%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV472^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:39:33 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV472^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:45:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26 % (492333)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (492339)% WARNING: option uhcvi not known.
% 0.08/0.26 % (492339)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3568638615:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.26 % (492339)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (492339)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.26 % (492339) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-492333-492339"...
% 0.08/0.26 % (492339)...printing done.
% 0.08/0.26 % (492339)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(type_def_6, type, sK0: $tType).
% 0.08/0.26 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:((X0 > X0))).
% 0.08/0.26 thf(func_def_1, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.08/0.26 thf(func_def_2, type, 'const/sets/SETSPEC': !>[X0: $tType]:((X0 > $o > X0 > $o))).
% 0.08/0.26 thf(func_def_3, type, 'const/sets/IN': !>[X0: $tType]:((X0 > (X0 > $o) > $o))).
% 0.08/0.26 thf(func_def_4, type, 'const/sets/GSPEC': !>[X0: $tType]:(((X0 > $o) > X0 > $o))).
% 0.08/0.26 thf(func_def_5, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.26 thf(func_def_9, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.26 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_11, type, vAND: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.26 thf(func_def_14, type, sK1: (sK0 > $o)).
% 0.08/0.26 thf(func_def_15, type, sK2: (sK0 > $o)).
% 0.08/0.26 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.08/0.26 thf(f2,axiom,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_')).
% 0.08/0.26 thf(f3,axiom,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ('const/sets/SUBSET' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X3 : X0] : (? [X4 : X0] : ('const/sets/SETSPEC' @ X0 @ X3 @ (X2 @ X4) & ('const/sets/IN' @ X0 @ X4 @ X1) @ X4)))) @ X1)),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_RESTRICT_')).
% 0.08/0.26 thf(f4,conjecture,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X1) => ('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X3 : X0] : (? [X4 : X0] : ('const/sets/SETSPEC' @ X0 @ X3 @ (X2 @ X4) & ('const/sets/IN' @ X0 @ X4 @ X1) @ X4))))))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_RESTRICT_')).
% 0.08/0.26 thf(f5,negated_conjecture,(
% 0.08/0.26 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X1) => ('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X3 : X0] : (? [X4 : X0] : ('const/sets/SETSPEC' @ X0 @ X3 @ (X2 @ X4) & ('const/sets/IN' @ X0 @ X4 @ X1) @ X4))))))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f4])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) => ((('const/sets/FINITE' @ X0 @ X1)) = $true))),
% 0.08/0.26 inference(fool_elimination,[],[f6])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ('const/sets/SUBSET' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X3 : X0] : (? [X4 : X0] : ('const/sets/SETSPEC' @ X0 @ X3 @ (X2 @ X4) & ('const/sets/IN' @ X0 @ X4 @ X1) @ X4)))) @ X1)),
% 0.08/0.26 inference(rectify,[],[f3])).
% 0.08/0.26 thf(f9,plain,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ($true = (('const/sets/SUBSET' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X1)))),
% 0.08/0.26 inference(fool_elimination,[],[f8])).
% 0.08/0.26 thf(f10,plain,(
% 0.08/0.26 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (('const/sets/FINITE' @ X0 @ X1) => ('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[X3 : X0] : (? [X4 : X0] : ('const/sets/SETSPEC' @ X0 @ X3 @ (X2 @ X4) & ('const/sets/IN' @ X0 @ X4 @ X1) @ X4))))))),
% 0.08/0.26 inference(rectify,[],[f5])).
% 0.08/0.26 thf(f11,plain,(
% 0.08/0.26 ~ ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) => ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1)))))))))),
% 0.08/0.26 inference(fool_elimination,[],[f10])).
% 0.08/0.26 thf(f12,plain,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) | (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)))),
% 0.08/0.26 inference(ennf_transformation,[],[f7])).
% 0.08/0.26 thf(f13,plain,(
% 0.08/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 0.08/0.26 inference(flattening,[],[f12])).
% 0.08/0.26 thf(f14,plain,(
% 0.08/0.26 ? [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (($true != (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1)))))))) & ((('const/sets/FINITE' @ X0 @ X1)) = $true))),
% 0.08/0.26 inference(ennf_transformation,[],[f11])).
% 0.08/0.26 thf(f15,plain,(
% 0.08/0.26 ($true != (('const/sets/FINITE' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ Y1)))))))) & ($true = (('const/sets/FINITE' @ sK0 @ sK1)))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14])).
% 0.08/0.26 thf(f17,plain,(
% 0.08/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f13])).
% 0.08/0.26 thf(f18,plain,(
% 0.08/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true = (('const/sets/SUBSET' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))) @ X1)))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f9])).
% 0.08/0.26 thf(f19,plain,(
% 0.08/0.26 ($true = (('const/sets/FINITE' @ sK0 @ sK1)))),
% 0.08/0.26 inference(cnf_transformation,[],[f15])).
% 0.08/0.26 thf(f20,plain,(
% 0.08/0.26 ($true != (('const/sets/FINITE' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ Y1))))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f15])).
% 0.08/0.26 thf(f22,definition,(
% 0.08/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.26 thf(f32,plain,(
% 0.08/0.26 ($true != $true) | ((('const/sets/FINITE' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ Y1))))))) = $false)),
% 0.08/0.26 inference(constrained_superposition,[],[f20,f22])).
% 0.08/0.26 thf(f33,plain,(
% 0.08/0.26 ((('const/sets/FINITE' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (sK2 @ Y1)) @ Y1))))))) = $false)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f32])).
% 0.08/0.26 thf(f45,plain,(
% 0.08/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true != $true) | ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1)))))))) | ((('const/sets/FINITE' @ X0 @ X1)) != $true)) )),
% 0.08/0.26 inference(constrained_superposition,[],[f17,f18])).
% 0.08/0.26 thf(f46,plain,(
% 0.08/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) != $true) | ($true = (('const/sets/FINITE' @ X0 @ ('const/sets/GSPEC' @ X0 @ (^[Y0 : X0]: (?? @ X0 @ (^[Y1 : X0]: ('const/sets/SETSPEC' @ X0 @ Y0 @ (('const/sets/IN' @ X0 @ Y1 @ X1) & (X2 @ Y1)) @ Y1))))))))) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f45])).
% 0.08/0.26 thf(f52,plain,(
% 0.08/0.26 ( ! [X0 : (sK0 > $o)] : (($true != $true) | ($true = (('const/sets/FINITE' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (X0 @ Y1)) @ Y1))))))))) )),
% 0.08/0.26 inference(constrained_superposition,[],[f46,f19])).
% 0.08/0.26 thf(f56,plain,(
% 0.08/0.26 ( ! [X0 : (sK0 > $o)] : (($true = (('const/sets/FINITE' @ sK0 @ ('const/sets/GSPEC' @ sK0 @ (^[Y0 : sK0]: (?? @ sK0 @ (^[Y1 : sK0]: ('const/sets/SETSPEC' @ sK0 @ Y0 @ (('const/sets/IN' @ sK0 @ Y1 @ sK1) & (X0 @ Y1)) @ Y1))))))))) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f52])).
% 0.08/0.26 thf(f67,plain,(
% 0.08/0.26 ($true = $false)),
% 0.08/0.26 inference(constrained_superposition,[],[f33,f56])).
% 0.08/0.26 thf(f72,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f67])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (492339)------------------------------
% 0.08/0.26 % (492339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (492339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (492339)CaDiCaL version: 2.1.3
% 0.08/0.26 % (492339)Termination reason: Refutation
% 0.08/0.26 % (492339)Time elapsed: 0.004 s
% 0.08/0.26 % (492339)Peak memory usage: 12 MB
% 0.08/0.26 % (492339)Instructions burned: 9 (million)
% 0.08/0.26 % (492333)Success in time 0.033 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------