%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL733^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:14:35 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL733^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 10:00:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.22/0.30 % (142415)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (142421)lrs+10_16_si=on:nwc=1.5:random_seed=590232939:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (142422)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2388756717:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (142423)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=535150300: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)
% 0.22/0.30 % (142424)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4140423006:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (142422) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-142415-142422"...
% 0.22/0.30 % (142423) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-142415-142423"...
% 0.22/0.30 % (142426)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (142426)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
% 0.22/0.30 % (142420)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1528550700:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (142423)...printing done.
% 0.22/0.30 % (142422)...printing done.
% 0.22/0.30 % (142423)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, b: $tType).
% 0.22/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_3, type, sK0: (((b > $o) > b) > b > $o)).
% 0.22/0.30 thf(func_def_4, type, sK1: (((b > $o) > b) > b)).
% 0.22/0.30 thf(func_def_5, type, sK2: (b > $o)).
% 0.22/0.30 thf(func_def_6, type, sK3: b).
% 0.22/0.30 thf(func_def_7, type, sK4: ((b > $o) > b)).
% 0.22/0.30 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.22/0.30 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.30 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.30 thf(f1,conjecture,(
% 0.22/0.30 ! [X0 : ((b > $o) > b > $o)] : (! [X1 : (b > $o)] : ? [X2 : b] : (? [X3 : b] : (X1 @ X3) => (X1 @ X2)) => ? [X4 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X3 : b] : (X1 @ X3) => (X1 @ (X4 @ X1)))) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : (? [X7 : b] : (X6 @ X7) => (X6 @ (X5 @ X6)))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5310_SUB4)).
% 0.22/0.30 thf(f2,negated_conjecture,(
% 0.22/0.30 ~(! [X0 : ((b > $o) > b > $o)] : (! [X1 : (b > $o)] : ? [X2 : b] : (? [X3 : b] : (X1 @ X3) => (X1 @ X2)) => ? [X4 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X3 : b] : (X1 @ X3) => (X1 @ (X4 @ X1)))) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : (? [X7 : b] : (X6 @ X7) => (X6 @ (X5 @ X6))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.30 thf(f3,plain,(
% 0.22/0.30 ~((! [X1 : (b > $o)] : ? [X2 : b] : (? [X3 : b] : (X1 @ X3) => (X1 @ X2)) => ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : (? [X6 : b] : (X5 @ X6) => (X5 @ (X4 @ X5)))) => ? [X7 : ((b > $o) > b)] : ! [X8 : (b > $o)] : (? [X9 : b] : (X8 @ X9) => (X8 @ (X7 @ X8))))),
% 0.22/0.30 inference(rectify,[],[f2])).
% 0.22/0.30 thf(f4,plain,(
% 0.22/0.30 ~((! [X1 : (b > $o)] : ? [X2 : b] : (? [X3 : b] : (((X1 @ X3)) = $true) => (((X1 @ X2)) = $true)) => ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : (? [X6 : b] : (((X5 @ X6)) = $true) => (((X5 @ (X4 @ X5))) = $true))) => ? [X7 : ((b > $o) > b)] : ! [X8 : (b > $o)] : (? [X9 : b] : (((X8 @ X9)) = $true) => (((X8 @ (X7 @ X8))) = $true)))),
% 0.22/0.30 inference(fool_elimination,[],[f3])).
% 0.22/0.30 thf(f5,plain,(
% 0.22/0.30 ~((! [X0 : (b > $o)] : ? [X1 : b] : (? [X2 : b] : (((X0 @ X2)) = $true) => (((X0 @ X1)) = $true)) => ? [X3 : ((b > $o) > b)] : ! [X4 : (b > $o)] : (? [X5 : b] : (((X4 @ X5)) = $true) => ($true = ((X4 @ (X3 @ X4)))))) => ? [X6 : ((b > $o) > b)] : ! [X7 : (b > $o)] : (? [X8 : b] : (((X7 @ X8)) = $true) => (((X7 @ (X6 @ X7))) = $true)))),
% 0.22/0.30 inference(rectify,[],[f4])).
% 0.22/0.30 thf(f6,plain,(
% 0.22/0.30 ! [X6 : ((b > $o) > b)] : ? [X7 : (b > $o)] : ((((X7 @ (X6 @ X7))) != $true) & ? [X8 : b] : (((X7 @ X8)) = $true)) & (? [X0 : (b > $o)] : ! [X1 : b] : (? [X2 : b] : (((X0 @ X2)) = $true) & (((X0 @ X1)) != $true)) | ? [X3 : ((b > $o) > b)] : ! [X4 : (b > $o)] : (($true = ((X4 @ (X3 @ X4)))) | ! [X5 : b] : (((X4 @ X5)) != $true)))),
% 0.22/0.30 inference(ennf_transformation,[],[f5])).
% 0.22/0.30 thf(f7,plain,(
% 0.22/0.30 ! [X0 : ((b > $o) > b)] : ? [X1 : (b > $o)] : ((((X1 @ (X0 @ X1))) != $true) & ? [X2 : b] : (((X1 @ X2)) = $true)) & (? [X3 : (b > $o)] : ! [X4 : b] : (? [X5 : b] : ($true = ((X3 @ X5))) & (((X3 @ X4)) != $true)) | ? [X6 : ((b > $o) > b)] : ! [X7 : (b > $o)] : ((((X7 @ (X6 @ X7))) = $true) | ! [X8 : b] : (((X7 @ X8)) != $true)))),
% 0.22/0.30 inference(rectify,[],[f6])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 ! [X0 : ((b > $o) > b)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0))))) & (((sK0 @ X0 @ (sK1 @ X0))) = $true)) & (! [X4 : b] : ((((sK2 @ sK3)) = $true) & (((sK2 @ X4)) != $true)) | ! [X7 : (b > $o)] : ((((X7 @ (sK4 @ X7))) = $true) | ! [X8 : b] : (((X7 @ X8)) != $true)))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,sK4]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0),skolemize(X3,sK2),skolemize(X5,sK3),skolemize(X6,sK4)],[f7])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 ( ! [X8 : b,X7 : (b > $o),X4 : b] : ((((X7 @ (sK4 @ X7))) = $true) | (((sK2 @ X4)) != $true) | (((X7 @ X8)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f8])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 ( ! [X8 : b,X7 : (b > $o)] : ((((X7 @ (sK4 @ X7))) = $true) | (((sK2 @ sK3)) = $true) | (((X7 @ X8)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f8])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ( ! [X0 : ((b > $o) > b)] : ((((sK0 @ X0 @ (sK1 @ X0))) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f8])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 ( ! [X0 : ((b > $o) > b)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0)))))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f8])).
% 0.22/0.30 thf(f15,definition,(
% 0.22/0.30 spl5_1 <=> ! [X4 : b] : (((sK2 @ X4)) != $true)),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 ( ! [X4 : b] : ((((sK2 @ X4)) != $true)) ) | ~spl5_1),
% 0.22/0.30 inference(avatar_component_clause,[],[f15])).
% 0.22/0.30 thf(f18,definition,(
% 0.22/0.30 spl5_2 <=> ! [X7 : (b > $o),X8 : b] : ((((X7 @ (sK4 @ X7))) = $true) | (((X7 @ X8)) != $true))),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 ( ! [X8 : b,X7 : (b > $o)] : ((((X7 @ (sK4 @ X7))) = $true) | (((X7 @ X8)) != $true)) ) | ~spl5_2),
% 0.22/0.30 inference(avatar_component_clause,[],[f18])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 spl5_1 | spl5_2),
% 0.22/0.30 inference(avatar_split_clause,[],[f9,f18,f15])).
% 0.22/0.30 thf(f22,definition,(
% 0.22/0.30 spl5_3 <=> (((sK2 @ sK3)) = $true)),
% 0.22/0.30 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.22/0.30 thf(f24,plain,(
% 0.22/0.30 (((sK2 @ sK3)) = $true) | ~spl5_3),
% 0.22/0.30 inference(avatar_component_clause,[],[f22])).
% 0.22/0.30 thf(f25,plain,(
% 0.22/0.30 spl5_3 | spl5_2),
% 0.22/0.30 inference(avatar_split_clause,[],[f10,f18,f22])).
% 0.22/0.30 thf(f30,plain,(
% 0.22/0.30 ( ! [X0 : b] : ((((sK0 @ sK4 @ X0)) != $true) | ($true != $true)) ) | ~spl5_2),
% 0.22/0.30 inference(superposition,[],[f12,f19])).
% 0.22/0.30 thf(f36,plain,(
% 0.22/0.30 ( ! [X0 : b] : ((((sK0 @ sK4 @ X0)) != $true)) ) | ~spl5_2),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f30])).
% 0.22/0.30 thf(f37,plain,(
% 0.22/0.30 ($true != $true) | ~spl5_2),
% 0.22/0.30 inference(superposition,[],[f36,f11])).
% 0.22/0.30 thf(f40,plain,(
% 0.22/0.30 $false | ~spl5_2),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f37])).
% 0.22/0.30 thf(f41,plain,(
% 0.22/0.30 ~spl5_2),
% 0.22/0.30 inference(avatar_contradiction_clause,[],[f40])).
% 0.22/0.30 thf(f42,plain,(
% 0.22/0.30 $false | (~spl5_1 | ~spl5_3)),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f24,f16])).
% 0.22/0.30 thf(f43,plain,(
% 0.22/0.30 ~spl5_1 | ~spl5_3),
% 0.22/0.30 inference(avatar_contradiction_clause,[],[f42])).
% 0.22/0.30 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f20])).
% 0.22/0.30 cnf(s2, plain, spl5_2 | spl5_3, inference(sat_conversion,[],[f25])).
% 0.22/0.30 cnf(s3, plain, ~spl5_2, inference(sat_conversion,[],[f41])).
% 0.22/0.30 cnf(s4, plain, ~spl5_1 | ~spl5_3, inference(sat_conversion,[],[f43])).
% 0.22/0.30 cnf(s5, plain, spl5_3, inference(rat,[],[s2,s3])).
% 0.22/0.30 cnf(s6, plain, ~spl5_1, inference(rat,[],[s4,s5])).
% 0.22/0.30 cnf(s7, plain, $false, inference(rat,[],[s1,s3,s6])).
% 0.22/0.30 thf(f44,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(avatar_sat_refutation,[],[s7])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (142423)------------------------------
% 0.22/0.30 % (142423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (142423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (142423)CaDiCaL version: 2.1.3
% 0.22/0.30 % (142423)Termination reason: Refutation
% 0.22/0.30 % (142423)Time elapsed: 0.003 s
% 0.22/0.30 % (142423)Peak memory usage: 13 MB
% 0.22/0.30 % (142423)Instructions burned: 3 (million)
% 0.22/0.30 % (142415)Success in time 0.043 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------