%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO221^5 : 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 : n005.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 08:47:13 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO221^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n005.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:39:46 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.21/0.30 % (1889405)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (1889412)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3622941895:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (1889412)Refutation not found, incomplete strategy
% 0.21/0.30 % (1889412)------------------------------
% 0.21/0.30 % (1889412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1889412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1889412)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1889412)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.30 % (1889412)Time elapsed: 0.002 s
% 0.21/0.30 % (1889412)Peak memory usage: 12 MB
% 0.21/0.30 % (1889412)Instructions burned: 2 (million)
% 0.21/0.30 % (1889412)------------------------------
% 0.21/0.30 % (1889412)------------------------------
% 0.21/0.30 % (1889416)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (1889416)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
% 0.21/0.30 % (1889411)lrs+10_16_si=on:nwc=1.5:random_seed=2996205533:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (1889414)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3963825836:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (1889410)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3774417586:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (1889413)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=1833629824: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)
% 0.21/0.30 % (1889415)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1909257371:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (1889416)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=3212864499:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (1889414) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1889405-1889414"...
% 0.21/0.30 % (1889410) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1889405-1889410"...
% 0.21/0.30 % (1889411) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1889405-1889411"...
% 0.21/0.30 % (1889414)...printing done.
% 0.21/0.30 % (1889413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1889405-1889413"...
% 0.21/0.30 % (1889410)...printing done.
% 0.21/0.30 % (1889415) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1889405-1889415"...
% 0.21/0.30 % (1889414)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% 0.21/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.30 thf(func_def_1, type, cP: ($i > $o)).
% 0.21/0.30 thf(func_def_6, type, sK0: (($i > $o) > $i)).
% 0.21/0.30 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.21/0.30 thf(func_def_8, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.30 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.30 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.30 thf(f1,conjecture,(
% 0.21/0.30 ? [X0 : ($i > $o)] : (((a != b) & (cP @ a)) => (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ~(X0 @ b) & ? [X2 : $i] : (X0 @ X2)))),
% 0.21/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE6)).
% 0.21/0.30 thf(f2,negated_conjecture,(
% 0.21/0.30 ~ ? [X0 : ($i > $o)] : (((a != b) & (cP @ a)) => (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ~(X0 @ b) & ? [X2 : $i] : (X0 @ X2)))),
% 0.21/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.30 thf(f3,plain,(
% 0.21/0.30 ~ ? [X0 : ($i > $o)] : (((a != b) & (cP @ a)) => (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ~(X0 @ b) & ? [X2 : $i] : (X0 @ X2)))),
% 0.21/0.30 inference(rectify,[],[f2])).
% 0.21/0.30 thf(f4,plain,(
% 0.21/0.30 ~ ? [X0 : ($i > $o)] : (((((cP @ a)) = $true) & (a != b)) => (! [X1 : $i] : ((((X0 @ X1)) = $true) => (((cP @ X1)) = $true)) & ~ (((X0 @ b)) = $true) & ? [X2 : $i] : (((X0 @ X2)) = $true)))),
% 0.21/0.30 inference(fool_elimination,[],[f3])).
% 0.21/0.30 thf(f5,plain,(
% 0.21/0.30 ~ ? [X0 : ($i > $o)] : (((((cP @ a)) = $true) & (a != b)) => (! [X1 : $i] : ((((X0 @ X1)) = $true) => (((cP @ X1)) = $true)) & ? [X2 : $i] : (((X0 @ X2)) = $true) & (((X0 @ b)) != $true)))),
% 0.21/0.30 inference(flattening,[],[f4])).
% 0.21/0.30 thf(f6,plain,(
% 0.21/0.30 ! [X0 : ($i > $o)] : (((((X0 @ b)) = $true) | ! [X2 : $i] : (((X0 @ X2)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((cP @ X1)) != $true))) & ((((cP @ a)) = $true) & (a != b)))),
% 0.21/0.30 inference(ennf_transformation,[],[f5])).
% 0.21/0.30 thf(f7,plain,(
% 0.21/0.30 ! [X0 : ($i > $o)] : ((a != b) & ((((X0 @ b)) = $true) | ! [X2 : $i] : (((X0 @ X2)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((cP @ X1)) != $true))) & (((cP @ a)) = $true))),
% 0.21/0.30 inference(flattening,[],[f6])).
% 0.21/0.30 thf(f8,plain,(
% 0.21/0.30 ! [X0 : ($i > $o)] : ((a != b) & ((((X0 @ b)) = $true) | ! [X1 : $i] : (((X0 @ X1)) != $true) | ? [X2 : $i] : ((((X0 @ X2)) = $true) & ($true != ((cP @ X2))))) & (((cP @ a)) = $true))),
% 0.21/0.30 inference(rectify,[],[f7])).
% 0.21/0.30 thf(f9,plain,(
% 0.21/0.30 ! [X0 : ($i > $o)] : ((a != b) & ((((X0 @ b)) = $true) | ! [X1 : $i] : (((X0 @ X1)) != $true) | (($true = ((X0 @ (sK0 @ X0)))) & ($true != ((cP @ (sK0 @ X0)))))) & (((cP @ a)) = $true))),
% 0.21/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f8])).
% 0.21/0.30 thf(f10,plain,(
% 0.21/0.30 (((cP @ a)) = $true)),
% 0.21/0.30 inference(cnf_transformation,[],[f9])).
% 0.21/0.30 thf(f11,plain,(
% 0.21/0.30 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((cP @ (sK0 @ X0)))) | (((X0 @ X1)) != $true) | (((X0 @ b)) = $true)) )),
% 0.21/0.30 inference(cnf_transformation,[],[f9])).
% 0.21/0.30 thf(f12,plain,(
% 0.21/0.30 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | (((X0 @ b)) = $true) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.21/0.30 inference(cnf_transformation,[],[f9])).
% 0.21/0.30 thf(f13,plain,(
% 0.21/0.30 (a != b)),
% 0.21/0.30 inference(cnf_transformation,[],[f9])).
% 0.21/0.30 thf(f15,plain,(
% 0.21/0.30 ( ! [X0 : $i] : (($true != ((cP @ (sK0 @ (= @ X0))))) | (b = X0)) )),
% 0.21/0.30 inference(leibniz_equality_elimination,[],[f11])).
% 0.21/0.30 thf(f17,plain,(
% 0.21/0.30 ( ! [X0 : $i] : ((b = X0) | ($true = ((X0 = (sK0 @ (= @ X0)))))) )),
% 0.21/0.30 inference(leibniz_equality_elimination,[],[f12])).
% 0.21/0.30 thf(f27,plain,(
% 0.21/0.30 ( ! [X0 : $i] : ((((sK0 @ (= @ X0))) = X0) | (b = X0)) )),
% 0.21/0.30 inference(equality_proxy_clausification,[],[f17])).
% 0.21/0.30 thf(f39,plain,(
% 0.21/0.30 ( ! [X0 : $i] : ((b = X0) | ($true != ((cP @ X0))) | (b = X0)) )),
% 0.21/0.30 inference(superposition,[],[f15,f27])).
% 0.21/0.30 thf(f41,plain,(
% 0.21/0.30 ( ! [X0 : $i] : (($true != ((cP @ X0))) | (b = X0)) )),
% 0.21/0.30 inference(duplicate_literal_removal,[],[f39])).
% 0.21/0.30 thf(f45,plain,(
% 0.21/0.30 ($true != $true) | (a = b)),
% 0.21/0.30 inference(superposition,[],[f41,f10])).
% 0.21/0.30 thf(f46,plain,(
% 0.21/0.30 (a = b)),
% 0.21/0.30 inference(trivial_inequality_removal,[],[f45])).
% 0.21/0.30 thf(f47,plain,(
% 0.21/0.30 $false),
% 0.21/0.30 inference(forward_subsumption_resolution,[],[f46,f13])).
% 0.21/0.30 % SZS output end Proof for theBenchmark
% 0.21/0.30 % (1889414)------------------------------
% 0.21/0.30 % (1889414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1889414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1889414)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1889414)Termination reason: Refutation
% 0.21/0.30 % (1889414)Time elapsed: 0.002 s
% 0.21/0.30 % (1889414)Peak memory usage: 12 MB
% 0.21/0.30 % (1889414)Instructions burned: 2 (million)
% 0.21/0.30 % (1889405)Success in time 0.046 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------