%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG298^5 : 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 : n008.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 07:45:22 AM UTC 2026
% Result : Theorem 0.12s 0.24s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG298^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.15 % Computer : n008.cluster.edu
% 0.12/0.15 % Model : x86_64 x86_64
% 0.12/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.15 % Memory : 8046.5625MB
% 0.12/0.15 % OS : Linux 6.8.0-71-generic
% 0.12/0.15 % CPULimit : 300
% 0.12/0.15 % WCLimit : 300
% 0.12/0.15 % DateTime : Tue Sep 29 17:38:39 UTC 2026
% 0.12/0.15 % CPUTime :
% 0.12/0.15 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.19 Running higher-order theorem proving
% 0.12/0.20 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
% 0.12/0.24 % (3480222)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.12/0.24 % (3480234)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3344497194:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.12/0.24 % (3480234) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3480222-3480234"...
% 0.12/0.24 % (3480234)...printing done.
% 0.12/0.24 % (3480234)Refutation found. Thanks to Tanya!
% 0.12/0.24 % SZS status Theorem for theBenchmark
% 0.12/0.24 % SZS output start Proof for theBenchmark
% 0.12/0.24 thf(type_def_5, type, c: $tType).
% 0.12/0.24 thf(type_def_6, type, b: $tType).
% 0.12/0.24 thf(type_def_7, type, a: $tType).
% 0.12/0.24 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.12/0.24 thf(func_def_0, type, c_starc: (c > c > c)).
% 0.12/0.24 thf(func_def_1, type, c_starb: (b > b > b)).
% 0.12/0.24 thf(func_def_2, type, c_stara: (a > a > a)).
% 0.12/0.24 thf(func_def_4, type, sK0: (b > c)).
% 0.12/0.24 thf(func_def_5, type, sK1: (a > b)).
% 0.12/0.24 thf(func_def_6, type, sK2: (a > c)).
% 0.12/0.24 thf(func_def_7, type, sK3: b).
% 0.12/0.24 thf(func_def_8, type, sK4: b).
% 0.12/0.24 thf(func_def_9, type, sK5: (b > a)).
% 0.12/0.24 thf(f1,conjecture,(
% 0.12/0.24 ! [X2 : (b > c),X0 : (a > b),X1 : (a > c)] : ((! [X4 : a,X3 : a] : (((X1 @ (c_stara @ X3 @ X4))) = ((c_starc @ (X1 @ X3) @ (X1 @ X4)))) & ! [X4 : a,X3 : a] : (((X0 @ (c_stara @ X3 @ X4))) = ((c_starb @ (X0 @ X3) @ (X0 @ X4)))) & ! [X4 : b] : ? [X3 : a] : (((X0 @ X3)) = X4) & ! [X3 : a] : (((X2 @ (X0 @ X3))) = ((X1 @ X3)))) => ! [X4 : b,X3 : b] : (((X2 @ (c_starb @ X3 @ X4))) = ((c_starc @ (X2 @ X3) @ (X2 @ X4)))))),
% 0.12/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM270_pme)).
% 0.12/0.24 thf(f2,negated_conjecture,(
% 0.12/0.24 ~ ! [X2 : (b > c),X0 : (a > b),X1 : (a > c)] : ((! [X4 : a,X3 : a] : (((X1 @ (c_stara @ X3 @ X4))) = ((c_starc @ (X1 @ X3) @ (X1 @ X4)))) & ! [X4 : a,X3 : a] : (((X0 @ (c_stara @ X3 @ X4))) = ((c_starb @ (X0 @ X3) @ (X0 @ X4)))) & ! [X4 : b] : ? [X3 : a] : (((X0 @ X3)) = X4) & ! [X3 : a] : (((X2 @ (X0 @ X3))) = ((X1 @ X3)))) => ! [X4 : b,X3 : b] : (((X2 @ (c_starb @ X3 @ X4))) = ((c_starc @ (X2 @ X3) @ (X2 @ X4)))))),
% 0.12/0.24 inference(negated_conjecture,[status(cth)],[f1])).
% 0.12/0.24 thf(f3,plain,(
% 0.12/0.24 ~ ! [X0 : (b > c),X1 : (a > b),X2 : (a > c)] : ((! [X9 : a] : (((X0 @ (X1 @ X9))) = ((X2 @ X9))) & ! [X6 : a,X5 : a] : (((X1 @ (c_stara @ X6 @ X5))) = ((c_starb @ (X1 @ X6) @ (X1 @ X5)))) & ! [X7 : b] : ? [X8 : a] : (((X1 @ X8)) = X7) & ! [X4 : a,X3 : a] : (((c_starc @ (X2 @ X4) @ (X2 @ X3))) = ((X2 @ (c_stara @ X4 @ X3))))) => ! [X10 : b,X11 : b] : (((X0 @ (c_starb @ X11 @ X10))) = ((c_starc @ (X0 @ X11) @ (X0 @ X10)))))),
% 0.12/0.24 inference(rectify,[],[f2])).
% 0.12/0.24 thf(f4,plain,(
% 0.12/0.24 ? [X0 : (b > c),X1 : (a > b),X2 : (a > c)] : (? [X10 : b,X11 : b] : (((X0 @ (c_starb @ X11 @ X10))) != ((c_starc @ (X0 @ X11) @ (X0 @ X10)))) & (! [X9 : a] : (((X0 @ (X1 @ X9))) = ((X2 @ X9))) & ! [X6 : a,X5 : a] : (((X1 @ (c_stara @ X6 @ X5))) = ((c_starb @ (X1 @ X6) @ (X1 @ X5)))) & ! [X7 : b] : ? [X8 : a] : (((X1 @ X8)) = X7) & ! [X4 : a,X3 : a] : (((c_starc @ (X2 @ X4) @ (X2 @ X3))) = ((X2 @ (c_stara @ X4 @ X3))))))),
% 0.12/0.24 inference(ennf_transformation,[],[f3])).
% 0.12/0.24 thf(f5,plain,(
% 0.12/0.24 ? [X0 : (b > c),X1 : (a > b),X2 : (a > c)] : (! [X4 : a,X3 : a] : (((c_starc @ (X2 @ X4) @ (X2 @ X3))) = ((X2 @ (c_stara @ X4 @ X3)))) & ! [X9 : a] : (((X0 @ (X1 @ X9))) = ((X2 @ X9))) & ! [X6 : a,X5 : a] : (((X1 @ (c_stara @ X6 @ X5))) = ((c_starb @ (X1 @ X6) @ (X1 @ X5)))) & ? [X10 : b,X11 : b] : (((X0 @ (c_starb @ X11 @ X10))) != ((c_starc @ (X0 @ X11) @ (X0 @ X10)))) & ! [X7 : b] : ? [X8 : a] : (((X1 @ X8)) = X7))),
% 0.12/0.24 inference(flattening,[],[f4])).
% 0.12/0.24 thf(f6,plain,(
% 0.12/0.24 ? [X0 : (b > c),X1 : (a > b),X2 : (a > c)] : (! [X3 : a,X4 : a] : (((c_starc @ (X2 @ X3) @ (X2 @ X4))) = ((X2 @ (c_stara @ X3 @ X4)))) & ! [X5 : a] : (((X0 @ (X1 @ X5))) = ((X2 @ X5))) & ! [X6 : a,X7 : a] : (((c_starb @ (X1 @ X6) @ (X1 @ X7))) = ((X1 @ (c_stara @ X6 @ X7)))) & ? [X8 : b,X9 : b] : (((X0 @ (c_starb @ X9 @ X8))) != ((c_starc @ (X0 @ X9) @ (X0 @ X8)))) & ! [X10 : b] : ? [X11 : a] : (((X1 @ X11)) = X10))),
% 0.12/0.24 inference(rectify,[],[f5])).
% 0.12/0.24 thf(f7,plain,(
% 0.12/0.24 ! [X3 : a,X4 : a] : (((c_starc @ (sK2 @ X3) @ (sK2 @ X4))) = ((sK2 @ (c_stara @ X3 @ X4)))) & ! [X5 : a] : (((sK2 @ X5)) = ((sK0 @ (sK1 @ X5)))) & ! [X6 : a,X7 : a] : (((c_starb @ (sK1 @ X6) @ (sK1 @ X7))) = ((sK1 @ (c_stara @ X6 @ X7)))) & (((c_starc @ (sK0 @ sK4) @ (sK0 @ sK3))) != ((sK0 @ (c_starb @ sK4 @ sK3)))) & ! [X10 : b] : (((sK1 @ (sK5 @ X10))) = X10)),
% 0.12/0.24 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X8,sK3),skolemize(X9,sK4),skolemize(X11,sK5 @ X10)],[f6])).
% 0.12/0.24 thf(f8,plain,(
% 0.12/0.24 ( ! [X10 : b] : ((((sK1 @ (sK5 @ X10))) = X10)) )),
% 0.12/0.24 inference(cnf_transformation,[],[f7])).
% 0.12/0.24 thf(f9,plain,(
% 0.12/0.24 (((c_starc @ (sK0 @ sK4) @ (sK0 @ sK3))) != ((sK0 @ (c_starb @ sK4 @ sK3))))),
% 0.12/0.24 inference(cnf_transformation,[],[f7])).
% 0.12/0.24 thf(f10,plain,(
% 0.12/0.24 ( ! [X6 : a,X7 : a] : ((((c_starb @ (sK1 @ X6) @ (sK1 @ X7))) = ((sK1 @ (c_stara @ X6 @ X7))))) )),
% 0.12/0.24 inference(cnf_transformation,[],[f7])).
% 0.12/0.24 thf(f11,plain,(
% 0.12/0.24 ( ! [X5 : a] : ((((sK2 @ X5)) = ((sK0 @ (sK1 @ X5))))) )),
% 0.12/0.24 inference(cnf_transformation,[],[f7])).
% 0.12/0.24 thf(f12,plain,(
% 0.12/0.24 ( ! [X3 : a,X4 : a] : ((((c_starc @ (sK2 @ X3) @ (sK2 @ X4))) = ((sK2 @ (c_stara @ X3 @ X4))))) )),
% 0.12/0.24 inference(cnf_transformation,[],[f7])).
% 0.12/0.24 thf(f13,plain,(
% 0.12/0.24 ( ! [X0 : b] : ((((sK0 @ X0)) = ((sK2 @ (sK5 @ X0))))) )),
% 0.12/0.24 inference(constrained_superposition,[],[f11,f8])).
% 0.12/0.24 thf(f14,plain,(
% 0.12/0.24 ( ! [X0 : b,X1 : a] : ((((c_starb @ (sK1 @ X1) @ X0)) = ((sK1 @ (c_stara @ X1 @ (sK5 @ X0)))))) )),
% 0.12/0.24 inference(constrained_superposition,[],[f10,f8])).
% 0.12/0.24 thf(f16,plain,(
% 0.12/0.24 ( ! [X0 : b,X1 : a] : ((((sK2 @ (c_stara @ X1 @ (sK5 @ X0)))) = ((c_starc @ (sK2 @ X1) @ (sK0 @ X0))))) )),
% 0.12/0.24 inference(constrained_superposition,[],[f12,f13])).
% 0.12/0.24 thf(f20,plain,(
% 0.12/0.24 ( ! [X0 : a,X1 : b] : ((((sK0 @ (c_starb @ (sK1 @ X0) @ X1))) = ((sK2 @ (c_stara @ X0 @ (sK5 @ X1)))))) )),
% 0.12/0.24 inference(constrained_superposition,[],[f11,f14])).
% 0.12/0.24 thf(f21,plain,(
% 0.12/0.24 ( ! [X0 : a,X1 : b] : ((((c_starc @ (sK2 @ X0) @ (sK0 @ X1))) = ((sK0 @ (c_starb @ (sK1 @ X0) @ X1))))) )),
% 0.12/0.24 inference(forward_demodulation,[],[f20,f16])).
% 0.12/0.24 thf(f51,plain,(
% 0.12/0.24 ( ! [X0 : b,X1 : b] : ((((sK0 @ (c_starb @ (sK1 @ (sK5 @ X0)) @ X1))) = ((c_starc @ (sK0 @ X0) @ (sK0 @ X1))))) )),
% 0.12/0.24 inference(constrained_superposition,[],[f21,f13])).
% 0.12/0.24 thf(f55,plain,(
% 0.12/0.24 ( ! [X0 : b,X1 : b] : ((((sK0 @ (c_starb @ X0 @ X1))) = ((c_starc @ (sK0 @ X0) @ (sK0 @ X1))))) )),
% 0.12/0.24 inference(forward_demodulation,[],[f51,f8])).
% 0.12/0.24 thf(f63,plain,(
% 0.12/0.24 (((sK0 @ (c_starb @ sK4 @ sK3))) != ((sK0 @ (c_starb @ sK4 @ sK3))))),
% 0.12/0.24 inference(constrained_superposition,[],[f9,f55])).
% 0.12/0.24 thf(f64,plain,(
% 0.12/0.24 $false),
% 0.12/0.24 inference(trivial_inequality_removal,[],[f63])).
% 0.12/0.24 % SZS output end Proof for theBenchmark
% 0.12/0.24 % (3480234)------------------------------
% 0.12/0.24 % (3480234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.24 % (3480234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.24 % (3480234)CaDiCaL version: 2.1.3
% 0.12/0.24 % (3480234)Termination reason: Refutation
% 0.12/0.24 % (3480234)Time elapsed: 0.003 s
% 0.12/0.24 % (3480234)Peak memory usage: 12 MB
% 0.12/0.24 % (3480234)Instructions burned: 9 (million)
% 0.12/0.24 % (3480222)Success in time 0.03 s
% 0.12/0.24 % Vampire exiting
%------------------------------------------------------------------------------