%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU796^2 : 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 : 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 08:31:26 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU796^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 14:31:04 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.13 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
% 0.08/0.16 % (181817)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.16 % (181828)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.16 % (181828)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
% 0.08/0.16 % (181822)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=509553834:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.16 % (181823)lrs+10_16_si=on:nwc=1.5:random_seed=73435157:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.16 % (181824)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3495945170:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.16 % (181828)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=578848011:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.16 % (181825)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=3677651395: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)
% 0.08/0.16 % (181826)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=342446077:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.16 % (181827)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3663246196:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.16 % (181824)Refutation not found, incomplete strategy
% 0.08/0.16 % (181824)------------------------------
% 0.08/0.16 % (181824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (181824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (181824)CaDiCaL version: 2.1.3
% 0.08/0.16 % (181824)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.16 % (181824)Time elapsed: 0.001 s
% 0.08/0.16 % (181824)Peak memory usage: 12 MB
% 0.08/0.16 % (181824)Instructions burned: 1 (million)
% 0.08/0.16 % (181824)------------------------------
% 0.08/0.16 % (181824)------------------------------
% 0.08/0.16 % (181822) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-181817-181822"...
% 0.08/0.16 % (181826) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-181817-181826"...
% 0.08/0.16 % (181827) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-181817-181827"...
% 0.08/0.16 % (181822)...printing done.
% 0.08/0.16 % (181826)...printing done.
% 0.08/0.16 % (181822)Refutation found. Thanks to Tanya!
% 0.08/0.16 % SZS status Theorem for theBenchmark
% 0.08/0.16 % SZS output start Proof for theBenchmark
% 0.08/0.16 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.16 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.16 thf(func_def_1, type, image1: ($i > ($i > $i) > $i)).
% 0.08/0.16 thf(func_def_2, type, image1Equiv: $o).
% 0.08/0.16 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.16 thf(func_def_7, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.16 thf(func_def_10, type, sK2: ($i > $i)).
% 0.08/0.16 thf(func_def_12, type, sK4: (($i > $i) > $i > $i > $i)).
% 0.08/0.16 thf(func_def_15, type, sK7: ($i > $i)).
% 0.08/0.16 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.08/0.16 thf(f1,axiom,(
% 0.08/0.16 (! [X0 : $i,X2 : $i,X1 : ($i > $i)] : (? [X3 : $i] : ((in @ X3 @ X0) & (X2 = ((X1 @ X3)))) <=> (in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : ((X1 @ X3)))))) = image1Equiv)),
% 0.08/0.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Equiv)).
% 0.08/0.16 thf(f2,conjecture,(
% 0.08/0.16 image1Equiv => ! [X1 : ($i > $i),X2 : $i,X0 : $i] : ((in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => ? [X3 : $i] : ((X2 = ((X1 @ X3))) & (in @ X3 @ X0)))),
% 0.08/0.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1E)).
% 0.08/0.16 thf(f3,negated_conjecture,(
% 0.08/0.16 ~(image1Equiv => ! [X1 : ($i > $i),X2 : $i,X0 : $i] : ((in @ X2 @ (image1 @ X0 @ (^[X3 : $i] : ((X1 @ X3))))) => ? [X3 : $i] : ((X2 = ((X1 @ X3))) & (in @ X3 @ X0))))),
% 0.08/0.16 inference(negated_conjecture,[status(cth)],[f2])).
% 0.08/0.16 thf(f4,plain,(
% 0.08/0.16 ~(image1Equiv => ! [X0 : ($i > $i),X1 : $i,X2 : $i] : ((in @ X1 @ (image1 @ X2 @ (^[X3 : $i] : ((X0 @ X3))))) => ? [X4 : $i] : ((((X0 @ X4)) = X1) & (in @ X4 @ X2))))),
% 0.08/0.16 inference(rectify,[],[f3])).
% 0.08/0.16 thf(f5,plain,(
% 0.08/0.16 ~((image1Equiv = $true) => ! [X0 : ($i > $i),X1 : $i,X2 : $i] : ((((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) => ? [X4 : $i] : ((((X0 @ X4)) = X1) & (((in @ X4 @ X2)) = $true))))),
% 0.08/0.16 inference(fool_elimination,[],[f4])).
% 0.08/0.16 thf(f6,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (? [X3 : $i] : ((in @ X3 @ X0) & (((X2 @ X3)) = X1)) <=> (in @ X1 @ (image1 @ X0 @ (^[X4 : $i] : ((X2 @ X4)))))) = image1Equiv)),
% 0.08/0.16 inference(rectify,[],[f1])).
% 0.08/0.16 thf(f7,plain,(
% 0.08/0.16 (image1Equiv = $true) <=> ! [X0 : $i,X1 : $i,X2 : ($i > $i)] : ((((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true) <=> ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((X2 @ X3)) = X1)))),
% 0.08/0.16 inference(fool_elimination,[],[f6])).
% 0.08/0.16 thf(f8,plain,(
% 0.08/0.16 ~((image1Equiv = $true) => ! [X1 : $i,X2 : $i,X0 : ($i > $i)] : ((((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true) => ? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((X0 @ X3)) = X1))))),
% 0.08/0.16 inference(rectify,[],[f5])).
% 0.08/0.16 thf(f9,plain,(
% 0.08/0.16 ? [X2 : $i,X1 : $i,X0 : ($i > $i)] : (! [X3 : $i] : ((((X0 @ X3)) != X1) | (((in @ X3 @ X2)) != $true)) & (((in @ X1 @ (image1 @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) = $true)) & (image1Equiv = $true)),
% 0.08/0.16 inference(ennf_transformation,[],[f8])).
% 0.08/0.16 thf(f10,plain,(
% 0.08/0.16 ((image1Equiv = $true) | ? [X0 : $i,X1 : $i,X2 : ($i > $i)] : ((! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((X2 @ X3)) != X1)) | (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) != $true)) & (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((X2 @ X3)) = X1)) | (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)))) & (! [X0 : $i,X1 : $i,X2 : ($i > $i)] : (((((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true) | ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((X2 @ X3)) != X1))) & (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((X2 @ X3)) = X1)) | (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) != $true))) | (image1Equiv != $true))),
% 0.08/0.16 inference(nnf_transformation,[],[f7])).
% 0.08/0.16 thf(f11,plain,(
% 0.08/0.16 ((image1Equiv = $true) | ? [X0 : $i,X1 : $i,X2 : ($i > $i)] : ((! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((X2 @ X3)) != X1)) | (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) != $true)) & (? [X4 : $i] : (($true = ((in @ X4 @ X0))) & (((X2 @ X4)) = X1)) | (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)))) & (! [X5 : $i,X6 : $i,X7 : ($i > $i)] : (((((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) = $true) | ! [X8 : $i] : (($true != ((in @ X8 @ X5))) | (((X7 @ X8)) != X6))) & (? [X9 : $i] : ((((in @ X9 @ X5)) = $true) & (((X7 @ X9)) = X6)) | (((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) != $true))) | (image1Equiv != $true))),
% 0.08/0.16 inference(rectify,[],[f10])).
% 0.08/0.16 thf(f12,plain,(
% 0.08/0.16 ((image1Equiv = $true) | ((! [X3 : $i] : (($true != ((in @ X3 @ sK0))) | (sK1 != ((sK2 @ X3)))) | (((in @ sK1 @ (image1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))))) != $true)) & ((($true = ((in @ sK3 @ sK0))) & (sK1 = ((sK2 @ sK3)))) | (((in @ sK1 @ (image1 @ sK0 @ (^[Y0 : $i]: (sK2 @ Y0))))) = $true)))) & (! [X5 : $i,X6 : $i,X7 : ($i > $i)] : (((((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) = $true) | ! [X8 : $i] : (($true != ((in @ X8 @ X5))) | (((X7 @ X8)) != X6))) & ((($true = ((in @ (sK4 @ X7 @ X6 @ X5) @ X5))) & (((X7 @ (sK4 @ X7 @ X6 @ X5))) = X6)) | (((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) != $true))) | (image1Equiv != $true))),
% 0.08/0.16 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(X9,sK4 @ X7 @ X6 @ X5)],[f11])).
% 0.08/0.16 thf(f13,plain,(
% 0.08/0.16 ? [X0 : $i,X1 : $i,X2 : ($i > $i)] : (! [X3 : $i] : ((((X2 @ X3)) != X1) | (((in @ X3 @ X0)) != $true)) & (((in @ X1 @ (image1 @ X0 @ (^[Y0 : $i]: (X2 @ Y0))))) = $true)) & (image1Equiv = $true)),
% 0.08/0.16 inference(rectify,[],[f9])).
% 0.08/0.16 thf(f14,plain,(
% 0.08/0.16 (! [X3 : $i] : ((sK6 != ((sK7 @ X3))) | (((in @ X3 @ sK5)) != $true)) & (((in @ sK6 @ (image1 @ sK5 @ (^[Y0 : $i]: (sK7 @ Y0))))) = $true)) & (image1Equiv = $true)),
% 0.08/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f13])).
% 0.08/0.16 thf(f15,plain,(
% 0.08/0.16 ( ! [X6 : $i,X7 : ($i > $i),X5 : $i] : ((((X7 @ (sK4 @ X7 @ X6 @ X5))) = X6) | (((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) != $true) | (image1Equiv != $true)) )),
% 0.08/0.16 inference(cnf_transformation,[],[f12])).
% 0.08/0.16 thf(f16,plain,(
% 0.08/0.16 ( ! [X6 : $i,X7 : ($i > $i),X5 : $i] : (($true = ((in @ (sK4 @ X7 @ X6 @ X5) @ X5))) | (((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) != $true) | (image1Equiv != $true)) )),
% 0.08/0.16 inference(cnf_transformation,[],[f12])).
% 0.08/0.16 thf(f21,plain,(
% 0.08/0.16 (image1Equiv = $true)),
% 0.08/0.16 inference(cnf_transformation,[],[f14])).
% 0.08/0.16 thf(f22,plain,(
% 0.08/0.16 (((in @ sK6 @ (image1 @ sK5 @ (^[Y0 : $i]: (sK7 @ Y0))))) = $true)),
% 0.08/0.16 inference(cnf_transformation,[],[f14])).
% 0.08/0.16 thf(f23,plain,(
% 0.08/0.16 ( ! [X3 : $i] : ((((in @ X3 @ sK5)) != $true) | (sK6 != ((sK7 @ X3)))) )),
% 0.08/0.16 inference(cnf_transformation,[],[f14])).
% 0.08/0.16 thf(f30,plain,(
% 0.08/0.16 ( ! [X6 : $i,X7 : ($i > $i),X5 : $i] : (($true = ((in @ (sK4 @ X7 @ X6 @ X5) @ X5))) | ($true != $true) | (((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) != $true)) )),
% 0.08/0.16 inference(definition_unfolding,[],[f16,f21])).
% 0.08/0.16 thf(f31,plain,(
% 0.08/0.16 ( ! [X6 : $i,X7 : ($i > $i),X5 : $i] : (($true != $true) | (((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) != $true) | (((X7 @ (sK4 @ X7 @ X6 @ X5))) = X6)) )),
% 0.08/0.16 inference(definition_unfolding,[],[f15,f21])).
% 0.08/0.16 thf(f33,plain,(
% 0.08/0.16 ( ! [X6 : $i,X7 : ($i > $i),X5 : $i] : ((((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) != $true) | ($true = ((in @ (sK4 @ X7 @ X6 @ X5) @ X5)))) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f30])).
% 0.08/0.16 thf(f34,plain,(
% 0.08/0.16 ( ! [X6 : $i,X7 : ($i > $i),X5 : $i] : (($true != ((in @ X6 @ (image1 @ X5 @ X7)))) | ($true = ((in @ (sK4 @ X7 @ X6 @ X5) @ X5)))) )),
% 0.08/0.16 inference(beta-eta_normalization,[],[f33])).
% 0.08/0.16 thf(f35,plain,(
% 0.08/0.16 (((in @ sK6 @ (image1 @ sK5 @ sK7))) = $true)),
% 0.08/0.16 inference(beta-eta_normalization,[],[f22])).
% 0.08/0.16 thf(f36,plain,(
% 0.08/0.16 ( ! [X6 : $i,X7 : ($i > $i),X5 : $i] : ((((X7 @ (sK4 @ X7 @ X6 @ X5))) = X6) | (((in @ X6 @ (image1 @ X5 @ (^[Y0 : $i]: (X7 @ Y0))))) != $true)) )),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f31])).
% 0.08/0.16 thf(f37,plain,(
% 0.08/0.16 ( ! [X6 : $i,X7 : ($i > $i),X5 : $i] : (($true != ((in @ X6 @ (image1 @ X5 @ X7)))) | (((X7 @ (sK4 @ X7 @ X6 @ X5))) = X6)) )),
% 0.08/0.16 inference(beta-eta_normalization,[],[f36])).
% 0.08/0.16 thf(f44,plain,(
% 0.08/0.16 (sK6 = ((sK7 @ (sK4 @ sK7 @ sK6 @ sK5)))) | ($true != $true)),
% 0.08/0.16 inference(constrained_superposition,[],[f37,f35])).
% 0.08/0.16 thf(f46,plain,(
% 0.08/0.16 (sK6 = ((sK7 @ (sK4 @ sK7 @ sK6 @ sK5))))),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f44])).
% 0.08/0.16 thf(f48,plain,(
% 0.08/0.16 ($true != $true) | (((in @ (sK4 @ sK7 @ sK6 @ sK5) @ sK5)) = $true)),
% 0.08/0.16 inference(constrained_superposition,[],[f34,f35])).
% 0.08/0.16 thf(f51,plain,(
% 0.08/0.16 (((in @ (sK4 @ sK7 @ sK6 @ sK5) @ sK5)) = $true)),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f48])).
% 0.08/0.16 thf(f52,plain,(
% 0.08/0.16 ($true != $true) | (sK6 != ((sK7 @ (sK4 @ sK7 @ sK6 @ sK5))))),
% 0.08/0.16 inference(constrained_superposition,[],[f23,f51])).
% 0.08/0.16 thf(f54,plain,(
% 0.08/0.16 (sK6 != ((sK7 @ (sK4 @ sK7 @ sK6 @ sK5))))),
% 0.08/0.16 inference(trivial_inequality_removal,[],[f52])).
% 0.08/0.16 thf(f56,plain,(
% 0.08/0.16 $false),
% 0.08/0.16 inference(forward_subsumption_resolution,[],[f54,f46])).
% 0.08/0.16 % SZS output end Proof for theBenchmark
% 0.08/0.16 % (181822)------------------------------
% 0.08/0.16 % (181822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (181822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (181822)CaDiCaL version: 2.1.3
% 0.08/0.16 % (181822)Termination reason: Refutation
% 0.08/0.16 % (181822)Time elapsed: 0.002 s
% 0.08/0.16 % (181822)Peak memory usage: 12 MB
% 0.08/0.16 % (181822)Instructions burned: 6 (million)
% 0.08/0.16 % (181817)Success in time 0.022 s
% 0.08/0.16 % Vampire exiting
%------------------------------------------------------------------------------