%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU906^5 : 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 : n011.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 08:31:55 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU906^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n011.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:45:01 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.21 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
% 0.07/0.25 % (179439)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.25 % (179445)lrs+10_16_si=on:nwc=1.5:random_seed=624417665:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.07/0.25 % (179450)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.07/0.25 % (179450)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
% 0.07/0.25 % (179445)Instruction limit reached!
% 0.07/0.25 % (179445)------------------------------
% 0.07/0.25 % (179445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (179445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (179445)CaDiCaL version: 2.1.3
% 0.07/0.25 % (179445)Termination reason: Instruction limit
% 0.07/0.25 % (179445)Termination phase: Saturation
% 0.07/0.25 % (179445)Time elapsed: 0.006 s
% 0.07/0.25 % (179445)Peak memory usage: 12 MB
% 0.07/0.25 % (179445)Instructions burned: 21 (million)
% 0.07/0.25 % (179444)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3813939813:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.07/0.25 % (179446)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3930613124:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.07/0.25 % (179448)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2081339819:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.07/0.25 % (179447)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=1710063319: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)
% 0.07/0.25 % (179450)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=1901797905:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.07/0.25 % (179446) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-179439-179446"...
% 0.07/0.25 % (179444)Refutation not found, incomplete strategy
% 0.07/0.25 % (179444)------------------------------
% 0.07/0.25 % (179444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (179444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (179444)CaDiCaL version: 2.1.3
% 0.07/0.25 % (179444)Termination reason: Refutation not found, incomplete strategy
% 0.07/0.25 % (179444)Time elapsed: 0.002 s
% 0.07/0.25 % (179444)Peak memory usage: 12 MB
% 0.07/0.25 % (179444)Instructions burned: 2 (million)
% 0.07/0.25 % (179448)Refutation not found, incomplete strategy
% 0.07/0.25 % (179448)------------------------------
% 0.07/0.25 % (179448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (179448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (179448)CaDiCaL version: 2.1.3
% 0.07/0.25 % (179448)Termination reason: Refutation not found, incomplete strategy
% 0.07/0.25 % (179448)Time elapsed: 0.002 s
% 0.07/0.25 % (179448)Peak memory usage: 12 MB
% 0.07/0.25 % (179448)Instructions burned: 3 (million)
% 0.07/0.25 % (179444)------------------------------
% 0.07/0.25 % (179444)------------------------------
% 0.07/0.25 % (179446)...printing done.
% 0.07/0.25 % (179447)Refutation not found, incomplete strategy
% 0.07/0.25 % (179447)------------------------------
% 0.07/0.25 % (179447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (179447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (179447)CaDiCaL version: 2.1.3
% 0.07/0.25 % (179447)Termination reason: Refutation not found, incomplete strategy
% 0.07/0.25 % (179447)Time elapsed: 0.003 s
% 0.07/0.25 % (179447)Peak memory usage: 12 MB
% 0.07/0.25 % (179447)Instructions burned: 3 (million)
% 0.07/0.25 % (179448)------------------------------
% 0.07/0.25 % (179448)------------------------------
% 0.07/0.25 % (179447)------------------------------
% 0.07/0.25 % (179447)------------------------------
% 0.07/0.25 % (179446)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% 0.07/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.25 thf(func_def_0, type, f: ($i > $i)).
% 0.07/0.25 thf(func_def_1, type, cS: ($i > $o)).
% 0.07/0.25 thf(func_def_3, type, sK0: (($i > $o) > $i)).
% 0.07/0.25 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.07/0.25 thf(func_def_7, type, inv_f_1: ($i > $i)).
% 0.07/0.25 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.07/0.25 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.07/0.25 thf(f1,conjecture,(
% 0.07/0.25 ! [X1 : $i,X0 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1)) => ? [X2 : ($i > $o)] : ! [X0 : $i] : ((X2 @ (f @ X0)) <=> (cS @ X0))),
% 0.07/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSV5_pme)).
% 0.07/0.25 thf(f2,negated_conjecture,(
% 0.07/0.25 ~(! [X1 : $i,X0 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1)) => ? [X2 : ($i > $o)] : ! [X0 : $i] : ((X2 @ (f @ X0)) <=> (cS @ X0)))),
% 0.07/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.07/0.25 thf(f3,plain,(
% 0.07/0.25 ~(! [X0 : $i,X1 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1)) => ? [X2 : ($i > $o)] : ! [X3 : $i] : ((X2 @ (f @ X3)) <=> (cS @ X3)))),
% 0.07/0.25 inference(rectify,[],[f2])).
% 0.07/0.25 thf(f4,plain,(
% 0.07/0.25 ~(! [X1 : $i,X0 : $i] : ((((f @ X0)) = ((f @ X1))) => (X0 = X1)) => ? [X2 : ($i > $o)] : ! [X3 : $i] : (((cS @ X3)) = ((X2 @ (f @ X3)))))),
% 0.07/0.25 inference(fool_elimination,[],[f3])).
% 0.07/0.25 thf(f5,plain,(
% 0.07/0.25 ! [X2 : ($i > $o)] : ? [X3 : $i] : (((cS @ X3)) != ((X2 @ (f @ X3)))) & ! [X1 : $i,X0 : $i] : ((X0 = X1) | (((f @ X0)) != ((f @ X1))))),
% 0.07/0.25 inference(ennf_transformation,[],[f4])).
% 0.07/0.25 thf(f6,plain,(
% 0.07/0.25 ! [X0 : ($i > $o)] : ? [X1 : $i] : (((X0 @ (f @ X1))) != ((cS @ X1))) & ! [X2 : $i,X3 : $i] : ((X2 = X3) | (((f @ X3)) != ((f @ X2))))),
% 0.07/0.25 inference(rectify,[],[f5])).
% 0.07/0.25 thf(f7,plain,(
% 0.07/0.25 ! [X0 : ($i > $o)] : (((X0 @ (f @ (sK0 @ X0)))) != ((cS @ (sK0 @ X0)))) & ! [X2 : $i,X3 : $i] : ((X2 = X3) | (((f @ X3)) != ((f @ X2))))),
% 0.07/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f6])).
% 0.07/0.25 thf(f8,plain,(
% 0.07/0.25 ( ! [X2 : $i,X3 : $i] : ((((f @ X3)) != ((f @ X2))) | (X2 = X3)) )),
% 0.07/0.25 inference(cnf_transformation,[],[f7])).
% 0.07/0.25 thf(f9,plain,(
% 0.07/0.25 ( ! [X0 : ($i > $o)] : ((((X0 @ (f @ (sK0 @ X0)))) != ((cS @ (sK0 @ X0))))) )),
% 0.07/0.25 inference(cnf_transformation,[],[f7])).
% 0.07/0.25 thf(f12,plain,(
% 0.07/0.25 ( ! [X3 : $i] : ((((inv_f_1 @ (f @ X3))) = X3)) )),
% 0.07/0.25 inference(injectivity,[],[f8])).
% 0.07/0.25 thf(f17,plain,(
% 0.07/0.25 ( ! [X1 : ($i > $i)] : ((((cS @ (sK0 @ (^[Y0 : $i]: (cS @ (X1 @ Y0)))))) != (((^[Y0 : $i]: (cS @ (X1 @ Y0))) @ (f @ (sK0 @ (^[Y0 : $i]: (cS @ (X1 @ Y0))))))))) )),
% 0.07/0.25 inference(imitation,[],[f9])).
% 0.07/0.25 thf(f19,plain,(
% 0.07/0.25 ( ! [X1 : ($i > $i)] : ((((cS @ (sK0 @ (^[Y0 : $i]: (cS @ (X1 @ Y0)))))) != ((cS @ (X1 @ (f @ (sK0 @ (^[Y0 : $i]: (cS @ (X1 @ Y0)))))))))) )),
% 0.07/0.25 inference(beta-eta_normalization,[],[f17])).
% 0.07/0.25 thf(f22,plain,(
% 0.07/0.25 (((cS @ (sK0 @ (^[Y0 : $i]: (cS @ (inv_f_1 @ Y0)))))) != ((cS @ (sK0 @ (^[Y0 : $i]: (cS @ (inv_f_1 @ Y0)))))))),
% 0.07/0.25 inference(constrained_superposition,[],[f19,f12])).
% 0.07/0.25 thf(f23,plain,(
% 0.07/0.25 $false),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f22])).
% 0.07/0.25 % SZS output end Proof for theBenchmark
% 0.07/0.25 % (179446)------------------------------
% 0.07/0.25 % (179446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (179446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (179446)CaDiCaL version: 2.1.3
% 0.07/0.25 % (179446)Termination reason: Refutation
% 0.07/0.25 % (179446)Time elapsed: 0.002 s
% 0.07/0.25 % (179446)Peak memory usage: 12 MB
% 0.07/0.25 % (179446)Instructions burned: 2 (million)
% 0.07/0.25 % (179439)Success in time 0.035 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------