%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM802^5 : 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 : 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 08:18:56 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM802^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n018.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.25 % WCLimit : 300
% 0.11/0.25 % DateTime : Tue Sep 29 13:02:56 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.32 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
% 0.25/0.36 % (34825)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.36 % (34831)lrs+10_16_si=on:nwc=1.5:random_seed=740312921:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.36 % (34831) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-34825-34831"...
% 0.25/0.36 % (34831)...printing done.
% 0.25/0.36 % (34831)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% 0.25/0.36 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.25/0.36 thf(func_def_1, type, absval: ($i > $i)).
% 0.25/0.36 thf(func_def_3, type, c_less_: ($i > $i > $o)).
% 0.25/0.36 thf(func_def_7, type, sK0: (($i > $o) > $i)).
% 0.25/0.36 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.25/0.36 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.25/0.36 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.25/0.36 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.25/0.36 thf(f1,conjecture,(
% 0.25/0.36 (c_less_ @ c_2 @ c0) => (! [X0 : $i,X1 : $i] : ((c_less_ @ X0 @ c0) => (X0 != ((absval @ X1)))) => ? [X2 : ($i > $o)] : ((X2 @ c_2) & ! [X3 : $i] : ~(X2 @ (absval @ X3))))),
% 0.25/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE_FENG_8)).
% 0.25/0.36 thf(f2,negated_conjecture,(
% 0.25/0.36 ~((c_less_ @ c_2 @ c0) => (! [X0 : $i,X1 : $i] : ((c_less_ @ X0 @ c0) => (X0 != ((absval @ X1)))) => ? [X2 : ($i > $o)] : ((X2 @ c_2) & ! [X3 : $i] : ~(X2 @ (absval @ X3)))))),
% 0.25/0.36 inference(negated_conjecture,[status(cth)],[f1])).
% 0.25/0.36 thf(f3,plain,(
% 0.25/0.36 ~((c_less_ @ c_2 @ c0) => (! [X0 : $i,X1 : $i] : ((c_less_ @ X0 @ c0) => (X0 != ((absval @ X1)))) => ? [X2 : ($i > $o)] : ((X2 @ c_2) & ! [X3 : $i] : ~(X2 @ (absval @ X3)))))),
% 0.25/0.36 inference(rectify,[],[f2])).
% 0.25/0.36 thf(f4,plain,(
% 0.25/0.36 ~((((c_less_ @ c_2 @ c0)) = $true) => (! [X1 : $i,X0 : $i] : ((((c_less_ @ X0 @ c0)) = $true) => (((absval @ X1)) != X0)) => ? [X2 : ($i > $o)] : ((((X2 @ c_2)) = $true) & ! [X3 : $i] : ~ (((X2 @ (absval @ X3))) = $true))))),
% 0.25/0.36 inference(fool_elimination,[],[f3])).
% 0.25/0.36 thf(f5,plain,(
% 0.25/0.36 ~((((c_less_ @ c_2 @ c0)) = $true) => (! [X1 : $i,X0 : $i] : ((((c_less_ @ X0 @ c0)) = $true) => (((absval @ X1)) != X0)) => ? [X2 : ($i > $o)] : (! [X3 : $i] : (((X2 @ (absval @ X3))) != $true) & (((X2 @ c_2)) = $true))))),
% 0.25/0.36 inference(flattening,[],[f4])).
% 0.25/0.36 thf(f6,plain,(
% 0.25/0.36 (! [X2 : ($i > $o)] : ((((X2 @ c_2)) != $true) | ? [X3 : $i] : (((X2 @ (absval @ X3))) = $true)) & ! [X1 : $i,X0 : $i] : ((((c_less_ @ X0 @ c0)) != $true) | (((absval @ X1)) != X0))) & (((c_less_ @ c_2 @ c0)) = $true)),
% 0.25/0.36 inference(ennf_transformation,[],[f5])).
% 0.25/0.36 thf(f7,plain,(
% 0.25/0.36 ! [X1 : $i,X0 : $i] : ((((c_less_ @ X0 @ c0)) != $true) | (((absval @ X1)) != X0)) & ! [X2 : ($i > $o)] : ((((X2 @ c_2)) != $true) | ? [X3 : $i] : (((X2 @ (absval @ X3))) = $true)) & (((c_less_ @ c_2 @ c0)) = $true)),
% 0.25/0.36 inference(flattening,[],[f6])).
% 0.25/0.36 thf(f8,plain,(
% 0.25/0.36 ! [X0 : $i,X1 : $i] : (($true != ((c_less_ @ X1 @ c0))) | (((absval @ X0)) != X1)) & ! [X2 : ($i > $o)] : ((((X2 @ c_2)) != $true) | ? [X3 : $i] : (((X2 @ (absval @ X3))) = $true)) & (((c_less_ @ c_2 @ c0)) = $true)),
% 0.25/0.36 inference(rectify,[],[f7])).
% 0.25/0.36 thf(f9,plain,(
% 0.25/0.36 ! [X0 : $i,X1 : $i] : (($true != ((c_less_ @ X1 @ c0))) | (((absval @ X0)) != X1)) & ! [X2 : ($i > $o)] : ((((X2 @ c_2)) != $true) | (((X2 @ (absval @ (sK0 @ X2)))) = $true)) & (((c_less_ @ c_2 @ c0)) = $true)),
% 0.25/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2)],[f8])).
% 0.25/0.36 thf(f10,plain,(
% 0.25/0.36 (((c_less_ @ c_2 @ c0)) = $true)),
% 0.25/0.36 inference(cnf_transformation,[],[f9])).
% 0.25/0.36 thf(f11,plain,(
% 0.25/0.36 ( ! [X2 : ($i > $o)] : ((((X2 @ c_2)) != $true) | (((X2 @ (absval @ (sK0 @ X2)))) = $true)) )),
% 0.25/0.36 inference(cnf_transformation,[],[f9])).
% 0.25/0.36 thf(f12,plain,(
% 0.25/0.36 ( ! [X0 : $i,X1 : $i] : (($true != ((c_less_ @ X1 @ c0))) | (((absval @ X0)) != X1)) )),
% 0.25/0.36 inference(cnf_transformation,[],[f9])).
% 0.25/0.36 thf(f15,plain,(
% 0.25/0.36 ( ! [X0 : $i] : ((((c_less_ @ (absval @ X0) @ c0)) != $true)) )),
% 0.25/0.36 inference(equality_resolution,[],[f12])).
% 0.25/0.36 thf(f16,plain,(
% 0.25/0.36 (c_2 = ((absval @ (sK0 @ (= @ c_2)))))),
% 0.25/0.36 inference(leibniz_equality_elimination,[],[f11])).
% 0.25/0.36 thf(f30,plain,(
% 0.25/0.36 (((c_less_ @ c_2 @ c0)) != $true)),
% 0.25/0.36 inference(constrained_superposition,[],[f15,f16])).
% 0.25/0.36 thf(f31,plain,(
% 0.25/0.36 $false),
% 0.25/0.36 inference(forward_subsumption_resolution,[],[f30,f10])).
% 0.25/0.36 % SZS output end Proof for theBenchmark
% 0.25/0.36 % (34831)------------------------------
% 0.25/0.36 % (34831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (34831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (34831)CaDiCaL version: 2.1.3
% 0.25/0.36 % (34831)Termination reason: Refutation
% 0.25/0.36 % (34831)Time elapsed: 0.002 s
% 0.25/0.36 % (34831)Peak memory usage: 12 MB
% 0.25/0.36 % (34831)Instructions burned: 2 (million)
% 0.25/0.36 % (34825)Success in time 0.024 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------