%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO375^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:49:49 AM UTC 2026
% Result : Theorem 0.06s 0.23s
% Output : Refutation 0.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO375^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 % Computer : n005.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 16:49:17 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.23 % (1909044)Will run a generic schedule for satisfiability detection.
% 0.06/0.23 % (1909058)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1502294475:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.06/0.23 % (1909058)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.06/0.23 % (1909058) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1909044-1909058"...
% 0.06/0.23 % (1909058)...printing done.
% 0.06/0.23 % (1909055)% WARNING: option uhcvi not known.
% 0.06/0.23 % (1909058)Refutation found. Thanks to Tanya!
% 0.06/0.23 % SZS status Theorem for theBenchmark
% 0.06/0.23 % SZS output start Proof for theBenchmark
% 0.06/0.23 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.06/0.23 thf(func_def_1, type, sK0: ($i > $o)).
% 0.06/0.23 thf(func_def_2, type, sK1: ($i > $o)).
% 0.06/0.23 thf(f1,conjecture,(
% 0.06/0.23 ! [X0 : ($i > $o),X1 : ($i > $o)] : (! [X2 : $i] : ((X0 @ X2) <=> (X1 @ X2)) => ! [X3 : $i] : ((X0 @ X3) <=> (X1 @ X3)))),
% 0.06/0.23 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT_SET1)).
% 0.06/0.23 thf(f2,negated_conjecture,(
% 0.06/0.23 ~ ! [X0 : ($i > $o),X1 : ($i > $o)] : (! [X2 : $i] : ((X0 @ X2) <=> (X1 @ X2)) => ! [X3 : $i] : ((X0 @ X3) <=> (X1 @ X3)))),
% 0.06/0.23 inference(negated_conjecture,[status(cth)],[f1])).
% 0.06/0.23 thf(f3,plain,(
% 0.06/0.23 ~ ! [X0 : ($i > $o),X1 : ($i > $o)] : (! [X2 : $i] : ((X0 @ X2) <=> (X1 @ X2)) => ! [X3 : $i] : ((X0 @ X3) <=> (X1 @ X3)))),
% 0.06/0.23 inference(rectify,[],[f2])).
% 0.06/0.23 thf(f4,plain,(
% 0.06/0.23 ~ ! [X0 : ($i > $o),X1 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))) => ! [X3 : $i] : (((X0 @ X3)) = ((X1 @ X3))))),
% 0.06/0.23 inference(fool_elimination,[],[f3])).
% 0.06/0.23 thf(f5,plain,(
% 0.06/0.23 ? [X0 : ($i > $o),X1 : ($i > $o)] : (? [X3 : $i] : (((X0 @ X3)) != ((X1 @ X3))) & ! [X2 : $i] : (((X0 @ X2)) = ((X1 @ X2))))),
% 0.06/0.23 inference(ennf_transformation,[],[f4])).
% 0.06/0.23 thf(f6,plain,(
% 0.06/0.23 ? [X0 : ($i > $o),X1 : ($i > $o)] : (? [X2 : $i] : (((X0 @ X2)) != ((X1 @ X2))) & ! [X3 : $i] : (((X0 @ X3)) = ((X1 @ X3))))),
% 0.06/0.23 inference(rectify,[],[f5])).
% 0.06/0.23 thf(f7,plain,(
% 0.06/0.23 (((sK0 @ sK2)) != ((sK1 @ sK2))) & ! [X3 : $i] : (((sK0 @ X3)) = ((sK1 @ X3)))),
% 0.06/0.23 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f6])).
% 0.06/0.23 thf(f8,plain,(
% 0.06/0.23 ( ! [X3 : $i] : ((((sK0 @ X3)) = ((sK1 @ X3)))) )),
% 0.06/0.23 inference(cnf_transformation,[],[f7])).
% 0.06/0.23 thf(f9,plain,(
% 0.06/0.23 (((sK0 @ sK2)) != ((sK1 @ sK2)))),
% 0.06/0.23 inference(cnf_transformation,[],[f7])).
% 0.06/0.23 thf(f11,definition,(
% 0.06/0.23 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.06/0.23 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.06/0.23 thf(f12,plain,(
% 0.06/0.23 ( ! [X3 : $i] : ((((sK1 @ X3)) = $false) | (((sK0 @ X3)) = $true)) )),
% 0.06/0.23 inference(iff_proxy_clausification,[],[f8])).
% 0.06/0.23 thf(f13,plain,(
% 0.06/0.23 ( ! [X3 : $i] : ((((sK1 @ X3)) = $true) | (((sK0 @ X3)) = $false)) )),
% 0.06/0.23 inference(iff_proxy_clausification,[],[f8])).
% 0.06/0.23 thf(f14,plain,(
% 0.06/0.23 (((sK0 @ sK2)) = $true) | (((sK1 @ sK2)) = $true)),
% 0.06/0.23 inference(xor_proxy_clausification,[],[f9])).
% 0.06/0.23 thf(f15,plain,(
% 0.06/0.23 (((sK0 @ sK2)) = $false) | (((sK1 @ sK2)) = $false)),
% 0.06/0.23 inference(xor_proxy_clausification,[],[f9])).
% 0.06/0.23 thf(f17,definition,(
% 0.06/0.23 spl3_1 <=> (((sK1 @ sK2)) = $false)),
% 0.06/0.23 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.06/0.23 thf(f19,plain,(
% 0.06/0.23 (((sK1 @ sK2)) = $false) | ~spl3_1),
% 0.06/0.23 inference(avatar_component_clause,[],[f17])).
% 0.06/0.23 thf(f21,definition,(
% 0.06/0.23 spl3_2 <=> (((sK0 @ sK2)) = $false)),
% 0.06/0.23 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.06/0.23 thf(f23,plain,(
% 0.06/0.23 (((sK0 @ sK2)) = $false) | ~spl3_2),
% 0.06/0.23 inference(avatar_component_clause,[],[f21])).
% 0.06/0.23 thf(f24,plain,(
% 0.06/0.23 spl3_1 | spl3_2),
% 0.06/0.23 inference(avatar_split_clause,[],[f15,f21,f17])).
% 0.06/0.23 thf(f26,definition,(
% 0.06/0.23 spl3_3 <=> (((sK1 @ sK2)) = $true)),
% 0.06/0.23 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.06/0.23 thf(f27,plain,(
% 0.06/0.23 (((sK1 @ sK2)) != $true) | spl3_3),
% 0.06/0.23 inference(avatar_component_clause,[],[f26])).
% 0.06/0.23 thf(f28,plain,(
% 0.06/0.23 (((sK1 @ sK2)) = $true) | ~spl3_3),
% 0.06/0.23 inference(avatar_component_clause,[],[f26])).
% 0.06/0.23 thf(f30,definition,(
% 0.06/0.23 spl3_4 <=> (((sK0 @ sK2)) = $true)),
% 0.06/0.23 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.06/0.23 thf(f32,plain,(
% 0.06/0.23 (((sK0 @ sK2)) = $true) | ~spl3_4),
% 0.06/0.23 inference(avatar_component_clause,[],[f30])).
% 0.06/0.23 thf(f33,plain,(
% 0.06/0.23 spl3_3 | spl3_4),
% 0.06/0.23 inference(avatar_split_clause,[],[f14,f30,f26])).
% 0.06/0.23 thf(f45,plain,(
% 0.06/0.23 ($true = $false) | (((sK0 @ sK2)) = $true) | ~spl3_3),
% 0.06/0.23 inference(constrained_superposition,[],[f28,f12])).
% 0.06/0.23 thf(f46,plain,(
% 0.06/0.23 (((sK0 @ sK2)) = $true) | ~spl3_3),
% 0.06/0.23 inference(trivial_inequality_removal,[],[f45])).
% 0.06/0.23 thf(f49,plain,(
% 0.06/0.23 ($true = $false) | (~spl3_2 | ~spl3_3)),
% 0.06/0.23 inference(forward_demodulation,[],[f46,f23])).
% 0.06/0.23 thf(f50,plain,(
% 0.06/0.23 $false | (~spl3_2 | ~spl3_3)),
% 0.06/0.23 inference(trivial_inequality_removal,[],[f49])).
% 0.06/0.23 thf(f51,plain,(
% 0.06/0.23 ~spl3_2 | ~spl3_3),
% 0.06/0.23 inference(avatar_contradiction_clause,[],[f50])).
% 0.06/0.23 thf(f56,plain,(
% 0.06/0.23 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 0.06/0.23 inference(constrained_superposition,[],[f19,f28])).
% 0.06/0.23 thf(f62,plain,(
% 0.06/0.23 $false | (~spl3_1 | ~spl3_3)),
% 0.06/0.23 inference(trivial_inequality_removal,[],[f56])).
% 0.06/0.23 thf(f63,plain,(
% 0.06/0.23 ~spl3_1 | ~spl3_3),
% 0.06/0.23 inference(avatar_contradiction_clause,[],[f62])).
% 0.06/0.23 thf(f67,plain,(
% 0.06/0.23 ($true != $true) | (((sK1 @ sK2)) = $false) | spl3_3),
% 0.06/0.23 inference(constrained_superposition,[],[f27,f11])).
% 0.06/0.23 thf(f68,plain,(
% 0.06/0.23 (((sK1 @ sK2)) = $false) | spl3_3),
% 0.06/0.23 inference(trivial_inequality_removal,[],[f67])).
% 0.06/0.23 thf(f69,plain,(
% 0.06/0.23 spl3_1 | spl3_3),
% 0.06/0.23 inference(avatar_split_clause,[],[f68,f26,f17])).
% 0.06/0.23 thf(f73,plain,(
% 0.06/0.23 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 0.06/0.23 inference(constrained_superposition,[],[f32,f23])).
% 0.06/0.23 thf(f77,plain,(
% 0.06/0.23 $false | (~spl3_2 | ~spl3_4)),
% 0.06/0.23 inference(trivial_inequality_removal,[],[f73])).
% 0.06/0.23 thf(f78,plain,(
% 0.06/0.23 ~spl3_2 | ~spl3_4),
% 0.06/0.23 inference(avatar_contradiction_clause,[],[f77])).
% 0.06/0.23 thf(f83,plain,(
% 0.06/0.23 ($true = $false) | (((sK0 @ sK2)) = $false) | ~spl3_1),
% 0.06/0.23 inference(constrained_superposition,[],[f19,f13])).
% 0.06/0.23 thf(f86,plain,(
% 0.06/0.23 (((sK0 @ sK2)) = $false) | ~spl3_1),
% 0.06/0.23 inference(trivial_inequality_removal,[],[f83])).
% 0.06/0.23 thf(f91,plain,(
% 0.06/0.23 spl3_2 | ~spl3_1),
% 0.06/0.23 inference(avatar_split_clause,[],[f86,f17,f21])).
% 0.06/0.23 cnf(s1, plain, spl3_1 | spl3_2, inference(sat_conversion,[],[f24])).
% 0.06/0.23 cnf(s2, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f33])).
% 0.06/0.23 cnf(s3, plain, ~spl3_2 | ~spl3_3, inference(sat_conversion,[],[f51])).
% 0.06/0.23 cnf(s8, plain, ~spl3_1 | ~spl3_3, inference(sat_conversion,[],[f63])).
% 0.06/0.23 cnf(s9, plain, spl3_1 | spl3_3, inference(sat_conversion,[],[f69])).
% 0.06/0.23 cnf(s11, plain, ~spl3_2 | ~spl3_4, inference(sat_conversion,[],[f78])).
% 0.06/0.23 cnf(s13, plain, ~spl3_1 | spl3_2, inference(sat_conversion,[],[f91])).
% 0.06/0.23 cnf(s15, plain, spl3_1, inference(rat,[],[s3,s1,s9])).
% 0.06/0.23 cnf(s16, plain, spl3_2, inference(rat,[],[s13,s15])).
% 0.06/0.23 cnf(s17, plain, ~spl3_3, inference(rat,[],[s8,s15])).
% 0.06/0.23 cnf(s18, plain, ~spl3_4, inference(rat,[],[s11,s16])).
% 0.06/0.23 cnf(s19, plain, $false, inference(rat,[],[s2,s18,s17])).
% 0.06/0.23 thf(f92,plain,(
% 0.06/0.23 $false),
% 0.06/0.23 inference(avatar_sat_refutation,[],[s19])).
% 0.06/0.23 % SZS output end Proof for theBenchmark
% 0.06/0.23 % (1909058)------------------------------
% 0.06/0.23 % (1909058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.23 % (1909058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.23 % (1909058)CaDiCaL version: 2.1.3
% 0.06/0.23 % (1909058)Termination reason: Refutation
% 0.06/0.23 % (1909058)Time elapsed: 0.002 s
% 0.06/0.23 % (1909058)Peak memory usage: 12 MB
% 0.06/0.23 % (1909058)Instructions burned: 3 (million)
% 0.06/0.23 % (1909044)Success in time 0.017 s
% 0.06/0.23 % Vampire exiting
%------------------------------------------------------------------------------