%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO270^5 : 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 : 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 08:47:19 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO270^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:43:05 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.20/0.27 % (1286445)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1286456)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (1286456)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
% 0.20/0.27 % (1286456)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=3711034192:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.27 % (1286456) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1286445-1286456"...
% 0.20/0.27 % (1286456)...printing done.
% 0.20/0.27 % (1286456)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_0, type, h: ($i > $i)).
% 0.20/0.27 thf(func_def_1, type, g: ($i > $i)).
% 0.20/0.27 thf(func_def_2, type, cP: ($i > $i > $o)).
% 0.20/0.27 thf(func_def_6, type, sK0: (($i > $i) > $i > $i)).
% 0.20/0.27 thf(func_def_7, type, sF1: ($i > ($i > $i) > $i)).
% 0.20/0.27 thf(func_def_8, type, sF2: (($i > $i) > $i > $i > $o)).
% 0.20/0.27 thf(func_def_9, type, sF3: ($i > ($i > $i) > $i)).
% 0.20/0.27 thf(func_def_10, type, sF4: (($i > $i) > $i > $i)).
% 0.20/0.27 thf(func_def_11, type, sF5: ($i > ($i > $i) > $i)).
% 0.20/0.27 thf(func_def_12, type, sF6: (($i > $i) > $i > $o)).
% 0.20/0.27 thf(func_def_13, type, sF7: (($i > $i) > $i > $o)).
% 0.20/0.27 thf(f1,conjecture,(
% 0.20/0.27 ? [X0 : $i,X1 : ($i > $i)] : ! [X2 : $i] : ((! [X3 : $i] : (cP @ X3 @ (X1 @ X0)) & (cP @ X0 @ X2)) => (cP @ X2 @ (g @ (h @ X2))))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM85)).
% 0.20/0.27 thf(f2,negated_conjecture,(
% 0.20/0.27 ~ ? [X0 : $i,X1 : ($i > $i)] : ! [X2 : $i] : ((! [X3 : $i] : (cP @ X3 @ (X1 @ X0)) & (cP @ X0 @ X2)) => (cP @ X2 @ (g @ (h @ X2))))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.27 thf(f3,plain,(
% 0.20/0.27 ~ ? [X0 : $i,X1 : ($i > $i)] : ! [X2 : $i] : ((! [X3 : $i] : (cP @ X3 @ (X1 @ X0)) & (cP @ X0 @ X2)) => (cP @ X2 @ (g @ (h @ X2))))),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ~ ? [X1 : ($i > $i),X0 : $i] : ! [X2 : $i] : ((! [X3 : $i] : (((cP @ X3 @ (X1 @ X0))) = $true) & (((cP @ X0 @ X2)) = $true)) => (((cP @ X2 @ (g @ (h @ X2)))) = $true))),
% 0.20/0.27 inference(fool_elimination,[],[f3])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 ! [X1 : ($i > $i),X0 : $i] : ? [X2 : $i] : ((((cP @ X2 @ (g @ (h @ X2)))) != $true) & (! [X3 : $i] : (((cP @ X3 @ (X1 @ X0))) = $true) & (((cP @ X0 @ X2)) = $true)))),
% 0.20/0.27 inference(ennf_transformation,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ! [X0 : $i,X1 : ($i > $i)] : ? [X2 : $i] : (! [X3 : $i] : (((cP @ X3 @ (X1 @ X0))) = $true) & (((cP @ X2 @ (g @ (h @ X2)))) != $true) & (((cP @ X0 @ X2)) = $true))),
% 0.20/0.27 inference(flattening,[],[f5])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 ! [X0 : $i,X1 : ($i > $i)] : (! [X3 : $i] : (((cP @ X3 @ (X1 @ X0))) = $true) & (((cP @ (sK0 @ X1 @ X0) @ (g @ (h @ (sK0 @ X1 @ X0))))) != $true) & (((cP @ X0 @ (sK0 @ X1 @ X0))) = $true))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X1 @ X0)],[f6])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((cP @ (sK0 @ X1 @ X0) @ (g @ (h @ (sK0 @ X1 @ X0))))) != $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f7])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 ( ! [X3 : $i,X0 : $i,X1 : ($i > $i)] : ((((cP @ X3 @ (X1 @ X0))) = $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f7])).
% 0.20/0.27 thf(f13,definition,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((sF1 @ X0 @ X1)) = ((X1 @ X0)))) )),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[sF1])],[function_definition])).
% 0.20/0.27 thf(f14,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((X1 @ X0)) = ((sF1 @ X0 @ X1)))) )),
% 0.20/0.27 inference(reorient_equations,[],[f13])).
% 0.20/0.27 thf(f15,definition,(
% 0.20/0.27 ( ! [X3 : $i,X0 : $i,X1 : ($i > $i)] : ((((sF2 @ X1 @ X0 @ X3)) = ((cP @ X3 @ (sF1 @ X0 @ X1))))) )),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[sF2])],[function_definition])).
% 0.20/0.27 thf(f16,plain,(
% 0.20/0.27 ( ! [X3 : $i,X0 : $i,X1 : ($i > $i)] : ((((cP @ X3 @ (sF1 @ X0 @ X1))) = ((sF2 @ X1 @ X0 @ X3)))) )),
% 0.20/0.27 inference(reorient_equations,[],[f15])).
% 0.20/0.27 thf(f17,plain,(
% 0.20/0.27 ( ! [X3 : $i,X0 : $i,X1 : ($i > $i)] : ((((sF2 @ X1 @ X0 @ X3)) = $true)) )),
% 0.20/0.27 inference(definition_folding,[],[f10,f16,f14])).
% 0.20/0.27 thf(f18,definition,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((sF3 @ X0 @ X1)) = ((sK0 @ X1 @ X0)))) )),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 0.20/0.27 thf(f19,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((sK0 @ X1 @ X0)) = ((sF3 @ X0 @ X1)))) )),
% 0.20/0.27 inference(reorient_equations,[],[f18])).
% 0.20/0.27 thf(f20,definition,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((sF4 @ X1 @ X0)) = ((h @ (sF3 @ X0 @ X1))))) )),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 0.20/0.27 thf(f21,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((h @ (sF3 @ X0 @ X1))) = ((sF4 @ X1 @ X0)))) )),
% 0.20/0.27 inference(reorient_equations,[],[f20])).
% 0.20/0.27 thf(f22,definition,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((sF5 @ X0 @ X1)) = ((g @ (sF4 @ X1 @ X0))))) )),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[sF5])],[function_definition])).
% 0.20/0.27 thf(f23,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((g @ (sF4 @ X1 @ X0))) = ((sF5 @ X0 @ X1)))) )),
% 0.20/0.27 inference(reorient_equations,[],[f22])).
% 0.20/0.27 thf(f24,definition,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((sF6 @ X1 @ X0)) = ((cP @ (sF3 @ X0 @ X1) @ (sF5 @ X0 @ X1))))) )),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[sF6])],[function_definition])).
% 0.20/0.27 thf(f25,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((cP @ (sF3 @ X0 @ X1) @ (sF5 @ X0 @ X1))) = ((sF6 @ X1 @ X0)))) )),
% 0.20/0.27 inference(reorient_equations,[],[f24])).
% 0.20/0.27 thf(f26,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : (($true != ((sF6 @ X1 @ X0)))) )),
% 0.20/0.27 inference(definition_folding,[],[f9,f25,f23,f21,f19,f19])).
% 0.20/0.27 thf(f31,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((cP @ (sF3 @ X0 @ X1) @ (sF5 @ X0 @ X1))) = $false) | ($true = ((sF6 @ X1 @ X0)))) )),
% 0.20/0.27 inference(iff_proxy_clausification,[],[f25])).
% 0.20/0.27 thf(f32,plain,(
% 0.20/0.27 ( ! [X3 : $i,X0 : $i,X1 : ($i > $i)] : ((((sF2 @ X1 @ X0 @ X3)) = $false) | (((cP @ X3 @ (sF1 @ X0 @ X1))) = $true)) )),
% 0.20/0.27 inference(iff_proxy_clausification,[],[f16])).
% 0.20/0.27 thf(f52,plain,(
% 0.20/0.27 ( ! [X3 : $i,X0 : $i,X1 : ($i > $i)] : (($true = $false) | (((cP @ X3 @ (sF1 @ X0 @ X1))) = $true)) )),
% 0.20/0.27 inference(forward_demodulation,[],[f32,f17])).
% 0.20/0.27 thf(f53,plain,(
% 0.20/0.27 ( ! [X3 : $i,X0 : $i,X1 : ($i > $i)] : ((((cP @ X3 @ (sF1 @ X0 @ X1))) = $true)) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f52])).
% 0.20/0.27 thf(f54,plain,(
% 0.20/0.27 ( ! [X3 : $i,X0 : $i,X1 : ($i > $i)] : ((((cP @ X3 @ (X1 @ X0))) = $true)) )),
% 0.20/0.27 inference(forward_demodulation,[],[f53,f14])).
% 0.20/0.27 thf(f56,plain,(
% 0.20/0.27 ( ! [X2 : $i,X0 : $i,X1 : ($i > $i)] : ((((cP @ X2 @ (sF5 @ X0 @ X1))) = $true)) )),
% 0.20/0.27 inference(constrained_superposition,[],[f54,f23])).
% 0.20/0.27 thf(f57,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : ($i > $i)] : ((((cP @ (sF3 @ X0 @ X1) @ (sF5 @ X0 @ X1))) = $false)) )),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f31,f26])).
% 0.20/0.27 thf(f58,plain,(
% 0.20/0.27 ($true = $false)),
% 0.20/0.27 inference(forward_demodulation,[],[f57,f56])).
% 0.20/0.27 thf(f59,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f58])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (1286456)------------------------------
% 0.20/0.27 % (1286456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1286456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1286456)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1286456)Termination reason: Refutation
% 0.20/0.27 % (1286456)Time elapsed: 0.002 s
% 0.20/0.27 % (1286456)Peak memory usage: 12 MB
% 0.20/0.27 % (1286456)Instructions burned: 5 (million)
% 0.20/0.27 % (1286445)Success in time 0.029 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------