%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU797^2 : 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 : n020.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 08:31:26 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU797^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:32:35 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.28 % (1132214)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1132221)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=264546632:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (1132221)Refutation not found, incomplete strategy
% 0.20/0.28 % (1132221)------------------------------
% 0.20/0.28 % (1132221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1132221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1132221)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1132221)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (1132221)Time elapsed: 0.001 s
% 0.20/0.28 % (1132221)Peak memory usage: 12 MB
% 0.20/0.28 % (1132221)Instructions burned: 1 (million)
% 0.20/0.28 % (1132221)------------------------------
% 0.20/0.28 % (1132221)------------------------------
% 0.20/0.28 % (1132225)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (1132225)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
% 0.20/0.28 % (1132219)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3732833777:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1132220)lrs+10_16_si=on:nwc=1.5:random_seed=567503148:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (1132223)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1624311976:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (1132222)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=2995294689: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)
% 0.20/0.28 % (1132224)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=138803769:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (1132225)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=2790539674:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (1132219) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1132214-1132219"...
% 0.20/0.28 % (1132223) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1132214-1132223"...
% 0.20/0.28 % (1132220) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1132214-1132220"...
% 0.20/0.28 % (1132224) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1132214-1132224"...
% 0.20/0.28 % (1132222) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1132214-1132222"...
% 0.20/0.28 % (1132227)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2800909110:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.28 % (1132219)...printing done.
% 0.20/0.28 % (1132223)...printing done.
% 0.20/0.28 % (1132219)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.28 thf(func_def_1, type, image1: ($i > ($i > $i) > $i)).
% 0.20/0.28 thf(func_def_2, type, image1Equiv: $o).
% 0.20/0.28 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.28 thf(func_def_9, type, sK1: ($i > $i)).
% 0.20/0.28 thf(func_def_12, type, sK4: ($i > ($i > $i) > $i > $i)).
% 0.20/0.28 thf(func_def_14, type, sK6: ($i > $i)).
% 0.20/0.28 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.20/0.28 thf(f1,axiom,(
% 0.20/0.28 (image1Equiv = ! [X1 : ($i > $i),X2 : $i,X0 : $i] : (? [X3 : $i] : ((X2 = ((X1 @ X3))) & (in @ X3 @ X0)) <=> (in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : ((X1 @ X3)))))))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Equiv)).
% 0.20/0.28 thf(f2,conjecture,(
% 0.20/0.28 image1Equiv => ! [X0 : $i,X1 : ($i > $i),X2 : $i] : (? [X3 : $i] : ((X2 = ((X1 @ X3))) & (in @ X3 @ X0)) => (in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : ((X1 @ X3))))))),
% 0.20/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1I)).
% 0.20/0.28 thf(f3,negated_conjecture,(
% 0.20/0.28 ~(image1Equiv => ! [X0 : $i,X1 : ($i > $i),X2 : $i] : (? [X3 : $i] : ((X2 = ((X1 @ X3))) & (in @ X3 @ X0)) => (in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : ((X1 @ X3)))))))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f2])).
% 0.20/0.28 thf(f4,plain,(
% 0.20/0.28 (image1Equiv = ! [X0 : ($i > $i),X1 : $i,X2 : $i] : (? [X3 : $i] : ((((X0 @ X3)) = X1) & (in @ X3 @ X2)) <=> (in @ X1 @ (image1 @ X2 @ (^[X4 : $i] : ((X0 @ X4)))))))),
% 0.20/0.28 inference(rectify,[],[f1])).
% 0.20/0.28 thf(f5,plain,(
% 0.20/0.28 (image1Equiv = $true) <=> ! [X2 : $i,X0 : ($i > $i),X1 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((X0 @ X3)) = X1)) <=> (((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ~(image1Equiv => ! [X0 : $i,X1 : ($i > $i),X2 : $i] : (? [X3 : $i] : ((X2 = ((X1 @ X3))) & (in @ X3 @ X0)) => (in @ X2 @ (image1 @ X0 @ (^[X4 : $i] : ((X1 @ X4)))))))),
% 0.20/0.28 inference(rectify,[],[f3])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ~((image1Equiv = $true) => ! [X0 : $i,X2 : $i,X1 : ($i > $i)] : (? [X3 : $i] : ((((X1 @ X3)) = X2) & (((in @ X3 @ X0)) = $true)) => ($true = ((in @ X2 @ (image1 @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))))))),
% 0.20/0.28 inference(fool_elimination,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 (image1Equiv = $true) & ? [X2 : $i,X1 : ($i > $i),X0 : $i] : (($true != ((in @ X2 @ (image1 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) & ? [X3 : $i] : ((((X1 @ X3)) = X2) & (((in @ X3 @ X0)) = $true)))),
% 0.20/0.28 inference(ennf_transformation,[],[f7])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ((image1Equiv = $true) | ? [X2 : $i,X0 : ($i > $i),X1 : $i] : (((((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true) | ! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | (((X0 @ X3)) != X1))) & ((((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | ? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((X0 @ X3)) = X1))))) & (! [X2 : $i,X0 : ($i > $i),X1 : $i] : ((? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((X0 @ X3)) = X1)) | (((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) != $true)) & ((((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) | ! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | (((X0 @ X3)) != X1)))) | (image1Equiv != $true))),
% 0.20/0.28 inference(nnf_transformation,[],[f5])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 ((image1Equiv = $true) | ? [X0 : $i,X1 : ($i > $i),X2 : $i] : ((($true != ((in @ X2 @ (image1 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((X1 @ X3)) != X2))) & (($true = ((in @ X2 @ (image1 @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | ? [X4 : $i] : (($true = ((in @ X4 @ X0))) & (((X1 @ X4)) = X2))))) & (! [X5 : $i,X6 : ($i > $i),X7 : $i] : ((? [X8 : $i] : (($true = ((in @ X8 @ X5))) & (((X6 @ X8)) = X7)) | ($true != ((in @ X7 @ (image1 @ X5 @ (^[Y0 : $i]: (X6 @ Y0))))))) & (($true = ((in @ X7 @ (image1 @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))))) | ! [X9 : $i] : ((((in @ X9 @ X5)) != $true) | (((X6 @ X9)) != X7)))) | (image1Equiv != $true))),
% 0.20/0.28 inference(rectify,[],[f9])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ((image1Equiv = $true) | ((($true != ((in @ sK2 @ (image1 @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))))) | ! [X3 : $i] : ((((in @ X3 @ sK0)) != $true) | (sK2 != ((sK1 @ X3))))) & (($true = ((in @ sK2 @ (image1 @ sK0 @ (^[Y0 : $i]: (sK1 @ Y0)))))) | (($true = ((in @ sK3 @ sK0))) & (((sK1 @ sK3)) = sK2))))) & (! [X5 : $i,X6 : ($i > $i),X7 : $i] : ((((((in @ (sK4 @ X7 @ X6 @ X5) @ X5)) = $true) & (((X6 @ (sK4 @ X7 @ X6 @ X5))) = X7)) | ($true != ((in @ X7 @ (image1 @ X5 @ (^[Y0 : $i]: (X6 @ Y0))))))) & (($true = ((in @ X7 @ (image1 @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))))) | ! [X9 : $i] : ((((in @ X9 @ X5)) != $true) | (((X6 @ X9)) != X7)))) | (image1Equiv != $true))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X4,sK3),skolemize(X8,sK4 @ X7 @ X6 @ X5)],[f10])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 (image1Equiv = $true) & ? [X0 : $i,X1 : ($i > $i),X2 : $i] : (($true != ((in @ X0 @ (image1 @ X2 @ (^[Y0 : $i]: (X1 @ Y0)))))) & ? [X3 : $i] : ((((X1 @ X3)) = X0) & (((in @ X3 @ X2)) = $true)))),
% 0.20/0.28 inference(rectify,[],[f8])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 (image1Equiv = $true) & (($true != ((in @ sK5 @ (image1 @ sK7 @ (^[Y0 : $i]: (sK6 @ Y0)))))) & ((sK5 = ((sK6 @ sK8))) & (((in @ sK8 @ sK7)) = $true)))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8)],[f12])).
% 0.20/0.28 thf(f14,plain,(
% 0.20/0.28 ( ! [X6 : ($i > $i),X9 : $i,X7 : $i,X5 : $i] : (($true = ((in @ X7 @ (image1 @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))))) | (((in @ X9 @ X5)) != $true) | (((X6 @ X9)) != X7) | (image1Equiv != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f11])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 (((in @ sK8 @ sK7)) = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 (sK5 = ((sK6 @ sK8)))),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f22,plain,(
% 0.20/0.28 ($true != ((in @ sK5 @ (image1 @ sK7 @ (^[Y0 : $i]: (sK6 @ Y0))))))),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f23,plain,(
% 0.20/0.28 (image1Equiv = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f13])).
% 0.20/0.28 thf(f31,plain,(
% 0.20/0.28 ( ! [X6 : ($i > $i),X9 : $i,X7 : $i,X5 : $i] : (($true = ((in @ X7 @ (image1 @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))))) | (((in @ X9 @ X5)) != $true) | (((X6 @ X9)) != X7) | ($true != $true)) )),
% 0.20/0.28 inference(definition_unfolding,[],[f14,f23])).
% 0.20/0.28 thf(f32,plain,(
% 0.20/0.28 ( ! [X6 : ($i > $i),X9 : $i,X5 : $i] : ((((in @ X9 @ X5)) != $true) | ($true = ((in @ (X6 @ X9) @ (image1 @ X5 @ (^[Y0 : $i]: (X6 @ Y0)))))) | ($true != $true)) )),
% 0.20/0.28 inference(equality_resolution,[],[f31])).
% 0.20/0.28 thf(f33,plain,(
% 0.20/0.28 ( ! [X6 : ($i > $i),X9 : $i,X5 : $i] : ((((in @ X9 @ X5)) != $true) | ($true = ((in @ (X6 @ X9) @ (image1 @ X5 @ (^[Y0 : $i]: (X6 @ Y0))))))) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f32])).
% 0.20/0.28 thf(f34,plain,(
% 0.20/0.28 ( ! [X6 : ($i > $i),X9 : $i,X5 : $i] : ((((in @ X9 @ X5)) != $true) | ($true = ((in @ (X6 @ X9) @ (image1 @ X5 @ X6))))) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f33])).
% 0.20/0.28 thf(f39,plain,(
% 0.20/0.28 ($true != ((in @ sK5 @ (image1 @ sK7 @ sK6))))),
% 0.20/0.28 inference(beta-eta_normalization,[],[f22])).
% 0.20/0.28 thf(f40,plain,(
% 0.20/0.28 ( ! [X0 : ($i > $i)] : (($true = ((in @ (X0 @ sK8) @ (image1 @ sK7 @ X0)))) | ($true != $true)) )),
% 0.20/0.28 inference(constrained_superposition,[],[f34,f20])).
% 0.20/0.28 thf(f41,plain,(
% 0.20/0.28 ( ! [X0 : ($i > $i)] : (($true = ((in @ (X0 @ sK8) @ (image1 @ sK7 @ X0))))) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f40])).
% 0.20/0.28 thf(f42,plain,(
% 0.20/0.28 ($true = ((in @ sK5 @ (image1 @ sK7 @ sK6))))),
% 0.20/0.28 inference(constrained_superposition,[],[f41,f21])).
% 0.20/0.28 thf(f45,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f42,f39])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (1132219)------------------------------
% 0.20/0.28 % (1132219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1132219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1132219)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1132219)Termination reason: Refutation
% 0.20/0.28 % (1132219)Time elapsed: 0.004 s
% 0.20/0.28 % (1132219)Peak memory usage: 12 MB
% 0.20/0.28 % (1132219)Instructions burned: 5 (million)
% 0.20/0.28 % (1132214)Success in time 0.038 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------