%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET044^5 : 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 : n011.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 08:23:12 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET044^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:36:17 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.28 % (96089)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (96098)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3837860606:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (96098) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-96089-96098"...
% 0.21/0.28 % (96098)...printing done.
% 0.21/0.28 % (96098)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, cF: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_4, type, sK0: ($i > $i)).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 ? [X0 : $i] : ! [X1 : $i] : ((cF @ X1 @ X0) <=> (cF @ X1 @ X1)) => ~ ! [X1 : $i] : ? [X0 : $i] : ! [X2 : $i] : ((cF @ X2 @ X0) <=> ~(cF @ X2 @ X1))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPELL40)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~(? [X0 : $i] : ! [X1 : $i] : ((cF @ X1 @ X0) <=> (cF @ X1 @ X1)) => ~ ! [X1 : $i] : ? [X0 : $i] : ! [X2 : $i] : ((cF @ X2 @ X0) <=> ~(cF @ X2 @ X1)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~(? [X0 : $i] : ! [X1 : $i] : ((cF @ X1 @ X0) <=> (cF @ X1 @ X1)) => ~ ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((cF @ X4 @ X3) <=> ~(cF @ X4 @ X2)))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~(? [X0 : $i] : ! [X1 : $i] : (((cF @ X1 @ X0)) = ((cF @ X1 @ X1))) => ~ ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((((cF @ X4 @ X3)) = $true) <=> ~ (((cF @ X4 @ X2)) = $true)))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ~(? [X0 : $i] : ! [X1 : $i] : (((cF @ X1 @ X0)) = ((cF @ X1 @ X1))) => ~ ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((((cF @ X4 @ X3)) = $true) <=> (((cF @ X4 @ X2)) != $true)))),
% 0.21/0.28 inference(flattening,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : ((((cF @ X4 @ X3)) = $true) <=> (((cF @ X4 @ X2)) != $true)) & ? [X0 : $i] : ! [X1 : $i] : (((cF @ X1 @ X0)) = ((cF @ X1 @ X1)))),
% 0.21/0.28 inference(ennf_transformation,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ! [X2 : $i] : ? [X3 : $i] : ! [X4 : $i] : (((((cF @ X4 @ X3)) = $true) | (((cF @ X4 @ X2)) = $true)) & ((((cF @ X4 @ X2)) != $true) | (((cF @ X4 @ X3)) != $true))) & ? [X0 : $i] : ! [X1 : $i] : (((cF @ X1 @ X0)) = ((cF @ X1 @ X1)))),
% 0.21/0.28 inference(nnf_transformation,[],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 ! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : (((((cF @ X2 @ X1)) = $true) | (((cF @ X2 @ X0)) = $true)) & ((((cF @ X2 @ X0)) != $true) | (((cF @ X2 @ X1)) != $true))) & ? [X3 : $i] : ! [X4 : $i] : (((cF @ X4 @ X4)) = ((cF @ X4 @ X3)))),
% 0.21/0.28 inference(rectify,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ! [X0 : $i] : ! [X2 : $i] : (((((cF @ X2 @ (sK0 @ X0))) = $true) | (((cF @ X2 @ X0)) = $true)) & ((((cF @ X2 @ X0)) != $true) | (((cF @ X2 @ (sK0 @ X0))) != $true))) & ! [X4 : $i] : (((cF @ X4 @ X4)) = ((cF @ X4 @ sK1)))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1]),skolemize(X1,sK0 @ X0),skolemize(X3,sK1)],[f8])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X4 : $i] : ((((cF @ X4 @ X4)) = ((cF @ X4 @ sK1)))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i] : ((((cF @ X2 @ (sK0 @ X0))) != $true) | (((cF @ X2 @ X0)) != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ( ! [X2 : $i,X0 : $i] : ((((cF @ X2 @ (sK0 @ X0))) = $true) | (((cF @ X2 @ X0)) = $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f9])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ( ! [X4 : $i] : ((((cF @ X4 @ X4)) = $true) | ($false = ((cF @ X4 @ sK1)))) )),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f10])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ( ! [X4 : $i] : ((((cF @ X4 @ sK1)) = $true) | (((cF @ X4 @ X4)) = $false)) )),
% 0.21/0.28 inference(iff_proxy_clausification,[],[f10])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($false = ((cF @ (sK0 @ X0) @ sK1))) | (((cF @ (sK0 @ X0) @ X0)) != $true) | ($true != $true)) )),
% 0.21/0.28 inference(superposition,[],[f11,f14])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 ( ! [X0 : $i] : ((((cF @ (sK0 @ X0) @ X0)) != $true) | ($false = ((cF @ (sK0 @ X0) @ sK1)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f17])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($false = $true) | (((cF @ X0 @ sK1)) = $true) | ($false = ((cF @ X0 @ sK1)))) )),
% 0.21/0.28 inference(superposition,[],[f15,f14])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ( ! [X0 : $i] : ((((cF @ X0 @ sK1)) = $true) | ($false = ((cF @ X0 @ sK1)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f21])).
% 0.21/0.28 thf(f41,plain,(
% 0.21/0.28 ( ! [X0 : $i] : ((((cF @ (sK0 @ X0) @ X0)) = $true) | (((cF @ (sK0 @ X0) @ sK1)) = $true) | ($false = $true)) )),
% 0.21/0.28 inference(superposition,[],[f15,f12])).
% 0.21/0.28 thf(f42,plain,(
% 0.21/0.28 ( ! [X0 : $i] : ((((cF @ (sK0 @ X0) @ X0)) = $true) | (((cF @ (sK0 @ X0) @ sK1)) = $true)) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f41])).
% 0.21/0.28 thf(f66,plain,(
% 0.21/0.28 ($false = ((cF @ (sK0 @ sK1) @ sK1))) | ($false = $true) | ($true != $true)),
% 0.21/0.28 inference(superposition,[],[f18,f27])).
% 0.21/0.28 thf(f69,plain,(
% 0.21/0.28 ($false = ((cF @ (sK0 @ sK1) @ sK1)))),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f66])).
% 0.21/0.28 thf(f85,plain,(
% 0.21/0.28 ($false = $true) | ($false = $true)),
% 0.21/0.28 inference(superposition,[],[f42,f69])).
% 0.21/0.28 thf(f89,plain,(
% 0.21/0.28 ($false = $true)),
% 0.21/0.28 inference(duplicate_literal_removal,[],[f85])).
% 0.21/0.28 thf(f90,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f89])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (96098)------------------------------
% 0.21/0.28 % (96098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (96098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (96098)CaDiCaL version: 2.1.3
% 0.21/0.28 % (96098)Termination reason: Refutation
% 0.21/0.28 % (96098)Time elapsed: 0.002 s
% 0.21/0.28 % (96098)Peak memory usage: 12 MB
% 0.21/0.28 % (96098)Instructions burned: 7 (million)
% 0.21/0.28 % (96089)Success in time 0.039 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------