%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV465^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:38:41 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV465^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:55:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.26 % (1410953)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (1410962)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3792900374:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.26 % (1410962) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1410953-1410962"...
% 0.20/0.26 % (1410964)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.26 % (1410964)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.26 % (1410962)...printing done.
% 0.20/0.26 % (1410962)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(type_def_6, type, sK0: $tType).
% 0.20/0.26 thf(type_def_7, type, sK1: $tType).
% 0.20/0.26 thf(func_def_0, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.20/0.26 thf(func_def_1, type, 'const/sets/IMAGE': !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X1 > $o))).
% 0.20/0.26 thf(func_def_5, type, sK2: (sK1 > sK0)).
% 0.20/0.26 thf(func_def_6, type, sK3: (sK1 > $o)).
% 0.20/0.26 thf(func_def_7, type, sK4: (sK0 > $o)).
% 0.20/0.26 thf(func_def_8, type, sK5: sK1).
% 0.20/0.26 thf(func_def_9, type, sK6: sK0).
% 0.20/0.26 thf(func_def_10, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X0 > X1))).
% 0.20/0.26 thf(f1,axiom,(
% 0.20/0.26 ! [X0 : $tType,X1 : $tType,X4 : (X0 > X1),X2 : X1,X3 : (X0 > $o)] : ((('const/sets/IN' @ X1 @ X2 @ ('const/sets/IMAGE' @ X0 @ X1 @ X4 @ X3))) = ? [X5 : X0] : ((X2 = ((X4 @ X5))) & ('const/sets/IN' @ X0 @ X5 @ X3)))),
% 0.20/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_IMAGE_')).
% 0.20/0.26 thf(f2,conjecture,(
% 0.20/0.26 ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : (! [X5 : X1] : (('const/sets/IN' @ X1 @ X5 @ X4) => (X2 @ (X3 @ X5))) = ! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)) => (X2 @ X5)))),
% 0.20/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FORALL_IN_IMAGE_')).
% 0.20/0.26 thf(f3,negated_conjecture,(
% 0.20/0.26 ~ ! [X1 : $tType,X0 : $tType,X2 : (X0 > $o),X3 : (X1 > X0),X4 : (X1 > $o)] : (! [X5 : X1] : (('const/sets/IN' @ X1 @ X5 @ X4) => (X2 @ (X3 @ X5))) = ! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4)) => (X2 @ X5)))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f2])).
% 0.20/0.26 thf(f4,plain,(
% 0.20/0.26 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : X1,X4 : (X0 > $o)] : ((('const/sets/IN' @ X1 @ X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) = ? [X5 : X0] : ((((X2 @ X5)) = X3) & ('const/sets/IN' @ X0 @ X5 @ X4)))),
% 0.20/0.26 inference(rectify,[],[f1])).
% 0.20/0.26 thf(f5,plain,(
% 0.20/0.26 ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : (X0 > X1),X4 : (X0 > $o)] : (((('const/sets/IN' @ X1 @ X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) = $true) <=> ? [X5 : X0] : (($true = (('const/sets/IN' @ X0 @ X5 @ X4))) & (((X2 @ X5)) = X3)))),
% 0.20/0.26 inference(fool_elimination,[],[f4])).
% 0.20/0.26 thf(f6,plain,(
% 0.20/0.26 ~ ! [X0 : $tType,X1 : $tType,X2 : (X1 > $o),X3 : (X0 > X1),X4 : (X0 > $o)] : (! [X5 : X0] : (('const/sets/IN' @ X0 @ X5 @ X4) => (X2 @ (X3 @ X5))) = ! [X6 : X1] : (('const/sets/IN' @ X1 @ X6 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4)) => (X2 @ X6)))),
% 0.20/0.26 inference(rectify,[],[f3])).
% 0.20/0.26 thf(f7,plain,(
% 0.20/0.26 ~ ! [X0 : $tType,X1 : $tType,X3 : (X0 > X1),X4 : (X0 > $o),X2 : (X1 > $o)] : (! [X5 : X0] : (($true = (('const/sets/IN' @ X0 @ X5 @ X4))) => (((X2 @ (X3 @ X5))) = $true)) <=> ! [X6 : X1] : (($true = (('const/sets/IN' @ X1 @ X6 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4)))) => ($true = ((X2 @ X6)))))),
% 0.20/0.26 inference(fool_elimination,[],[f6])).
% 0.20/0.26 thf(f8,plain,(
% 0.20/0.26 ? [X1 : $tType,X0 : $tType,X3 : (X0 > X1),X4 : (X0 > $o),X2 : (X1 > $o)] : (! [X6 : X1] : (($true = ((X2 @ X6))) | ($true != (('const/sets/IN' @ X1 @ X6 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4))))) <~> ! [X5 : X0] : (($true != (('const/sets/IN' @ X0 @ X5 @ X4))) | (((X2 @ (X3 @ X5))) = $true)))),
% 0.20/0.26 inference(ennf_transformation,[],[f7])).
% 0.20/0.26 thf(f9,plain,(
% 0.20/0.26 ? [X1 : $tType,X0 : $tType,X3 : (X0 > X1),X4 : (X0 > $o),X2 : (X1 > $o)] : ((? [X5 : X0] : (($true = (('const/sets/IN' @ X0 @ X5 @ X4))) & (((X2 @ (X3 @ X5))) != $true)) | ? [X6 : X1] : (($true != ((X2 @ X6))) & ($true = (('const/sets/IN' @ X1 @ X6 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4)))))) & (! [X5 : X0] : (($true != (('const/sets/IN' @ X0 @ X5 @ X4))) | (((X2 @ (X3 @ X5))) = $true)) | ! [X6 : X1] : (($true = ((X2 @ X6))) | ($true != (('const/sets/IN' @ X1 @ X6 @ ('const/sets/IMAGE' @ X0 @ X1 @ X3 @ X4)))))))),
% 0.20/0.26 inference(nnf_transformation,[],[f8])).
% 0.20/0.26 thf(f10,plain,(
% 0.20/0.26 ? [X0 : $tType,X1 : $tType,X2 : (X1 > X0),X3 : (X1 > $o),X4 : (X0 > $o)] : ((? [X5 : X1] : (((('const/sets/IN' @ X1 @ X5 @ X3)) = $true) & (((X4 @ (X2 @ X5))) != $true)) | ? [X6 : X0] : (($true != ((X4 @ X6))) & ((('const/sets/IN' @ X0 @ X6 @ ('const/sets/IMAGE' @ X1 @ X0 @ X2 @ X3))) = $true))) & (! [X7 : X1] : (((('const/sets/IN' @ X1 @ X7 @ X3)) != $true) | (((X4 @ (X2 @ X7))) = $true)) | ! [X8 : X0] : ((((X4 @ X8)) = $true) | ((('const/sets/IN' @ X0 @ X8 @ ('const/sets/IMAGE' @ X1 @ X0 @ X2 @ X3))) != $true))))),
% 0.20/0.26 inference(rectify,[],[f9])).
% 0.20/0.26 thf(f11,plain,(
% 0.20/0.26 ((((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) & (((sK4 @ (sK2 @ sK5))) != $true)) | ((((sK4 @ sK6)) != $true) & ((('const/sets/IN' @ sK0 @ sK6 @ ('const/sets/IMAGE' @ sK1 @ sK0 @ sK2 @ sK3))) = $true))) & (! [X7 : sK1] : (($true != (('const/sets/IN' @ sK1 @ X7 @ sK3))) | (((sK4 @ (sK2 @ X7))) = $true)) | ! [X8 : sK0] : ((((sK4 @ X8)) = $true) | ((('const/sets/IN' @ sK0 @ X8 @ ('const/sets/IMAGE' @ sK1 @ sK0 @ sK2 @ sK3))) != $true)))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f10])).
% 0.20/0.26 thf(f12,plain,(
% 0.20/0.26 ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : (X0 > X1),X4 : (X0 > $o)] : ((((('const/sets/IN' @ X1 @ X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) = $true) | ! [X5 : X0] : (($true != (('const/sets/IN' @ X0 @ X5 @ X4))) | (((X2 @ X5)) != X3))) & (? [X5 : X0] : (($true = (('const/sets/IN' @ X0 @ X5 @ X4))) & (((X2 @ X5)) = X3)) | ((('const/sets/IN' @ X1 @ X3 @ ('const/sets/IMAGE' @ X0 @ X1 @ X2 @ X4))) != $true)))),
% 0.20/0.26 inference(nnf_transformation,[],[f5])).
% 0.20/0.26 thf(f13,plain,(
% 0.20/0.26 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X1 > X0),X4 : (X1 > $o)] : ((((('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = $true) | ! [X5 : X1] : (((('const/sets/IN' @ X1 @ X5 @ X4)) != $true) | (((X3 @ X5)) != X2))) & (? [X6 : X1] : (((('const/sets/IN' @ X1 @ X6 @ X4)) = $true) & (((X3 @ X6)) = X2)) | ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) != $true)))),
% 0.20/0.26 inference(rectify,[],[f12])).
% 0.20/0.26 thf(f14,plain,(
% 0.20/0.26 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X1 > X0),X4 : (X1 > $o)] : ((((('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = $true) | ! [X5 : X1] : (((('const/sets/IN' @ X1 @ X5 @ X4)) != $true) | (((X3 @ X5)) != X2))) & ((((('const/sets/IN' @ X1 @ (sK7 @ X0 @ X1 @ X4 @ X3 @ X2) @ X4)) = $true) & (((X3 @ (sK7 @ X0 @ X1 @ X4 @ X3 @ X2))) = X2)) | ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) != $true)))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X6,sK7 @ X0 @ X1 @ X4 @ X3 @ X2)],[f13])).
% 0.20/0.26 thf(f15,plain,(
% 0.20/0.26 ( ! [X8 : sK0,X7 : sK1] : (((('const/sets/IN' @ sK0 @ X8 @ ('const/sets/IMAGE' @ sK1 @ sK0 @ sK2 @ sK3))) != $true) | (((sK4 @ (sK2 @ X7))) = $true) | ($true != (('const/sets/IN' @ sK1 @ X7 @ sK3))) | (((sK4 @ X8)) = $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f11])).
% 0.20/0.26 thf(f16,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK0 @ sK6 @ ('const/sets/IMAGE' @ sK1 @ sK0 @ sK2 @ sK3))) = $true) | (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f11])).
% 0.20/0.26 thf(f17,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ sK5))) != $true) | (((sK4 @ sK6)) != $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f11])).
% 0.20/0.26 thf(f18,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK0 @ sK6 @ ('const/sets/IMAGE' @ sK1 @ sK0 @ sK2 @ sK3))) = $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f11])).
% 0.20/0.26 thf(f19,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | (((sK4 @ sK6)) != $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f11])).
% 0.20/0.26 thf(f20,plain,(
% 0.20/0.26 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X1 > X0),X4 : (X1 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) != $true) | (((X3 @ (sK7 @ X0 @ X1 @ X4 @ X3 @ X2))) = X2)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f14])).
% 0.20/0.26 thf(f21,plain,(
% 0.20/0.26 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X1 > X0),X4 : (X1 > $o)] : (((('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) != $true) | ((('const/sets/IN' @ X1 @ (sK7 @ X0 @ X1 @ X4 @ X3 @ X2) @ X4)) = $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f14])).
% 0.20/0.26 thf(f22,plain,(
% 0.20/0.26 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X1 > X0),X4 : (X1 > $o),X5 : X1] : (((('const/sets/IN' @ X0 @ X2 @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = $true) | ((('const/sets/IN' @ X1 @ X5 @ X4)) != $true) | (((X3 @ X5)) != X2)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f14])).
% 0.20/0.26 thf(f24,plain,(
% 0.20/0.26 ( ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X4 : (X1 > $o),X5 : X1] : (((('const/sets/IN' @ X0 @ (X3 @ X5) @ ('const/sets/IMAGE' @ X1 @ X0 @ X3 @ X4))) = $true) | ((('const/sets/IN' @ X1 @ X5 @ X4)) != $true)) )),
% 0.20/0.26 inference(equality_resolution,[],[f22])).
% 0.20/0.26 thf(f25,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : (($true != $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | (((sK4 @ (sK2 @ X0))) = $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | (((sK4 @ sK6)) = $true)) )),
% 0.20/0.26 inference(superposition,[],[f15,f18])).
% 0.20/0.26 thf(f26,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : (($true != $true) | (((sK4 @ (sK2 @ X0))) = $true) | (((sK4 @ sK6)) = $true) | (((sK4 @ (sK2 @ sK5))) != $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true)) )),
% 0.20/0.26 inference(superposition,[],[f15,f16])).
% 0.20/0.26 thf(f27,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | (((sK4 @ (sK2 @ sK5))) != $true) | (((sK4 @ sK6)) = $true) | (((sK4 @ (sK2 @ X0))) = $true)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f26])).
% 0.20/0.26 thf(f28,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | (((sK4 @ sK6)) = $true) | (((sK4 @ (sK2 @ X0))) = $true)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f25])).
% 0.20/0.26 thf(f29,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | (((sK4 @ (sK2 @ X0))) = $true) | (((sK4 @ (sK2 @ sK5))) != $true)) )),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f27,f17])).
% 0.20/0.26 thf(f30,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | (((sK4 @ (sK2 @ X0))) = $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true)) )),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f28,f19])).
% 0.20/0.26 thf(f35,plain,(
% 0.20/0.26 ( ! [X0 : sK1,X1 : sK1] : ((((sK4 @ (sK2 @ X1))) = $true) | ($true != (('const/sets/IN' @ sK1 @ X1 @ sK3))) | ($true != $true) | (((sK4 @ (sK2 @ X0))) = $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true)) )),
% 0.20/0.26 inference(superposition,[],[f15,f24])).
% 0.20/0.26 thf(f36,plain,(
% 0.20/0.26 ( ! [X0 : sK1,X1 : sK1] : (($true != (('const/sets/IN' @ sK1 @ X1 @ sK3))) | (((sK4 @ (sK2 @ X1))) = $true) | (((sK4 @ (sK2 @ X0))) = $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f35])).
% 0.20/0.26 thf(f45,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | (sK6 = ((sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) | ($true != $true)),
% 0.20/0.26 inference(superposition,[],[f20,f18])).
% 0.20/0.26 thf(f46,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ sK5))) != $true) | ($true != $true) | (sK6 = ((sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6))))),
% 0.20/0.26 inference(superposition,[],[f20,f16])).
% 0.20/0.26 thf(f49,plain,(
% 0.20/0.26 (sK6 = ((sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) | (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f46])).
% 0.20/0.26 thf(f50,plain,(
% 0.20/0.26 (sK6 = ((sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f45])).
% 0.20/0.26 thf(f53,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | ($true != $true) | ((('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6) @ sK3)) = $true)),
% 0.20/0.26 inference(superposition,[],[f21,f18])).
% 0.20/0.26 thf(f54,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6) @ sK3)) = $true) | (((sK4 @ (sK2 @ sK5))) != $true) | ($true != $true)),
% 0.20/0.26 inference(superposition,[],[f21,f16])).
% 0.20/0.26 thf(f56,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6) @ sK3)) = $true) | (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f54])).
% 0.20/0.26 thf(f58,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6) @ sK3)) = $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f53])).
% 0.20/0.26 thf(f62,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) = $true) | ($true != $true) | (((sK4 @ (sK2 @ sK5))) != $true) | (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(superposition,[],[f29,f56])).
% 0.20/0.26 thf(f66,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) = $true) | ($true != $true) | (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(duplicate_literal_removal,[],[f62])).
% 0.20/0.26 thf(f67,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) = $true) | (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f66])).
% 0.20/0.26 thf(f70,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ sK5))) != $true) | (((sK4 @ sK6)) = $true) | (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(superposition,[],[f67,f49])).
% 0.20/0.26 thf(f72,plain,(
% 0.20/0.26 (((sK4 @ sK6)) = $true) | (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(duplicate_literal_removal,[],[f70])).
% 0.20/0.26 thf(f74,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ sK5))) != $true)),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f72,f17])).
% 0.20/0.26 thf(f77,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | ($true != $true) | (((sK4 @ (sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) = $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true)),
% 0.20/0.26 inference(superposition,[],[f30,f58])).
% 0.20/0.26 thf(f81,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | (((sK4 @ (sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) = $true) | ($true != $true)),
% 0.20/0.26 inference(duplicate_literal_removal,[],[f77])).
% 0.20/0.26 thf(f82,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ (sK7 @ sK0 @ sK1 @ sK3 @ sK2 @ sK6)))) = $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f81])).
% 0.20/0.26 thf(f85,plain,(
% 0.20/0.26 (((sK4 @ sK6)) = $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true)),
% 0.20/0.26 inference(superposition,[],[f82,f50])).
% 0.20/0.26 thf(f88,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true) | (((sK4 @ sK6)) = $true)),
% 0.20/0.26 inference(duplicate_literal_removal,[],[f85])).
% 0.20/0.26 thf(f89,plain,(
% 0.20/0.26 ((('const/sets/IN' @ sK1 @ sK5 @ sK3)) = $true)),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f88,f19])).
% 0.20/0.26 thf(f91,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : ((((sK4 @ (sK2 @ sK5))) = $true) | ($true != $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | (((sK4 @ (sK2 @ X0))) = $true)) )),
% 0.20/0.26 inference(superposition,[],[f36,f89])).
% 0.20/0.26 thf(f94,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : ((((sK4 @ (sK2 @ sK5))) = $true) | ((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | (((sK4 @ (sK2 @ X0))) = $true)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f91])).
% 0.20/0.26 thf(f96,plain,(
% 0.20/0.26 ( ! [X0 : sK1] : (((('const/sets/IN' @ sK1 @ X0 @ sK3)) != $true) | (((sK4 @ (sK2 @ X0))) = $true)) )),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f94,f29])).
% 0.20/0.26 thf(f97,plain,(
% 0.20/0.26 ($true != $true) | (((sK4 @ (sK2 @ sK5))) = $true)),
% 0.20/0.26 inference(superposition,[],[f96,f89])).
% 0.20/0.26 thf(f101,plain,(
% 0.20/0.26 (((sK4 @ (sK2 @ sK5))) = $true)),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f97])).
% 0.20/0.26 thf(f105,plain,(
% 0.20/0.26 $false),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f101,f74])).
% 0.20/0.26 % SZS output end Proof for theBenchmark
% 0.20/0.26 % (1410962)------------------------------
% 0.20/0.26 % (1410962)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (1410962)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (1410962)CaDiCaL version: 2.1.3
% 0.20/0.26 % (1410962)Termination reason: Refutation
% 0.20/0.26 % (1410962)Time elapsed: 0.005 s
% 0.20/0.26 % (1410962)Peak memory usage: 12 MB
% 0.20/0.26 % (1410962)Instructions burned: 14 (million)
% 0.20/0.26 % (1410953)Success in time 0.03 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------