%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO274^5 : 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 : 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 08:47:20 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 : SYO274^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:48:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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 % (1488728)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (1488740)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=2486872855: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 % (1488740) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1488728-1488740"...
% 0.22/0.28 % (1488743)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 % (1488743)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 % (1488740)...printing done.
% 0.22/0.28 % (1488740)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, c: $tType).
% 0.22/0.28 thf(type_def_6, type, b: $tType).
% 0.22/0.28 thf(type_def_7, type, a: $tType).
% 0.22/0.28 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, cG: (c > b)).
% 0.22/0.28 thf(func_def_1, type, cF: (b > a)).
% 0.22/0.28 thf(func_def_5, type, sK0: (b > b > a > $o)).
% 0.22/0.28 thf(func_def_6, type, sK1: (c > c > b > $o)).
% 0.22/0.28 thf(func_def_7, type, sK2: c).
% 0.22/0.28 thf(func_def_8, type, sK3: c).
% 0.22/0.28 thf(func_def_9, type, sK4: (c > $o)).
% 0.22/0.28 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.22/0.28 thf(func_def_12, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.28 thf(func_def_13, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.28 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.28 thf(f1,conjecture,(
% 0.22/0.28 (! [X1 : b,X0 : b] : (! [X2 : (a > $o)] : ((X2 @ (cF @ X0)) => (X2 @ (cF @ X1))) => ! [X2 : (b > $o)] : ((X2 @ X0) => (X2 @ X1))) & ! [X1 : c,X0 : c] : (! [X2 : (b > $o)] : ((X2 @ (cG @ X0)) => (X2 @ (cG @ X1))) => ! [X2 : (c > $o)] : ((X2 @ X0) => (X2 @ X1)))) => ! [X0 : c,X1 : c] : (! [X2 : (a > $o)] : ((X2 @ (cF @ (cG @ X0))) => (X2 @ (cF @ (cG @ X1)))) => ! [X2 : (c > $o)] : ((X2 @ X0) => (X2 @ X1)))),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM48_EXPD)).
% 0.22/0.28 thf(f2,negated_conjecture,(
% 0.22/0.28 ~((! [X1 : b,X0 : b] : (! [X2 : (a > $o)] : ((X2 @ (cF @ X0)) => (X2 @ (cF @ X1))) => ! [X2 : (b > $o)] : ((X2 @ X0) => (X2 @ X1))) & ! [X1 : c,X0 : c] : (! [X2 : (b > $o)] : ((X2 @ (cG @ X0)) => (X2 @ (cG @ X1))) => ! [X2 : (c > $o)] : ((X2 @ X0) => (X2 @ X1)))) => ! [X0 : c,X1 : c] : (! [X2 : (a > $o)] : ((X2 @ (cF @ (cG @ X0))) => (X2 @ (cF @ (cG @ X1)))) => ! [X2 : (c > $o)] : ((X2 @ X0) => (X2 @ X1))))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.28 thf(f3,plain,(
% 0.22/0.28 ~((! [X0 : b,X1 : b] : (! [X2 : (a > $o)] : ((X2 @ (cF @ X1)) => (X2 @ (cF @ X0))) => ! [X3 : (b > $o)] : ((X3 @ X1) => (X3 @ X0))) & ! [X4 : c,X5 : c] : (! [X6 : (b > $o)] : ((X6 @ (cG @ X5)) => (X6 @ (cG @ X4))) => ! [X7 : (c > $o)] : ((X7 @ X5) => (X7 @ X4)))) => ! [X8 : c,X9 : c] : (! [X10 : (a > $o)] : ((X10 @ (cF @ (cG @ X8))) => (X10 @ (cF @ (cG @ X9)))) => ! [X11 : (c > $o)] : ((X11 @ X8) => (X11 @ X9))))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f4,plain,(
% 0.22/0.28 ~((! [X5 : c,X4 : c] : (! [X6 : (b > $o)] : ((((X6 @ (cG @ X5))) = $true) => ($true = ((X6 @ (cG @ X4))))) => ! [X7 : (c > $o)] : (($true = ((X7 @ X5))) => (((X7 @ X4)) = $true))) & ! [X0 : b,X1 : b] : (! [X2 : (a > $o)] : ((((X2 @ (cF @ X1))) = $true) => (((X2 @ (cF @ X0))) = $true)) => ! [X3 : (b > $o)] : ((((X3 @ X1)) = $true) => (((X3 @ X0)) = $true)))) => ! [X8 : c,X9 : c] : (! [X10 : (a > $o)] : ((((X10 @ (cF @ (cG @ X8)))) = $true) => (((X10 @ (cF @ (cG @ X9)))) = $true)) => ! [X11 : (c > $o)] : (($true = ((X11 @ X8))) => (((X11 @ X9)) = $true))))),
% 0.22/0.28 inference(fool_elimination,[],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 ? [X8 : c,X9 : c] : (? [X11 : (c > $o)] : (($true = ((X11 @ X8))) & (((X11 @ X9)) != $true)) & ! [X10 : (a > $o)] : ((((X10 @ (cF @ (cG @ X8)))) != $true) | (((X10 @ (cF @ (cG @ X9)))) = $true))) & (! [X5 : c,X4 : c] : (! [X7 : (c > $o)] : ((((X7 @ X4)) = $true) | ($true != ((X7 @ X5)))) | ? [X6 : (b > $o)] : (($true != ((X6 @ (cG @ X4)))) & (((X6 @ (cG @ X5))) = $true))) & ! [X1 : b,X0 : b] : (? [X2 : (a > $o)] : ((((X2 @ (cF @ X1))) = $true) & (((X2 @ (cF @ X0))) != $true)) | ! [X3 : (b > $o)] : ((((X3 @ X1)) != $true) | (((X3 @ X0)) = $true))))),
% 0.22/0.28 inference(ennf_transformation,[],[f4])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 ! [X1 : b,X0 : b] : (? [X2 : (a > $o)] : ((((X2 @ (cF @ X1))) = $true) & (((X2 @ (cF @ X0))) != $true)) | ! [X3 : (b > $o)] : ((((X3 @ X1)) != $true) | (((X3 @ X0)) = $true))) & ! [X5 : c,X4 : c] : (! [X7 : (c > $o)] : ((((X7 @ X4)) = $true) | ($true != ((X7 @ X5)))) | ? [X6 : (b > $o)] : (($true != ((X6 @ (cG @ X4)))) & (((X6 @ (cG @ X5))) = $true))) & ? [X8 : c,X9 : c] : (? [X11 : (c > $o)] : (($true = ((X11 @ X8))) & (((X11 @ X9)) != $true)) & ! [X10 : (a > $o)] : ((((X10 @ (cF @ (cG @ X8)))) != $true) | (((X10 @ (cF @ (cG @ X9)))) = $true)))),
% 0.22/0.28 inference(flattening,[],[f5])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ! [X0 : b,X1 : b] : (? [X2 : (a > $o)] : ((((X2 @ (cF @ X0))) = $true) & (((X2 @ (cF @ X1))) != $true)) | ! [X3 : (b > $o)] : ((((X3 @ X0)) != $true) | (((X3 @ X1)) = $true))) & ! [X4 : c,X5 : c] : (! [X6 : (c > $o)] : ((((X6 @ X5)) = $true) | (((X6 @ X4)) != $true)) | ? [X7 : (b > $o)] : ((((X7 @ (cG @ X5))) != $true) & (((X7 @ (cG @ X4))) = $true))) & ? [X8 : c,X9 : c] : (? [X10 : (c > $o)] : (($true = ((X10 @ X8))) & (((X10 @ X9)) != $true)) & ! [X11 : (a > $o)] : ((((X11 @ (cF @ (cG @ X8)))) != $true) | ($true = ((X11 @ (cF @ (cG @ X9)))))))),
% 0.22/0.28 inference(rectify,[],[f6])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 ! [X0 : b,X1 : b] : ((($true = ((sK0 @ X1 @ X0 @ (cF @ X0)))) & (((sK0 @ X1 @ X0 @ (cF @ X1))) != $true)) | ! [X3 : (b > $o)] : ((((X3 @ X0)) != $true) | (((X3 @ X1)) = $true))) & ! [X4 : c,X5 : c] : (! [X6 : (c > $o)] : ((((X6 @ X5)) = $true) | (((X6 @ X4)) != $true)) | ((((sK1 @ X5 @ X4 @ (cG @ X5))) != $true) & (((sK1 @ X5 @ X4 @ (cG @ X4))) = $true))) & ((($true = ((sK4 @ sK2))) & ($true != ((sK4 @ sK3)))) & ! [X11 : (a > $o)] : ((((X11 @ (cF @ (cG @ sK2)))) != $true) | (((X11 @ (cF @ (cG @ sK3)))) = $true)))),
% 0.22/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,sK4]),skolemize(X7,sK1 @ X5 @ X4),skolemize(X7,sK1 @ X5 @ X4),skolemize(X8,sK2),skolemize(X9,sK3),skolemize(X10,sK4)],[f7])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 ( ! [X11 : (a > $o)] : ((((X11 @ (cF @ (cG @ sK3)))) = $true) | (((X11 @ (cF @ (cG @ sK2)))) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f10,plain,(
% 0.22/0.28 ($true != ((sK4 @ sK3)))),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f11,plain,(
% 0.22/0.28 ($true = ((sK4 @ sK2)))),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f12,plain,(
% 0.22/0.28 ( ! [X6 : (c > $o),X4 : c,X5 : c] : ((((sK1 @ X5 @ X4 @ (cG @ X4))) = $true) | (((X6 @ X4)) != $true) | (((X6 @ X5)) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f13,plain,(
% 0.22/0.28 ( ! [X6 : (c > $o),X4 : c,X5 : c] : ((((sK1 @ X5 @ X4 @ (cG @ X5))) != $true) | (((X6 @ X5)) = $true) | (((X6 @ X4)) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 ( ! [X3 : (b > $o),X0 : b,X1 : b] : ((((sK0 @ X1 @ X0 @ (cF @ X1))) != $true) | (((X3 @ X0)) != $true) | (((X3 @ X1)) = $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 ( ! [X3 : (b > $o),X0 : b,X1 : b] : (($true = ((sK0 @ X1 @ X0 @ (cF @ X0)))) | (((X3 @ X1)) = $true) | (((X3 @ X0)) != $true)) )),
% 0.22/0.28 inference(cnf_transformation,[],[f8])).
% 0.22/0.28 thf(f18,definition,(
% 0.22/0.28 spl5_1 <=> ($true = ((sK4 @ sK3)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.22/0.28 thf(f21,plain,(
% 0.22/0.28 ~spl5_1),
% 0.22/0.28 inference(avatar_split_clause,[],[f10,f18])).
% 0.22/0.28 thf(f23,definition,(
% 0.22/0.28 spl5_2 <=> ($true = ((sK4 @ sK2)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.22/0.28 thf(f26,plain,(
% 0.22/0.28 spl5_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f11,f23])).
% 0.22/0.28 thf(f28,plain,(
% 0.22/0.28 (((cF @ (cG @ sK3))) = ((cF @ (cG @ sK2))))),
% 0.22/0.28 inference(leibniz_equality_elimination,[],[f9])).
% 0.22/0.28 thf(f38,definition,(
% 0.22/0.28 spl5_3 <=> (((cF @ (cG @ sK3))) = ((cF @ (cG @ sK2))))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.22/0.28 thf(f40,plain,(
% 0.22/0.28 (((cF @ (cG @ sK3))) = ((cF @ (cG @ sK2)))) | ~spl5_3),
% 0.22/0.28 inference(avatar_component_clause,[],[f38])).
% 0.22/0.28 thf(f41,plain,(
% 0.22/0.28 spl5_3),
% 0.22/0.28 inference(avatar_split_clause,[],[f28,f38])).
% 0.22/0.28 thf(f42,plain,(
% 0.22/0.28 ( ! [X0 : c,X1 : c] : ((((sK1 @ X1 @ X0 @ (cG @ X0))) = $true) | (X0 = X1)) )),
% 0.22/0.28 inference(leibniz_equality_elimination,[],[f12])).
% 0.22/0.28 thf(f44,plain,(
% 0.22/0.28 ( ! [X0 : c,X1 : c] : ((((sK1 @ X1 @ X0 @ (cG @ X1))) != $true) | (X0 = X1)) )),
% 0.22/0.28 inference(leibniz_equality_elimination,[],[f13])).
% 0.22/0.28 thf(f47,plain,(
% 0.22/0.28 ( ! [X0 : b,X1 : b] : ((((sK0 @ X1 @ X0 @ (cF @ X1))) != $true) | (X0 = X1)) )),
% 0.22/0.28 inference(leibniz_equality_elimination,[],[f14])).
% 0.22/0.28 thf(f53,plain,(
% 0.22/0.28 ( ! [X0 : b] : ((((sK0 @ (cG @ sK2) @ X0 @ (cF @ (cG @ sK3)))) != $true) | (((cG @ sK2)) = X0)) ) | ~spl5_3),
% 0.22/0.28 inference(superposition,[],[f47,f40])).
% 0.22/0.28 thf(f59,plain,(
% 0.22/0.28 ( ! [X0 : b,X1 : b] : (($true = ((sK0 @ X1 @ X0 @ (cF @ X0)))) | (X0 = X1)) )),
% 0.22/0.28 inference(leibniz_equality_elimination,[],[f15])).
% 0.22/0.28 thf(f66,definition,(
% 0.22/0.28 spl5_4 <=> (((cG @ sK3)) = ((cG @ sK2)))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.22/0.28 thf(f68,plain,(
% 0.22/0.28 (((cG @ sK3)) = ((cG @ sK2))) | ~spl5_4),
% 0.22/0.28 inference(avatar_component_clause,[],[f66])).
% 0.22/0.28 thf(f74,plain,(
% 0.22/0.28 (((cG @ sK3)) = ((cG @ sK2))) | (((cG @ sK3)) = ((cG @ sK2))) | ($true != $true) | ~spl5_3),
% 0.22/0.28 inference(superposition,[],[f53,f59])).
% 0.22/0.28 thf(f75,plain,(
% 0.22/0.28 ($true != $true) | (((cG @ sK3)) = ((cG @ sK2))) | ~spl5_3),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f74])).
% 0.22/0.28 thf(f76,plain,(
% 0.22/0.28 (((cG @ sK3)) = ((cG @ sK2))) | ~spl5_3),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f75])).
% 0.22/0.28 thf(f77,plain,(
% 0.22/0.28 spl5_4 | ~spl5_3),
% 0.22/0.28 inference(avatar_split_clause,[],[f76,f38,f66])).
% 0.22/0.28 thf(f79,plain,(
% 0.22/0.28 ( ! [X0 : c] : ((((sK1 @ sK2 @ X0 @ (cG @ sK3))) != $true) | (sK2 = X0)) ) | ~spl5_4),
% 0.22/0.28 inference(superposition,[],[f44,f68])).
% 0.22/0.28 thf(f85,plain,(
% 0.22/0.28 ($true != $true) | (sK2 = sK3) | (sK2 = sK3) | ~spl5_4),
% 0.22/0.28 inference(superposition,[],[f79,f42])).
% 0.22/0.28 thf(f87,plain,(
% 0.22/0.28 (sK2 = sK3) | ($true != $true) | ~spl5_4),
% 0.22/0.28 inference(duplicate_literal_removal,[],[f85])).
% 0.22/0.28 thf(f88,plain,(
% 0.22/0.28 (sK2 = sK3) | ~spl5_4),
% 0.22/0.28 inference(trivial_inequality_removal,[],[f87])).
% 0.22/0.28 thf(f91,definition,(
% 0.22/0.28 spl5_6 <=> (sK2 = sK3)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 0.22/0.28 thf(f94,plain,(
% 0.22/0.28 spl5_6 | ~spl5_4),
% 0.22/0.28 inference(avatar_split_clause,[],[f88,f66,f91])).
% 0.22/0.28 thf(f99,definition,(
% 0.22/0.28 (sK2 != sK3) | ($true != ((sK4 @ sK2))) | ($true = ((sK4 @ sK3)))),
% 0.22/0.28 introduced(theory,[theory_tautology_sat_conflict])).
% 0.22/0.28 cnf(s1, plain, ~spl5_1, inference(sat_conversion,[],[f21])).
% 0.22/0.28 cnf(s2, plain, spl5_2, inference(sat_conversion,[],[f26])).
% 0.22/0.28 cnf(s3, plain, spl5_3, inference(sat_conversion,[],[f41])).
% 0.22/0.28 cnf(s6, plain, ~spl5_3 | spl5_4, inference(sat_conversion,[],[f77])).
% 0.22/0.28 cnf(s7, plain, ~spl5_4 | spl5_6, inference(sat_conversion,[],[f94])).
% 0.22/0.28 cnf(s9, plain, spl5_1 | ~spl5_2 | ~spl5_6, inference(sat_conversion,[],[f99])).
% 0.22/0.28 cnf(s10, plain, spl5_4, inference(rat,[],[s6,s3])).
% 0.22/0.28 cnf(s11, plain, spl5_6, inference(rat,[],[s7,s10])).
% 0.22/0.28 cnf(s12, plain, spl5_1, inference(rat,[],[s9,s11,s2])).
% 0.22/0.28 cnf(s13, plain, $false, inference(rat,[],[s1,s12])).
% 0.22/0.28 thf(f100,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(avatar_sat_refutation,[],[s13])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (1488740)------------------------------
% 0.22/0.28 % (1488740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1488740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1488740)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1488740)Termination reason: Refutation
% 0.22/0.28 % (1488740)Time elapsed: 0.004 s
% 0.22/0.28 % (1488740)Peak memory usage: 13 MB
% 0.22/0.28 % (1488740)Instructions burned: 9 (million)
% 0.22/0.28 % (1488728)Success in time 0.035 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------