%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO268^5 : 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 : n015.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 08:49:38 AM UTC 2026
% Result : Theorem 0.24s 0.27s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO268^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n015.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 16:45:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.24/0.27 % (3775014)Will run a generic schedule for satisfiability detection.
% 0.24/0.27 % (3775027)% WARNING: option uhcvi not known.
% 0.24/0.27 % (3775026)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=371944800_2999 on theBenchmark for (2999ds/0Mi)
% 0.24/0.27 % (3775027)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3522147651:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.27 % (3775030)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3294096888:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.24/0.27 % (3775029)dis+10_1_sil=32000:sp=arity:random_seed=1252273258:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.27 % (3775027)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.27 % (3775030)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.27 % (3775027)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.24/0.27 % Exception at run slice level
% 0.24/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.27 % (3775028)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=322546195:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.27 % (3775033)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1992580605:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.24/0.27 % (3775029) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3775014-3775029"...
% 0.24/0.27 % (3775027) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3775014-3775027"...
% 0.24/0.27 % (3775031)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=890560714:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.24/0.27 % (3775030) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3775014-3775030"...
% 0.24/0.27 % (3775027)...printing done.
% 0.24/0.27 % (3775029)...printing done.
% 0.24/0.27 % (3775027)Refutation found. Thanks to Tanya!
% 0.24/0.27 % SZS status Theorem for theBenchmark
% 0.24/0.27 % SZS output start Proof for theBenchmark
% 0.24/0.27 thf(type_def_5, type, a: $tType).
% 0.24/0.27 thf(type_def_6, type, b: $tType).
% 0.24/0.27 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.27 thf(func_def_0, type, r: (a > b > $o)).
% 0.24/0.27 thf(func_def_4, type, sK0: ((a > b) > a)).
% 0.24/0.27 thf(func_def_5, type, sK1: a).
% 0.24/0.27 thf(func_def_6, type, sK2: (a > b)).
% 0.24/0.27 thf(func_def_7, type, sK3: (a > b)).
% 0.24/0.27 thf(func_def_8, type, sK4: ((b > $o) > b)).
% 0.24/0.27 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.24/0.27 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.24/0.27 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.24/0.27 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.24/0.27 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 0.24/0.27 thf(f1,conjecture,(
% 0.24/0.27 ? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (! [X2 : a] : ? [X3 : b] : (r @ X2 @ X3) <=> ? [X4 : (a > b)] : ! [X2 : a] : (r @ X2 @ (X4 @ X2)))),
% 0.24/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5308)).
% 0.24/0.27 thf(f2,negated_conjecture,(
% 0.24/0.27 ~(? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (! [X2 : a] : ? [X3 : b] : (r @ X2 @ X3) <=> ? [X4 : (a > b)] : ! [X2 : a] : (r @ X2 @ (X4 @ X2))))),
% 0.24/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.24/0.27 thf(f3,plain,(
% 0.24/0.27 ~(? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X2 : b] : (X1 @ X2) => (X1 @ (X0 @ X1))) => (! [X3 : a] : ? [X4 : b] : (r @ X3 @ X4) <=> ? [X5 : (a > b)] : ! [X6 : a] : (r @ X6 @ (X5 @ X6))))),
% 0.24/0.27 inference(rectify,[],[f2])).
% 0.24/0.27 thf(f4,plain,(
% 0.24/0.27 ~(? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X2 : b] : (((X1 @ X2)) = $true) => (((X1 @ (X0 @ X1))) = $true)) => (! [X3 : a] : ? [X4 : b] : (((r @ X3 @ X4)) = $true) <=> ? [X5 : (a > b)] : ! [X6 : a] : (((r @ X6 @ (X5 @ X6))) = $true)))),
% 0.24/0.27 inference(fool_elimination,[],[f3])).
% 0.24/0.27 thf(f5,plain,(
% 0.24/0.27 (! [X3 : a] : ? [X4 : b] : (((r @ X3 @ X4)) = $true) <~> ? [X5 : (a > b)] : ! [X6 : a] : (((r @ X6 @ (X5 @ X6))) = $true)) & ? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : ((((X1 @ (X0 @ X1))) = $true) | ! [X2 : b] : (((X1 @ X2)) != $true))),
% 0.24/0.27 inference(ennf_transformation,[],[f4])).
% 0.24/0.27 thf(f6,plain,(
% 0.24/0.27 ((! [X5 : (a > b)] : ? [X6 : a] : (((r @ X6 @ (X5 @ X6))) != $true) | ? [X3 : a] : ! [X4 : b] : (((r @ X3 @ X4)) != $true)) & (? [X5 : (a > b)] : ! [X6 : a] : (((r @ X6 @ (X5 @ X6))) = $true) | ! [X3 : a] : ? [X4 : b] : (((r @ X3 @ X4)) = $true))) & ? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : ((((X1 @ (X0 @ X1))) = $true) | ! [X2 : b] : (((X1 @ X2)) != $true))),
% 0.24/0.27 inference(nnf_transformation,[],[f5])).
% 0.24/0.27 thf(f7,plain,(
% 0.24/0.27 (! [X5 : (a > b)] : ? [X6 : a] : (((r @ X6 @ (X5 @ X6))) != $true) | ? [X3 : a] : ! [X4 : b] : (((r @ X3 @ X4)) != $true)) & (? [X5 : (a > b)] : ! [X6 : a] : (((r @ X6 @ (X5 @ X6))) = $true) | ! [X3 : a] : ? [X4 : b] : (((r @ X3 @ X4)) = $true)) & ? [X0 : ((b > $o) > b)] : ! [X1 : (b > $o)] : ((((X1 @ (X0 @ X1))) = $true) | ! [X2 : b] : (((X1 @ X2)) != $true))),
% 0.24/0.27 inference(flattening,[],[f6])).
% 0.24/0.27 thf(f8,plain,(
% 0.24/0.27 (! [X0 : (a > b)] : ? [X1 : a] : ($true != ((r @ X1 @ (X0 @ X1)))) | ? [X2 : a] : ! [X3 : b] : (((r @ X2 @ X3)) != $true)) & (? [X4 : (a > b)] : ! [X5 : a] : ($true = ((r @ X5 @ (X4 @ X5)))) | ! [X6 : a] : ? [X7 : b] : ($true = ((r @ X6 @ X7)))) & ? [X8 : ((b > $o) > b)] : ! [X9 : (b > $o)] : (($true = ((X9 @ (X8 @ X9)))) | ! [X10 : b] : ($true != ((X9 @ X10))))),
% 0.24/0.27 inference(rectify,[],[f7])).
% 0.24/0.27 thf(f9,plain,(
% 0.24/0.27 (! [X0 : (a > b)] : ($true != ((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0))))) | ! [X3 : b] : ($true != ((r @ sK1 @ X3)))) & (! [X5 : a] : ($true = ((r @ X5 @ (sK2 @ X5)))) | ! [X6 : a] : ($true = ((r @ X6 @ (sK3 @ X6))))) & ! [X9 : (b > $o)] : (($true = ((X9 @ (sK4 @ X9)))) | ! [X10 : b] : ($true != ((X9 @ X10))))),
% 0.24/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2,vAPP,sK4]),skolemize(X7,sK3 @ X6),skolemize(X2,sK1),skolemize(X4,sK2),skolemize(X7,sK3 @ X6),skolemize(X8,sK4)],[f8])).
% 0.24/0.27 thf(f11,plain,(
% 0.24/0.27 ( ! [X6 : a,X5 : a] : (($true = ((r @ X5 @ (sK2 @ X5)))) | ($true = ((r @ X6 @ (sK3 @ X6))))) )),
% 0.24/0.27 inference(cnf_transformation,[],[f9])).
% 0.24/0.27 thf(f12,plain,(
% 0.24/0.27 ( ! [X3 : b,X0 : (a > b)] : (($true != ((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0))))) | ($true != ((r @ sK1 @ X3)))) )),
% 0.24/0.27 inference(cnf_transformation,[],[f9])).
% 0.24/0.27 thf(f16,definition,(
% 0.24/0.27 spl5_1 <=> ! [X6 : a] : ($true = ((r @ X6 @ (sK3 @ X6))))),
% 0.24/0.27 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.24/0.27 thf(f17,plain,(
% 0.24/0.27 ( ! [X6 : a] : (($true = ((r @ X6 @ (sK3 @ X6))))) ) | ~spl5_1),
% 0.24/0.27 inference(avatar_component_clause,[],[f16])).
% 0.24/0.27 thf(f19,definition,(
% 0.24/0.27 spl5_2 <=> ! [X5 : a] : ($true = ((r @ X5 @ (sK2 @ X5))))),
% 0.24/0.27 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.24/0.27 thf(f20,plain,(
% 0.24/0.27 ( ! [X5 : a] : (($true = ((r @ X5 @ (sK2 @ X5))))) ) | ~spl5_2),
% 0.24/0.27 inference(avatar_component_clause,[],[f19])).
% 0.24/0.27 thf(f21,plain,(
% 0.24/0.27 spl5_1 | spl5_2),
% 0.24/0.27 inference(avatar_split_clause,[],[f11,f19,f16])).
% 0.24/0.27 thf(f23,definition,(
% 0.24/0.27 spl5_3 <=> ! [X3 : b] : ($true != ((r @ sK1 @ X3)))),
% 0.24/0.27 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 0.24/0.27 thf(f24,plain,(
% 0.24/0.27 ( ! [X3 : b] : (($true != ((r @ sK1 @ X3)))) ) | ~spl5_3),
% 0.24/0.27 inference(avatar_component_clause,[],[f23])).
% 0.24/0.27 thf(f26,definition,(
% 0.24/0.27 spl5_4 <=> ! [X0 : (a > b)] : ($true != ((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))))),
% 0.24/0.27 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.24/0.27 thf(f27,plain,(
% 0.24/0.27 ( ! [X0 : (a > b)] : (($true != ((r @ (sK0 @ X0) @ (X0 @ (sK0 @ X0)))))) ) | ~spl5_4),
% 0.24/0.27 inference(avatar_component_clause,[],[f26])).
% 0.24/0.27 thf(f28,plain,(
% 0.24/0.27 spl5_3 | spl5_4),
% 0.24/0.27 inference(avatar_split_clause,[],[f12,f26,f23])).
% 0.24/0.27 thf(f29,plain,(
% 0.24/0.27 ($true != $true) | (~spl5_2 | ~spl5_3)),
% 0.24/0.27 inference(constrained_superposition,[],[f24,f20])).
% 0.24/0.27 thf(f30,plain,(
% 0.24/0.27 $false | (~spl5_2 | ~spl5_3)),
% 0.24/0.27 inference(trivial_inequality_removal,[],[f29])).
% 0.24/0.27 thf(f31,plain,(
% 0.24/0.27 ~spl5_2 | ~spl5_3),
% 0.24/0.27 inference(avatar_contradiction_clause,[],[f30])).
% 0.24/0.27 thf(f32,plain,(
% 0.24/0.27 ($true != $true) | (~spl5_1 | ~spl5_3)),
% 0.24/0.27 inference(constrained_superposition,[],[f24,f17])).
% 0.24/0.27 thf(f33,plain,(
% 0.24/0.27 $false | (~spl5_1 | ~spl5_3)),
% 0.24/0.27 inference(trivial_inequality_removal,[],[f32])).
% 0.24/0.27 thf(f34,plain,(
% 0.24/0.27 ~spl5_1 | ~spl5_3),
% 0.24/0.27 inference(avatar_contradiction_clause,[],[f33])).
% 0.24/0.27 thf(f53,plain,(
% 0.24/0.27 ($true != $true) | (sK2 != (^[Y0 : a]: (sK2 @ ((^[Y1 : a]: (Y1)) @ Y0)))) | (~spl5_2 | ~spl5_4)),
% 0.24/0.27 inference(constrained_superposition,[],[f27,f20])).
% 0.24/0.27 thf(f57,plain,(
% 0.24/0.27 (sK2 != (^[Y0 : a]: (sK2 @ ((^[Y1 : a]: (Y1)) @ Y0)))) | (~spl5_2 | ~spl5_4)),
% 0.24/0.27 inference(trivial_inequality_removal,[],[f53])).
% 0.24/0.27 thf(f58,plain,(
% 0.24/0.27 (sK2 != sK2) | (~spl5_2 | ~spl5_4)),
% 0.24/0.27 inference(beta-eta_normalization,[],[f57])).
% 0.24/0.27 thf(f59,plain,(
% 0.24/0.27 $false | (~spl5_2 | ~spl5_4)),
% 0.24/0.27 inference(trivial_inequality_removal,[],[f58])).
% 0.24/0.27 thf(f60,plain,(
% 0.24/0.27 ~spl5_2 | ~spl5_4),
% 0.24/0.27 inference(avatar_contradiction_clause,[],[f59])).
% 0.24/0.27 thf(f62,plain,(
% 0.24/0.27 ($true != $true) | (sK3 != (^[Y0 : a]: (sK3 @ ((^[Y1 : a]: (Y1)) @ Y0)))) | (~spl5_1 | ~spl5_4)),
% 0.24/0.27 inference(constrained_superposition,[],[f27,f17])).
% 0.24/0.27 thf(f72,plain,(
% 0.24/0.27 (sK3 != (^[Y0 : a]: (sK3 @ ((^[Y1 : a]: (Y1)) @ Y0)))) | (~spl5_1 | ~spl5_4)),
% 0.24/0.27 inference(trivial_inequality_removal,[],[f62])).
% 0.24/0.27 thf(f73,plain,(
% 0.24/0.27 (sK3 != sK3) | (~spl5_1 | ~spl5_4)),
% 0.24/0.27 inference(beta-eta_normalization,[],[f72])).
% 0.24/0.27 thf(f74,plain,(
% 0.24/0.27 $false | (~spl5_1 | ~spl5_4)),
% 0.24/0.27 inference(trivial_inequality_removal,[],[f73])).
% 0.24/0.27 thf(f75,plain,(
% 0.24/0.27 ~spl5_1 | ~spl5_4),
% 0.24/0.27 inference(avatar_contradiction_clause,[],[f74])).
% 0.24/0.27 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f21])).
% 0.24/0.27 cnf(s2, plain, spl5_3 | spl5_4, inference(sat_conversion,[],[f28])).
% 0.24/0.27 cnf(s3, plain, ~spl5_2 | ~spl5_3, inference(sat_conversion,[],[f31])).
% 0.24/0.27 cnf(s4, plain, ~spl5_1 | ~spl5_3, inference(sat_conversion,[],[f34])).
% 0.24/0.27 cnf(s5, plain, ~spl5_2 | ~spl5_4, inference(sat_conversion,[],[f60])).
% 0.24/0.27 cnf(s6, plain, ~spl5_1 | ~spl5_4, inference(sat_conversion,[],[f75])).
% 0.24/0.27 cnf(s7, plain, ~spl5_2, inference(rat,[],[s2,s3,s5])).
% 0.24/0.27 cnf(s8, plain, spl5_1, inference(rat,[],[s1,s7])).
% 0.24/0.27 cnf(s9, plain, ~spl5_4, inference(rat,[],[s6,s8])).
% 0.24/0.27 cnf(s10, plain, ~spl5_3, inference(rat,[],[s4,s8])).
% 0.24/0.27 cnf(s11, plain, $false, inference(rat,[],[s2,s9,s10])).
% 0.24/0.27 thf(f76,plain,(
% 0.24/0.27 $false),
% 0.24/0.27 inference(avatar_sat_refutation,[],[s11])).
% 0.24/0.27 % SZS output end Proof for theBenchmark
% 0.24/0.27 % (3775027)------------------------------
% 0.24/0.27 % (3775027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.27 % (3775027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.27 % (3775027)CaDiCaL version: 2.1.3
% 0.24/0.27 % (3775027)Termination reason: Refutation
% 0.24/0.27 % (3775027)Time elapsed: 0.006 s
% 0.24/0.27 % (3775027)Peak memory usage: 12 MB
% 0.24/0.27 % (3775027)Instructions burned: 7 (million)
% 0.24/0.27 % (3775014)Success in time 0.044 s
% 0.24/0.28 % Vampire exiting
%------------------------------------------------------------------------------