sK3 @ sK5 @ sK2))))),
% 0.22/0.28 inference(forward_demodulation,[],[f21,f17])).
% 0.22/0.28 thf(f23,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f22])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (171572)------------------------------
% 0.22/0.28 % (171572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (171572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (171572)CaDiCaL version: 2.1.3
% 0.22/0.28 % (171572)Termination reason: Refutation
% 0.22/0.28 % (171572)Time elapsed: 0.003 s
% 0.22/0.28 % (171572)Peak memory usage: 12 MB
% 0.22/0.28 % (171572)Instructions burned: 3 (million)
% 0.22/0.28 % (171562)Success in time 0.041 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------