%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO212^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:47:12 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO212^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n016.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 16:44:20 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (590320)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (590327)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=181344839:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (590327)Refutation not found, incomplete strategy
% 0.20/0.28 % (590327)------------------------------
% 0.20/0.28 % (590327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (590327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (590327)CaDiCaL version: 2.1.3
% 0.20/0.28 % (590327)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (590327)Time elapsed: 0.0000 s
% 0.20/0.28 % (590327)Peak memory usage: 12 MB
% 0.20/0.28 % (590327)------------------------------
% 0.20/0.28 % (590327)------------------------------
% 0.20/0.28 % (590325)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=94261701:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (590326)lrs+10_16_si=on:nwc=1.5:random_seed=682057381:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (590326)Refutation not found, incomplete strategy
% 0.20/0.28 % (590326)------------------------------
% 0.20/0.28 % (590326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (590325)Refutation not found, incomplete strategy
% 0.20/0.28 % (590325)------------------------------
% 0.20/0.28 % (590325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (590325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (590326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (590325)CaDiCaL version: 2.1.3
% 0.20/0.28 % (590326)CaDiCaL version: 2.1.3
% 0.20/0.28 % (590326)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (590326)Time elapsed: 0.001 s
% 0.20/0.28 % (590325)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (590325)Time elapsed: 0.001 s
% 0.20/0.28 % (590326)Peak memory usage: 11 MB
% 0.20/0.28 % (590325)Peak memory usage: 12 MB
% 0.20/0.28 % (590328)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=3498532557: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)
% 0.20/0.28 % (590325)------------------------------
% 0.20/0.28 % (590325)------------------------------
% 0.20/0.28 % (590326)------------------------------
% 0.20/0.28 % (590326)------------------------------
% 0.20/0.28 % (590333)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=465862064:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.28 % (590328) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-590320-590328"...
% 0.20/0.28 % (590333)Instruction limit reached!
% 0.20/0.28 % (590333)------------------------------
% 0.20/0.28 % (590333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (590333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (590333)CaDiCaL version: 2.1.3
% 0.20/0.28 % (590333)Termination reason: Instruction limit
% 0.20/0.28 % (590333)Termination phase: Saturation
% 0.20/0.28 % (590333)Time elapsed: 0.001 s
% 0.20/0.28 % (590333)Peak memory usage: 12 MB
% 0.20/0.28 % (590333)Instructions burned: 2 (million)
% 0.20/0.28 % (590328)...printing done.
% 0.20/0.28 % (590328)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_0, type, b: $o).
% 0.20/0.28 thf(func_def_1, type, a: $o).
% 0.20/0.28 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.20/0.28 thf(func_def_6, type, sK0: ($o > $o)).
% 0.20/0.28 thf(f1,conjecture,(
% 0.20/0.28 ! [X0 : ($o > $o)] : (((X0 @ b) & (X0 @ a)) => (X0 @ b & a))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEMB2)).
% 0.20/0.28 thf(f2,negated_conjecture,(
% 0.20/0.28 ~ ! [X0 : ($o > $o)] : (((X0 @ b) & (X0 @ a)) => (X0 @ b & a))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.28 thf(f3,plain,(
% 0.20/0.28 ~ ! [X0 : ($o > $o)] : (((X0 @ b) & (X0 @ a)) => (X0 @ b & a))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f4,plain,(
% 0.20/0.28 ~ ! [X0 : ($o > $o)] : (((((X0 @ b)) = $true) & (((X0 @ a)) = $true)) => (((X0 @ (a & b))) = $true))),
% 0.20/0.28 inference(fool_elimination,[],[f3])).
% 0.20/0.28 thf(f5,plain,(
% 0.20/0.28 ? [X0 : ($o > $o)] : ((((X0 @ (a & b))) != $true) & ((((X0 @ b)) = $true) & (((X0 @ a)) = $true)))),
% 0.20/0.28 inference(ennf_transformation,[],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ? [X0 : ($o > $o)] : ((((X0 @ a)) = $true) & (((X0 @ (a & b))) != $true) & (((X0 @ b)) = $true))),
% 0.20/0.28 inference(flattening,[],[f5])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 (((sK0 @ a)) = $true) & (((sK0 @ (a & b))) != $true) & (((sK0 @ b)) = $true)),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 (((sK0 @ b)) = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 (((sK0 @ (a & b))) != $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 (((sK0 @ a)) = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 thf(f13,definition,(
% 0.20/0.28 spl1_1 <=> (((sK0 @ a)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 (((sK0 @ a)) = $true) | ~spl1_1),
% 0.20/0.28 inference(avatar_component_clause,[],[f13])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 spl1_1),
% 0.20/0.28 inference(avatar_split_clause,[],[f10,f13])).
% 0.20/0.28 thf(f18,definition,(
% 0.20/0.28 spl1_2 <=> (((sK0 @ (a & b))) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 (((sK0 @ (a & b))) != $true) | spl1_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f18])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 ~spl1_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f9,f18])).
% 0.20/0.28 thf(f23,definition,(
% 0.20/0.28 spl1_3 <=> (((sK0 @ b)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 spl1_3),
% 0.20/0.28 inference(avatar_split_clause,[],[f8,f23])).
% 0.20/0.28 thf(f34,definition,(
% 0.20/0.28 spl1_5 <=> (a = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 0.20/0.28 thf(f36,plain,(
% 0.20/0.28 (a = $false) | ~spl1_5),
% 0.20/0.28 inference(avatar_component_clause,[],[f34])).
% 0.20/0.28 thf(f39,plain,(
% 0.20/0.28 (a = $false) | (((sK0 @ ($true & b))) != $true) | spl1_2),
% 0.20/0.28 inference(fool_paramodulation,[],[f20])).
% 0.20/0.28 thf(f44,plain,(
% 0.20/0.28 (((sK0 @ b)) != $true) | (a = $false) | spl1_2),
% 0.20/0.28 inference(boolean_simplification,[],[f39])).
% 0.20/0.28 thf(f52,plain,(
% 0.20/0.28 spl1_5 | ~spl1_3 | spl1_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f44,f18,f23,f34])).
% 0.20/0.28 thf(f56,plain,(
% 0.20/0.28 (((sK0 @ ($false & b))) != $true) | (spl1_2 | ~spl1_5)),
% 0.20/0.28 inference(superposition,[],[f20,f36])).
% 0.20/0.28 thf(f57,plain,(
% 0.20/0.28 (((sK0 @ $false)) = $true) | (~spl1_1 | ~spl1_5)),
% 0.20/0.28 inference(superposition,[],[f15,f36])).
% 0.20/0.28 thf(f58,plain,(
% 0.20/0.28 (((sK0 @ $false)) != $true) | (spl1_2 | ~spl1_5)),
% 0.20/0.28 inference(boolean_simplification,[],[f56])).
% 0.20/0.28 thf(f60,definition,(
% 0.20/0.28 spl1_7 <=> (((sK0 @ $false)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition])).
% 0.20/0.28 thf(f63,plain,(
% 0.20/0.28 spl1_7 | ~spl1_1 | ~spl1_5),
% 0.20/0.28 inference(avatar_split_clause,[],[f57,f34,f13,f60])).
% 0.20/0.28 thf(f64,plain,(
% 0.20/0.28 ~spl1_7 | spl1_2 | ~spl1_5),
% 0.20/0.28 inference(avatar_split_clause,[],[f58,f34,f18,f60])).
% 0.20/0.28 cnf(s1, plain, spl1_1, inference(sat_conversion,[],[f16])).
% 0.20/0.28 cnf(s2, plain, ~spl1_2, inference(sat_conversion,[],[f21])).
% 0.20/0.28 cnf(s3, plain, spl1_3, inference(sat_conversion,[],[f26])).
% 0.20/0.28 cnf(s7, plain, spl1_2 | ~spl1_3 | spl1_5, inference(sat_conversion,[],[f52])).
% 0.20/0.28 cnf(s10, plain, ~spl1_1 | ~spl1_5 | spl1_7, inference(sat_conversion,[],[f63])).
% 0.20/0.28 cnf(s11, plain, spl1_2 | ~spl1_5 | ~spl1_7, inference(sat_conversion,[],[f64])).
% 0.20/0.28 cnf(s12, plain, spl1_5, inference(rat,[],[s7,s3,s2])).
% 0.20/0.28 cnf(s13, plain, ~spl1_7, inference(rat,[],[s11,s2,s12])).
% 0.20/0.28 cnf(s14, plain, ~spl1_1, inference(rat,[],[s10,s13,s12])).
% 0.20/0.28 cnf(s15, plain, $false, inference(rat,[],[s1,s14])).
% 0.20/0.28 thf(f65,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(avatar_sat_refutation,[],[s15])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (590328)------------------------------
% 0.20/0.28 % (590328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (590328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (590328)CaDiCaL version: 2.1.3
% 0.20/0.28 % (590328)Termination reason: Refutation
% 0.20/0.28 % (590328)Time elapsed: 0.003 s
% 0.20/0.28 % (590328)Peak memory usage: 13 MB
% 0.20/0.28 % (590328)Instructions burned: 2 (million)
% 0.20/0.28 % (590320)Success in time 0.039 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------