%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO268^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:47:19 AM UTC 2026
% Result : Theorem 0.09s 0.16s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO268^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 16:42:04 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running higher-order theorem proving
% 0.09/0.13 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.16 % (350357)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.16 % (350368)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.16 % (350368)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
% 0.09/0.16 % (350366)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4164863739:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.16 % (350362)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3569157036:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.16 % (350363)lrs+10_16_si=on:nwc=1.5:random_seed=463515387:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.16 % (350367)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1467549766:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.16 % (350364)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1155216056:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.16 % (350368)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=4067295932:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.16 % (350365)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=2392413486: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)
% 0.09/0.16 % (350362) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-350357-350362"...
% 0.09/0.16 % (350364) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-350357-350364"...
% 0.09/0.16 % (350365) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-350357-350365"...
% 0.09/0.16 % (350364)...printing done.
% 0.09/0.16 % (350362)...printing done.
% 0.09/0.16 % (350363) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-350357-350363"...
% 0.09/0.16 % (350367) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-350357-350367"...
% 0.09/0.16 % (350364)Refutation found. Thanks to Tanya!
% 0.09/0.16 % SZS status Theorem for theBenchmark
% 0.09/0.16 % SZS output start Proof for theBenchmark
% 0.09/0.16 thf(type_def_5, type, a: $tType).
% 0.09/0.16 thf(type_def_6, type, b: $tType).
% 0.09/0.16 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.16 thf(func_def_0, type, r: (a > b > $o)).
% 0.09/0.16 thf(func_def_4, type, sK0: a).
% 0.09/0.16 thf(func_def_5, type, sK1: ((a > b) > a)).
% 0.09/0.16 thf(func_def_6, type, sK2: (a > b)).
% 0.09/0.16 thf(func_def_7, type, sK3: (a > b)).
% 0.09/0.16 thf(func_def_8, type, sK4: ((b > $o) > b)).
% 0.09/0.16 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.09/0.16 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.16 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.16 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.16 thf(f1,conjecture,(
% 0.09/0.16 ? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X4 : (a > b)] : ! [X2 : a] : (r @ X2 @ (X4 @ X2)) <=> ! [X2 : a] : ? [X3 : b] : (r @ X2 @ X3))),
% 0.09/0.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5308)).
% 0.09/0.16 thf(f2,negated_conjecture,(
% 0.09/0.16 ~(? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X4 : (a > b)] : ! [X2 : a] : (r @ X2 @ (X4 @ X2)) <=> ! [X2 : a] : ? [X3 : b] : (r @ X2 @ X3)))),
% 0.09/0.16 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.16 thf(f3,plain,(
% 0.09/0.16 ~(? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (? [X3 : (a > b)] : ! [X4 : a] : (r @ X4 @ (X3 @ X4)) <=> ! [X5 : a] : ? [X6 : b] : (r @ X5 @ X6)))),
% 0.09/0.16 inference(rectify,[],[f2])).
% 0.09/0.16 thf(f4,plain,(
% 0.09/0.16 ~(? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X2 : b] : (((X1 @ X2)) = $true) => (((X1 @ (X0 @ X1))) = $true)) => (! [X5 : a] : ? [X6 : b] : (((r @ X5 @ X6)) = $true) <=> ? [X3 : (a > b)] : ! [X4 : a] : (((r @ X4 @ (X3 @ X4))) = $true)))),
% 0.09/0.16 inference(fool_elimination,[],[f3])).
% 0.09/0.16 thf(f5,plain,(
% 0.09/0.16 (? [X3 : (a > b)] : ! [X4 : a] : (((r @ X4 @ (X3 @ X4))) = $true) <~> ! [X5 : a] : ? [X6 : b] : (((r @ X5 @ X6)) = $true)) & ? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : ((((X1 @ (X0 @ X1))) = $true) | ! [X2 : b] : (((X1 @ X2)) != $true))),
% 0.09/0.16 inference(ennf_transformation,[],[f4])).
% 0.09/0.16 thf(f6,plain,(
% 0.09/0.16 ((? [X5 : a] : ! [X6 : b] : (((r @ X5 @ X6)) != $true) | ! [X3 : (a > b)] : ? [X4 : a] : (((r @ X4 @ (X3 @ X4))) != $true)) & (! [X5 : a] : ? [X6 : b] : (((r @ X5 @ X6)) = $true) | ? [X3 : (a > b)] : ! [X4 : a] : (((r @ X4 @ (X3 @ X4))) = $true))) & ? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : ((((X1 @ (X0 @ X1))) = $true) | ! [X2 : b] : (((X1 @ X2)) != $true))),
% 0.09/0.16 inference(nnf_transformation,[],[f5])).
% 0.09/0.16 thf(f7,plain,(
% 0.09/0.16 (? [X5 : a] : ! [X6 : b] : (((r @ X5 @ X6)) != $true) | ! [X3 : (a > b)] : ? [X4 : a] : (((r @ X4 @ (X3 @ X4))) != $true)) & (! [X5 : a] : ? [X6 : b] : (((r @ X5 @ X6)) = $true) | ? [X3 : (a > b)] : ! [X4 : a] : (((r @ X4 @ (X3 @ X4))) = $true)) & ? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : ((((X1 @ (X0 @ X1))) = $true) | ! [X2 : b] : (((X1 @ X2)) != $true))),
% 0.09/0.16 inference(flattening,[],[f6])).
% 0.09/0.16 thf(f8,plain,(
% 0.09/0.16 (? [X0 : a] : ! [X1 : b] : ($true != ((r @ X0 @ X1))) | ! [X2 : (a > b)] : ? [X3 : a] : (((r @ X3 @ (X2 @ X3))) != $true)) & (! [X4 : a] : ? [X5 : b] : (((r @ X4 @ X5)) = $true) | ? [X6 : (a > b)] : ! [X7 : a] : (((r @ X7 @ (X6 @ X7))) = $true)) & ? [X8 : ((b > $o) > b)] : ! [X9 : (b > $o)] : (($true = ((X9 @ (X8 @ X9)))) | ! [X10 : b] : (((X9 @ X10)) != $true))),
% 0.09/0.16 inference(rectify,[],[f7])).
% 0.09/0.16 thf(f9,plain,(
% 0.09/0.16 (! [X1 : b] : ($true != ((r @ sK0 @ X1))) | ! [X2 : (a > b)] : (((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2)))) != $true)) & (! [X4 : a] : (((r @ X4 @ (sK2 @ X4))) = $true) | ! [X7 : a] : ($true = ((r @ X7 @ (sK3 @ X7))))) & ! [X9 : (b > $o)] : (($true = ((X9 @ (sK4 @ X9)))) | ! [X10 : b] : (((X9 @ X10)) != $true))),
% 0.09/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP,sK3,sK4]),skolemize(X0,sK0),skolemize(X5,sK2 @ X4),skolemize(X5,sK2 @ X4),skolemize(X6,sK3),skolemize(X8,sK4)],[f8])).
% 0.09/0.16 thf(f11,plain,(
% 0.09/0.16 ( ! [X7 : a,X4 : a] : (($true = ((r @ X7 @ (sK3 @ X7)))) | (((r @ X4 @ (sK2 @ X4))) = $true)) )),
% 0.09/0.16 inference(cnf_transformation,[],[f9])).
% 0.09/0.16 thf(f12,plain,(
% 0.09/0.16 ( ! [X2 : (a > b),X1 : b] : ((((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2)))) != $true) | ($true != ((r @ sK0 @ X1)))) )),
% 0.09/0.16 inference(cnf_transformation,[],[f9])).
% 0.09/0.16 thf(f16,definition,(
% 0.09/0.16 spl5_1 <=> ! [X1 : b] : ($true != ((r @ sK0 @ X1)))),
% 0.09/0.16 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.09/0.16 thf(f17,plain,(
% 0.09/0.16 ( ! [X1 : b] : (($true != ((r @ sK0 @ X1)))) ) | ~spl5_1),
% 0.09/0.16 inference(avatar_component_clause,[],[f16])).
% 0.09/0.16 thf(f19,definition,(
% 0.09/0.16 spl5_2 <=> ! [X2 : (a > b)] : (((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2)))) != $true)),
% 0.09/0.16 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.09/0.16 thf(f20,plain,(
% 0.09/0.16 ( ! [X2 : (a > b)] : ((((r @ (sK1 @ X2) @ (X2 @ (sK1 @ X2)))) != $true)) ) | ~spl5_2),
% 0.09/0.16 inference(avatar_component_clause,[],[f19])).
% 0.09/0.16 thf(f21,plain,(
% 0.09/0.16 spl5_1 | spl5_2),
% 0.09/0.16 inference(avatar_split_clause,[],[f12,f19,f16])).
% 0.09/0.16 thf(f23,definition,(
% 0.09/0.16 spl5_3 <=> ! [X7 : a] : ($true = ((r @ X7 @ (sK3 @ X7))))),
% 0.09/0.16 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.09/0.16 thf(f24,plain,(
% 0.09/0.16 ( ! [X7 : a] : (($true = ((r @ X7 @ (sK3 @ X7))))) ) | ~spl5_3),
% 0.09/0.16 inference(avatar_component_clause,[],[f23])).
% 0.09/0.16 thf(f26,definition,(
% 0.09/0.16 spl5_4 <=> ! [X4 : a] : (((r @ X4 @ (sK2 @ X4))) = $true)),
% 0.09/0.16 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.09/0.16 thf(f27,plain,(
% 0.09/0.16 ( ! [X4 : a] : ((((r @ X4 @ (sK2 @ X4))) = $true)) ) | ~spl5_4),
% 0.09/0.16 inference(avatar_component_clause,[],[f26])).
% 0.09/0.16 thf(f28,plain,(
% 0.09/0.16 spl5_3 | spl5_4),
% 0.09/0.16 inference(avatar_split_clause,[],[f11,f26,f23])).
% 0.09/0.16 thf(f40,plain,(
% 0.09/0.16 ($true != $true) | (~spl5_2 | ~spl5_3)),
% 0.09/0.16 inference(constrained_superposition,[],[f20,f24])).
% 0.09/0.16 thf(f41,plain,(
% 0.09/0.16 $false | (~spl5_2 | ~spl5_3)),
% 0.09/0.16 inference(trivial_inequality_removal,[],[f40])).
% 0.09/0.16 thf(f42,plain,(
% 0.09/0.16 ~spl5_2 | ~spl5_3),
% 0.09/0.16 inference(avatar_contradiction_clause,[],[f41])).
% 0.09/0.16 thf(f43,plain,(
% 0.09/0.16 ($true != $true) | (~spl5_1 | ~spl5_3)),
% 0.09/0.16 inference(constrained_superposition,[],[f17,f24])).
% 0.09/0.16 thf(f44,plain,(
% 0.09/0.16 $false | (~spl5_1 | ~spl5_3)),
% 0.09/0.16 inference(trivial_inequality_removal,[],[f43])).
% 0.09/0.16 thf(f45,plain,(
% 0.09/0.16 ~spl5_1 | ~spl5_3),
% 0.09/0.16 inference(avatar_contradiction_clause,[],[f44])).
% 0.09/0.16 thf(f48,plain,(
% 0.09/0.16 ($true != $true) | (~spl5_2 | ~spl5_4)),
% 0.09/0.16 inference(constrained_superposition,[],[f20,f27])).
% 0.09/0.16 thf(f49,plain,(
% 0.09/0.16 $false | (~spl5_2 | ~spl5_4)),
% 0.09/0.16 inference(trivial_inequality_removal,[],[f48])).
% 0.09/0.16 thf(f50,plain,(
% 0.09/0.16 ~spl5_2 | ~spl5_4),
% 0.09/0.16 inference(avatar_contradiction_clause,[],[f49])).
% 0.09/0.16 thf(f51,plain,(
% 0.09/0.16 ($true != $true) | (~spl5_1 | ~spl5_4)),
% 0.09/0.16 inference(constrained_superposition,[],[f17,f27])).
% 0.09/0.16 thf(f55,plain,(
% 0.09/0.16 $false | (~spl5_1 | ~spl5_4)),
% 0.09/0.16 inference(trivial_inequality_removal,[],[f51])).
% 0.09/0.16 thf(f56,plain,(
% 0.09/0.16 ~spl5_1 | ~spl5_4),
% 0.09/0.16 inference(avatar_contradiction_clause,[],[f55])).
% 0.09/0.16 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f21])).
% 0.09/0.16 cnf(s2, plain, spl5_3 | spl5_4, inference(sat_conversion,[],[f28])).
% 0.09/0.16 cnf(s3, plain, ~spl5_2 | ~spl5_3, inference(sat_conversion,[],[f42])).
% 0.09/0.16 cnf(s4, plain, ~spl5_1 | ~spl5_3, inference(sat_conversion,[],[f45])).
% 0.09/0.16 cnf(s5, plain, ~spl5_2 | ~spl5_4, inference(sat_conversion,[],[f50])).
% 0.09/0.16 cnf(s7, plain, ~spl5_1 | ~spl5_4, inference(sat_conversion,[],[f56])).
% 0.09/0.16 cnf(s8, plain, ~spl5_2, inference(rat,[],[s2,s3,s5])).
% 0.09/0.16 cnf(s9, plain, spl5_1, inference(rat,[],[s1,s8])).
% 0.09/0.16 cnf(s10, plain, ~spl5_4, inference(rat,[],[s7,s9])).
% 0.09/0.16 cnf(s11, plain, ~spl5_3, inference(rat,[],[s4,s9])).
% 0.09/0.16 cnf(s12, plain, $false, inference(rat,[],[s2,s10,s11])).
% 0.09/0.16 thf(f57,plain,(
% 0.09/0.16 $false),
% 0.09/0.16 inference(avatar_sat_refutation,[],[s12])).
% 0.09/0.16 % SZS output end Proof for theBenchmark
% 0.09/0.16 % (350364)------------------------------
% 0.09/0.16 % (350364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.16 % (350364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.16 % (350364)CaDiCaL version: 2.1.3
% 0.09/0.16 % (350364)Termination reason: Refutation
% 0.09/0.16 % (350364)Time elapsed: 0.002 s
% 0.09/0.16 % (350364)Peak memory usage: 13 MB
% 0.09/0.16 % (350364)Instructions burned: 4 (million)
% 0.09/0.16 % (350357)Success in time 0.028 s
% 0.09/0.16 % Vampire exiting
%------------------------------------------------------------------------------