0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.38	% Computer : n006.cluster.edu
0.11/0.38	% Model    : x86_64 x86_64
0.11/0.38	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.38	% Memory   : 8046.5625MB
0.11/0.38	% OS       : Linux 6.8.0-71-generic
0.11/0.38	% CPULimit : 1440
0.11/0.38	% WCLimit  : 180
0.11/0.38	% DateTime : Mon Jul 27 10:09:04 UTC 2026
0.11/0.38	% CPUTime  : 
0.11/0.38	Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.42	Running higher-order theorem proving
0.11/0.43	Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p
0.17/0.49	% (2680993)Detected a higher-order problem, will run a greedy HOL sequence.
0.17/0.49	% (2680998)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2949253978:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.17/0.49	% (2680998) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2680993-2680998"...
0.17/0.49	% (2680998)...printing done.
0.17/0.49	% (2680998)Refutation found. Thanks to Tanya!
0.17/0.49	% SZS status Theorem for theBenchmark
0.17/0.49	% SZS output start Proof for theBenchmark
0.17/0.49	thf(type_def_5, type, g: $tType).
0.17/0.49	thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
0.17/0.49	thf(func_def_0, type, cGRP_RIGHT_INVERSE: ((g > g > g) > g > $o)).
0.17/0.49	thf(func_def_1, type, cGRP_RIGHT_UNIT: ((g > g > g) > g > $o)).
0.17/0.49	thf(func_def_3, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
0.17/0.49	thf(func_def_4, type, db2: !>[X0: $tType]:(X0)).
0.17/0.49	thf(func_def_5, type, db0: !>[X0: $tType]:(X0)).
0.17/0.49	thf(func_def_6, type, db1: !>[X0: $tType]:(X0)).
0.17/0.49	thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
0.17/0.49	thf(func_def_8, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
0.17/0.49	thf(func_def_11, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
0.17/0.49	thf(func_def_12, type, db3: !>[X0: $tType]:(X0)).
0.17/0.49	thf(func_def_13, type, sK0: (g > g > g)).
0.17/0.49	thf(func_def_14, type, sK1: g).
0.17/0.49	thf(func_def_15, type, sK2: g).
0.17/0.49	thf(func_def_16, type, vNOT: ($o > $o)).
0.17/0.49	thf(func_def_17, type, sK3: (g > g)).
0.17/0.49	thf(f1,axiom,(
0.17/0.49	  ((^[X0 : (g > g > g), X1 : g] : (! [X2 : g] : ? [X3 : g] : (((X0 @ X2 @ X3)) = X1))) = cGRP_RIGHT_INVERSE)),
0.17/0.49	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def)).
0.17/0.49	thf(f2,axiom,(
0.17/0.49	  ((^[X0 : (g > g > g), X1 : g] : (! [X2 : g] : (((X0 @ X2 @ X1)) = X2))) = cGRP_RIGHT_UNIT)),
0.17/0.49	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def)).
0.17/0.49	thf(f3,conjecture,(
0.17/0.49	  ! [X0 : (g > g > g),X1 : g] : ((! [X4 : g,X2 : g,X3 : g] : (((X0 @ (X0 @ X4 @ X2) @ X3)) = ((X0 @ X4 @ (X0 @ X2 @ X3)))) & (cGRP_RIGHT_UNIT @ X0 @ X1) & (cGRP_RIGHT_INVERSE @ X0 @ X1)) => ! [X4 : g] : (((X0 @ X1 @ X4)) = X4))),
0.17/0.49	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE13A2A)).
0.17/0.49	thf(f4,negated_conjecture,(
0.17/0.49	  ~ ! [X0 : (g > g > g),X1 : g] : ((! [X4 : g,X2 : g,X3 : g] : (((X0 @ (X0 @ X4 @ X2) @ X3)) = ((X0 @ X4 @ (X0 @ X2 @ X3)))) & (cGRP_RIGHT_UNIT @ X0 @ X1) & (cGRP_RIGHT_INVERSE @ X0 @ X1)) => ! [X4 : g] : (((X0 @ X1 @ X4)) = X4))),
0.17/0.49	  inference(negated_conjecture,[status(cth)],[f3])).
0.17/0.49	thf(f5,plain,(
0.17/0.49	  (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
0.17/0.49	  inference(fool_elimination,[],[f2])).
0.17/0.49	thf(f6,plain,(
0.17/0.49	  ~ ! [X0 : (g > g > g),X1 : g] : ((! [X2 : g,X3 : g,X4 : g] : (((X0 @ X2 @ (X0 @ X3 @ X4))) = ((X0 @ (X0 @ X2 @ X3) @ X4))) & (cGRP_RIGHT_UNIT @ X0 @ X1) & (cGRP_RIGHT_INVERSE @ X0 @ X1)) => ! [X5 : g] : (((X0 @ X1 @ X5)) = X5))),
0.17/0.49	  inference(rectify,[],[f4])).
0.17/0.49	thf(f7,plain,(
0.17/0.49	  ~ ! [X1 : g,X0 : (g > g > g)] : ((! [X2 : g,X4 : g,X3 : g] : (((X0 @ X2 @ (X0 @ X3 @ X4))) = ((X0 @ (X0 @ X2 @ X3) @ X4))) & (((cGRP_RIGHT_INVERSE @ X0 @ X1)) = $true) & (((cGRP_RIGHT_UNIT @ X0 @ X1)) = $true)) => ! [X5 : g] : (((X0 @ X1 @ X5)) = X5))),
0.17/0.49	  inference(fool_elimination,[],[f6])).
0.17/0.49	thf(f8,plain,(
0.17/0.49	  (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
0.17/0.49	  inference(fool_elimination,[],[f1])).
0.17/0.49	thf(f9,plain,(
0.17/0.49	  ? [X1 : g,X0 : (g > g > g)] : (? [X5 : g] : (((X0 @ X1 @ X5)) != X5) & (! [X2 : g,X4 : g,X3 : g] : (((X0 @ X2 @ (X0 @ X3 @ X4))) = ((X0 @ (X0 @ X2 @ X3) @ X4))) & (((cGRP_RIGHT_INVERSE @ X0 @ X1)) = $true) & (((cGRP_RIGHT_UNIT @ X0 @ X1)) = $true)))),
0.17/0.49	  inference(ennf_transformation,[],[f7])).
0.17/0.49	thf(f10,plain,(
0.17/0.49	  ? [X0 : (g > g > g),X1 : g] : (? [X5 : g] : (((X0 @ X1 @ X5)) != X5) & (((cGRP_RIGHT_INVERSE @ X0 @ X1)) = $true) & ! [X2 : g,X4 : g,X3 : g] : (((X0 @ X2 @ (X0 @ X3 @ X4))) = ((X0 @ (X0 @ X2 @ X3) @ X4))) & (((cGRP_RIGHT_UNIT @ X0 @ X1)) = $true))),
0.17/0.49	  inference(flattening,[],[f9])).
0.17/0.49	thf(f11,plain,(
0.17/0.49	  ? [X0 : (g > g > g),X1 : g] : (? [X2 : g] : (((X0 @ X1 @ X2)) != X2) & (((cGRP_RIGHT_INVERSE @ X0 @ X1)) = $true) & ! [X3 : g,X4 : g,X5 : g] : (((X0 @ X3 @ (X0 @ X5 @ X4))) = ((X0 @ (X0 @ X3 @ X5) @ X4))) & (((cGRP_RIGHT_UNIT @ X0 @ X1)) = $true))),
0.17/0.49	  inference(rectify,[],[f10])).
0.17/0.49	thf(f12,plain,(
0.17/0.49	  (sK2 != ((sK0 @ sK1 @ sK2))) & ($true = ((cGRP_RIGHT_INVERSE @ sK0 @ sK1))) & ! [X3 : g,X4 : g,X5 : g] : (((sK0 @ X3 @ (sK0 @ X5 @ X4))) = ((sK0 @ (sK0 @ X3 @ X5) @ X4))) & ($true = ((cGRP_RIGHT_UNIT @ sK0 @ sK1)))),
0.17/0.49	  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f11])).
0.17/0.49	thf(f13,plain,(
0.17/0.49	  (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))),
0.17/0.49	  inference(cnf_transformation,[],[f5])).
0.17/0.49	thf(f14,plain,(
0.17/0.49	  (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))),
0.17/0.49	  inference(cnf_transformation,[],[f8])).
0.17/0.49	thf(f15,plain,(
0.17/0.49	  ($true = ((cGRP_RIGHT_UNIT @ sK0 @ sK1)))),
0.17/0.49	  inference(cnf_transformation,[],[f12])).
0.17/0.49	thf(f16,plain,(
0.17/0.49	  ( ! [X3 : g,X4 : g,X5 : g] : ((((sK0 @ X3 @ (sK0 @ X5 @ X4))) = ((sK0 @ (sK0 @ X3 @ X5) @ X4)))) )),
0.17/0.49	  inference(cnf_transformation,[],[f12])).
0.17/0.49	thf(f17,plain,(
0.17/0.49	  ($true = ((cGRP_RIGHT_INVERSE @ sK0 @ sK1)))),
0.17/0.49	  inference(cnf_transformation,[],[f12])).
0.17/0.49	thf(f18,plain,(
0.17/0.49	  (sK2 != ((sK0 @ sK1 @ sK2)))),
0.17/0.49	  inference(cnf_transformation,[],[f12])).
0.17/0.49	thf(f21,plain,(
0.17/0.49	  ($true = (((^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))) @ sK0 @ sK1)))),
0.17/0.49	  inference(definition_unfolding,[],[f17,f14])).
0.17/0.49	thf(f22,plain,(
0.17/0.49	  ((((^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))) @ sK0 @ sK1)) = $true)),
0.17/0.49	  inference(definition_unfolding,[],[f15,f13])).
0.17/0.49	thf(f23,plain,(
0.17/0.49	  ($true = ((!! @ g @ (^[Y0 : g]: ((sK0 @ Y0 @ sK1) = Y0)))))),
0.17/0.49	  inference(beta-eta_normalization,[],[f22])).
0.17/0.49	thf(f24,plain,(
0.17/0.49	  ( ! [X1 : g] : (($true = (((^[Y0 : g]: ((sK0 @ Y0 @ sK1) = Y0)) @ X1)))) )),
0.17/0.49	  inference(pi_proxy_clausification,[],[f23])).
0.17/0.49	thf(f25,plain,(
0.17/0.49	  ( ! [X1 : g] : (($true = (((sK0 @ X1 @ sK1) = X1)))) )),
0.17/0.49	  inference(beta-eta_normalization,[],[f24])).
0.17/0.49	thf(f26,plain,(
0.17/0.49	  ( ! [X1 : g] : ((((sK0 @ X1 @ sK1)) = X1)) )),
0.17/0.49	  inference(equality_proxy_clausification,[],[f25])).
0.17/0.49	thf(f27,plain,(
0.17/0.49	  (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK0 @ Y0 @ Y1) = sK1)))))) = $true)),
0.17/0.49	  inference(beta-eta_normalization,[],[f21])).
0.17/0.49	thf(f28,plain,(
0.17/0.49	  ( ! [X1 : g] : (($true = (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK0 @ Y0 @ Y1) = sK1)))) @ X1)))) )),
0.17/0.49	  inference(pi_proxy_clausification,[],[f27])).
0.17/0.49	thf(f29,plain,(
0.17/0.49	  ( ! [X1 : g] : (($true = ((?? @ g @ (^[Y0 : g]: ((sK0 @ X1 @ Y0) = sK1)))))) )),
0.17/0.49	  inference(beta-eta_normalization,[],[f28])).
0.17/0.49	thf(f30,plain,(
0.17/0.49	  ( ! [X1 : g] : (($true = (((^[Y0 : g]: ((sK0 @ X1 @ Y0) = sK1)) @ (sK3 @ X1))))) )),
0.17/0.49	  inference(sigma_proxy_clausification,[],[f29])).
0.17/0.49	thf(f31,plain,(
0.17/0.49	  ( ! [X1 : g] : (($true = (((sK0 @ X1 @ (sK3 @ X1)) = sK1)))) )),
0.17/0.49	  inference(beta-eta_normalization,[],[f30])).
0.17/0.49	thf(f32,plain,(
0.17/0.49	  ( ! [X1 : g] : ((sK1 = ((sK0 @ X1 @ (sK3 @ X1))))) )),
0.17/0.49	  inference(equality_proxy_clausification,[],[f31])).
0.17/0.49	thf(f33,plain,(
0.17/0.49	  ( ! [X0 : g,X1 : g] : ((((sK0 @ X0 @ (sK0 @ sK1 @ X1))) = ((sK0 @ X0 @ X1)))) )),
0.17/0.49	  inference(constrained_superposition,[],[f16,f26])).
0.17/0.49	thf(f34,plain,(
0.17/0.49	  ( ! [X0 : g,X1 : g] : ((((sK0 @ X0 @ (sK0 @ (sK3 @ X0) @ X1))) = ((sK0 @ sK1 @ X1)))) )),
0.17/0.49	  inference(constrained_superposition,[],[f16,f32])).
0.17/0.49	thf(f57,plain,(
0.17/0.49	  ( ! [X0 : g] : ((((sK0 @ X0 @ sK1)) = ((sK0 @ sK1 @ (sK3 @ (sK3 @ X0)))))) )),
0.17/0.49	  inference(constrained_superposition,[],[f34,f32])).
0.17/0.49	thf(f67,plain,(
0.17/0.49	  ( ! [X0 : g] : ((((sK0 @ sK1 @ (sK3 @ (sK3 @ X0)))) = X0)) )),
0.17/0.49	  inference(forward_demodulation,[],[f57,f26])).
0.17/0.49	thf(f73,plain,(
0.17/0.49	  ( ! [X0 : g,X1 : g] : ((((sK0 @ X1 @ (sK3 @ (sK3 @ X0)))) = ((sK0 @ X1 @ X0)))) )),
0.17/0.49	  inference(constrained_superposition,[],[f33,f67])).
0.17/0.49	thf(f77,plain,(
0.17/0.49	  ( ! [X0 : g] : ((((sK0 @ sK1 @ X0)) = X0)) )),
0.17/0.49	  inference(constrained_superposition,[],[f73,f67])).
0.17/0.49	thf(f94,plain,(
0.17/0.49	  (sK2 != sK2)),
0.17/0.49	  inference(constrained_superposition,[],[f18,f77])).
0.17/0.49	thf(f101,plain,(
0.17/0.49	  $false),
0.17/0.49	  inference(trivial_inequality_removal,[],[f94])).
0.17/0.49	% SZS output end Proof for theBenchmark
0.17/0.49	% (2680998)------------------------------
0.17/0.49	% (2680998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.17/0.49	% (2680998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.17/0.49	% (2680998)CaDiCaL version: 2.1.3
0.17/0.49	% (2680998)Termination reason: Refutation
0.17/0.49	% (2680998)Time elapsed: 0.006 s
0.17/0.49	% (2680998)Peak memory usage: 12 MB
0.17/0.49	% (2680998)Instructions burned: 9 (million)
0.17/0.49	% (2680993)Success in time 0.044 s
0.17/0.49	% Vampire exiting
0.17/0.49	EOF