%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO041^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 0.24s 0.37s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO041^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n020.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 16:25:04 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 Running higher-order theorem proving
% 0.24/0.30 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
% 0.24/0.37 % (1249391)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.37 % (1249397)lrs+10_16_si=on:nwc=1.5:random_seed=1818856334:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.37 % (1249397)Refutation not found, incomplete strategy
% 0.24/0.37 % (1249397)------------------------------
% 0.24/0.37 % (1249397)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (1249397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (1249397)CaDiCaL version: 2.1.3
% 0.24/0.37 % (1249397)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (1249397)Time elapsed: 0.002 s
% 0.24/0.37 % (1249397)Peak memory usage: 12 MB
% 0.24/0.37 % (1249397)Instructions burned: 2 (million)
% 0.24/0.37 % (1249397)------------------------------
% 0.24/0.37 % (1249397)------------------------------
% 0.24/0.37 % (1249402)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.37 % (1249402)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.24/0.37 % (1249396)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2365017250:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.37 % (1249398)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2487020022:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.37 % (1249399)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=2449149078: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)
% 0.24/0.37 % (1249400)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3524005436:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.37 % (1249401)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3153182358:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.37 % (1249398)Refutation not found, incomplete strategy
% 0.24/0.37 % (1249398)------------------------------
% 0.24/0.37 % (1249398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (1249398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (1249398)CaDiCaL version: 2.1.3
% 0.24/0.37 % (1249398)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (1249398)Time elapsed: 0.002 s
% 0.24/0.37 % (1249398)Peak memory usage: 12 MB
% 0.24/0.37 % (1249396)Refutation not found, incomplete strategy
% 0.24/0.37 % (1249396)------------------------------
% 0.24/0.37 % (1249396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (1249396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (1249396)CaDiCaL version: 2.1.3
% 0.24/0.37 % (1249396)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (1249396)Time elapsed: 0.003 s
% 0.24/0.37 % (1249396)Peak memory usage: 12 MB
% 0.24/0.37 % (1249396)Instructions burned: 1 (million)
% 0.24/0.37 % (1249398)------------------------------
% 0.24/0.37 % (1249398)------------------------------
% 0.24/0.37 % (1249396)------------------------------
% 0.24/0.37 % (1249396)------------------------------
% 0.24/0.37 % (1249402)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=926349536:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.37 % (1249400)Refutation not found, incomplete strategy
% 0.24/0.37 % (1249400)------------------------------
% 0.24/0.37 % (1249400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (1249400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (1249400)CaDiCaL version: 2.1.3
% 0.24/0.37 % (1249400)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (1249400)Time elapsed: 0.004 s
% 0.24/0.37 % (1249400)Peak memory usage: 12 MB
% 0.24/0.37 % (1249400)Instructions burned: 4 (million)
% 0.24/0.37 % (1249400)------------------------------
% 0.24/0.37 % (1249400)------------------------------
% 0.24/0.37 % (1249404)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2848467107:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.37 % (1249404)Instruction limit reached!
% 0.24/0.37 % (1249404)------------------------------
% 0.24/0.37 % (1249404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (1249399) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1249391-1249399"...
% 0.24/0.37 % (1249404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (1249404)CaDiCaL version: 2.1.3
% 0.24/0.37 % (1249404)Termination reason: Instruction limit
% 0.24/0.37 % (1249404)Termination phase: Saturation
% 0.24/0.37 % (1249404)Time elapsed: 0.001 s
% 0.24/0.37 % (1249404)Peak memory usage: 12 MB
% 0.24/0.37 % (1249404)Instructions burned: 2 (million)
% 0.24/0.37 % (1249401) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1249391-1249401"...
% 0.24/0.37 % (1249399)...printing done.
% 0.24/0.37 % (1249399)Refutation found. Thanks to Tanya!
% 0.24/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.24/0.37 % SZS output start Proof for theBenchmark
% 0.24/0.37 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.24/0.37 thf(func_def_0, type, a: $o).
% 0.24/0.37 thf(func_def_1, type, f: ($o > $o)).
% 0.24/0.37 thf(func_def_2, type, g: ($o > $o)).
% 0.24/0.37 thf(func_def_3, type, x: $o).
% 0.24/0.37 thf(func_def_4, type, y: $o).
% 0.24/0.37 thf(f1,axiom,(
% 0.24/0.37 (((g @ x)) = y) & (x != y) & (((f @ (f @ (f @ x)))) = ((g @ (f @ x)))) & (((g @ y)) = x)),
% 0.24/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',3)).
% 0.24/0.37 thf(f2,plain,(
% 0.24/0.37 (x = ((g @ y)))),
% 0.24/0.37 inference(cnf_transformation,[],[f1])).
% 0.24/0.37 thf(f3,plain,(
% 0.24/0.37 (((f @ (f @ (f @ x)))) = ((g @ (f @ x))))),
% 0.24/0.37 inference(cnf_transformation,[],[f1])).
% 0.24/0.37 thf(f4,plain,(
% 0.24/0.37 (x != y)),
% 0.24/0.37 inference(cnf_transformation,[],[f1])).
% 0.24/0.37 thf(f5,plain,(
% 0.24/0.37 (y = ((g @ x)))),
% 0.24/0.37 inference(cnf_transformation,[],[f1])).
% 0.24/0.37 thf(f7,plain,(
% 0.24/0.37 (y = $true) | (((g @ x)) = $false)),
% 0.24/0.37 inference(iff_proxy_clausification,[],[f5])).
% 0.24/0.37 thf(f8,plain,(
% 0.24/0.37 (y = $false) | (((g @ x)) = $true)),
% 0.24/0.37 inference(iff_proxy_clausification,[],[f5])).
% 0.24/0.37 thf(f9,plain,(
% 0.24/0.37 (x = $true) | (y = $true)),
% 0.24/0.37 inference(xor_proxy_clausification,[],[f4])).
% 0.24/0.37 thf(f10,plain,(
% 0.24/0.37 (x = $false) | (y = $false)),
% 0.24/0.37 inference(xor_proxy_clausification,[],[f4])).
% 0.24/0.37 thf(f11,plain,(
% 0.24/0.37 (((g @ y)) = $false) | (x = $true)),
% 0.24/0.37 inference(iff_proxy_clausification,[],[f2])).
% 0.24/0.37 thf(f12,plain,(
% 0.24/0.37 (x = $false) | (((g @ y)) = $true)),
% 0.24/0.37 inference(iff_proxy_clausification,[],[f2])).
% 0.24/0.37 thf(f13,plain,(
% 0.24/0.37 (((g @ (f @ x))) = $false) | (((f @ (f @ (f @ x)))) = $true)),
% 0.24/0.37 inference(iff_proxy_clausification,[],[f3])).
% 0.24/0.37 thf(f14,plain,(
% 0.24/0.37 (((f @ (f @ (f @ x)))) = $false) | (((g @ (f @ x))) = $true)),
% 0.24/0.37 inference(iff_proxy_clausification,[],[f3])).
% 0.24/0.37 thf(f16,definition,(
% 0.24/0.37 spl0_1 <=> (y = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.24/0.37 thf(f18,plain,(
% 0.24/0.37 (y = $false) | ~spl0_1),
% 0.24/0.37 inference(avatar_component_clause,[],[f16])).
% 0.24/0.37 thf(f20,definition,(
% 0.24/0.37 spl0_2 <=> (((g @ x)) = $true)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.24/0.37 thf(f23,plain,(
% 0.24/0.37 spl0_1 | spl0_2),
% 0.24/0.37 inference(avatar_split_clause,[],[f8,f20,f16])).
% 0.24/0.37 thf(f25,definition,(
% 0.24/0.37 spl0_3 <=> (y = $true)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.24/0.37 thf(f26,plain,(
% 0.24/0.37 (y != $true) | spl0_3),
% 0.24/0.37 inference(avatar_component_clause,[],[f25])).
% 0.24/0.37 thf(f27,plain,(
% 0.24/0.37 (y = $true) | ~spl0_3),
% 0.24/0.37 inference(avatar_component_clause,[],[f25])).
% 0.24/0.37 thf(f29,definition,(
% 0.24/0.37 spl0_4 <=> (((g @ x)) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.24/0.37 thf(f32,plain,(
% 0.24/0.37 spl0_3 | spl0_4),
% 0.24/0.37 inference(avatar_split_clause,[],[f7,f29,f25])).
% 0.24/0.37 thf(f34,definition,(
% 0.24/0.37 spl0_5 <=> (x = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition])).
% 0.24/0.37 thf(f36,plain,(
% 0.24/0.37 (x = $false) | ~spl0_5),
% 0.24/0.37 inference(avatar_component_clause,[],[f34])).
% 0.24/0.37 thf(f37,plain,(
% 0.24/0.37 spl0_5 | spl0_1),
% 0.24/0.37 inference(avatar_split_clause,[],[f10,f16,f34])).
% 0.24/0.37 thf(f39,definition,(
% 0.24/0.37 spl0_6 <=> (x = $true)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
% 0.24/0.37 thf(f41,plain,(
% 0.24/0.37 (x = $true) | ~spl0_6),
% 0.24/0.37 inference(avatar_component_clause,[],[f39])).
% 0.24/0.37 thf(f42,plain,(
% 0.24/0.37 spl0_3 | spl0_6),
% 0.24/0.37 inference(avatar_split_clause,[],[f9,f39,f25])).
% 0.24/0.37 thf(f44,definition,(
% 0.24/0.37 spl0_7 <=> (((g @ y)) = $true)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition])).
% 0.24/0.37 thf(f47,plain,(
% 0.24/0.37 spl0_5 | spl0_7),
% 0.24/0.37 inference(avatar_split_clause,[],[f12,f44,f34])).
% 0.24/0.37 thf(f49,definition,(
% 0.24/0.37 spl0_8 <=> (((g @ y)) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])).
% 0.24/0.37 thf(f51,plain,(
% 0.24/0.37 (((g @ y)) = $false) | ~spl0_8),
% 0.24/0.37 inference(avatar_component_clause,[],[f49])).
% 0.24/0.37 thf(f52,plain,(
% 0.24/0.37 spl0_8 | spl0_6),
% 0.24/0.37 inference(avatar_split_clause,[],[f11,f39,f49])).
% 0.24/0.37 thf(f54,definition,(
% 0.24/0.37 spl0_9 <=> (((f @ (f @ (f @ x)))) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition])).
% 0.24/0.37 thf(f56,plain,(
% 0.24/0.37 (((f @ (f @ (f @ x)))) = $false) | ~spl0_9),
% 0.24/0.37 inference(avatar_component_clause,[],[f54])).
% 0.24/0.37 thf(f58,definition,(
% 0.24/0.37 spl0_10 <=> (((g @ (f @ x))) = $true)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
% 0.24/0.37 thf(f60,plain,(
% 0.24/0.37 (((g @ (f @ x))) = $true) | ~spl0_10),
% 0.24/0.37 inference(avatar_component_clause,[],[f58])).
% 0.24/0.37 thf(f61,plain,(
% 0.24/0.37 spl0_9 | spl0_10),
% 0.24/0.37 inference(avatar_split_clause,[],[f14,f58,f54])).
% 0.24/0.37 thf(f63,definition,(
% 0.24/0.37 spl0_11 <=> (((g @ (f @ x))) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition])).
% 0.24/0.37 thf(f65,plain,(
% 0.24/0.37 (((g @ (f @ x))) = $false) | ~spl0_11),
% 0.24/0.37 inference(avatar_component_clause,[],[f63])).
% 0.24/0.37 thf(f67,definition,(
% 0.24/0.37 spl0_12 <=> (((f @ (f @ (f @ x)))) = $true)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition])).
% 0.24/0.37 thf(f70,plain,(
% 0.24/0.37 spl0_11 | spl0_12),
% 0.24/0.37 inference(avatar_split_clause,[],[f13,f67,f63])).
% 0.24/0.37 thf(f72,plain,(
% 0.24/0.37 ($true = $false) | (~spl0_5 | ~spl0_6)),
% 0.24/0.37 inference(forward_demodulation,[],[f41,f36])).
% 0.24/0.37 thf(f73,plain,(
% 0.24/0.37 $false | (~spl0_5 | ~spl0_6)),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f72])).
% 0.24/0.37 thf(f74,plain,(
% 0.24/0.37 ~spl0_5 | ~spl0_6),
% 0.24/0.37 inference(avatar_contradiction_clause,[],[f73])).
% 0.24/0.37 thf(f75,plain,(
% 0.24/0.37 (((g @ $true)) = $false) | (~spl0_3 | ~spl0_8)),
% 0.24/0.37 inference(forward_demodulation,[],[f51,f27])).
% 0.24/0.37 thf(f78,definition,(
% 0.24/0.37 spl0_13 <=> (((g @ $true)) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition])).
% 0.24/0.37 thf(f80,plain,(
% 0.24/0.37 (((g @ $true)) = $false) | ~spl0_13),
% 0.24/0.37 inference(avatar_component_clause,[],[f78])).
% 0.24/0.37 thf(f81,plain,(
% 0.24/0.37 spl0_13 | ~spl0_3 | ~spl0_8),
% 0.24/0.37 inference(avatar_split_clause,[],[f75,f49,f25,f78])).
% 0.24/0.37 thf(f91,plain,(
% 0.24/0.37 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.24/0.37 inference(superposition,[],[f27,f18])).
% 0.24/0.37 thf(f94,plain,(
% 0.24/0.37 $false | (~spl0_1 | ~spl0_3)),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f91])).
% 0.24/0.37 thf(f95,plain,(
% 0.24/0.37 ~spl0_1 | ~spl0_3),
% 0.24/0.37 inference(avatar_contradiction_clause,[],[f94])).
% 0.24/0.37 thf(f98,definition,(
% 0.24/0.37 (y != $true) | ($true != ((g @ $true))) | (((g @ y)) != $false) | (y = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f118,definition,(
% 0.24/0.37 (y != $true) | (((f @ (f @ (f @ x)))) != $true) | (((f @ (f @ (f @ x)))) != $false) | (((g @ y)) != $false) | ($true = ((g @ $true)))),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f127,plain,(
% 0.24/0.37 (((f @ (f @ (f @ $false)))) = $false) | (~spl0_5 | ~spl0_9)),
% 0.24/0.37 inference(forward_demodulation,[],[f56,f36])).
% 0.24/0.37 thf(f129,definition,(
% 0.24/0.37 spl0_18 <=> (((f @ (f @ (f @ $false)))) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition])).
% 0.24/0.37 thf(f131,plain,(
% 0.24/0.37 (((f @ (f @ (f @ $false)))) = $false) | ~spl0_18),
% 0.24/0.37 inference(avatar_component_clause,[],[f129])).
% 0.24/0.37 thf(f132,plain,(
% 0.24/0.37 spl0_18 | ~spl0_5 | ~spl0_9),
% 0.24/0.37 inference(avatar_split_clause,[],[f127,f54,f34,f129])).
% 0.24/0.37 thf(f133,plain,(
% 0.24/0.37 (((f @ $false)) = $false) | (((f @ (f @ $true))) = $false) | ~spl0_18),
% 0.24/0.37 inference(fool_paramodulation,[],[f131])).
% 0.24/0.37 thf(f134,plain,(
% 0.24/0.37 (((f @ (f @ $false))) = $false) | (((f @ $true)) = $false) | ~spl0_18),
% 0.24/0.37 inference(fool_paramodulation,[],[f131])).
% 0.24/0.37 thf(f136,definition,(
% 0.24/0.37 spl0_19 <=> (((f @ (f @ $false))) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition])).
% 0.24/0.37 thf(f140,definition,(
% 0.24/0.37 spl0_20 <=> (((f @ $true)) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition])).
% 0.24/0.37 thf(f143,plain,(
% 0.24/0.37 spl0_19 | spl0_20 | ~spl0_18),
% 0.24/0.37 inference(avatar_split_clause,[],[f134,f129,f140,f136])).
% 0.24/0.37 thf(f145,definition,(
% 0.24/0.37 spl0_21 <=> (((f @ (f @ $true))) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition])).
% 0.24/0.37 thf(f147,plain,(
% 0.24/0.37 (((f @ (f @ $true))) = $false) | ~spl0_21),
% 0.24/0.37 inference(avatar_component_clause,[],[f145])).
% 0.24/0.37 thf(f149,definition,(
% 0.24/0.37 spl0_22 <=> (((f @ $false)) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition])).
% 0.24/0.37 thf(f152,plain,(
% 0.24/0.37 spl0_21 | spl0_22 | ~spl0_18),
% 0.24/0.37 inference(avatar_split_clause,[],[f133,f129,f149,f145])).
% 0.24/0.37 thf(f153,definition,(
% 0.24/0.37 (((f @ $true)) != $false) | (((f @ (f @ $true))) != $false) | (x != $false) | (y != $true) | (((g @ x)) != $true) | (((g @ (f @ x))) != $false) | (y = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f158,definition,(
% 0.24/0.37 (((f @ $true)) != $false) | (((f @ $false)) != $false) | (((f @ (f @ $true))) = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f162,definition,(
% 0.24/0.37 (((f @ (f @ $false))) != $false) | (x != $false) | (((g @ x)) != $true) | (((g @ (f @ x))) != $false) | (((f @ (f @ (f @ x)))) != $false) | (((f @ (f @ (f @ x)))) = $true)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f179,definition,(
% 0.24/0.37 (x != $false) | (((f @ $false)) != $false) | (((f @ (f @ (f @ x)))) = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f181,definition,(
% 0.24/0.37 (x != $false) | (((f @ $false)) != $false) | (((f @ (f @ $false))) = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f187,plain,(
% 0.24/0.37 ($true = ((g @ (f @ $false)))) | (~spl0_5 | ~spl0_10)),
% 0.24/0.37 inference(forward_demodulation,[],[f60,f36])).
% 0.24/0.37 thf(f192,definition,(
% 0.24/0.37 spl0_23 <=> ($true = ((g @ (f @ $false))))),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition])).
% 0.24/0.37 thf(f194,plain,(
% 0.24/0.37 ($true = ((g @ (f @ $false)))) | ~spl0_23),
% 0.24/0.37 inference(avatar_component_clause,[],[f192])).
% 0.24/0.37 thf(f195,plain,(
% 0.24/0.37 spl0_23 | ~spl0_5 | ~spl0_10),
% 0.24/0.37 inference(avatar_split_clause,[],[f187,f58,f34,f192])).
% 0.24/0.37 thf(f196,plain,(
% 0.24/0.37 ($true = ((g @ $true))) | (((f @ $false)) = $false) | ~spl0_23),
% 0.24/0.37 inference(fool_paramodulation,[],[f194])).
% 0.24/0.37 thf(f197,plain,(
% 0.24/0.37 (((f @ $false)) = $false) | ($true = $false) | (~spl0_13 | ~spl0_23)),
% 0.24/0.37 inference(forward_demodulation,[],[f196,f80])).
% 0.24/0.37 thf(f198,plain,(
% 0.24/0.37 (((f @ $false)) = $false) | (~spl0_13 | ~spl0_23)),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f197])).
% 0.24/0.37 thf(f199,plain,(
% 0.24/0.37 spl0_22 | ~spl0_13 | ~spl0_23),
% 0.24/0.37 inference(avatar_split_clause,[],[f198,f192,f78,f149])).
% 0.24/0.37 thf(f204,definition,(
% 0.24/0.37 (((g @ y)) != $true) | (((g @ y)) != $false) | (y != $false) | (y = $true)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f209,plain,(
% 0.24/0.37 (y = $false) | ($true != $true) | spl0_3),
% 0.24/0.37 inference(fool_paramodulation,[],[f26])).
% 0.24/0.37 thf(f210,plain,(
% 0.24/0.37 (y = $false) | spl0_3),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f209])).
% 0.24/0.37 thf(f211,plain,(
% 0.24/0.37 spl0_1 | spl0_3),
% 0.24/0.37 inference(avatar_split_clause,[],[f210,f25,f16])).
% 0.24/0.37 thf(f223,plain,(
% 0.24/0.37 (((g @ (f @ $true))) = $false) | (~spl0_6 | ~spl0_11)),
% 0.24/0.37 inference(forward_demodulation,[],[f65,f41])).
% 0.24/0.37 thf(f225,definition,(
% 0.24/0.37 spl0_24 <=> (((g @ (f @ $true))) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition])).
% 0.24/0.37 thf(f228,plain,(
% 0.24/0.37 spl0_24 | ~spl0_6 | ~spl0_11),
% 0.24/0.37 inference(avatar_split_clause,[],[f223,f63,f39,f225])).
% 0.24/0.37 thf(f230,plain,(
% 0.24/0.37 (((f @ (f @ (f @ $true)))) = $false) | (~spl0_6 | ~spl0_9)),
% 0.24/0.37 inference(forward_demodulation,[],[f56,f41])).
% 0.24/0.37 thf(f232,definition,(
% 0.24/0.37 spl0_25 <=> (((f @ (f @ (f @ $true)))) = $false)),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition])).
% 0.24/0.37 thf(f234,plain,(
% 0.24/0.37 (((f @ (f @ (f @ $true)))) = $false) | ~spl0_25),
% 0.24/0.37 inference(avatar_component_clause,[],[f232])).
% 0.24/0.37 thf(f235,plain,(
% 0.24/0.37 spl0_25 | ~spl0_6 | ~spl0_9),
% 0.24/0.37 inference(avatar_split_clause,[],[f230,f54,f39,f232])).
% 0.24/0.37 thf(f236,plain,(
% 0.24/0.37 (((f @ $true)) = $false) | (((f @ (f @ $true))) = $false) | ~spl0_25),
% 0.24/0.37 inference(fool_paramodulation,[],[f234])).
% 0.24/0.37 thf(f239,plain,(
% 0.24/0.37 spl0_21 | spl0_20 | ~spl0_25),
% 0.24/0.37 inference(avatar_split_clause,[],[f236,f232,f140,f145])).
% 0.24/0.37 thf(f241,plain,(
% 0.24/0.37 (((f @ $true)) = $false) | (((f @ $true)) = $false) | ~spl0_21),
% 0.24/0.37 inference(fool_paramodulation,[],[f147])).
% 0.24/0.37 thf(f243,plain,(
% 0.24/0.37 (((f @ $true)) = $false) | ~spl0_21),
% 0.24/0.37 inference(duplicate_literal_removal,[],[f241])).
% 0.24/0.37 thf(f244,plain,(
% 0.24/0.37 spl0_20 | ~spl0_21),
% 0.24/0.37 inference(avatar_split_clause,[],[f243,f145,f140])).
% 0.24/0.37 thf(f248,definition,(
% 0.24/0.37 (x != $true) | (((f @ $true)) != $false) | (y != $false) | (((g @ (f @ x))) != $false) | (((g @ y)) = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f252,definition,(
% 0.24/0.37 (y != $false) | (((f @ (f @ (f @ x)))) != $false) | (((f @ (f @ (f @ x)))) != $true) | (y = $true)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f265,definition,(
% 0.24/0.37 (x != $true) | (((f @ $true)) != $false) | (((f @ (f @ $true))) != $false) | (((f @ (f @ (f @ x)))) = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f269,definition,(
% 0.24/0.37 (((g @ (f @ $true))) != $false) | (((g @ (f @ x))) != $true) | (x != $true) | (x = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f273,definition,(
% 0.24/0.37 (x != $true) | (((g @ x)) != $false) | (((g @ $true)) = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f282,definition,(
% 0.24/0.37 (x != $true) | (((f @ (f @ (f @ x)))) != $true) | (((f @ $true)) != $false) | (((f @ (f @ (f @ $false)))) = $false)),
% 0.24/0.37 introduced(theory,[theory_tautology_sat_conflict])).
% 0.24/0.37 thf(f285,plain,(
% 0.24/0.37 ($true = ((g @ (f @ $true)))) | (~spl0_6 | ~spl0_10)),
% 0.24/0.37 inference(forward_demodulation,[],[f60,f41])).
% 0.24/0.37 thf(f290,definition,(
% 0.24/0.37 spl0_26 <=> ($true = ((g @ (f @ $true))))),
% 0.24/0.37 introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition])).
% 0.24/0.37 thf(f292,plain,(
% 0.24/0.37 ($true = ((g @ (f @ $true)))) | ~spl0_26),
% 0.24/0.37 inference(avatar_component_clause,[],[f290])).
% 0.24/0.37 thf(f293,plain,(
% 0.24/0.37 spl0_26 | ~spl0_6 | ~spl0_10),
% 0.24/0.37 inference(avatar_split_clause,[],[f285,f58,f39,f290])).
% 0.24/0.37 thf(f302,plain,(
% 0.24/0.37 ($true = ((g @ $true))) | (((f @ $true)) = $false) | ~spl0_26),
% 0.24/0.37 inference(fool_paramodulation,[],[f292])).
% 0.24/0.37 thf(f303,plain,(
% 0.24/0.37 ($true = $false) | (((f @ $true)) = $false) | (~spl0_13 | ~spl0_26)),
% 0.24/0.37 inference(forward_demodulation,[],[f302,f80])).
% 0.24/0.37 thf(f304,plain,(
% 0.24/0.37 (((f @ $true)) = $false) | (~spl0_13 | ~spl0_26)),
% 0.24/0.37 inference(trivial_inequality_removal,[],[f303])).
% 0.24/0.37 thf(f305,plain,(
% 0.24/0.37 spl0_20 | ~spl0_13 | ~spl0_26),
% 0.24/0.37 inference(avatar_split_clause,[],[f304,f290,f78,f140])).
% 0.24/0.37 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f23])).
% 0.24/0.37 cnf(s2, plain, spl0_3 | spl0_4, inference(sat_conversion,[],[f32])).
% 0.24/0.37 cnf(s3, plain, spl0_1 | spl0_5, inference(sat_conversion,[],[f37])).
% 0.24/0.37 cnf(s4, plain, spl0_3 | spl0_6, inference(sat_conversion,[],[f42])).
% 0.24/0.37 cnf(s5, plain, spl0_5 | spl0_7, inference(sat_conversion,[],[f47])).
% 0.24/0.37 cnf(s6, plain, spl0_6 | spl0_8, inference(sat_conversion,[],[f52])).
% 0.24/0.37 cnf(s7, plain, spl0_9 | spl0_10, inference(sat_conversion,[],[f61])).
% 0.24/0.37 cnf(s8, plain, spl0_11 | spl0_12, inference(sat_conversion,[],[f70])).
% 0.24/0.37 cnf(s9, plain, ~spl0_5 | ~spl0_6, inference(sat_conversion,[],[f74])).
% 0.24/0.37 cnf(s10, plain, ~spl0_3 | ~spl0_8 | spl0_13, inference(sat_conversion,[],[f81])).
% 0.24/0.37 cnf(s15, plain, ~spl0_1 | ~spl0_3, inference(sat_conversion,[],[f95])).
% 0.24/0.37 cnf(s18, plain, spl0_1 | ~spl0_3 | ~spl0_8 | ~spl0_14, inference(sat_conversion,[],[f98])).
% 0.24/0.37 cnf(s26, plain, ~spl0_3 | ~spl0_8 | ~spl0_9 | ~spl0_12 | spl0_14, inference(sat_conversion,[],[f118])).
% 0.24/0.37 cnf(s28, plain, ~spl0_5 | ~spl0_9 | spl0_18, inference(sat_conversion,[],[f132])).
% 0.24/0.37 cnf(s29, plain, ~spl0_18 | spl0_19 | spl0_20, inference(sat_conversion,[],[f143])).
% 0.24/0.37 cnf(s30, plain, ~spl0_18 | spl0_21 | spl0_22, inference(sat_conversion,[],[f152])).
% 0.24/0.37 cnf(s31, plain, spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_5 | ~spl0_11 | ~spl0_20 | ~spl0_21, inference(sat_conversion,[],[f153])).
% 0.24/0.37 cnf(s36, plain, ~spl0_20 | spl0_21 | ~spl0_22, inference(sat_conversion,[],[f158])).
% 0.24/0.37 cnf(s40, plain, ~spl0_2 | ~spl0_5 | ~spl0_9 | ~spl0_11 | spl0_12 | ~spl0_19, inference(sat_conversion,[],[f162])).
% 0.24/0.37 cnf(s57, plain, ~spl0_5 | spl0_9 | ~spl0_22, inference(sat_conversion,[],[f179])).
% 0.24/0.37 cnf(s59, plain, ~spl0_5 | spl0_19 | ~spl0_22, inference(sat_conversion,[],[f181])).
% 0.24/0.37 cnf(s65, plain, ~spl0_5 | ~spl0_10 | spl0_23, inference(sat_conversion,[],[f195])).
% 0.24/0.37 cnf(s66, plain, ~spl0_13 | spl0_22 | ~spl0_23, inference(sat_conversion,[],[f199])).
% 0.24/0.37 cnf(s71, plain, ~spl0_1 | spl0_3 | ~spl0_7 | ~spl0_8, inference(sat_conversion,[],[f204])).
% 0.24/0.37 cnf(s76, plain, spl0_1 | spl0_3, inference(sat_conversion,[],[f211])).
% 0.24/0.37 cnf(s77, plain, ~spl0_6 | ~spl0_11 | spl0_24, inference(sat_conversion,[],[f228])).
% 0.24/0.37 cnf(s78, plain, ~spl0_6 | ~spl0_9 | spl0_25, inference(sat_conversion,[],[f235])).
% 0.24/0.37 cnf(s80, plain, spl0_20 | spl0_21 | ~spl0_25, inference(sat_conversion,[],[f239])).
% 0.24/0.37 cnf(s81, plain, spl0_20 | ~spl0_21, inference(sat_conversion,[],[f244])).
% 0.24/0.37 cnf(s85, plain, ~spl0_1 | ~spl0_6 | spl0_8 | ~spl0_11 | ~spl0_20, inference(sat_conversion,[],[f248])).
% 0.24/0.37 cnf(s89, plain, ~spl0_1 | spl0_3 | ~spl0_9 | ~spl0_12, inference(sat_conversion,[],[f252])).
% 0.24/0.37 cnf(s102, plain, ~spl0_6 | spl0_9 | ~spl0_20 | ~spl0_21, inference(sat_conversion,[],[f265])).
% 0.24/0.37 cnf(s106, plain, spl0_5 | ~spl0_6 | ~spl0_10 | ~spl0_24, inference(sat_conversion,[],[f269])).
% 0.24/0.37 cnf(s110, plain, ~spl0_4 | ~spl0_6 | spl0_13, inference(sat_conversion,[],[f273])).
% 0.24/0.37 cnf(s119, plain, ~spl0_6 | ~spl0_12 | spl0_18 | ~spl0_20, inference(sat_conversion,[],[f282])).
% 0.24/0.37 cnf(s122, plain, ~spl0_6 | ~spl0_10 | spl0_26, inference(sat_conversion,[],[f293])).
% 0.24/0.37 cnf(s126, plain, ~spl0_13 | spl0_20 | ~spl0_26, inference(sat_conversion,[],[f305])).
% 0.24/0.37 cnf(s127, plain, spl0_9 | spl0_1, inference(rat,[],[s65,s66,s7,s57,s10,s6,s9,s3,s76])).
% 0.24/0.37 cnf(s128, plain, spl0_1, inference(rat,[],[s31,s30,s29,s59,s40,s8,s28,s26,s127,s18,s6,s9,s1,s3,s76])).
% 0.24/0.37 cnf(s129, plain, ~spl0_3, inference(rat,[],[s15,s128])).
% 0.24/0.37 cnf(s130, plain, spl0_6, inference(rat,[],[s4,s129])).
% 0.24/0.37 cnf(s131, plain, spl0_4, inference(rat,[],[s2,s129])).
% 0.24/0.37 cnf(s133, plain, ~spl0_5, inference(rat,[],[s9,s130])).
% 0.24/0.37 cnf(s134, plain, spl0_13, inference(rat,[],[s110,s130,s131])).
% 0.24/0.37 cnf(s135, plain, spl0_7, inference(rat,[],[s5,s133])).
% 0.24/0.37 cnf(s136, plain, ~spl0_8, inference(rat,[],[s71,s129,s128,s135])).
% 0.24/0.37 cnf(s137, plain, spl0_9, inference(rat,[],[s30,s119,s36,s8,s102,s77,s126,s106,s122,s7,s130,s134,s133])).
% 0.24/0.37 cnf(s138, plain, ~spl0_12, inference(rat,[],[s89,s129,s128,s137])).
% 0.24/0.37 cnf(s139, plain, spl0_25, inference(rat,[],[s78,s130,s137])).
% 0.24/0.37 cnf(s140, plain, spl0_11, inference(rat,[],[s8,s138])).
% 0.24/0.37 cnf(s141, plain, ~spl0_20, inference(rat,[],[s85,s136,s130,s128,s140])).
% 0.24/0.37 cnf(s144, plain, ~spl0_21, inference(rat,[],[s81,s141])).
% 0.24/0.37 cnf(s145, plain, $false, inference(rat,[],[s80,s139,s144,s141])).
% 0.24/0.37 thf(f306,plain,(
% 0.24/0.37 $false),
% 0.24/0.37 inference(avatar_sat_refutation,[],[s145])).
% 0.24/0.37 % SZS output end Proof for theBenchmark
% 0.24/0.37 % (1249399)------------------------------
% 0.24/0.37 % (1249399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (1249399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (1249399)CaDiCaL version: 2.1.3
% 0.24/0.37 % (1249399)Termination reason: Refutation
% 0.24/0.37 % (1249399)Time elapsed: 0.013 s
% 0.24/0.37 % (1249399)Peak memory usage: 13 MB
% 0.24/0.37 % (1249399)Instructions burned: 11 (million)
% 0.24/0.37 % (1249391)Success in time 0.052 s
% 0.24/0.37 % Vampire exiting
%------------------------------------------------------------------------------