%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM761^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:19:29 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 : NUM761^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n018.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 12:55:41 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 % (26800)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (26809)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3473242990:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (26809)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (26809) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-26800-26809"...
% 0.20/0.27 % (26806)% WARNING: option uhcvi not known.
% 0.20/0.27 % (26809)...printing done.
% 0.20/0.27 % (26809)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, frac: $tType).
% 0.20/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(func_def_0, type, x: frac).
% 0.20/0.27 thf(func_def_1, type, y: frac).
% 0.20/0.27 thf(func_def_2, type, z: frac).
% 0.20/0.27 thf(func_def_3, type, u: frac).
% 0.20/0.27 thf(func_def_4, type, moref: (frac > frac > $o)).
% 0.20/0.27 thf(func_def_5, type, eq: (frac > frac > $o)).
% 0.20/0.27 thf(func_def_7, type, pf: (frac > frac > frac)).
% 0.20/0.27 thf(func_def_10, type, vNOT: ($o > $o)).
% 0.20/0.27 thf(f1,axiom,(
% 0.20/0.27 ~(moref @ x @ y) => (eq @ x @ y)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m)).
% 0.20/0.27 thf(f2,axiom,(
% 0.20/0.27 (moref @ z @ u)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n)).
% 0.20/0.27 thf(f4,axiom,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((moref @ X2 @ X3) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62g)).
% 0.20/0.27 thf(f5,axiom,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((moref @ X2 @ X3) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz64)).
% 0.20/0.27 thf(f6,conjecture,(
% 0.20/0.27 (moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz65a)).
% 0.20/0.27 thf(f7,negated_conjecture,(
% 0.20/0.27 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f6])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 ~(moref @ x @ y) => (eq @ x @ y)),
% 0.20/0.27 inference(rectify,[],[f1])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 ~ (((moref @ x @ y)) = $true) => (((eq @ x @ y)) = $true)),
% 0.20/0.27 inference(fool_elimination,[],[f8])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 (moref @ z @ u)),
% 0.20/0.27 inference(rectify,[],[f2])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 (((moref @ z @ u)) = $true)),
% 0.20/0.27 inference(fool_elimination,[],[f10])).
% 0.20/0.27 thf(f14,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((eq @ X0 @ X1) => ((moref @ X2 @ X3) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.20/0.27 inference(rectify,[],[f4])).
% 0.20/0.27 thf(f15,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((eq @ X0 @ X1)) = $true) => ((((moref @ X2 @ X3)) = $true) => (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)))),
% 0.20/0.27 inference(fool_elimination,[],[f14])).
% 0.20/0.27 thf(f16,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((moref @ X0 @ X1) => ((moref @ X2 @ X3) => (moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))))),
% 0.20/0.27 inference(rectify,[],[f5])).
% 0.20/0.27 thf(f17,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ X0 @ X1)) = $true) => ((((moref @ X2 @ X3)) = $true) => (((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true)))),
% 0.20/0.27 inference(fool_elimination,[],[f16])).
% 0.20/0.27 thf(f18,plain,(
% 0.20/0.27 ~(moref @ (pf @ x @ z) @ (pf @ y @ u))),
% 0.20/0.27 inference(rectify,[],[f7])).
% 0.20/0.27 thf(f19,plain,(
% 0.20/0.27 ~ (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $true)),
% 0.20/0.27 inference(fool_elimination,[],[f18])).
% 0.20/0.27 thf(f20,plain,(
% 0.20/0.27 (((moref @ x @ y)) != $true) => (((eq @ x @ y)) = $true)),
% 0.20/0.27 inference(flattening,[],[f9])).
% 0.20/0.27 thf(f22,plain,(
% 0.20/0.27 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) != $true)),
% 0.20/0.27 inference(flattening,[],[f19])).
% 0.20/0.27 thf(f23,plain,(
% 0.20/0.27 (((eq @ x @ y)) = $true) | (((moref @ x @ y)) = $true)),
% 0.20/0.27 inference(ennf_transformation,[],[f20])).
% 0.20/0.27 thf(f25,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((moref @ X2 @ X3)) != $true)) | (((eq @ X0 @ X1)) != $true))),
% 0.20/0.27 inference(ennf_transformation,[],[f15])).
% 0.20/0.27 thf(f26,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((moref @ X2 @ X3)) != $true) | (((eq @ X0 @ X1)) != $true))),
% 0.20/0.27 inference(flattening,[],[f25])).
% 0.20/0.27 thf(f27,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : (((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((moref @ X2 @ X3)) != $true)) | (((moref @ X0 @ X1)) != $true))),
% 0.20/0.27 inference(ennf_transformation,[],[f17])).
% 0.20/0.27 thf(f28,plain,(
% 0.20/0.27 ! [X0 : frac,X1 : frac,X2 : frac,X3 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((moref @ X2 @ X3)) != $true) | (((moref @ X0 @ X1)) != $true))),
% 0.20/0.27 inference(flattening,[],[f27])).
% 0.20/0.27 thf(f29,plain,(
% 0.20/0.27 (((eq @ x @ y)) = $true) | (((moref @ x @ y)) = $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f23])).
% 0.20/0.27 thf(f30,plain,(
% 0.20/0.27 (((moref @ z @ u)) = $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f11])).
% 0.20/0.27 thf(f32,plain,(
% 0.20/0.27 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((moref @ X2 @ X3)) != $true) | (((eq @ X0 @ X1)) != $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f26])).
% 0.20/0.27 thf(f33,plain,(
% 0.20/0.27 ( ! [X2 : frac,X3 : frac,X0 : frac,X1 : frac] : ((((moref @ (pf @ X0 @ X2) @ (pf @ X1 @ X3))) = $true) | (((moref @ X2 @ X3)) != $true) | (((moref @ X0 @ X1)) != $true)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f28])).
% 0.20/0.27 thf(f34,plain,(
% 0.20/0.27 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) != $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f22])).
% 0.20/0.27 thf(f36,definition,(
% 0.20/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.27 thf(f39,definition,(
% 0.20/0.27 spl0_1 <=> (((moref @ x @ y)) = $true)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.20/0.27 thf(f41,plain,(
% 0.20/0.27 (((moref @ x @ y)) = $true) | ~spl0_1),
% 0.20/0.27 inference(avatar_component_clause,[],[f39])).
% 0.20/0.27 thf(f43,definition,(
% 0.20/0.27 spl0_2 <=> (((eq @ x @ y)) = $true)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.20/0.27 thf(f45,plain,(
% 0.20/0.27 (((eq @ x @ y)) = $true) | ~spl0_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f43])).
% 0.20/0.27 thf(f46,plain,(
% 0.20/0.27 spl0_1 | spl0_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f29,f43,f39])).
% 0.20/0.27 thf(f49,plain,(
% 0.20/0.27 ($true != $true) | (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $false)),
% 0.20/0.27 inference(constrained_superposition,[],[f34,f36])).
% 0.20/0.27 thf(f51,plain,(
% 0.20/0.27 (((moref @ (pf @ x @ z) @ (pf @ y @ u))) = $false)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f49])).
% 0.20/0.27 thf(f59,plain,(
% 0.20/0.27 ($true = $false) | (((moref @ z @ u)) != $true) | (((eq @ x @ y)) != $true)),
% 0.20/0.27 inference(constrained_superposition,[],[f32,f51])).
% 0.20/0.27 thf(f64,plain,(
% 0.20/0.27 (((moref @ z @ u)) != $true) | (((eq @ x @ y)) != $true)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f59])).
% 0.20/0.27 thf(f67,plain,(
% 0.20/0.27 (((eq @ x @ y)) != $true)),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f64,f30])).
% 0.20/0.27 thf(f72,plain,(
% 0.20/0.27 $false | ~spl0_2),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f67,f45])).
% 0.20/0.27 thf(f73,plain,(
% 0.20/0.27 ~spl0_2),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f72])).
% 0.20/0.27 thf(f76,plain,(
% 0.20/0.27 ($true = $false) | (((moref @ z @ u)) != $true) | (((moref @ x @ y)) != $true)),
% 0.20/0.27 inference(constrained_superposition,[],[f33,f51])).
% 0.20/0.27 thf(f81,plain,(
% 0.20/0.27 (((moref @ z @ u)) != $true) | (((moref @ x @ y)) != $true)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f76])).
% 0.20/0.27 thf(f84,plain,(
% 0.20/0.27 (((moref @ x @ y)) != $true)),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f81,f30])).
% 0.20/0.27 thf(f89,plain,(
% 0.20/0.27 $false | ~spl0_1),
% 0.20/0.27 inference(forward_subsumption_resolution,[],[f84,f41])).
% 0.20/0.27 thf(f90,plain,(
% 0.20/0.27 ~spl0_1),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f89])).
% 0.20/0.27 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f46])).
% 0.20/0.27 cnf(s4, plain, ~spl0_2, inference(sat_conversion,[],[f73])).
% 0.20/0.27 cnf(s7, plain, ~spl0_1, inference(sat_conversion,[],[f90])).
% 0.20/0.27 cnf(s8, plain, $false, inference(rat,[],[s1,s4,s7])).
% 0.20/0.27 thf(f91,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s8])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (26809)------------------------------
% 0.20/0.27 % (26809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (26809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (26809)CaDiCaL version: 2.1.3
% 0.20/0.27 % (26809)Termination reason: Refutation
% 0.20/0.27 % (26809)Time elapsed: 0.003 s
% 0.20/0.27 % (26809)Peak memory usage: 12 MB
% 0.20/0.27 % (26809)Instructions burned: 5 (million)
% 0.20/0.27 % (26800)Success in time 0.027 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------