%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Tue Sep 29 12:47:06 PM UTC 2026
% Result : Theorem 0.42s 0.84s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 15 unt; 0 def)
% Number of atoms : 173 ( 75 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 228 ( 104 ~; 99 |; 17 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 52 ( 51 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f14,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f35,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( relation_rng(X0) = relation_dom(X1)
& relation_composition(X0,X1) = X0 )
=> X1 = identity_relation(relation_dom(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
fof(f37,axiom,
! [X0] : one_to_one(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(f38,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f40,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f41,conjecture,
! [X0] : function_inverse(identity_relation(X0)) = identity_relation(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_funct_1) ).
fof(f42,negated_conjecture,
~ ! [X0] : function_inverse(identity_relation(X0)) = identity_relation(X0),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f44,axiom,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
& relation_rng(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f47,plain,
? [X0] : identity_relation(X0) != function_inverse(identity_relation(X0)),
inference(ennf_transformation,[],[f42]) ).
fof(f49,plain,
! [X0] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f50,plain,
! [X0] :
( ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f52,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f54,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( X1 = identity_relation(relation_dom(X1))
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != X0
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( X1 = identity_relation(relation_dom(X1))
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != X0
| ~ relation(X1)
| ~ function(X1) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f55]) ).
fof(f75,plain,
identity_relation(sK0) != function_inverse(identity_relation(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f47]) ).
fof(f83,plain,
identity_relation(sK0) != function_inverse(identity_relation(sK0)),
inference(cnf_transformation,[],[f75]) ).
fof(f86,plain,
! [X0] :
( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f88,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f89,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f90,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f91,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f92,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f96,plain,
! [X0,X1] :
( relation_rng(X0) != relation_dom(X1)
| identity_relation(relation_dom(X1)) = X1
| relation_composition(X0,X1) != X0
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f115,plain,
! [X0] : one_to_one(identity_relation(X0)),
inference(cnf_transformation,[],[f37]) ).
fof(f122,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f123,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f196,plain,
! [X0,X1] :
( relation_dom(X1) != X0
| identity_relation(relation_dom(X1)) = X1
| identity_relation(X0) != relation_composition(identity_relation(X0),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(superposition,[],[f96,f122]) ).
fof(f201,plain,
! [X0,X1] :
( relation_dom(X1) != X0
| identity_relation(relation_dom(X1)) = X1
| identity_relation(X0) != relation_composition(identity_relation(X0),X1)
| ~ relation(X1)
| ~ function(X1)
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f196,f92]) ).
fof(f204,plain,
! [X0,X1] :
( identity_relation(X0) != relation_composition(identity_relation(X0),X1)
| identity_relation(relation_dom(X1)) = X1
| relation_dom(X1) != X0
| ~ relation(X1)
| ~ function(X1) ),
inference(forward_subsumption_resolution,[],[f201,f91]) ).
fof(f258,plain,
! [X0] :
( identity_relation(X0) != identity_relation(relation_dom(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0))))
| relation_dom(function_inverse(identity_relation(X0))) != X0
| ~ relation(function_inverse(identity_relation(X0)))
| ~ function(function_inverse(identity_relation(X0)))
| ~ one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(superposition,[],[f204,f86]) ).
fof(f259,plain,
! [X0] :
( identity_relation(X0) != identity_relation(relation_dom(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0))))
| relation_dom(function_inverse(identity_relation(X0))) != X0
| ~ function(function_inverse(identity_relation(X0)))
| ~ one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f258,f90]) ).
fof(f260,plain,
! [X0] :
( identity_relation(X0) != identity_relation(relation_dom(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0))))
| relation_dom(function_inverse(identity_relation(X0))) != X0
| ~ one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f259,f89]) ).
fof(f261,plain,
! [X0] :
( identity_relation(X0) != identity_relation(relation_dom(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0))))
| relation_dom(function_inverse(identity_relation(X0))) != X0
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f260,f115]) ).
fof(f262,plain,
! [X0] :
( identity_relation(X0) != identity_relation(relation_dom(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0))))
| relation_dom(function_inverse(identity_relation(X0))) != X0
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f261,f92]) ).
fof(f263,plain,
! [X0] :
( identity_relation(X0) != identity_relation(relation_dom(identity_relation(X0)))
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0))))
| relation_dom(function_inverse(identity_relation(X0))) != X0 ),
inference(forward_subsumption_resolution,[],[f262,f91]) ).
fof(f264,plain,
! [X0] :
( identity_relation(X0) != identity_relation(X0)
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0))))
| relation_dom(function_inverse(identity_relation(X0))) != X0 ),
inference(forward_demodulation,[],[f263,f123]) ).
fof(f265,plain,
! [X0] :
( relation_dom(function_inverse(identity_relation(X0))) != X0
| function_inverse(identity_relation(X0)) = identity_relation(relation_dom(function_inverse(identity_relation(X0)))) ),
inference(trivial_inequality_removal,[],[f264]) ).
fof(f266,plain,
! [X0] :
( relation_rng(identity_relation(X0)) != X0
| function_inverse(identity_relation(X0)) = identity_relation(relation_rng(identity_relation(X0)))
| ~ one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(superposition,[],[f265,f88]) ).
fof(f267,plain,
! [X0] :
( function_inverse(identity_relation(X0)) = identity_relation(relation_rng(identity_relation(X0)))
| ~ one_to_one(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f266,f122]) ).
fof(f268,plain,
! [X0] :
( function_inverse(identity_relation(X0)) = identity_relation(relation_rng(identity_relation(X0)))
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f267,f115]) ).
fof(f269,plain,
! [X0] :
( function_inverse(identity_relation(X0)) = identity_relation(relation_rng(identity_relation(X0)))
| ~ function(identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f268,f92]) ).
fof(f270,plain,
! [X0] : function_inverse(identity_relation(X0)) = identity_relation(relation_rng(identity_relation(X0))),
inference(forward_subsumption_resolution,[],[f269,f91]) ).
fof(f271,plain,
! [X0] : identity_relation(X0) = function_inverse(identity_relation(X0)),
inference(forward_demodulation,[],[f270,f122]) ).
fof(f280,plain,
identity_relation(sK0) != identity_relation(sK0),
inference(superposition,[],[f83,f271]) ).
fof(f294,plain,
$false,
inference(trivial_inequality_removal,[],[f280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU034+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 28 03:25:04 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.84 % (2988619)Detected formulas, will run a generic FOF schedule.
% 0.42/0.84 % (2988628)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2506341713:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.42/0.84 % (2988626)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=909471491:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.42/0.84 % (2988625)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=222586650:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.42/0.84 % (2988630)dis-21_1_sil=8000:lcm=predicate:random_seed=699517976:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.42/0.84 % (2988627)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1589268148:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.42/0.84 % (2988624)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2714575041:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.42/0.84 % (2988627)Refutation not found, incomplete strategy
% 0.42/0.84 % (2988627)------------------------------
% 0.42/0.84 % (2988627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.84 % (2988627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.84 % (2988627)CaDiCaL version: 2.1.3
% 0.42/0.84 % (2988627)Termination reason: Refutation not found, incomplete strategy
% 0.42/0.84 % (2988627)Time elapsed: 0.001 s
% 0.42/0.84 % (2988627)Peak memory usage: 87 MB
% 0.42/0.84 % (2988628)First to succeed.
% 0.42/0.84 % (2988628)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2988619"
% 0.42/0.84 % (2988629)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2646834054:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.42/0.84 % (2988629)Also succeeded, but the first one will report.
% 0.42/0.84 % (2988630)Instruction limit reached!
% 0.42/0.84 % (2988630)------------------------------
% 0.42/0.84 % (2988630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.42/0.84 % (2988630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.42/0.84 % (2988630)CaDiCaL version: 2.1.3
% 0.42/0.84 % (2988630)Termination reason: Instruction limit
% 0.42/0.84 % (2988630)Termination phase: Saturation
% 0.42/0.84 % (2988630)Time elapsed: 0.041 s
% 0.42/0.84 % (2988630)Peak memory usage: 89 MB
% 0.42/0.84 % (2988630)Instructions burned: 130 (million)
% 0.42/0.84 % (2988627)------------------------------
% 0.42/0.84 % (2988627)------------------------------
% 0.42/0.84 % (2988628)Refutation found. Thanks to Tanya!
% 0.42/0.84 % SZS status Theorem for theBenchmark
% 0.42/0.84 % SZS output start Proof for theBenchmark
% See solution above
% 2.34/0.93 % (2988628)------------------------------
% 2.34/0.93 % (2988628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.93 % (2988628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.93 % (2988628)CaDiCaL version: 2.1.3
% 2.34/0.93 % (2988628)Termination reason: Refutation
% 2.34/0.93 % (2988628)Time elapsed: 0.003 s
% 2.34/0.93 % (2988628)Peak memory usage: 88 MB
% 2.34/0.93 % (2988628)Instructions burned: 9 (million)
% 2.34/0.93 % (2988628)------------------------------
% 2.34/0.93 % (2988628)------------------------------
% 2.34/0.93 % (2988619)Success in time 0.302 s
% 2.34/0.93 % Vampire exiting
%------------------------------------------------------------------------------