%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO043^1 : 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 : n010.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 08:46:21 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.26s
% Output : Refutation 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO043^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n010.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:24:48 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 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
% 0.09/0.26 % (3079314)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (3079321)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4074979888:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.26 % (3079321)Refutation not found, incomplete strategy
% 0.09/0.26 % (3079321)------------------------------
% 0.09/0.26 % (3079321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3079321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3079321)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3079321)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.26 % (3079321)Time elapsed: 0.001 s
% 0.09/0.26 % (3079321)Peak memory usage: 12 MB
% 0.09/0.26 % (3079321)------------------------------
% 0.09/0.26 % (3079321)------------------------------
% 0.09/0.26 % (3079320)lrs+10_16_si=on:nwc=1.5:random_seed=1857791459:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.26 % (3079319)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=234106114:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.26 % (3079322)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=2499026316: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)
% 0.09/0.26 % (3079319)Refutation not found, incomplete strategy
% 0.09/0.26 % (3079319)------------------------------
% 0.09/0.26 % (3079319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3079319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3079320)Refutation not found, incomplete strategy
% 0.09/0.26 % (3079320)------------------------------
% 0.09/0.26 % (3079320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3079320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3079319)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3079319)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.26 % (3079319)Time elapsed: 0.001 s
% 0.09/0.26 % (3079320)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3079319)Peak memory usage: 12 MB
% 0.09/0.26 % (3079320)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.26 % (3079320)Time elapsed: 0.001 s
% 0.09/0.26 % (3079319)Instructions burned: 1 (million)
% 0.09/0.26 % (3079320)Peak memory usage: 12 MB
% 0.09/0.26 % (3079320)Instructions burned: 1 (million)
% 0.09/0.26 % (3079320)------------------------------
% 0.09/0.26 % (3079320)------------------------------
% 0.09/0.26 % (3079319)------------------------------
% 0.09/0.26 % (3079319)------------------------------
% 0.09/0.26 % (3079323)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1827569605:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.26 % (3079322) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3079314-3079322"...
% 0.09/0.26 % (3079327)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3852394124:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.09/0.26 % (3079323)Refutation not found, incomplete strategy
% 0.09/0.26 % (3079323)------------------------------
% 0.09/0.26 % (3079323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3079323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3079323)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3079323)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.26 % (3079323)Time elapsed: 0.001 s
% 0.09/0.26 % (3079323)Peak memory usage: 12 MB
% 0.09/0.26 % (3079323)Instructions burned: 1 (million)
% 0.09/0.26 % (3079322)...printing done.
% 0.09/0.26 % (3079323)------------------------------
% 0.09/0.26 % (3079323)------------------------------
% 0.09/0.26 % (3079327)Instruction limit reached!
% 0.09/0.26 % (3079327)------------------------------
% 0.09/0.26 % (3079327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3079327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3079327)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3079327)Termination reason: Instruction limit
% 0.09/0.26 % (3079327)Termination phase: Saturation
% 0.09/0.26 % (3079327)Time elapsed: 0.002 s
% 0.09/0.26 % (3079327)Peak memory usage: 12 MB
% 0.09/0.26 % (3079327)Instructions burned: 6 (million)
% 0.09/0.26 % (3079322)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% 0.09/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.26 thf(func_def_0, type, f: ($o > $o)).
% 0.09/0.26 thf(func_def_1, type, q: (($o > $o) > $o > $o)).
% 0.09/0.26 thf(func_def_2, type, x: $o).
% 0.09/0.26 thf(f1,axiom,(
% 0.09/0.26 (((f @ (q @ f @ x))) != ((f @ x))) & (q @ f @ x) & (f @ (f @ x))),
% 0.09/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',5)).
% 0.09/0.26 thf(f2,plain,(
% 0.09/0.26 (((f @ (q @ f @ x))) != ((f @ x))) & (q @ f @ x) & (f @ (f @ x))),
% 0.09/0.26 inference(rectify,[],[f1])).
% 0.09/0.26 thf(f3,plain,(
% 0.09/0.26 (((f @ x)) != ((f @ (q @ f @ x)))) & (((q @ f @ x)) = $true) & (((f @ (f @ x))) = $true)),
% 0.09/0.26 inference(fool_elimination,[],[f2])).
% 0.09/0.26 thf(f4,plain,(
% 0.09/0.26 (((f @ (f @ x))) = $true)),
% 0.09/0.26 inference(cnf_transformation,[],[f3])).
% 0.09/0.26 thf(f5,plain,(
% 0.09/0.26 (((q @ f @ x)) = $true)),
% 0.09/0.26 inference(cnf_transformation,[],[f3])).
% 0.09/0.26 thf(f6,plain,(
% 0.09/0.26 (((f @ x)) != ((f @ (q @ f @ x))))),
% 0.09/0.26 inference(cnf_transformation,[],[f3])).
% 0.09/0.26 thf(f8,plain,(
% 0.09/0.26 (((f @ (q @ f @ x))) = $true) | (((f @ x)) = $true)),
% 0.09/0.26 inference(xor_proxy_clausification,[],[f6])).
% 0.09/0.26 thf(f9,plain,(
% 0.09/0.26 (((f @ x)) = $false) | (((f @ (q @ f @ x))) = $false)),
% 0.09/0.26 inference(xor_proxy_clausification,[],[f6])).
% 0.09/0.26 thf(f11,definition,(
% 0.09/0.26 spl0_1 <=> (((q @ f @ x)) = $true)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.09/0.26 thf(f13,plain,(
% 0.09/0.26 (((q @ f @ x)) = $true) | ~spl0_1),
% 0.09/0.26 inference(avatar_component_clause,[],[f11])).
% 0.09/0.26 thf(f14,plain,(
% 0.09/0.26 spl0_1),
% 0.09/0.26 inference(avatar_split_clause,[],[f5,f11])).
% 0.09/0.26 thf(f16,definition,(
% 0.09/0.26 spl0_2 <=> (((f @ x)) = $false)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.09/0.26 thf(f18,plain,(
% 0.09/0.26 (((f @ x)) = $false) | ~spl0_2),
% 0.09/0.26 inference(avatar_component_clause,[],[f16])).
% 0.09/0.26 thf(f20,definition,(
% 0.09/0.26 spl0_3 <=> (((f @ (q @ f @ x))) = $false)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.09/0.26 thf(f23,plain,(
% 0.09/0.26 spl0_2 | spl0_3),
% 0.09/0.26 inference(avatar_split_clause,[],[f9,f20,f16])).
% 0.09/0.26 thf(f25,definition,(
% 0.09/0.26 spl0_4 <=> (((f @ x)) = $true)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.09/0.26 thf(f27,plain,(
% 0.09/0.26 (((f @ x)) = $true) | ~spl0_4),
% 0.09/0.26 inference(avatar_component_clause,[],[f25])).
% 0.09/0.26 thf(f29,definition,(
% 0.09/0.26 spl0_5 <=> (((f @ (q @ f @ x))) = $true)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.09/0.26 thf(f31,plain,(
% 0.09/0.26 (((f @ (q @ f @ x))) = $true) | ~spl0_5),
% 0.09/0.26 inference(avatar_component_clause,[],[f29])).
% 0.09/0.26 thf(f32,plain,(
% 0.09/0.26 spl0_4 | spl0_5),
% 0.09/0.26 inference(avatar_split_clause,[],[f8,f29,f25])).
% 0.09/0.26 thf(f34,definition,(
% 0.09/0.26 spl0_6 <=> (((f @ (f @ x))) = $true)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.09/0.26 thf(f36,plain,(
% 0.09/0.26 (((f @ (f @ x))) = $true) | ~spl0_6),
% 0.09/0.26 inference(avatar_component_clause,[],[f34])).
% 0.09/0.26 thf(f37,plain,(
% 0.09/0.26 spl0_6),
% 0.09/0.26 inference(avatar_split_clause,[],[f4,f34])).
% 0.09/0.26 thf(f39,plain,(
% 0.09/0.26 (((f @ $true)) = $true) | (((f @ x)) = $false) | ~spl0_6),
% 0.09/0.26 inference(fool_paramodulation,[],[f36])).
% 0.09/0.26 thf(f42,definition,(
% 0.09/0.26 spl0_7 <=> (x = $false)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.09/0.26 thf(f51,definition,(
% 0.09/0.26 spl0_9 <=> (((f @ $true)) = $true)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 0.09/0.26 thf(f53,plain,(
% 0.09/0.26 (((f @ $true)) = $true) | ~spl0_9),
% 0.09/0.26 inference(avatar_component_clause,[],[f51])).
% 0.09/0.26 thf(f54,plain,(
% 0.09/0.26 spl0_9 | spl0_2 | ~spl0_6),
% 0.09/0.26 inference(avatar_split_clause,[],[f39,f34,f16,f51])).
% 0.09/0.26 thf(f77,plain,(
% 0.09/0.26 (x = $false) | (((f @ $true)) = $false) | ~spl0_2),
% 0.09/0.26 inference(fool_paramodulation,[],[f18])).
% 0.09/0.26 thf(f80,definition,(
% 0.09/0.26 spl0_13 <=> (((f @ $true)) = $false)),
% 0.09/0.26 introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])).
% 0.09/0.26 thf(f82,plain,(
% 0.09/0.26 (((f @ $true)) = $false) | ~spl0_13),
% 0.09/0.26 inference(avatar_component_clause,[],[f80])).
% 0.09/0.26 thf(f83,plain,(
% 0.09/0.26 spl0_7 | spl0_13 | ~spl0_2),
% 0.09/0.26 inference(avatar_split_clause,[],[f77,f16,f80,f42])).
% 0.09/0.26 thf(f97,plain,(
% 0.09/0.26 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.09/0.26 inference(forward_demodulation,[],[f27,f18])).
% 0.09/0.26 thf(f98,plain,(
% 0.09/0.26 $false | (~spl0_2 | ~spl0_4)),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f97])).
% 0.09/0.26 thf(f99,plain,(
% 0.09/0.26 ~spl0_2 | ~spl0_4),
% 0.09/0.26 inference(avatar_contradiction_clause,[],[f98])).
% 0.09/0.26 thf(f101,plain,(
% 0.09/0.26 (((f @ $true)) = $true) | (~spl0_1 | ~spl0_5)),
% 0.09/0.26 inference(forward_demodulation,[],[f31,f13])).
% 0.09/0.26 thf(f102,plain,(
% 0.09/0.26 spl0_9 | ~spl0_1 | ~spl0_5),
% 0.09/0.26 inference(avatar_split_clause,[],[f101,f29,f11,f51])).
% 0.09/0.26 thf(f104,plain,(
% 0.09/0.26 ($true = $false) | (~spl0_9 | ~spl0_13)),
% 0.09/0.26 inference(superposition,[],[f82,f53])).
% 0.09/0.26 thf(f105,plain,(
% 0.09/0.26 ($true = $false) | (~spl0_9 | ~spl0_13)),
% 0.09/0.26 inference(superposition,[],[f53,f82])).
% 0.09/0.26 thf(f106,plain,(
% 0.09/0.26 $false | (~spl0_9 | ~spl0_13)),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f105])).
% 0.09/0.26 thf(f107,plain,(
% 0.09/0.26 ~spl0_9 | ~spl0_13),
% 0.09/0.26 inference(avatar_contradiction_clause,[],[f106])).
% 0.09/0.26 thf(f108,plain,(
% 0.09/0.26 $false | (~spl0_9 | ~spl0_13)),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f104])).
% 0.09/0.26 thf(f109,plain,(
% 0.09/0.26 ~spl0_9 | ~spl0_13),
% 0.09/0.26 inference(avatar_contradiction_clause,[],[f108])).
% 0.09/0.26 thf(f110,definition,(
% 0.09/0.26 (((q @ f @ x)) != $true) | (((f @ (q @ f @ x))) != $false) | (((f @ $true)) = $false)),
% 0.09/0.26 introduced(theory,[theory_tautology_sat_conflict])).
% 0.09/0.26 thf(f112,definition,(
% 0.09/0.26 (((f @ x)) != $false) | (x != $false) | (((f @ (f @ x))) != $true) | (((f @ x)) = $true)),
% 0.09/0.26 introduced(theory,[theory_tautology_sat_conflict])).
% 0.09/0.26 cnf(s1, plain, spl0_1, inference(sat_conversion,[],[f14])).
% 0.09/0.26 cnf(s2, plain, spl0_2 | spl0_3, inference(sat_conversion,[],[f23])).
% 0.09/0.26 cnf(s3, plain, spl0_4 | spl0_5, inference(sat_conversion,[],[f32])).
% 0.09/0.26 cnf(s4, plain, spl0_6, inference(sat_conversion,[],[f37])).
% 0.09/0.26 cnf(s6, plain, spl0_2 | ~spl0_6 | spl0_9, inference(sat_conversion,[],[f54])).
% 0.09/0.26 cnf(s13, plain, ~spl0_2 | spl0_7 | spl0_13, inference(sat_conversion,[],[f83])).
% 0.09/0.26 cnf(s18, plain, ~spl0_2 | ~spl0_4, inference(sat_conversion,[],[f99])).
% 0.09/0.26 cnf(s20, plain, ~spl0_1 | ~spl0_5 | spl0_9, inference(sat_conversion,[],[f102])).
% 0.09/0.26 cnf(s21, plain, ~spl0_9 | ~spl0_13, inference(sat_conversion,[],[f107])).
% 0.09/0.26 cnf(s22, plain, ~spl0_9 | ~spl0_13, inference(sat_conversion,[],[f109])).
% 0.38/0.26 cnf(s23, plain, ~spl0_1 | ~spl0_3 | spl0_13, inference(sat_conversion,[],[f110])).
% 0.38/0.26 cnf(s25, plain, ~spl0_2 | spl0_4 | ~spl0_6 | ~spl0_7, inference(sat_conversion,[],[f112])).
% 0.38/0.26 cnf(s27, plain, spl0_2, inference(rat,[],[s23,s22,s2,s6,s1,s4])).
% 0.38/0.26 cnf(s28, plain, ~spl0_4, inference(rat,[],[s18,s27])).
% 0.38/0.26 cnf(s30, plain, ~spl0_7, inference(rat,[],[s25,s27,s4,s28])).
% 0.38/0.26 cnf(s31, plain, spl0_5, inference(rat,[],[s3,s28])).
% 0.38/0.26 cnf(s32, plain, spl0_13, inference(rat,[],[s13,s27,s30])).
% 0.38/0.26 cnf(s35, plain, spl0_9, inference(rat,[],[s20,s1,s31])).
% 0.38/0.26 cnf(s36, plain, $false, inference(rat,[],[s21,s32,s35])).
% 0.38/0.26 thf(f114,plain,(
% 0.38/0.26 $false),
% 0.38/0.26 inference(avatar_sat_refutation,[],[s36])).
% 0.38/0.26 % SZS output end Proof for theBenchmark
% 0.38/0.26 % (3079322)------------------------------
% 0.38/0.26 % (3079322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.26 % (3079322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.26 % (3079322)CaDiCaL version: 2.1.3
% 0.38/0.27 % (3079322)Termination reason: Refutation
% 0.38/0.27 % (3079322)Time elapsed: 0.004 s
% 0.38/0.27 % (3079322)Peak memory usage: 13 MB
% 0.38/0.27 % (3079322)Instructions burned: 4 (million)
% 0.38/0.27 % (3079314)Success in time 0.044 s
% 0.38/0.27 % Vampire exiting
%------------------------------------------------------------------------------