%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN374^5 : 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 : n013.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 08:41:41 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN374^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:14:51 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.29 % (2307914)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (2307923)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=94144384:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (2307923)Instruction limit reached!
% 0.20/0.29 % (2307923)------------------------------
% 0.20/0.29 % (2307923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2307923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2307923)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2307923)Termination reason: Instruction limit
% 0.20/0.29 % (2307923)Termination phase: Saturation
% 0.20/0.29 % (2307923)Time elapsed: 0.006 s
% 0.20/0.29 % (2307923)Peak memory usage: 12 MB
% 0.20/0.29 % (2307923)Instructions burned: 24 (million)
% 0.20/0.29 % (2307920)lrs+10_16_si=on:nwc=1.5:random_seed=1816651614:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (2307919)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1027871287:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (2307921)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2998760078:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (2307922)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=2792569579: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)
% 0.20/0.29 % (2307921)Refutation not found, incomplete strategy
% 0.20/0.29 % (2307921)------------------------------
% 0.20/0.29 % (2307921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2307921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2307921)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2307921)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (2307921)Time elapsed: 0.003 s
% 0.20/0.29 % (2307921)Peak memory usage: 12 MB
% 0.20/0.29 % (2307921)Instructions burned: 2 (million)
% 0.20/0.29 % (2307920) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2307914-2307920"...
% 0.20/0.29 % (2307919) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2307914-2307919"...
% 0.20/0.29 % (2307921)------------------------------
% 0.20/0.29 % (2307921)------------------------------
% 0.20/0.29 % (2307922) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2307914-2307922"...
% 0.20/0.29 % (2307925)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (2307925)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
% 0.20/0.29 % (2307920)...printing done.
% 0.20/0.29 % (2307919)...printing done.
% 0.20/0.29 % (2307920)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, cP: ($i > $o)).
% 0.20/0.29 thf(func_def_6, type, sK2: ($i > $i)).
% 0.20/0.29 thf(f1,conjecture,(
% 0.20/0.29 ? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) <=> (cP @ X1)) <=> (? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cP @ X1))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2125)).
% 0.20/0.29 thf(f2,negated_conjecture,(
% 0.20/0.29 ~(? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) <=> (cP @ X1)) <=> (? [X0 : $i] : (cP @ X0) <=> ! [X1 : $i] : (cP @ X1)))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.29 thf(f3,plain,(
% 0.20/0.29 ~(? [X0 : $i] : ! [X1 : $i] : ((cP @ X0) <=> (cP @ X1)) <=> (? [X2 : $i] : (cP @ X2) <=> ! [X3 : $i] : (cP @ X3)))),
% 0.20/0.29 inference(rectify,[],[f2])).
% 0.20/0.29 thf(f4,plain,(
% 0.20/0.29 ~((! [X3 : $i] : ($true = ((cP @ X3))) <=> ? [X2 : $i] : ($true = ((cP @ X2)))) <=> ? [X0 : $i] : ! [X1 : $i] : (((cP @ X0)) = ((cP @ X1))))),
% 0.20/0.29 inference(fool_elimination,[],[f3])).
% 0.20/0.29 thf(f5,plain,(
% 0.20/0.29 ? [X0 : $i] : ! [X1 : $i] : (((cP @ X0)) = ((cP @ X1))) <~> (! [X3 : $i] : ($true = ((cP @ X3))) <=> ? [X2 : $i] : ($true = ((cP @ X2))))),
% 0.20/0.29 inference(ennf_transformation,[],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 (((! [X2 : $i] : ($true != ((cP @ X2))) | ? [X3 : $i] : ($true != ((cP @ X3)))) & (? [X2 : $i] : ($true = ((cP @ X2))) | ! [X3 : $i] : ($true = ((cP @ X3))))) | ! [X0 : $i] : ? [X1 : $i] : (((cP @ X0)) != ((cP @ X1)))) & (((! [X3 : $i] : ($true = ((cP @ X3))) | ! [X2 : $i] : ($true != ((cP @ X2)))) & (? [X2 : $i] : ($true = ((cP @ X2))) | ? [X3 : $i] : ($true != ((cP @ X3))))) | ? [X0 : $i] : ! [X1 : $i] : (((cP @ X0)) = ((cP @ X1))))),
% 0.20/0.29 inference(nnf_transformation,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 (((! [X0 : $i] : (((cP @ X0)) != $true) | ? [X1 : $i] : (((cP @ X1)) != $true)) & (? [X2 : $i] : ($true = ((cP @ X2))) | ! [X3 : $i] : ($true = ((cP @ X3))))) | ! [X4 : $i] : ? [X5 : $i] : (((cP @ X5)) != ((cP @ X4)))) & (((! [X6 : $i] : ($true = ((cP @ X6))) | ! [X7 : $i] : ($true != ((cP @ X7)))) & (? [X8 : $i] : ($true = ((cP @ X8))) | ? [X9 : $i] : ($true != ((cP @ X9))))) | ? [X10 : $i] : ! [X11 : $i] : (((cP @ X10)) = ((cP @ X11))))),
% 0.20/0.29 inference(rectify,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 (((! [X0 : $i] : (((cP @ X0)) != $true) | ($true != ((cP @ sK0)))) & (($true = ((cP @ sK1))) | ! [X3 : $i] : ($true = ((cP @ X3))))) | ! [X4 : $i] : (((cP @ X4)) != ((cP @ (sK2 @ X4))))) & (((! [X6 : $i] : ($true = ((cP @ X6))) | ! [X7 : $i] : ($true != ((cP @ X7)))) & (($true = ((cP @ sK3))) | ($true != ((cP @ sK4))))) | ! [X11 : $i] : (((cP @ sK5)) = ((cP @ X11))))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,sK3,sK4,sK5]),skolemize(X1,sK0),skolemize(X2,sK1),skolemize(X5,sK2 @ X4),skolemize(X8,sK3),skolemize(X9,sK4),skolemize(X10,sK5)],[f7])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 ( ! [X11 : $i,X6 : $i,X7 : $i] : (($true != ((cP @ X7))) | (((cP @ sK5)) = ((cP @ X11))) | ($true = ((cP @ X6)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((cP @ X3))) | ($true = ((cP @ sK1))) | (((cP @ X4)) != ((cP @ (sK2 @ X4))))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f12,plain,(
% 0.20/0.29 ( ! [X0 : $i,X4 : $i] : ((((cP @ X4)) != ((cP @ (sK2 @ X4)))) | (((cP @ X0)) != $true) | ($true != ((cP @ sK0)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f8])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 ( ! [X11 : $i,X6 : $i,X7 : $i] : ((((cP @ X11)) = $false) | ($true = ((cP @ X6))) | ($true != ((cP @ X7))) | ($true = ((cP @ sK5)))) )),
% 0.20/0.29 inference(iff_proxy_clausification,[],[f10])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 ( ! [X11 : $i,X6 : $i,X7 : $i] : (($true = ((cP @ X6))) | ($true != ((cP @ X7))) | ($true = ((cP @ X11))) | (((cP @ sK5)) = $false)) )),
% 0.20/0.29 inference(iff_proxy_clausification,[],[f10])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 ( ! [X0 : $i,X4 : $i] : ((((cP @ X4)) = $false) | ($true != ((cP @ sK0))) | (((cP @ X0)) != $true) | ($false = ((cP @ (sK2 @ X4))))) )),
% 0.20/0.29 inference(xor_proxy_clausification,[],[f12])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i] : (($true = ((cP @ (sK2 @ X4)))) | ($true = ((cP @ X3))) | ($true = ((cP @ sK1))) | ($true = ((cP @ X4)))) )),
% 0.20/0.29 inference(xor_proxy_clausification,[],[f11])).
% 0.20/0.29 thf(f24,definition,(
% 0.20/0.29 spl6_1 <=> (((cP @ sK5)) = $false)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 (((cP @ sK5)) = $false) | ~spl6_1),
% 0.20/0.29 inference(avatar_component_clause,[],[f24])).
% 0.20/0.29 thf(f28,definition,(
% 0.20/0.29 spl6_2 <=> ! [X7 : $i] : ($true != ((cP @ X7)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 0.20/0.29 thf(f29,plain,(
% 0.20/0.29 ( ! [X7 : $i] : (($true != ((cP @ X7)))) ) | ~spl6_2),
% 0.20/0.29 inference(avatar_component_clause,[],[f28])).
% 0.20/0.29 thf(f31,definition,(
% 0.20/0.29 spl6_3 <=> ! [X11 : $i] : ($true = ((cP @ X11)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ( ! [X11 : $i] : (($true = ((cP @ X11)))) ) | ~spl6_3),
% 0.20/0.29 inference(avatar_component_clause,[],[f31])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 spl6_1 | spl6_2 | spl6_3 | spl6_3),
% 0.20/0.29 inference(avatar_split_clause,[],[f16,f31,f31,f28,f24])).
% 0.20/0.29 thf(f35,definition,(
% 0.20/0.29 spl6_4 <=> ($true = ((cP @ sK5)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition])).
% 0.20/0.29 thf(f37,plain,(
% 0.20/0.29 ($true = ((cP @ sK5))) | ~spl6_4),
% 0.20/0.29 inference(avatar_component_clause,[],[f35])).
% 0.20/0.29 thf(f39,definition,(
% 0.20/0.29 spl6_5 <=> ! [X11 : $i] : (((cP @ X11)) = $false)),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition])).
% 0.20/0.29 thf(f40,plain,(
% 0.20/0.29 ( ! [X11 : $i] : ((((cP @ X11)) = $false)) ) | ~spl6_5),
% 0.20/0.29 inference(avatar_component_clause,[],[f39])).
% 0.20/0.29 thf(f41,plain,(
% 0.20/0.29 spl6_4 | spl6_5 | spl6_3 | spl6_2),
% 0.20/0.29 inference(avatar_split_clause,[],[f15,f28,f31,f39,f35])).
% 0.20/0.29 thf(f43,definition,(
% 0.20/0.29 spl6_6 <=> ($true = ((cP @ sK0)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition])).
% 0.20/0.29 thf(f44,plain,(
% 0.20/0.29 ($true = ((cP @ sK0))) | ~spl6_6),
% 0.20/0.29 inference(avatar_component_clause,[],[f43])).
% 0.20/0.29 thf(f45,plain,(
% 0.20/0.29 ($true != ((cP @ sK0))) | spl6_6),
% 0.20/0.29 inference(avatar_component_clause,[],[f43])).
% 0.20/0.29 thf(f47,definition,(
% 0.20/0.29 spl6_7 <=> ! [X4 : $i] : ((((cP @ X4)) = $false) | ($false = ((cP @ (sK2 @ X4)))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition])).
% 0.20/0.29 thf(f48,plain,(
% 0.20/0.29 ( ! [X4 : $i] : (($false = ((cP @ (sK2 @ X4)))) | (((cP @ X4)) = $false)) ) | ~spl6_7),
% 0.20/0.29 inference(avatar_component_clause,[],[f47])).
% 0.20/0.29 thf(f49,plain,(
% 0.20/0.29 ~spl6_6 | spl6_2 | spl6_7),
% 0.20/0.29 inference(avatar_split_clause,[],[f18,f47,f28,f43])).
% 0.20/0.29 thf(f51,definition,(
% 0.20/0.29 spl6_8 <=> ! [X4 : $i] : (($true = ((cP @ (sK2 @ X4)))) | ($true = ((cP @ X4))))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition])).
% 0.20/0.29 thf(f52,plain,(
% 0.20/0.29 ( ! [X4 : $i] : (($true = ((cP @ (sK2 @ X4)))) | ($true = ((cP @ X4)))) ) | ~spl6_8),
% 0.20/0.29 inference(avatar_component_clause,[],[f51])).
% 0.20/0.29 thf(f55,definition,(
% 0.20/0.29 spl6_9 <=> ($true = ((cP @ sK1)))),
% 0.20/0.29 introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition])).
% 0.20/0.29 thf(f57,plain,(
% 0.20/0.29 ($true = ((cP @ sK1))) | ~spl6_9),
% 0.20/0.29 inference(avatar_component_clause,[],[f55])).
% 0.20/0.29 thf(f59,plain,(
% 0.20/0.29 spl6_3 | spl6_8 | spl6_9),
% 0.20/0.29 inference(avatar_split_clause,[],[f19,f55,f51,f31])).
% 0.20/0.29 thf(f70,plain,(
% 0.20/0.29 $false | (~spl6_3 | spl6_6)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f45,f32])).
% 0.20/0.29 thf(f71,plain,(
% 0.20/0.29 ~spl6_3 | spl6_6),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f70])).
% 0.20/0.29 thf(f72,plain,(
% 0.20/0.29 ( ! [X4 : $i] : (($true = $false) | (((cP @ X4)) = $false)) ) | (~spl6_3 | ~spl6_7)),
% 0.20/0.29 inference(forward_demodulation,[],[f48,f32])).
% 0.20/0.29 thf(f73,plain,(
% 0.20/0.29 ( ! [X4 : $i] : ((((cP @ X4)) = $false)) ) | (~spl6_3 | ~spl6_7)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f72])).
% 0.20/0.29 thf(f74,plain,(
% 0.20/0.29 spl6_5 | ~spl6_3 | ~spl6_7),
% 0.20/0.29 inference(avatar_split_clause,[],[f73,f47,f31,f39])).
% 0.20/0.29 thf(f75,plain,(
% 0.20/0.29 ($true = $false) | (~spl6_3 | ~spl6_5)),
% 0.20/0.29 inference(constrained_superposition,[],[f40,f32])).
% 0.20/0.29 thf(f79,plain,(
% 0.20/0.29 $false | (~spl6_3 | ~spl6_5)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f75])).
% 0.20/0.29 thf(f80,plain,(
% 0.20/0.29 ~spl6_3 | ~spl6_5),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f79])).
% 0.20/0.29 thf(f81,plain,(
% 0.20/0.29 ( ! [X4 : $i] : (($true = $false) | ($true = ((cP @ X4)))) ) | (~spl6_5 | ~spl6_8)),
% 0.20/0.29 inference(forward_demodulation,[],[f52,f40])).
% 0.20/0.29 thf(f82,plain,(
% 0.20/0.29 ( ! [X4 : $i] : (($true = ((cP @ X4)))) ) | (~spl6_5 | ~spl6_8)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f81])).
% 0.20/0.29 thf(f86,plain,(
% 0.20/0.29 ($true = $false) | (~spl6_5 | ~spl6_8)),
% 0.20/0.29 inference(forward_demodulation,[],[f82,f40])).
% 0.20/0.29 thf(f87,plain,(
% 0.20/0.29 $false | (~spl6_5 | ~spl6_8)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f86])).
% 0.20/0.29 thf(f88,plain,(
% 0.20/0.29 ~spl6_5 | ~spl6_8),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f87])).
% 0.20/0.29 thf(f90,plain,(
% 0.20/0.29 ($true = $false) | (~spl6_1 | ~spl6_4)),
% 0.20/0.29 inference(constrained_superposition,[],[f26,f37])).
% 0.20/0.29 thf(f93,plain,(
% 0.20/0.29 $false | (~spl6_1 | ~spl6_4)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f90])).
% 0.20/0.29 thf(f94,plain,(
% 0.20/0.29 ~spl6_1 | ~spl6_4),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f93])).
% 0.20/0.29 thf(f96,plain,(
% 0.20/0.29 ($true != $true) | (~spl6_2 | ~spl6_6)),
% 0.20/0.29 inference(constrained_superposition,[],[f29,f44])).
% 0.20/0.29 thf(f97,plain,(
% 0.20/0.29 $false | (~spl6_2 | ~spl6_6)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f96])).
% 0.20/0.29 thf(f98,plain,(
% 0.20/0.29 ~spl6_2 | ~spl6_6),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f97])).
% 0.20/0.29 thf(f101,plain,(
% 0.20/0.29 ( ! [X0 : $i] : (($true != $true) | (((cP @ X0)) = $true)) ) | (~spl6_2 | ~spl6_8)),
% 0.20/0.29 inference(constrained_superposition,[],[f29,f52])).
% 0.20/0.29 thf(f103,plain,(
% 0.20/0.29 ( ! [X0 : $i] : ((((cP @ X0)) = $true)) ) | (~spl6_2 | ~spl6_8)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f101])).
% 0.20/0.29 thf(f104,plain,(
% 0.20/0.29 $false | (~spl6_2 | ~spl6_8)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f103,f29])).
% 0.20/0.29 thf(f105,plain,(
% 0.20/0.29 ~spl6_2 | ~spl6_8),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f104])).
% 0.20/0.29 thf(f106,plain,(
% 0.20/0.29 $false | (~spl6_2 | ~spl6_9)),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f57,f29])).
% 0.20/0.29 thf(f107,plain,(
% 0.20/0.29 ~spl6_2 | ~spl6_9),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f106])).
% 0.20/0.29 thf(f108,plain,(
% 0.20/0.29 ($true = $false) | (~spl6_5 | ~spl6_9)),
% 0.20/0.29 inference(forward_demodulation,[],[f57,f40])).
% 0.20/0.29 thf(f109,plain,(
% 0.20/0.29 $false | (~spl6_5 | ~spl6_9)),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f108])).
% 0.20/0.29 thf(f110,plain,(
% 0.20/0.29 ~spl6_5 | ~spl6_9),
% 0.20/0.29 inference(avatar_contradiction_clause,[],[f109])).
% 0.20/0.29 cnf(s1, plain, spl6_3 | spl6_2 | spl6_1 | spl6_3, inference(sat_conversion,[],[f33])).
% 0.20/0.29 cnf(s2, plain, spl6_1 | spl6_2 | spl6_3, inference(rat,[],[s1])).
% 0.20/0.29 cnf(s3, plain, spl6_2 | spl6_3 | spl6_4 | spl6_5, inference(sat_conversion,[],[f41])).
% 0.20/0.29 cnf(s4, plain, spl6_2 | ~spl6_6 | spl6_7, inference(sat_conversion,[],[f49])).
% 0.20/0.29 cnf(s7, plain, spl6_3 | spl6_8 | spl6_9, inference(sat_conversion,[],[f59])).
% 0.20/0.29 cnf(s10, plain, ~spl6_3 | spl6_6, inference(sat_conversion,[],[f71])).
% 0.20/0.29 cnf(s11, plain, ~spl6_3 | spl6_5 | ~spl6_7, inference(sat_conversion,[],[f74])).
% 0.20/0.29 cnf(s13, plain, ~spl6_3 | ~spl6_5, inference(sat_conversion,[],[f80])).
% 0.20/0.29 cnf(s15, plain, ~spl6_5 | ~spl6_8, inference(sat_conversion,[],[f88])).
% 0.20/0.29 cnf(s17, plain, ~spl6_1 | ~spl6_4, inference(sat_conversion,[],[f94])).
% 0.20/0.29 cnf(s18, plain, ~spl6_2 | ~spl6_6, inference(sat_conversion,[],[f98])).
% 0.20/0.29 cnf(s19, plain, ~spl6_2 | ~spl6_8, inference(sat_conversion,[],[f105])).
% 0.20/0.29 cnf(s20, plain, ~spl6_2 | ~spl6_9, inference(sat_conversion,[],[f107])).
% 0.20/0.29 cnf(s21, plain, ~spl6_5 | ~spl6_9, inference(sat_conversion,[],[f110])).
% 0.20/0.29 cnf(s22, plain, spl6_2 | spl6_1, inference(rat,[],[s4,s11,s10,s13,s2])).
% 0.20/0.29 cnf(s23, plain, ~spl6_2, inference(rat,[],[s10,s7,s18,s19,s20])).
% 0.20/0.29 cnf(s24, plain, spl6_1, inference(rat,[],[s22,s23])).
% 0.20/0.29 cnf(s25, plain, ~spl6_4, inference(rat,[],[s17,s24])).
% 0.20/0.29 cnf(s26, plain, ~spl6_3, inference(rat,[],[s4,s11,s10,s13,s23])).
% 0.20/0.29 cnf(s27, plain, spl6_5, inference(rat,[],[s3,s25,s23,s26])).
% 0.20/0.29 cnf(s28, plain, ~spl6_9, inference(rat,[],[s21,s27])).
% 0.20/0.29 cnf(s29, plain, ~spl6_8, inference(rat,[],[s15,s27])).
% 0.20/0.29 cnf(s31, plain, $false, inference(rat,[],[s7,s26,s28,s29])).
% 0.20/0.29 thf(f113,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(avatar_sat_refutation,[],[s31])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (2307920)------------------------------
% 0.20/0.29 % (2307920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (2307920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (2307920)CaDiCaL version: 2.1.3
% 0.20/0.29 % (2307920)Termination reason: Refutation
% 0.20/0.29 % (2307920)Time elapsed: 0.004 s
% 0.20/0.29 % (2307920)Peak memory usage: 13 MB
% 0.20/0.29 % (2307920)Instructions burned: 5 (million)
% 0.20/0.29 % (2307914)Success in time 0.049 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------