%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV197^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:39:08 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV197^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:20:54 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.25 % (3292759)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (3292768)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=140916056:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (3292768)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (3292765)% WARNING: option uhcvi not known.
% 0.09/0.25 % (3292768) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3292759-3292768"...
% 0.09/0.25 % (3292764)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2082004917_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.25 % (3292769)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2233255264:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.25 % (3292765)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2747040524:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.25 % (3292768)...printing done.
% 0.09/0.25 % (3292766)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2196735294:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (3292765)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % (3292770)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=72419219:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (3292765)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.25 % Exception at run slice level
% 0.09/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.25 % (3292768)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, iS: $tType).
% 0.09/0.25 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_0, type, c0: iS).
% 0.09/0.25 thf(func_def_1, type, cP: (iS > iS > iS)).
% 0.09/0.25 thf(func_def_5, type, sK0: iS).
% 0.09/0.25 thf(func_def_6, type, sK1: iS).
% 0.09/0.25 thf(func_def_7, type, sK2: iS).
% 0.09/0.25 thf(func_def_8, type, sK3: iS).
% 0.09/0.25 thf(func_def_9, type, sK4: iS).
% 0.09/0.25 thf(func_def_10, type, sK5: iS).
% 0.09/0.25 thf(func_def_11, type, sK6: ((iS > $o) > iS)).
% 0.09/0.25 thf(func_def_12, type, sK7: ((iS > $o) > iS)).
% 0.09/0.25 thf(func_def_13, type, vNOT: ($o > $o)).
% 0.09/0.25 thf(func_def_15, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.09/0.25 thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.25 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.25 thf(f1,conjecture,(
% 0.09/0.25 (! [X4 : (iS > $o)] : ((! [X0 : iS,X1 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X0 : iS,X1 : iS,X2 : iS,X3 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X2 = X3) & (X0 = X1))) & ! [X0 : iS,X1 : iS] : (((cP @ X0 @ X1)) != c0)) => (! [X0 : iS,X1 : iS] : (((cP @ X0 @ X1)) != c0) & ! [X0 : iS,X1 : iS,X2 : iS,X3 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X2 = X3) & (X0 = X1))))),
% 0.09/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_ALG02_pme)).
% 0.09/0.25 thf(f2,negated_conjecture,(
% 0.09/0.25 ~((! [X4 : (iS > $o)] : ((! [X0 : iS,X1 : iS] : (((X4 @ X1) & (X4 @ X0)) => (X4 @ (cP @ X0 @ X1))) & (X4 @ c0)) => ! [X0 : iS] : (X4 @ X0)) & ! [X0 : iS,X1 : iS,X2 : iS,X3 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X2 = X3) & (X0 = X1))) & ! [X0 : iS,X1 : iS] : (((cP @ X0 @ X1)) != c0)) => (! [X0 : iS,X1 : iS] : (((cP @ X0 @ X1)) != c0) & ! [X0 : iS,X1 : iS,X2 : iS,X3 : iS] : ((((cP @ X0 @ X2)) = ((cP @ X1 @ X3))) => ((X2 = X3) & (X0 = X1)))))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.25 thf(f3,plain,(
% 0.09/0.25 ~((! [X0 : (iS > $o)] : ((! [X1 : iS,X2 : iS] : (((X0 @ X2) & (X0 @ X1)) => (X0 @ (cP @ X1 @ X2))) & (X0 @ c0)) => ! [X3 : iS] : (X0 @ X3)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : ((((cP @ X4 @ X6)) = ((cP @ X5 @ X7))) => ((X6 = X7) & (X4 = X5))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9)))) => (! [X10 : iS,X11 : iS] : (c0 != ((cP @ X10 @ X11))) & ! [X12 : iS,X13 : iS,X14 : iS,X15 : iS] : ((((cP @ X12 @ X14)) = ((cP @ X13 @ X15))) => ((X14 = X15) & (X12 = X13)))))),
% 0.09/0.25 inference(rectify,[],[f2])).
% 0.09/0.25 thf(f4,plain,(
% 0.09/0.25 ~((! [X0 : (iS > $o)] : ((! [X1 : iS,X2 : iS] : (((((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) => (((X0 @ (cP @ X1 @ X2))) = $true)) & (((X0 @ c0)) = $true)) => ! [X3 : iS] : (((X0 @ X3)) = $true)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : ((((cP @ X4 @ X6)) = ((cP @ X5 @ X7))) => ((X6 = X7) & (X4 = X5))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9)))) => (! [X10 : iS,X11 : iS] : (c0 != ((cP @ X10 @ X11))) & ! [X12 : iS,X13 : iS,X14 : iS,X15 : iS] : ((((cP @ X12 @ X14)) = ((cP @ X13 @ X15))) => ((X14 = X15) & (X12 = X13)))))),
% 0.09/0.25 inference(fool_elimination,[],[f3])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 (? [X10 : iS,X11 : iS] : (c0 = ((cP @ X10 @ X11))) | ? [X12 : iS,X13 : iS,X14 : iS,X15 : iS] : (((X14 != X15) | (X12 != X13)) & (((cP @ X12 @ X14)) = ((cP @ X13 @ X15))))) & (! [X0 : (iS > $o)] : (! [X3 : iS] : (((X0 @ X3)) = $true) | (? [X1 : iS,X2 : iS] : ((((X0 @ (cP @ X1 @ X2))) != $true) & ((((X0 @ X2)) = $true) & (((X0 @ X1)) = $true))) | (((X0 @ c0)) != $true))) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((X6 = X7) & (X4 = X5)) | (((cP @ X4 @ X6)) != ((cP @ X5 @ X7)))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9))))),
% 0.09/0.25 inference(ennf_transformation,[],[f4])).
% 0.09/0.25 thf(f6,plain,(
% 0.09/0.25 (? [X10 : iS,X11 : iS] : (c0 = ((cP @ X10 @ X11))) | ? [X12 : iS,X13 : iS,X14 : iS,X15 : iS] : (((X14 != X15) | (X12 != X13)) & (((cP @ X12 @ X14)) = ((cP @ X13 @ X15))))) & ! [X0 : (iS > $o)] : (! [X3 : iS] : (((X0 @ X3)) = $true) | ? [X1 : iS,X2 : iS] : ((((X0 @ (cP @ X1 @ X2))) != $true) & (((X0 @ X2)) = $true) & (((X0 @ X1)) = $true)) | (((X0 @ c0)) != $true)) & ! [X4 : iS,X5 : iS,X6 : iS,X7 : iS] : (((X6 = X7) & (X4 = X5)) | (((cP @ X4 @ X6)) != ((cP @ X5 @ X7)))) & ! [X8 : iS,X9 : iS] : (c0 != ((cP @ X8 @ X9)))),
% 0.09/0.25 inference(flattening,[],[f5])).
% 0.09/0.25 thf(f7,plain,(
% 0.09/0.25 (? [X0 : iS,X1 : iS] : (((cP @ X0 @ X1)) = c0) | ? [X2 : iS,X3 : iS,X4 : iS,X5 : iS] : (((X4 != X5) | (X2 != X3)) & (((cP @ X2 @ X4)) = ((cP @ X3 @ X5))))) & ! [X6 : (iS > $o)] : (! [X7 : iS] : ($true = ((X6 @ X7))) | ? [X8 : iS,X9 : iS] : (($true != ((X6 @ (cP @ X8 @ X9)))) & ($true = ((X6 @ X9))) & ($true = ((X6 @ X8)))) | ($true != ((X6 @ c0)))) & ! [X10 : iS,X11 : iS,X12 : iS,X13 : iS] : (((X12 = X13) & (X10 = X11)) | (((cP @ X10 @ X12)) != ((cP @ X11 @ X13)))) & ! [X14 : iS,X15 : iS] : (c0 != ((cP @ X14 @ X15)))),
% 0.09/0.25 inference(rectify,[],[f6])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 ((c0 = ((cP @ sK0 @ sK1))) | (((sK4 != sK5) | (sK2 != sK3)) & (((cP @ sK2 @ sK4)) = ((cP @ sK3 @ sK5))))) & ! [X6 : (iS > $o)] : (! [X7 : iS] : ($true = ((X6 @ X7))) | (($true != ((X6 @ (cP @ (sK6 @ X6) @ (sK7 @ X6))))) & ($true = ((X6 @ (sK7 @ X6)))) & ($true = ((X6 @ (sK6 @ X6))))) | ($true != ((X6 @ c0)))) & ! [X10 : iS,X11 : iS,X12 : iS,X13 : iS] : (((X12 = X13) & (X10 = X11)) | (((cP @ X10 @ X12)) != ((cP @ X11 @ X13)))) & ! [X14 : iS,X15 : iS] : (c0 != ((cP @ X14 @ X15)))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X9,sK7 @ X6),skolemize(X9,sK7 @ X6)],[f7])).
% 0.09/0.25 thf(f9,plain,(
% 0.09/0.25 ( ! [X14 : iS,X15 : iS] : ((c0 != ((cP @ X14 @ X15)))) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f10,plain,(
% 0.09/0.25 ( ! [X10 : iS,X11 : iS,X12 : iS,X13 : iS] : ((((cP @ X10 @ X12)) != ((cP @ X11 @ X13))) | (X10 = X11)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f11,plain,(
% 0.09/0.25 ( ! [X10 : iS,X11 : iS,X12 : iS,X13 : iS] : ((((cP @ X10 @ X12)) != ((cP @ X11 @ X13))) | (X12 = X13)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f15,plain,(
% 0.09/0.25 (c0 = ((cP @ sK0 @ sK1))) | (((cP @ sK2 @ sK4)) = ((cP @ sK3 @ sK5)))),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f16,plain,(
% 0.09/0.25 (c0 = ((cP @ sK0 @ sK1))) | (sK4 != sK5) | (sK2 != sK3)),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f19,plain,(
% 0.09/0.25 (((cP @ sK2 @ sK4)) = ((cP @ sK3 @ sK5)))),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f15,f9])).
% 0.09/0.25 thf(f20,plain,(
% 0.09/0.25 (sK4 != sK5) | (sK2 != sK3)),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f16,f9])).
% 0.09/0.25 thf(f22,definition,(
% 0.09/0.25 spl8_1 <=> (sK2 = sK3)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.09/0.25 thf(f24,plain,(
% 0.09/0.25 (sK2 != sK3) | spl8_1),
% 0.09/0.25 inference(avatar_component_clause,[],[f22])).
% 0.09/0.25 thf(f26,definition,(
% 0.09/0.25 spl8_2 <=> (sK4 = sK5)),
% 0.09/0.25 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.09/0.25 thf(f28,plain,(
% 0.09/0.25 (sK4 != sK5) | spl8_2),
% 0.09/0.25 inference(avatar_component_clause,[],[f26])).
% 0.09/0.25 thf(f29,plain,(
% 0.09/0.25 ~spl8_1 | ~spl8_2),
% 0.09/0.25 inference(avatar_split_clause,[],[f20,f26,f22])).
% 0.09/0.25 thf(f32,plain,(
% 0.09/0.25 ( ! [X0 : iS,X1 : iS] : ((((cP @ X0 @ X1)) != ((cP @ sK2 @ sK4))) | (sK3 = X0)) )),
% 0.09/0.25 inference(constrained_superposition,[],[f10,f19])).
% 0.09/0.25 thf(f35,plain,(
% 0.09/0.25 ( ! [X0 : iS,X1 : iS] : ((((cP @ X0 @ X1)) != ((cP @ sK2 @ sK4))) | (sK5 = X1)) )),
% 0.09/0.25 inference(constrained_superposition,[],[f11,f19])).
% 0.09/0.25 thf(f249,plain,(
% 0.09/0.25 (sK2 = sK3)),
% 0.09/0.25 inference(equality_resolution,[],[f32])).
% 0.09/0.25 thf(f250,plain,(
% 0.09/0.25 $false | spl8_1),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f249,f24])).
% 0.09/0.25 thf(f251,plain,(
% 0.09/0.25 spl8_1),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f250])).
% 0.09/0.25 thf(f283,plain,(
% 0.09/0.25 (sK4 = sK5)),
% 0.09/0.25 inference(equality_resolution,[],[f35])).
% 0.09/0.25 thf(f284,plain,(
% 0.09/0.25 $false | spl8_2),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f283,f28])).
% 0.09/0.25 thf(f285,plain,(
% 0.09/0.25 spl8_2),
% 0.09/0.25 inference(avatar_contradiction_clause,[],[f284])).
% 0.09/0.25 cnf(s1, plain, ~spl8_1 | ~spl8_2, inference(sat_conversion,[],[f29])).
% 0.09/0.25 cnf(s11, plain, spl8_1, inference(sat_conversion,[],[f251])).
% 0.09/0.25 cnf(s12, plain, spl8_2, inference(sat_conversion,[],[f285])).
% 0.09/0.25 cnf(s15, plain, $false, inference(rat,[],[s1,s12,s11])).
% 0.09/0.25 thf(f286,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(avatar_sat_refutation,[],[s15])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (3292768)------------------------------
% 0.09/0.25 % (3292768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (3292768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (3292768)CaDiCaL version: 2.1.3
% 0.09/0.25 % (3292768)Termination reason: Refutation
% 0.09/0.25 % (3292768)Time elapsed: 0.006 s
% 0.09/0.25 % (3292768)Peak memory usage: 12 MB
% 0.09/0.25 % (3292768)Instructions burned: 13 (million)
% 0.09/0.25 % (3292759)Success in time 0.036 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------