%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU810^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 08:31:36 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU810^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n008.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 14:34:09 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 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
% 0.19/0.27 % (3246922)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (3246929)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=848930799:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.27 % (3246929)Refutation not found, incomplete strategy
% 0.19/0.27 % (3246929)------------------------------
% 0.19/0.27 % (3246929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3246929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3246929)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3246929)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.27 % (3246929)Time elapsed: 0.001 s
% 0.19/0.27 % (3246929)Peak memory usage: 12 MB
% 0.19/0.27 % (3246929)Instructions burned: 2 (million)
% 0.19/0.27 % (3246929)------------------------------
% 0.19/0.27 % (3246929)------------------------------
% 0.19/0.27 % (3246927)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2816605213:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.27 % (3246928)lrs+10_16_si=on:nwc=1.5:random_seed=1188021570:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.27 % (3246931)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3657600679:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.27 % (3246930)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=4044816901: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)
% 0.19/0.27 % (3246933)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.27 % (3246933)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
% 0.19/0.27 % (3246927)Refutation not found, incomplete strategy
% 0.19/0.27 % (3246927)------------------------------
% 0.19/0.27 % (3246927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3246927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3246927)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3246927)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.27 % (3246927)Time elapsed: 0.002 s
% 0.19/0.27 % (3246927)Peak memory usage: 12 MB
% 0.19/0.27 % (3246927)Instructions burned: 2 (million)
% 0.19/0.27 % (3246931) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3246922-3246931"...
% 0.19/0.27 % (3246928)Refutation not found, incomplete strategy
% 0.19/0.27 % (3246928)------------------------------
% 0.19/0.27 % (3246928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3246928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3246928)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3246928)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.27 % (3246928)Time elapsed: 0.003 s
% 0.19/0.27 % (3246928)Peak memory usage: 12 MB
% 0.19/0.27 % (3246928)Instructions burned: 3 (million)
% 0.19/0.27 % (3246927)------------------------------
% 0.19/0.27 % (3246927)------------------------------
% 0.19/0.27 % (3246930)Refutation not found, incomplete strategy
% 0.19/0.27 % (3246930)------------------------------
% 0.19/0.27 % (3246930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3246930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3246930)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3246930)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.27 % (3246930)Time elapsed: 0.003 s
% 0.19/0.27 % (3246930)Peak memory usage: 12 MB
% 0.19/0.27 % (3246930)Instructions burned: 4 (million)
% 0.19/0.27 % (3246928)------------------------------
% 0.19/0.27 % (3246928)------------------------------
% 0.19/0.27 % (3246933)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=3399481637:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.27 % (3246931)...printing done.
% 0.19/0.27 % (3246930)------------------------------
% 0.19/0.27 % (3246930)------------------------------
% 0.19/0.27 % (3246935)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=747781506:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.27 % (3246931)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.19/0.27 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.19/0.27 thf(func_def_4, type, emptysetE: $o).
% 0.19/0.27 thf(func_def_6, type, setadjoinIL: $o).
% 0.19/0.27 thf(func_def_7, type, in__Cong: $o).
% 0.19/0.27 thf(func_def_8, type, omegaS: ($i > $i)).
% 0.19/0.27 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.27 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.27 thf(func_def_14, type, sK1: $o).
% 0.19/0.27 thf(func_def_22, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.19/0.27 thf(f2,axiom,(
% 0.19/0.27 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL)).
% 0.19/0.27 thf(f4,axiom,(
% 0.19/0.27 (omegaS = (^[X0 : $i] : ((setadjoin @ X0 @ X0))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaS)).
% 0.19/0.27 thf(f5,conjecture,(
% 0.19/0.27 emptysetE => (setadjoinIL => (in__Cong => ! [X0 : $i] : ((in @ X0 @ omega) => (((omegaS @ X0)) != emptyset))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',peano0notS)).
% 0.19/0.27 thf(f6,negated_conjecture,(
% 0.19/0.27 ~(emptysetE => (setadjoinIL => (in__Cong => ! [X0 : $i] : ((in @ X0 @ omega) => (((omegaS @ X0)) != emptyset)))))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f5])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 (setadjoinIL = $true) <=> ! [X1 : $i,X0 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1))) = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f9])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 (omegaS = (^[Y0 : $i]: (setadjoin @ Y0 @ Y0)))),
% 0.19/0.27 inference(fool_elimination,[],[f4])).
% 0.19/0.27 thf(f12,plain,(
% 0.19/0.27 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f13,plain,(
% 0.19/0.27 (emptysetE = $true) <=> ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => ! [X1 : $o] : ($true = X1))),
% 0.19/0.27 inference(fool_elimination,[],[f12])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 ~(emptysetE => (setadjoinIL => (in__Cong => ! [X0 : $i] : ((in @ X0 @ omega) => (((omegaS @ X0)) != emptyset)))))),
% 0.19/0.27 inference(rectify,[],[f6])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ~((emptysetE = $true) => ((setadjoinIL = $true) => ((in__Cong = $true) => ! [X0 : $i] : ((((in @ X0 @ omega)) = $true) => (emptyset != ((omegaS @ X0)))))))),
% 0.19/0.27 inference(fool_elimination,[],[f14])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ((? [X0 : $i] : ((emptyset = ((omegaS @ X0))) & (((in @ X0 @ omega)) = $true)) & (in__Cong = $true)) & (setadjoinIL = $true)) & (emptysetE = $true)),
% 0.19/0.27 inference(ennf_transformation,[],[f15])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 (in__Cong = $true) & ? [X0 : $i] : ((emptyset = ((omegaS @ X0))) & (((in @ X0 @ omega)) = $true)) & (emptysetE = $true) & (setadjoinIL = $true)),
% 0.19/0.27 inference(flattening,[],[f16])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.19/0.27 inference(ennf_transformation,[],[f13])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) & ? [X1 : $o] : ($true != X1)))),
% 0.19/0.27 inference(nnf_transformation,[],[f18])).
% 0.19/0.27 thf(f21,plain,(
% 0.19/0.27 (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | ? [X2 : $i] : (($true = ((in @ X2 @ emptyset))) & ? [X3 : $o] : ($true != X3)))),
% 0.19/0.27 inference(rectify,[],[f20])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true)) & ((emptysetE = $true) | (($true = ((in @ sK0 @ emptyset))) & (sK1 != $true)))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f21])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 ((setadjoinIL = $true) | ? [X1 : $i,X0 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1))) != $true)) & (! [X1 : $i,X0 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1))) = $true) | (setadjoinIL != $true))),
% 0.19/0.27 inference(nnf_transformation,[],[f10])).
% 0.19/0.27 thf(f24,plain,(
% 0.19/0.27 ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) != $true)) & (! [X2 : $i,X3 : $i] : ($true = ((in @ X3 @ (setadjoin @ X3 @ X2)))) | (setadjoinIL != $true))),
% 0.19/0.27 inference(rectify,[],[f23])).
% 0.19/0.27 thf(f25,plain,(
% 0.19/0.27 ((setadjoinIL = $true) | ($true != ((in @ sK3 @ (setadjoin @ sK3 @ sK2))))) & (! [X2 : $i,X3 : $i] : ($true = ((in @ X3 @ (setadjoin @ X3 @ X2)))) | (setadjoinIL != $true))),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f24])).
% 0.19/0.27 thf(f29,plain,(
% 0.19/0.27 (in__Cong = $true) & ((emptyset = ((omegaS @ sK8))) & (((in @ sK8 @ omega)) = $true)) & (emptysetE = $true) & (setadjoinIL = $true)),
% 0.19/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X0,sK8)],[f17])).
% 0.19/0.27 thf(f32,plain,(
% 0.19/0.27 ( ! [X0 : $i,X1 : $o] : ((emptysetE != $true) | (((in @ X0 @ emptyset)) != $true) | ($true = X1)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f22])).
% 0.19/0.27 thf(f33,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i] : ((setadjoinIL != $true) | ($true = ((in @ X3 @ (setadjoin @ X3 @ X2))))) )),
% 0.19/0.27 inference(cnf_transformation,[],[f25])).
% 0.19/0.27 thf(f39,plain,(
% 0.19/0.27 (omegaS = (^[Y0 : $i]: (setadjoin @ Y0 @ Y0)))),
% 0.19/0.27 inference(cnf_transformation,[],[f11])).
% 0.19/0.27 thf(f40,plain,(
% 0.19/0.27 (setadjoinIL = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f29])).
% 0.19/0.27 thf(f41,plain,(
% 0.19/0.27 (emptysetE = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f29])).
% 0.19/0.27 thf(f43,plain,(
% 0.19/0.27 (emptyset = ((omegaS @ sK8)))),
% 0.19/0.27 inference(cnf_transformation,[],[f29])).
% 0.19/0.27 thf(f45,definition,(
% 0.19/0.27 ($true != $false)),
% 0.19/0.27 introduced(theory,[fool_distinctness_axiom])).
% 0.19/0.27 thf(f55,plain,(
% 0.19/0.27 ( ! [X0 : $i,X1 : $o] : ((((in @ X0 @ emptyset)) != $true) | ($true = X1)) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f32,f41])).
% 0.19/0.27 thf(f56,plain,(
% 0.19/0.27 ( ! [X1 : $i] : ((((omegaS @ X1)) = (((^[Y0 : $i]: (setadjoin @ Y0 @ Y0)) @ X1)))) )),
% 0.19/0.27 inference(argument_congruence,[],[f39])).
% 0.19/0.27 thf(f57,plain,(
% 0.19/0.27 ( ! [X1 : $i] : ((((omegaS @ X1)) = ((setadjoin @ X1 @ X1)))) )),
% 0.19/0.27 inference(beta-eta_normalization,[],[f56])).
% 0.19/0.27 thf(f58,plain,(
% 0.19/0.27 ( ! [X2 : $i,X3 : $i] : (($true = ((in @ X3 @ (setadjoin @ X3 @ X2))))) )),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f33,f40])).
% 0.19/0.27 thf(f59,plain,(
% 0.19/0.27 ( ! [X0 : $i] : (($true = ((in @ X0 @ (omegaS @ X0))))) )),
% 0.19/0.27 inference(superposition,[],[f58,f57])).
% 0.19/0.27 thf(f60,plain,(
% 0.19/0.27 ($true = ((in @ sK8 @ emptyset)))),
% 0.19/0.27 inference(superposition,[],[f59,f43])).
% 0.19/0.27 thf(f61,plain,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($true != $true)) )),
% 0.19/0.27 inference(superposition,[],[f55,f60])).
% 0.19/0.27 thf(f62,plain,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0)) )),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f61])).
% 0.19/0.27 thf(f64,plain,(
% 0.19/0.27 ( ! [X0 : $o] : (($false != X0)) )),
% 0.19/0.27 inference(superposition,[],[f45,f62])).
% 0.19/0.27 thf(f70,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(equality_resolution,[],[f64])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (3246931)------------------------------
% 0.19/0.27 % (3246931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (3246931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (3246931)CaDiCaL version: 2.1.3
% 0.19/0.27 % (3246931)Termination reason: Refutation
% 0.19/0.27 % (3246931)Time elapsed: 0.003 s
% 0.19/0.27 % (3246931)Peak memory usage: 12 MB
% 0.19/0.27 % (3246931)Instructions burned: 4 (million)
% 0.19/0.27 % (3246922)Success in time 0.041 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------