%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN983^1 : TPTP v9.3.1. Released v3.6.0.
% 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 08:41:45 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN983^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 % Computer : n011.cluster.edu
% 0.12/0.19 % Model : x86_64 x86_64
% 0.12/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.19 % Memory : 8046.5625MB
% 0.12/0.19 % OS : Linux 6.8.0-71-generic
% 0.12/0.19 % CPULimit : 300
% 0.12/0.19 % WCLimit : 300
% 0.12/0.19 % DateTime : Tue Sep 29 16:19:46 UTC 2026
% 0.12/0.19 % CPUTime :
% 0.12/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.22 Running higher-order theorem proving
% 0.12/0.24 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
% 0.22/0.28 % (283985)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (284006)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=1153354677: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)
% 0.22/0.28 % (284006) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-283985-284006"...
% 0.22/0.28 % (284006)...printing done.
% 0.22/0.28 % (284006)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% 0.22/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.28 thf(func_def_0, type, a: $o).
% 0.22/0.28 thf(func_def_1, type, b: $o).
% 0.22/0.28 thf(func_def_2, type, p: ($o > $o)).
% 0.22/0.28 thf(func_def_6, type, vAND: ($o > $o > $o)).
% 0.22/0.28 thf(f1,conjecture,(
% 0.22/0.28 ((p @ a) & (p @ b)) => (p @ b & a)),
% 0.22/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.22/0.28 thf(f2,negated_conjecture,(
% 0.22/0.28 ~(((p @ a) & (p @ b)) => (p @ b & a))),
% 0.22/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.28 thf(f3,plain,(
% 0.22/0.28 ~(((p @ a) & (p @ b)) => (p @ b & a))),
% 0.22/0.28 inference(rectify,[],[f2])).
% 0.22/0.28 thf(f4,plain,(
% 0.22/0.28 ~(((((p @ b)) = $true) & (((p @ a)) = $true)) => ($true = ((p @ (a & b)))))),
% 0.22/0.28 inference(fool_elimination,[],[f3])).
% 0.22/0.28 thf(f5,plain,(
% 0.22/0.28 ($true != ((p @ (a & b)))) & ((((p @ b)) = $true) & (((p @ a)) = $true))),
% 0.22/0.28 inference(ennf_transformation,[],[f4])).
% 0.22/0.28 thf(f6,plain,(
% 0.22/0.28 (((p @ a)) = $true) & (((p @ b)) = $true) & ($true != ((p @ (a & b))))),
% 0.22/0.28 inference(flattening,[],[f5])).
% 0.22/0.28 thf(f7,plain,(
% 0.22/0.28 ($true != ((p @ (a & b))))),
% 0.22/0.28 inference(cnf_transformation,[],[f6])).
% 0.22/0.28 thf(f8,plain,(
% 0.22/0.28 (((p @ b)) = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f6])).
% 0.22/0.28 thf(f9,plain,(
% 0.22/0.28 (((p @ a)) = $true)),
% 0.22/0.28 inference(cnf_transformation,[],[f6])).
% 0.22/0.28 thf(f12,definition,(
% 0.22/0.28 spl0_1 <=> (((p @ a)) = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.22/0.28 thf(f14,plain,(
% 0.22/0.28 (((p @ a)) = $true) | ~spl0_1),
% 0.22/0.28 inference(avatar_component_clause,[],[f12])).
% 0.22/0.28 thf(f15,plain,(
% 0.22/0.28 spl0_1),
% 0.22/0.28 inference(avatar_split_clause,[],[f9,f12])).
% 0.22/0.28 thf(f17,definition,(
% 0.22/0.28 spl0_2 <=> ($true = ((p @ (a & b))))),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.22/0.28 thf(f19,plain,(
% 0.22/0.28 ($true != ((p @ (a & b)))) | spl0_2),
% 0.22/0.28 inference(avatar_component_clause,[],[f17])).
% 0.22/0.28 thf(f20,plain,(
% 0.22/0.28 ~spl0_2),
% 0.22/0.28 inference(avatar_split_clause,[],[f7,f17])).
% 0.22/0.28 thf(f22,definition,(
% 0.22/0.28 spl0_3 <=> (((p @ b)) = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.22/0.28 thf(f24,plain,(
% 0.22/0.28 (((p @ b)) = $true) | ~spl0_3),
% 0.22/0.28 inference(avatar_component_clause,[],[f22])).
% 0.22/0.28 thf(f25,plain,(
% 0.22/0.28 spl0_3),
% 0.22/0.28 inference(avatar_split_clause,[],[f8,f22])).
% 0.22/0.28 thf(f33,definition,(
% 0.22/0.28 spl0_5 <=> (a = $false)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.22/0.28 thf(f35,plain,(
% 0.22/0.28 (a = $false) | ~spl0_5),
% 0.22/0.28 inference(avatar_component_clause,[],[f33])).
% 0.22/0.28 thf(f46,plain,(
% 0.22/0.28 (a = $false) | ($true != ((p @ ($true & b)))) | spl0_2),
% 0.22/0.28 inference(fool_paramodulation,[],[f19])).
% 0.22/0.28 thf(f50,plain,(
% 0.22/0.28 (a = $false) | (((p @ b)) != $true) | spl0_2),
% 0.22/0.28 inference(boolean_simplification,[],[f46])).
% 0.22/0.28 thf(f54,plain,(
% 0.22/0.28 (a = $false) | (spl0_2 | ~spl0_3)),
% 0.22/0.28 inference(forward_subsumption_resolution,[],[f50,f24])).
% 0.22/0.28 thf(f58,plain,(
% 0.22/0.28 spl0_5 | spl0_2 | ~spl0_3),
% 0.22/0.28 inference(avatar_split_clause,[],[f54,f22,f17,f33])).
% 0.22/0.28 thf(f60,plain,(
% 0.22/0.28 ($true != ((p @ ($false & b)))) | (spl0_2 | ~spl0_5)),
% 0.22/0.28 inference(superposition,[],[f19,f35])).
% 0.22/0.28 thf(f61,plain,(
% 0.22/0.28 (((p @ $false)) = $true) | (~spl0_1 | ~spl0_5)),
% 0.22/0.28 inference(superposition,[],[f14,f35])).
% 0.22/0.28 thf(f62,plain,(
% 0.22/0.28 (((p @ $false)) != $true) | (spl0_2 | ~spl0_5)),
% 0.22/0.28 inference(boolean_simplification,[],[f60])).
% 0.22/0.28 thf(f64,definition,(
% 0.22/0.28 spl0_7 <=> (((p @ $false)) = $true)),
% 0.22/0.28 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.22/0.28 thf(f67,plain,(
% 0.22/0.28 ~spl0_7 | spl0_2 | ~spl0_5),
% 0.22/0.28 inference(avatar_split_clause,[],[f62,f33,f17,f64])).
% 0.22/0.28 thf(f68,plain,(
% 0.22/0.28 spl0_7 | ~spl0_1 | ~spl0_5),
% 0.22/0.28 inference(avatar_split_clause,[],[f61,f33,f12,f64])).
% 0.22/0.28 cnf(s1, plain, spl0_1, inference(sat_conversion,[],[f15])).
% 0.22/0.28 cnf(s2, plain, ~spl0_2, inference(sat_conversion,[],[f20])).
% 0.22/0.28 cnf(s3, plain, spl0_3, inference(sat_conversion,[],[f25])).
% 0.22/0.28 cnf(s9, plain, spl0_2 | ~spl0_3 | spl0_5, inference(sat_conversion,[],[f58])).
% 0.22/0.28 cnf(s12, plain, spl0_2 | ~spl0_5 | ~spl0_7, inference(sat_conversion,[],[f67])).
% 0.22/0.28 cnf(s13, plain, ~spl0_1 | ~spl0_5 | spl0_7, inference(sat_conversion,[],[f68])).
% 0.22/0.28 cnf(s14, plain, spl0_5, inference(rat,[],[s9,s3,s2])).
% 0.22/0.28 cnf(s15, plain, ~spl0_7, inference(rat,[],[s12,s2,s14])).
% 0.22/0.28 cnf(s16, plain, ~spl0_1, inference(rat,[],[s13,s14,s15])).
% 0.22/0.28 cnf(s17, plain, $false, inference(rat,[],[s1,s16])).
% 0.22/0.28 thf(f69,plain,(
% 0.22/0.28 $false),
% 0.22/0.28 inference(avatar_sat_refutation,[],[s17])).
% 0.22/0.28 % SZS output end Proof for theBenchmark
% 0.22/0.28 % (284006)------------------------------
% 0.22/0.28 % (284006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (284006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (284006)CaDiCaL version: 2.1.3
% 0.22/0.28 % (284006)Termination reason: Refutation
% 0.22/0.28 % (284006)Time elapsed: 0.002 s
% 0.22/0.28 % (284006)Peak memory usage: 12 MB
% 0.22/0.28 % (284006)Instructions burned: 2 (million)
% 0.22/0.28 % (283985)Success in time 0.035 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------