%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO516^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:50:21 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO516^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:13:59 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (2788356)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (2788362)% WARNING: option uhcvi not known.
% 0.21/0.28 % (2788365)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2858502835:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.28 % (2788365)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.28 % (2788365) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2788356-2788365"...
% 0.21/0.28 % (2788364)dis+10_1_sil=32000:sp=arity:random_seed=2384662610:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.28 % (2788365)...printing done.
% 0.21/0.28 % (2788361)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1751249530_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (2788362)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3696810650:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (2788363)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3158572094:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.28 % (2788365)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, r: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_2, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_3, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.28 thf(func_def_4, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_7, type, sK0: (($i > $i) > $i)).
% 0.21/0.28 thf(func_def_8, type, sK1: ($i > $i)).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ! [X0 : $i] : ? [X1 : $i] : (((r @ X0)) = (^[X2 : $i] : ((X1 = X2)))) => ? [X3 : ($i > $i)] : ! [X0 : $i] : (r @ X0 @ (X3 @ X0))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr2)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~(! [X0 : $i] : ? [X1 : $i] : (((r @ X0)) = (^[X2 : $i] : ((X1 = X2)))) => ? [X3 : ($i > $i)] : ! [X0 : $i] : (r @ X0 @ (X3 @ X0)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~(! [X0 : $i] : ? [X1 : $i] : (((r @ X0)) = (^[X2 : $i] : ((X1 = X2)))) => ? [X3 : ($i > $i)] : ! [X4 : $i] : (r @ X4 @ (X3 @ X4)))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~(! [X0 : $i] : ? [X1 : $i] : (((r @ X0)) = (^[Y0 : $i]: (X1 = Y0))) => ? [X3 : ($i > $i)] : ! [X4 : $i] : (((r @ X4 @ (X3 @ X4))) = $true))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~(! [X0 : $i] : ? [X1 : $i] : (((r @ X0)) = (^[Y0 : $i]: (X1 = Y0))) => ? [X2 : ($i > $i)] : ! [X3 : $i] : ($true = ((r @ X3 @ (X2 @ X3)))))),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ! [X2 : ($i > $i)] : ? [X3 : $i] : ($true != ((r @ X3 @ (X2 @ X3)))) & ! [X0 : $i] : ? [X1 : $i] : (((r @ X0)) = (^[Y0 : $i]: (X1 = Y0)))),
% 0.21/0.28 inference(ennf_transformation,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ! [X0 : ($i > $i)] : ? [X1 : $i] : ($true != ((r @ X1 @ (X0 @ X1)))) & ! [X2 : $i] : ? [X3 : $i] : (((r @ X2)) = (^[Y0 : $i]: (X3 = Y0)))),
% 0.21/0.28 inference(rectify,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ! [X0 : ($i > $i)] : ($true != ((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0))))) & ! [X2 : $i] : (((r @ X2)) = (^[Y0 : $i]: ((sK1 @ X2) = Y0)))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK1 @ X2),skolemize(X3,sK1 @ X2)],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ( ! [X2 : $i] : ((((r @ X2)) = (^[Y0 : $i]: ((sK1 @ X2) = Y0)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X0 : ($i > $i)] : (($true != ((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f8])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 ( ! [X2 : $i] : ((((r @ X2)) = ((= @ (sK1 @ X2))))) )),
% 0.21/0.28 inference(beta-eta_normalization,[],[f9])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ( ! [X2 : $i,X3 : $i] : ((((r @ X2 @ X3)) = (((sK1 @ X2) = X3)))) )),
% 0.21/0.28 inference(argument_congruence,[],[f13])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ( ! [X2 : $i,X3 : $i] : (($true = ((r @ X2 @ X3))) | ($false = (((sK1 @ X2) = X3)))) )),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f14])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 ( ! [X2 : $i,X3 : $i] : (($true = ((r @ X2 @ X3))) | (((sK1 @ X2)) != X3)) )),
% 0.21/0.28 inference(equality_proxy_clausification,[],[f15])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ( ! [X0 : ($i > $i)] : (($true != $true) | (((X0 @ (sK0 @ X0))) != ((sK1 @ (sK0 @ X0))))) )),
% 0.21/0.28 inference(constrained_superposition,[],[f10,f18])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 ( ! [X0 : ($i > $i)] : ((((X0 @ (sK0 @ X0))) != ((sK1 @ (sK0 @ X0))))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f21])).
% 0.21/0.28 thf(f35,plain,(
% 0.21/0.28 (sK1 != (^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0))))),
% 0.21/0.28 inference(equality_resolution,[],[f23])).
% 0.21/0.28 thf(f38,plain,(
% 0.21/0.28 (sK1 != sK1)),
% 0.21/0.28 inference(beta-eta_normalization,[],[f35])).
% 0.21/0.28 thf(f39,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f38])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (2788365)------------------------------
% 0.21/0.28 % (2788365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2788365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2788365)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2788365)Termination reason: Refutation
% 0.21/0.28 % (2788365)Time elapsed: 0.002 s
% 0.21/0.28 % (2788365)Peak memory usage: 12 MB
% 0.21/0.28 % (2788365)Instructions burned: 3 (million)
% 0.21/0.28 % (2788356)Success in time 0.04 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------